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Table of Contents
Introduction
Basic Electronics
Conductor and Insulator
Resistor Value Test
Simple Dc Circuits
Types Of Switching
Variable Voltages
Ohm's Law
DC Voltage
DC Current
Series and Parallel Resistors
AC Measurement
AC Voltage and Current
AC Theory
RCL Series
RCL Parallel
Capacitance
Capacitors
Inductance
Inductors
Impedance
Radio and Communication
Tuned Circuits
Attenuators
Passive Filters
Active Filters
Oscillators
Circuit Theorems
Complex Numbers
DC Power
AC Power
Silicon Controlled Rectifier
Power Supply
Voltage Regulation
Electro-Magnetism
Electrical Machines
Transformers
Three Phase Systems
Energy Transfer and Cost
Atomic Structures
Diode Theory
Diode Applications
Transistor Theory
Bipolar Transistors
Transistor Configurations
Active Transistor Circuits
Field Effect Transistors
Basic Operational Amplifier
Op-Amp Theory
Op-Amp Applications
Sum and Difference Amplifiers
Analogue Multi-Meter
Component Testing
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Electronics V11 Home Study
by Clive W. Humphris M0DXJ
Portable Learning, Reference and Revision Tools.
Copyright by eptsoft limited 2018
All rights reserved.
Acknowledgement
Our thanks and appreciation goes to John D. Ransley MIEE from
Whitbourne in Worcestershire for all his help and expert guidance in
developing this eBook and additional app content.
Introduction
An enhanced eBook published in full colour. Now including extensive
interactive content enabling exploration by inserting any values that would
occur in a real situation whereby the graphics are redrawn to reflect those
changes.
Calculations can be also tested against any standard subject textbook to
compare the results.
Interactive Technology when used in the classroom can motivate passive
students by encouraging their active participation where STEM subjects are
ideally suited to Mobile Interactive Technology.
Students are more likely to be comfortable with technology they understand
i.e. their phone and can interact with, often preferring 'Learning-by-Doing'
over traditional pencil and paper methods.
Full colour graphics that are redrawn for every input change will make the
learning experience more enjoyable and effective as it encourages
experimentation of real world situations as almost any practical values are
accepted.
Students who struggle to be fully engaged in normal classroom activity can
often achieve the unexpected once sat in front of a digital screen where they
can learn without the embarrassment of full class exposure.
Mobile Interactive Technology can bring any STEM textbook to life by
inserting printed values from the book into their mobile device and
comparing the results.
Colourful visual presentation assists the learning process as students will
more likely remember, thereby increasing their personal confidence as they
believe they are learning more as a result. Knowing the content is on their
phone encourages them to dip-in in a spare moment more than open a
traditional textbook.
Conclusion: Students will spend more time engaged with the Mobile
Interactive Technology than with a traditional textbook.
For each topic group students can TEST THEIR UNDERSTANDING by
considering an open question whereby their ease of answering will provide
an indication of personal progress.
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BASIC ELECTRONICS: Finding Circuit Voltages.
Interactive Content!
When calculating a voltage, in this case a DC we are determining the
potential difference (PD) developed across an electrical device due to the
current flowing through it. This will be explained further when we come to
explore Ohm's Law. In this instance we are finding the voltages developed
across the resistor and the lamp.
The components shown are in what is called a series circuit, the resistor is in
series with the lamp as the electron current flow is through one followed by
the other. Remove either the resistor or the lamp and the circuit ceases to
function, what's known as an open-circuit.
This simple circuit provides the opportunity to introduce some electronics
mathematics which for the moment its sufficient to say that if we want to
find how much current is being drawn from the battery when the lamp is lit,
we can calculate it. Found by dividing the sum of the voltages across the
resistor and lamp by the total circuit resistance. When the individual
potential differences are added they will always equal the supply potential of
the battery. This is known as Kirchhoff's Voltage Law.
Note: the polarity of the voltage. This is important when it comes to
connecting your Voltage Test Meter where the black lead is applied to the
more negative part of the circuit and the red lead to the more positive.
BASIC ELECTRONICS: Measuring Voltage and Current.
The electric current which flows through a circuit is a measure of the rate of
flow of electric charge (electron movement) past any given point.
An ammeter is used to measure current flow, but before we can do this, it is
first necessary to insert the meter into the current path within the circuit.
Note voltages appear across electrical devices (shown by the voltmeter
connections) which posses resistance, whereas current flows through them.
The current can also be calculated using the formula for Ohm's Law. The
ammeter can be placed at any point in the circuit and will always give the
same current reading, which is determined by the battery potential voltage
divided by the resistor value added to the lamp resistance or the total circuit
resistance.
As the value of R1 is increased then the current is limited around the circuit
and in a practical situation the lamp would glow less brightly. As the
resistance of the lamp is fixed the voltage developed across the filament will
also fall in direct proportion to the current I.
BASIC ELECTRONICS: Variable Resistance.
A variable resistor (known as a potentiometer) is a fixed value resistor onto
which a slider is attached to tap off the resistance at any given point across a
carbon track. VR1 is connected to form a potential divider circuit, the output
voltage depending upon the slider position. Move the slider towards point [a]
and the output voltage increases, towards [c] and it decreases. Is there a
linear relationship between voltage output and slider position i.e. do you get
half the voltage output at the control mid point?
The answer should be yes, but only because the output is open circuit. As
soon as a load resistance is connected across the output this smooth linear
voltage variation from one end of the control to the other will be upset and
will be explained when we come to voltage dividers.
Variable resistors are commonly found in modern audio amplifiers where the
variable DC voltage is used to adjust the level of volume, bass and treble
within an integrated circuit amplifier using a DC controlled attenuator.
Variable resistors can also be found in AC circuits where the signal
attenuation can be adjusted from maximum to zero by varying the slider
position.
There are two types of potentiometer, linear, where the resistance across the
track increases evenly from one end to the other and logarithmic where there
is a greater change of resistance to angle of rotation at one end than the
other. The latter are less common now, but can upset measurements if the
wrong type is used. Where higher currents are involved potentiometers are
available with a wire wound track and printed circuit boards demand subminiature horizontal and vertical mounting types. Finally for greater
precision multiple turn resistors should be used.
BASIC ELECTRONICS: Adding Positive Values.
When the numbers to be added are all positive the total will be the
cumulative addition of each new value.
An example is when adding resistor values in series, as each resistor is
connected the total resistance becomes larger.
Voltages and currents, as we shall see later, can only be added directly when
they have the same phase angle or direction.
BASIC ELECTRONICS: Adding Negative Values.
A negative current is simply a way of mathematically defining a current
flowing in the opposite direction to a positive one.
When -I1, -I2 and -I3 are added together at point X to become -I total.
Normally its good practice to include brackets ( ) around a negative number.
It avoids confusion of + and - operators appearing next to one another.
It's useful to remember that a minus added to a minus is just a bigger minus.
BASIC ELECTRONICS: Adding Signed Values.
Positive and negative voltages developed across a circuit will cancel each
other when added together, the resultant or total taking the sign of the greater
quantity. Voltages and currents normally represent peak or RMS values or
any other instantaneous measurement, any can be used so long as the same
method is applied throughout.
Adding positive and negative numbers is common in AC circuits, the (+) and
(-) signs indicating voltages or currents in phase opposition.
During the first half of the waveform the resultant will be in one phase, then
reversed during the following half cycle.
BASIC ELECTRONICS: Algebraic Addition of Currents.
Currents can be made to flow in both directions through a conductor, or as in
this example a resistor.
Some electrons moving from left to right will be cancelled out by those
moving right to left, the sign just represents one or other direction.
The resultant current being I1 - I2 or I2 - I1. This is the same as adding a
positive current (flowing in one direction) to a negative current (in the
opposite direction).
You will note the sign is not included for the final result as the answer just
represents an amount of current flowing in the circuit, the direction is
usually unimportant for further calculations and could complicate the result
of say, Ohm's Law by showing a negative voltage.
BASIC ELECTRONICS: Subtracting Signed Voltages.
As an example of subtracting a negative value from a positive.
Consider a series resistor network, which measures 20V at one end and -11V
at the other. What is the potential difference between the two ends?
The rule for subtracting a negative value from a positive is, change the sign
of the negative (-n2) and add.
When calculating the voltage or potential difference, ignore the sign of the
final answer.
BASIC ELECTRONICS: Subtracting Negative Currents.
Calculations in electronics often involve negative numbers.
Remember that a negative value is usually a current or voltage with the
opposite phase to that of a similar amount or value which is positive.
This calculation can be made easier by changing the sign of n2 and adding.
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CONDUCTOR AND INSULATOR: Conductor.
Interactive Content!
For an electric current to flow there has to be a source of electrons, i.e. a
battery. Closing the switch completes the circuit. This electron flow causes
the lamp to light. If the switch is opened the electron movement ceases and
the lamp is therefore turned off.
Electrons are released from the negative battery terminal (-), and attracted by
the positive terminal (+) through the circuit. The amount of electron
movement being limited by the resistance of the lamp, the filament of which
is made of tungsten. Filament resistance causes more work (power) in
moving the electrons and heat is generated, up to as much as 1000°C which
is white hot and emits visible light.
The direction of current flow can be considered in two ways, either as
conventional current when the flow is from positive (+) to negative (-) or as
electron flow, where electrons are released from the negative battery
terminal and attracted by positive terminal.
Both are valid. In simple DC circuits conventional current is appropriate.
However, to explain the operation of a semiconductor, which is a transistor
or diode, then electron flow must be considered as we are then primarily
interested in the combination of negative electrons and positive holes.
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CONDUCTOR AND INSULATOR: Insulator.
An insulator placed within the conducting path will prevent current flow, the
electric current cannot pass through the insulating material as there are no
free electrons to enable current to flow.
The air space between the open contacts of a switch is a typical insulator.
Insulating materials are chosen because they have very few free electrons
with which to form an electron flow. Closing the switch in this instance
therefore has no effect.
Within any material there is always some electron movement (even
insulators) this can be caused by external events, heat for example,
especially in good conductors such as copper which have very loosely
coupled electrons in their outer shell and easily dislodged.
Relative to normal current flow this activity is minute and as the electron
movement is random in all directions it cancels out. However, remove the
insulator and close the switch and these random electrons are pulled towards
the positive potential of the battery. Contributing to current flow as others
are released. The negative terminal of the battery provides a supply of
electrons to balance those attracted away by the positive potential.
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CONDUCTOR AND INSULATOR: Measuring an Electric Current.
The amount of current flowing in a circuit is dependent upon two factors, the
circuit resistance R and the applied voltage or electromotive force (EMF).
EMF is electrical force and is required to move electrons (current flow) in a
conductor.
Electrons don't actually travel around a conducting path. Each is pulled away
from its parent atom by the attraction of a positively charged atom (+ION)
close by. This in turn leaves a positive charge behind to attract an electron
from an adjacent neutral atom further down the line; the effect is the
negatively charged stream of electrons move in the direction of the positive
potential. Millions and millions of them in an instant.
It is important to understand that if the EMF is increased the current or
electron movement also increases in direct proportion. Double the voltage
and the current doubles. The value of R will remain fixed. We will explore
this further with the calculations for Ohm's Law.
For the moment its sufficient to just have an appreciation for what is
happening within a simple electric circuit. It's this intuitive feel for what is
actually going on which helps in the understanding of circuits, you get to
know what to expect in any given situation, which only comes from
spending time playing with electronics. Remember you can't see voltage and
current only the effect of it, but you can feel it!
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CONDUCTOR AND INSULATOR: Conductor Resistance.
This topic is simply a voltage supply, feeding a reel of cable with a load
resistance connected to the end. However, all conductors contain resistance
and for long lengths of cable carrying large currents this can result in a
significant loss of voltage across the load. This difference between the
supply voltage and the load voltage is called a 'voltage drop'. Voltage
starvation across an electric motor can cause it to run slow, or lamps will be
dimmed, or heating becomes inefficient.
When calculating the volts drop on a length of cable, it should be
remembered that it consists of two parallel conductors and so the cable
resistance-per-metre must be doubled for the length of cable on the drum.
Cable should always be unwound from the drum before use, as it acts as a
large inductor and can cause the core to melt due to the heat generated by
stray eddy currents.
The equivalent circuit shows the cable and load resistances as a series
resistive circuit where the calculations are for a voltage divider, these will all
be investigated later and you can come back to them.
Inadequate cable diameters for a given load will also cause the cable to run
hot, eventually resulting in failure. This is the exact principle of a fuse.
Fortunately there is a solution to voltage drop. Just use a thicker cable,
where the resistance-per-meter will be less for your particular load
requirements.
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RESISTOR VALUE TEST: Select Random Value.
Interactive Content!
Resistor values can be determined using the Resistor Colour Code. For the
4-band type, the first two bands are numerical values the third is the
multiplier or number of noughts.
For example 3.9kOhms = orange(3), white(9), red(2) = 3900ohms or
3.9kOhms. For values below 10ohms the third band is coloured gold which
is a multiplier of 0.1. The fourth band indicates tolerance.
Resistor values are also available as 5-band types. You can select a routine to
determine the value of both types Resistor Colour Codes in the Toolbox
menu along with another selection for Preferred Resistor Values. Resistors
are available in a number of ranges, the most common being the E12(10%)
and E24(5%) series, the latter having a closer tolerance, therefore more
values are required to ensure every likely value is covered.
The Toolbox also contains a routine for finding preferred types. Calculations
will often produce odd resistor values and in some cases very close tolerance
high stability types may be required. For this purpose the E48(2%), E96(1%)
and E192(0.5%) ranges are available, obviously this closer precision is
reflected in their cost.
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SIMPLE DC CIRCUITS: Three Resistors in Series.
Interactive Content!
In a practical circuit consisting of just three resistors, connected in series
across a battery, four circuit parameters can be measured using a simple
multi-meter. Firstly the current I flowing which is determined by inserting an
ammeter in series with the resistors and then the three voltage drops across
the individual resistors.
The current is a result of the applied voltage divided by the total series
circuit resistance. Apply the formula for series resistance to determine the
total resistance R.
Individual resistor voltage drops are each found by applying Ohm's Law.
Resistance R1, R2 or R3 multiplied by the series circuit current. Adding the
individual voltage drops together will always equal the applied battery
voltage.
SIMPLE DC CIRCUITS: Two Parallel Resistors.
Shown are three components connected together forming a circuit. A battery
or source of electric current and two resistors. From this diagram a number
of circuit parameters may be found. Some are known others need to be
calculated.
Considering the current as being 'conventional' where it flows from the
battery positive terminal and divides into two branches. The amount of
current in each branch will be inversely proportional to the resistor value, i.e.
the larger resistor value the less current flows.
Firstly we need to find the total current I, but before we can do this we
require the equivalent circuit resistance from the formula. We know the
applied battery voltage. However each individual branch current could just
as easily be calculated by applying Ohm's Law and the two current values
added together which will equal I. Current is never lost (Kirchhoff's Law)
the sum of individual currents will always equal the total current.
As you can see there are several ways of solving this problem. If you were
given the total current and the resistor values, could you have found the
battery voltage?
SIMPLE DC CIRCUITS: Potential Divider.
A simple potential divider is just two resistors connected in series across a
battery. So long as we don't have large variations in load current the voltage
at the resistor junction will be remain fixed.
The voltage dropped across the lower resistor provides the output voltage,
determined by the relationship between Ra and Rb. The calculations will
demonstrate this in more detail. What is the output voltage if the lower
resistor is made a quarter of the resistance of the upper value?
The simple voltage divider circuit is commonly used to make a transistor
base biasing network where the base current requirements are small.
However, there are further considerations when the current requirements
increase or are subject to large variations.
SIMPLE DC CIRCUITS: Loading a Potential Divider.
Loading the voltage divider connects the resistance of the load in parallel
with the lower resistance Rb. We will call this parallel combination Rx. Note
the shorthand for resistors in parallel. To determine the total current, first
calculate the value of Rx, then divide the battery or supply voltage by the
addition of Ra + Rx.
Load current Iout is simply the resistor junction voltage over the load
resistance RL.
In practice the value of Rb is chosen to be about one tenth of the value of the
load. This ensures that any fluctuations in load current have a limited effect
on the divided output voltage.
Experiment with the values of Rb relative to RL and note the changes on the
Ra, Rb junction voltage.
SIMPLE DC CIRCUITS: Pull Up, Down Resistors.
The use of pull up and pull down resistors is a common feature in
electronics. Closing S1 in the left hand diagram pulls down the voltage at the
lower end of Ra by shorting it to the zero line. Current flowing in Ra will
then depend solely upon the resistor value and the supply voltage.
In the diagram to the right, the voltage at the top of Rb is pulled up to the
supply voltage by closing S2. With equal value resistors will the current
flowing be the same in both circuits when the switches are closed?
S1 and S2 could be replaced by transistors acting as switches which
effectively become short circuited between the collector and emitter
terminals when made to conduct heavily. Resistor Ra is a collector load and
Rb an emitter resistor.
When a transistor is biased OFF, i.e. no base volts the transistor is open
circuit. For T1 the collector voltage would be high, no collector current
flowing and for T2 the emitter voltage would be zero, with no emitter
current flowing. Biasing ON T1 and its collector output voltage is pulled
down and for T2 the emitter voltage is pulled up.
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TYPES OF SWITCHING: Push Switch.
Interactive Content!
Switch contacts when open provide an interruption of the current flow
within a circuit and when closed completes the conducting path. Shown is
one of the simplest of schematic diagrams that consists of just three
components, indicated by appropriate symbols. Clearly shown are the
component connections and the effect of what happens when the switch
button is pushed. One of the simplest types of switch has to be the push-tomake, i.e. for a doorbell, here is a push-to-break.
Within the pages of a components catalogue you can find dozens of different
combinations of switch types. When selecting a switch there are two main
considerations, current rating and the maximum working voltage. Using a
switch that is under-rated can be unreliable and dangerous because of arcing
of the contacts or physically expose the user to an electric shock because of a
voltage breakdown of the insulation.
In this diagram the battery can represent any number of cells connected in
series which increase the supply voltage (potential difference) as each cell is
added. Battery cells are usually in multiples of 1.5V, and those of the
rechargeable type are lower at 1.2V.
To calculate the current I flowing in this simple circuit we can use Ohm's
Law by applying the formula shown. Try changing the battery supply
voltage and note the changing current. In a practical circuit the more current
that flows the brighter the lamp would glow. Increasing the voltage and
thereby the current, above that permitted by the bulb and the filament acts
like a fuse.
TYPES OF SWITCHING: Change-over Switch.
Switches are available in many different types. Here is an example of a
changeover switch that redirects the battery connection to either the lamp or
the buzzer. This is a break-before-make switch.
Others are make-before-break, where power is connected to both parts of the
circuit during changeover. Switches are used as relay contacts, rotary
selectors, slider contacts etc.
Here we have given the two devices a different working resistance. This
demonstrates that the current drawn from the battery changes as the switch is
thrown. As the battery has what is called 'internal resistance' this can cause a
reduction in the potential difference PD between the battery terminals as the
load resistance increases.
Electronic buzzers have no moving contacts and therefore do not generate
RF interference, but produce a clear penetrating sound. Typical uses are in
internal burglar alarm sounders. The output frequency is around 400Hz with
impedance of a few hundred ohms, consuming approximately 35mA when a
voltage between four to twenty volts is applied.
TYPES OF SWITCHING: Stair-case Switch.
The staircase switch arrangement derives its name from its purpose in
domestic house wiring, where it is often necessary to be able to switch a
single lamp from any number of different places. There are two types of
switch used, A and D are normal changeover types. The others B and C are
called intermediate switches (of which there can be any number) are
crossover types.
What happens is the intermediate switches changeover the central pair of
conductors.
There is no need for a clever logic diagram to explain or carry out this
action, its simply the bulb lights or extinguishes for every switch action.
Follow the lamp current path for yourself for all the available switch states.
TYPES OF SWITCHING: Relay Switch.
A relay is a device, which is an electrically operated switch. It works by
energising an electromagnet that pulls or releases switch contacts that are
make (shorted out) or break (open circuit) depending upon whether the relay
coil is energised. Close S1 and a current is made to flow in the relay coil.
This causes a magnetic field to develop which pulls the central switch
contact [b] to the left, making the circuit with [a] for the bulb to light.
Release S1 and the magnetic field collapses and the contact [b] returns to its
rest position, against the right hand contact [c], causing the buzzer to sound.
In use a reverse biased diode should be connected across the energising coil
for protection as the high back-EMF that is generated when the current is
switched off can easily damage any associated circuitry.
Relays are available in both single-pole and double-pole switch actions.
Typical switch contact resistance is measured as 50mOhms (milli-Ohms)
with operating times of around a couple of milliseconds. Maximum
switching currents can exceed 10Amps, but for most applications, a much
smaller and less expensive device would suffice.
A relay has a mechanical switching operation, not electronic, as is the case
of a thyristor semiconductor device. The electromagnetic coil resistance is
between 80 and 1kOhms depending on the type when designed for an
operating voltage of around 5Volts to 30Volts. The life of the contacts can
exceed 100,000 operations but this depends largely on the amount of current
being switched and if it is AC or DC as the former tends to maintain cleaner
switch contacts due to its uni-polar direction.
TYPES OF SWITCHING: Three-level Switch.
Most switches found in component catalogues are fairly standard, where
only the method of mounting or presentation differs. However, there will be
times when a specialist action is called for. Typical examples are found in
electric cookers and washing machines. As the latter can be very
complicated we will concentrate on the former to switch the heating
elements in an oven or cooker hot plate.
The example shown consists of three switch positions, plus an ON/OFF,
which also forms part of the thermostat. The thermostat will be bi-metal
strip, which bends and makes or breaks a pair of switch contacts to complete
the circuit depending upon the temperature setting. But it's the switching
action, which is of interest here.
The two elements Re1 and Re2 are resistances which are designed to make
use of their dissipated heat which is normally wasted. They could be
considered as underrated wire wound types, which become hot due to
excessive current owing to their low value. In the 'Low Heat' setting they are
connected in series, as their combined resistance increases across the (L) (N) terminals the current flow and therefore heat dissipated will be relatively
low. 'Medium Heat' and just one element is connected and for 'High Heat'
both are switched ON, which for purposes of calculations are in connected in
parallel.
Note the supply voltage is AC, but we use the RMS value, because it has the
same energy content as an equivalent DC voltage. Select <Electrical: DC
Power> for more details of the calculations. As both Re1 and Re2 are always
the same we can use a simplified method of finding the equivalent series and
parallel values.
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VARIABLE VOLTAGES: DC Voltage.
Interactive Content!
DC voltages are constant over time. The voltage range is determined by the
battery, which could equally be some form of regulated DC power supply.
In practice the lamp would glow brighter as the battery voltage is increased,
but it will always remain at the same level whilst the voltage is constant.
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VARIABLE VOLTAGES: Switching a DC Voltage.
A switch causes the lamp to light when the contacts are closed, by placing a
voltage across the bulb filament. Operating the switch makes the lamp to go
ON and OFF as the applied voltage is first present and current flows and
which then falls to zero as the voltage is removed.
In a practical circuit the ON-OFF periods would not necessarily be constant
as shown here, but would vary with the on-off time.
The output has what is commonly called a square-wave-form. The ON
period is referred to as the mark and the OFF as the space. We will explore
this effect later when we look at timing circuits.
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VARIABLE VOLTAGES: Variable DC Voltage.
By introducing a variable resistor across our battery, some interesting
changes can be observed over time, i.e. the output voltage will vary. The
output is changed slowly, not switched, so between slider positions the
voltage will be made to increase or decrease gradually.
You will probably by now see the variable resistor as a voltage divider
circuit. The output voltage will depend upon the slider position, which
effectively splits the variable resistor track into two quite separate resistor
sections. Changing the variable resistor component value will increase or
decrease the current drawn from the battery and can be calculated using
Ohm's Law.
Variable resistors can be linear as in this case, when the track has the same
relationship between slider position and resistor value or logarithmic, having
very small changes in resistance to slider position at one end and very large
changes at the other.
Logarithmic resistors are less common now and were mostly used as volume
controls, and now with the introduction of IC's these components have been
largely replaced with DC controlled circuits.
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VARIABLE VOLTAGES: Alternating DC Voltage.
Again a variable resistor is used to simulate an AC waveform. That is one
that goes above and below the zero volt line. The battery potentials provide
the maximum and minimum voltage swings.
Note the polarity of the batteries at their junction and the variable resistor
slider, then observe the output voltage. What would be the effect if the
batteries had unequal voltages?
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OHM'S LAW: Current.
Interactive Content!
A simple DC circuit consists of a current source (the battery) connected
across a resistor. Electrons are propelled by the electromotive force (voltage)
of the battery. Expelled from the negative terminal (-) and attracted by the
positive (+) terminal.
Using Ohm's Law the circuit voltage, current or resistance can be found. An
easy way of remembering each of the formulae is to draw a triangle as
shown. Covering the result variable in the triangle leaves the required
formula.
The graph shows a linear relationship between V, I and R, i.e. an increase in
the voltage across the resistor causes a proportional increase in the current
through the resistor.
The plot Window shows an accurate representation for your chosen values.
OHM'S LAW: Voltage.
A simple DC circuit consists of a current source (the battery) connected
across a resistor. Electrons are propelled by the electromotive force (voltage)
of the battery. Expelled from the negative terminal (-) and attracted by the
positive (+) terminal.
Using Ohm's Law the circuit voltage, current or resistance can be found. An
easy way of remembering each of the formulae is to draw a triangle as
shown. Covering the result variable in the triangle leaves the required
formula.
The graph shows a linear relationship between V, I and R, i.e. an increase in
the voltage across the resistor causes a proportional increase in the current
through the resistor.
The plot Window shows an accurate representation for your chosen values.
OHM'S LAW: Resistance.
A simple DC circuit consists of a current source (the battery) connected
across a resistor. Electrons are propelled by the electromotive force (voltage)
of the battery. Expelled from the negative terminal (-) and attracted by the
positive (+) terminal.
Using Ohm's Law the circuit voltage, current or resistance can be found. An
easy way of remembering each of the formulae is to draw a triangle as
shown. Covering the result variable in the triangle leaves the required
formula.
The graph shows a linear relationship between V, I and R, i.e. an increase in
the voltage across the resistor causes a proportional increase in the current
through the resistor.
The plot Window shows an accurate representation for your chosen values.
OHM'S LAW: Formula Transformation.
The subject of the equation is the variable we are attempting to find. In the
first example its V, and R in the second. Note: that the expression is in
algebraic form. Formulae transformations should be made before inserting
the final values and not as in the case of the calculations Window where the
process is shown using actual values.
Manipulation of the variables is across the equals sign (shorthand L.H.S left
hand side and R.H.S for right hand side) also above and below the division
line. Variables with the same sign above and below the line can be cancelled.
The formulae shown are used in electronics to determine the voltage, current
and resistance in a simple DC circuit. By transposing the formula the value
of the third variable can always be found, providing the other two are
known.
Practically all electronics formulae are derived from Ohm's Law and so a
grasp of these transformation principles is essential to aid your
understanding of more complex calculations.
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DC VOLTAGE: Voltage Divider.
Interactive Content!
A simple voltage divider circuit can be constructed as shown, using just two
resistors connected across a voltage supply.
Current I will flow through R1 and R2 determined by their combined value.
The lower voltage (Vout) across R2 is found by Ohm's Law I × R2.
Circuits connected to the Vout junction are referred to as the Load. Load
current will flow through R1 in addition to R2 current and effectively pull
down the voltage at this junction due to the increased voltage drop across
R1.
DC VOLTAGE: Loading a Voltage Divider.
A voltage divider produces a fixed voltage reference. If the current drawn
from the junction of R1 and R2 is small relative to the current through R1
then the loading effect can be ignored. However, increased loading current
can pull down this junction voltage, thereby removing any voltage
stabilisation.
Basically, if the load conditions are fixed by a steady current then the voltage
divider is ideal and the circuit voltages can be calculated as shown. Where
the load current varies considerably then the use of a series voltage regulator
would be a better approach.
Vout is determined by the ratio of R2 : (R1 + R2). Connecting a load across
R2 increases the total current through R1 causing a greater voltage drop
across R1, which lowers the junction output voltage.
To stabilise the output voltage against load current changes, a practical rule
of thumb is to choose the values of R1 and R2 in the correct ratio so that the
divider current is 10 times greater than the load current.
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DC CURRENT: Current Divider.
Interactive Content!
Connecting resistors in parallel divides the total circuit current into n
branches. I equals the sum of the individual branch currents.
Total circuit current I can also be found using Ohm's Law, by dividing the
applied battery voltage by the equivalent circuit resistance.
Note: there is an inverse relationship between each branch current and that
branch resistance.
DC CURRENT: Further Current Dividing.
A current will flow in R1, R2 and R3 which is inversely proportional to their
values. The total current will always equal the combined branch currents.
Individual branch currents can be found by multiplying total current I by the
ratio of the branch resistance to the total circuit resistance.
DC CURRENT: Kirchhoff's Current Law.
Kirchhoff's current law states that the current flowing into a node (circuit
joining point) will always equal the current flowing out. Nodes are identified
in this diagram as the small magenta circles.
The current at any of these points will be measured as equal to I. Similarly
individual parallel section branch currents between the nodes when added
will equal the total current.
To find the individual branch currents, calculate the equivalent parallel
resistance for each section and using Ohm's Law find the voltage between
the nodes.
The current flowing in R1 for example will be the parallel resistor section
(R1, R2, and R3) voltage (potential difference) divided by the value of R1.
Each of the other branch currents can be found in the same way.
DC CURRENT: Further Current Law.
The current flowing into a node or junction will always equal the current
flowing out. Here voltage source Va causes Ia to flow via R3 and R1 and Vb
causes a current Ib to flow in R3 and R2. The total current into the node via
R3 consists of Ia + Ib, where it divides and flows out of the junction back to
Va and Vb to complete each loop.
There are more accurate ways of making these calculations by applying the
various circuit theorems which we shall explore later.
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SERIES AND PARALLEL RESISTORS: Series Resistors.
Interactive Content!
The total circuit resistance of n resistors connected in series can be found by
adding the values together.
Current (electron flow) is common for all values of R1, R2 and R3.
As the current makes its way through the circuit each resistor will develop a
voltage across it which can be calculated using Ohm's Law. The individual
resistor voltage drops when added will equal the applied (battery) voltage.
SERIES AND PARALLEL RESISTORS: Two Resistors in Parallel.
When resistors are connected in parallel their combined resistance will
always be lower than the smallest value. The equivalent for two equal value
resistors will be half either value.
The simple formula shown can be applied in this instance.
SERIES AND PARALLEL RESISTORS: Three or more Resistors in
Parallel.
Connecting three or more resistors in parallel involves a slightly more
complex approach. As for two resistors their combined total will always be
lower than the smallest value.
The reciprocal of resistance is called Conductance this is the ease by which
current can flow. To calculate, first find the conductance of each value and
add them together, the reciprocal of the total is the equivalent resistance.
SERIES AND PARALLEL RESISTORS: Series Parallel Resistors.
When resistors are connected in series/parallel or any other combination the
total circuit current will be dependent upon their combined resistance.
Here the equivalent value of R2 and R3 is found first and then added to the
value of R1.
Circuit current flows through R1 before dividing into I1 and I2 branches,
when added together these branch currents will equal the circuit current. R1
× I is another way of stating 'voltage across R1' using Ohm's Law.
SERIES AND PARALLEL RESISTORS: Further Series Parallel
Resistors.
To calculate the total resistance you will need to determine the equivalent
values of each parallel section first. Then simply add the equivalent and
actual values as for series resistors, where R = R1 || R2 + R3 + R4 || R5. '||'
being shorthand for in parallel.
Combining resistors in this way can be useful to obtain a non-preferred
value.
SERIES AND PARALLEL RESISTORS: Triangle Method.
For a practical electronics application of trigonometry a method of
graphically finding the value of the equivalent resistance Requ for a parallel
circuit is shown. R1 or R2 can also be found when only one is known along
with the equivalent circuit resistance. Position the pointers on the R1 and R2
scales. The equivalent resistor value can be read off on the middle scale.
Alternatively, place R1 or R2 and fit the line to read Requ. The second
resistor value can then be determined.
Scales must represent equal value ranges, i.e. Ohms, kOhms or Mohms.
This method employs the right angle triangle with a 60, 30° relationship
between the sides and where the opposite is found to be half or (0.5) of the
length of the hypotenuse.
Within the calculations the formula is shown as proof by a simultaneous
equation.
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AC MEASUREMENTS: RMS Voltage.
Interactive Content!
The sine wave is the accepted way of representing an alternating voltage or
current. Its wave shape is derived from the output of a voltage generator
during one complete revolution using a single loop of wire. Amplitudes may
be measured as Peak, Peak-to-Peak and RMS (root-mean-square).
RMS values are considered to have the equivalent energy content (heating
effect) as comparable DC voltages and currents. 250V AC mains has an
RMS value with a peak voltage of approximately 350V and a Peak-to-Peak
value of 700V.
Unless otherwise stated AC voltage and current measurements are taken to
be RMS values. Applying the appropriate formula easily makes the
conversion.
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AC MEASUREMENTS: Peak Voltage.
The sine wave is the accepted way of representing an alternating voltage or
current. Its wave shape is derived from the output of a voltage generator
during one complete revolution using a single loop of wire. Amplitudes may
be measured as Peak, Peak-to-Peak and RMS (root-mean-square).
RMS values are considered to have the equivalent energy content (heating
effect) as comparable DC voltages and currents. 250V AC mains has an
RMS value with a peak voltage of approximately 350V and a Peak-to-Peak
value of 700V.
Unless otherwise stated AC voltage and current measurements are taken to
be RMS values. Applying the appropriate formula easily makes the
conversion.
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AC MEASUREMENTS: Peak - Peak Voltage.
The sine wave is the accepted way of representing an alternating voltage or
current. Its wave shape is derived from the output of a voltage generator
during one complete revolution using a single loop of wire. Amplitudes may
be measured as Peak, Peak-to-Peak and RMS (root-mean-square).
RMS values are considered to have the equivalent energy content (heating
effect) as comparable DC voltages and currents. 250V AC mains has an
RMS value with a peak voltage of approximately 350V and a Peak-to-Peak
value of 700V.
Unless otherwise stated AC voltage and current measurements are taken to
be RMS values. Applying the appropriate formula easily makes the
conversion.
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AC MEASUREMENTS: Combining AC Voltages.
When two out-of-phase AC voltages appear across a circuit their resultant
phase angle will depend upon the capacitive and inductive elements within
that circuit. A series or parallel tuned circuit for example.
Out-of-phase voltages cannot be added directly. The resulting amplitude and
phase angle will be dependent upon the relative amplitudes and angles of V1
and V2.
To make this easier to understand, V1 is fixed at 0° and V2 is displaced by
the phase difference ø. Va and Vb represent the values of V1 and V2 with
phase correction. (Va and Vb are simply two temporary variables used to
simplify the formula.) To prove this, give the sine waves equal amplitudes
and make the phase angle ø = 90°, and then compare the calculations as the
phase angle is changed.
Pythagorean Theorem is applied to the corrected values.
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AC MEASUREMENTS: Angular Values.
A sine wave comprises two parameters, amplitude and frequency, each
expressing a continually changing voltage or current. Instantaneous values of
V or I will occur throughout the sine wave cycle.
The angular value (voltage or current) is that amplitude measurement at a
particular angle throughout 360°.
Angular values are not frequency dependent. However, it is useful to be able
to calculate the time t1. A typical example is for SCR or thyristor power
regulation, using t1 as the turn on time. The time t1 is made to vary as the
load power requirements change.
This is explained when we look at SCR power regulation.
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AC MEASUREMENTS: Frequency Measurement.
Here is shown a further representation of the sine wave. This time we are
required to determine the frequency of the waveform. Amplitude is always
measured on the vertical scale and time on the horizontal.
Frequency is therefore the number of complete waveforms that occur during
a period of one second. The period or length of one cycle is also known as
the signal wavelength.
The formula shows this as the reciprocal of t. A reciprocal is simply the
decimal result of dividing a value into 1 or the number of times the value
will fit into a whole, in this case one second. For example the reciprocal of a
period of 25 milliseconds = 1/.025 = 40.
If the frequency is increased will there be more or less cycles per second?
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AC MEASUREMENTS: Period of AC Sine Wave.
The period of a sine waveform is a measure of its frequency. Input a value of
50Hz, the UK mains frequency and the period of one complete cycle will be
20ms or 0.02 of a second.
Now try increasing and decreasing the frequency about this point and note
the period. Does the period increase or decrease with frequency?
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AC VOLTAGE AND CURRENT: Resistor, Voltage and Current
Relationship.
Interactive Content!
As a current flows through a series circuit containing a resistor, a voltage
will develop across the end terminals of that component. The voltage will be
in phase with the current.
The value of the resistor is found by applying AC Ohm's Law where R = V
÷ I.
AC VOLTAGE AND CURRENT: Capacitor, Voltage and Current
Relationship.
As a current flows through a series circuit containing a capacitor, a voltage
will develop across the component end terminals.
From the current waveform on the horizontal scale, voltages peaking to the
right of the current waveform are said to be lagging by 90° as the capacitor
takes time to charge. Changing the relative values of the voltage and current
has no effect on their phase relationship.
The value of the capacitor reactance (AC resistance) can be found by
applying Ohm's Law where Xc = V ÷ I.
AC VOLTAGE AND CURRENT: Inductor, Voltage and Current
Relationship.
As a current flows through a series circuit containing an inductor, a voltage
will develop across the end terminals of the coil. The voltage will lead by
90° across the inductor as the current cannot change instantly due to the
opposition from the magnetic field which is developed around the coil.
From the current waveform on the horizontal scale voltages peaking to the
left are said to be leading by 90°. The value for the inductor reactance (AC
resistance) is found by applying AC Ohm's Law where XL = V ÷ I.
AC VOLTAGE AND CURRENT: Series RCL Voltage Current
Relationships.
Applying a voltage across a resistor, inductor and capacitor, connected in
series will cause a current I to flow through the circuit. The individual
voltages developed across C and L will have 'lagging' and 'leading' phase
angles respectively.
The voltage amplitudes produced will depend upon the resistance or
reactance of C and L at the applied frequency.
The voltages across the inductor and capacitor will to some extent cancel
depending upon their relative amplitudes, as they are 180° out of phase. In
practice the both capacitance and inductance contain some resistance, but for
our purposes this can be ignored as we are only interested in the principle of
circuit operation.
AC VOLTAGE AND CURRENT: Angle of Rotation.
AC voltages and currents measured across a resistive circuit have a
constantly changing amplitude throughout the 360° cycle. Beginning at 0°
increasing to a maximum positive at 90° and declining to zero at the 180°
point. Then repeated in the negative direction from 180 to 360° for the other
half cycle.
The voltage or current measured at any point is known as its instantaneous
value. As these follow the waveform shape they will reflect the peak
amplitudes.
You have the opportunity to examine these values more fully by selecting
'Angular values'.
AC VOLTAGE AND CURRENT: Parallelogram for Voltage Phase
Angles.
A convenient way of representing AC voltages is to use a phasor diagram.
Phase angles for inductive circuits will be plotted above the zero line as V
leads I and below zero for capacitive circuits, as V lags I.
Resistor currents and voltages are always in phase and therefore will be
drawn on the 0° line. The diagram is completed as a parallelogram. The
resultant phasor length and angle, provide a useful visual indication of the
AC circuit conditions.
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AC THEORY: AC Ohm's Law.
Interactive Content!
Ohm's Law can also be applied to AC circuits. However, alternating currents
and voltages are continually changing. At the beginning of the cycle the
voltage and current are zero, building to peak positive values at 90°, before
declining back to zero, and then repeated in a negative direction.
It is therefore only possible to calculate instantaneous values of V or I
throughout the cycle. Peak or RMS values are normally used.
The AC resistance of capacitors and inductors is called 'reactance' (measured
in Ohms). As the frequency is increased, capacitive reactance decreases,
whereas inductive reactance increases.
Once the reactance is calculated for C or L at the applied frequency, the
value can be inserted in the formula as for resistance. Where there is a
combination of resistance and reactance the calculation refers to 'impedance',
symbol Z.
AC THEORY: Combining Alternating Currents.
When two or more currents flow in a DC circuit they can be added or
subtracted directly. For parallel AC circuits the currents will be at phase
angles determined by the circuit capacitive and inductive elements.
One way the resultant can be found is graphically as shown, by measuring
the amplitudes of the instantaneous values for A and B throughout the
waveform and adding. The resultant phase angle will tend to be towards the
current making the greatest contribution to the resultant.
Phase differences greater than 90° are not considered, but it should be
understood that they do arise in practical circuits.
The use of phasors is another approach. Select 'phasor diagrams topic' for an
explanation.
AC THEORY: Voltage and Current for R.
For the parallel AC circuit the voltage is common across all current branches
of R, C and L. However, the current for each branch will have a phase angle
determined by the resistive, capacitive or inductive element of that
component.
For the capacitor, the current will 'lead' the voltage and for the inductor
current will 'lag' the voltage. Whereas resistor currents and voltages will
always be in phase.
The instantaneous amplitudes of both voltage and current can be found at
any point throughout the AC waveform for phase angles of 0 to 360°.
AC THEORY: Voltage and Current for C.
For the parallel AC circuit the voltage is common across all current branches
of R, C and L. However, the current for each branch will have a phase angle
determined by the resistive, capacitive or inductive element of that
component.
For the capacitor, the current will 'lead' the voltage and for the inductor
current will 'lag' the voltage. Whereas resistor currents and voltages will
always be in phase.
The instantaneous amplitudes of both voltage and current can be found at
any point throughout the AC waveform for phase angles of 0 to 360°.
AC THEORY: Voltage and Current for L.
For the parallel AC circuit the voltage is common across all current branches
of R, C and L. However, the current for each branch will have a phase angle
determined by the resistive, capacitive or inductive element of that
component.
For the capacitor, the current will 'lead' the voltage and for the inductor
current will 'lag' the voltage. Whereas resistor currents and voltages will
always be in phase.
The instantaneous amplitudes of both voltage and current can be found at
any point throughout the AC waveform for phase angles of 0 to 360°.
AC THEORY: Capacitive and Inductive Current Phasors.
The phasor diagram is a useful way to determine the resultant of out-ofphase AC currents. These can be measured as peak or RMS values.
As alternating currents are continuously changing throughout the sine wave
cycle then only instantaneous points throughout the cycle can be used.
Negative phase angles indicate a lagging or inductive current, whereas a
positive or leading phase angle will indicate a capacitive current. The phase
angle of the resultant indicates a predominantly capacitive or inductive
circuit.
Calculations to prove the resultant values can be determined using the
formulae for adding complex numbers.
AC THEORY: Oscilloscope Measurements.
This topic shows you how to measure the frequency and peak-to-peak
amplitude of the sine wave. The oscilloscope graticule scale will be marked
as TIME/DIV on the horizontal and VOLTS/DIV on the vertical. Period t is
the time duration of one cycle. To calculate the sine wave frequency simply
multiply the number of horizontal divisions (including any fractional parts)
by the TIME/DIV value and find the reciprocal.
The amplitude is determined in the same way, count the vertical divisions
including any fractional part and multiply by the VOLTS/DIV switch setting.
To find the peak amplitude divide peak-to-peak measurement by two. You
are left to investigate the RMS value.
Typical features to be found on an oscilloscope are as follows. Large 150mm
(6ins) High Luminance CRT with internal graticule, 1cm/div Sensitivity ×10
Sweep magnification. TV Sync. Separator Circuit for Stable TV Signal
Observation. ALT Triggering Function (Vert Mode), CH2 Polarity Inversion
Switch. High Sensitivity X-Y Mode.
The functions are now also available as 'virtual instruments' which are
viewed on a computer screen display One advantage of these over the
conventional oscilloscope instrument is they are able to digitally analyse the
display thereby providing additional information to the user.
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RCL SERIES: RC Series Circuit.
Interactive Content!
When a capacitor and resistor are connected in series a current will flow to
charge the capacitor. Current I is shown as being in phase with VR. VC will
lag I by 90°. The two voltages VR and VC cannot be added directly and the
phasor diagram is used to find the resultant or applied voltage amplitude and
phase angle.
Voltage VC can be found using AC Ohm's Law where VC = Xc × I.
The resultant or applied voltage is that which is required or developed across
the circuit with these particular component values. Note the resultant voltage
can be greater than the individual values of VR or VC.
As this is a capacitive circuit the resultant voltage phase angle will lag the
current I.
RCL SERIES: RL Series Circuit.
Voltages developed across R and L cannot be added directly. The phasor
diagram is used to show the resultant voltage and phase angle.
VR and VL are a result of the values for R, XL (inductive reactance) and the
series current.
The larger the relative value of XL to R the closer the resultant phase angle
will be to 90° which is an indication of the amount of inductance in the
circuit.
As it's an inductive circuit the resultant or applied voltage will lead the
current I which is given an arbitrary value in this instance to show that it is
in phase with VR.
RCL SERIES: RCL Series Circuit.
The series current is common for R, C and L. VR will be in phase with I.
Whereas the voltages of VC and VL will be in 180° phase opposition,
resulting in some cancellation.
The phasor diagram will produce the resultant circuit voltage and its phase
angle. Positive angles indicate a greater inductive circuit influence and
negative angles capacitive.
We will go on to examine how these voltages are calculated when
considering the reactance's of capacitance and inductance.
For this example the value of the current is of no importance other than to
show it flows through all three components.
RCL SERIES: Series RC Voltages.
In the series RC circuit, voltages developed across R and C have a 90° phase
relationship.
Our objective here is to determine the value of V and its resultant phase
angle, to that of the series current and VR which both sit on a phase angle of
0°.
As the proportion of the voltage V is increased across R, the resulting phase
angle across the circuit gets smaller, lowering voltage across C. VR is in
phase with the current and VC at -90° for a perfect capacitor.
The phase angle is always negative as the capacitor voltage lags the series
circuit current.
RCL SERIES: Series RC Phase Angle.
This example of applying trigonometry to electronics uses the right angle
triangle to find the circuit impedance and the effect on the resultant phase
angle for a series RC circuit.
The 'hypotenuse' of the triangle represents the total circuit impedance Z. The
value of R is shown as the triangle 'base or adjacent'. Therefore, the 'height
or opposite' will represent Xc. The resulting phase angle is dependent on the
relationship between values of resistance R and the capacitor reactance Xc.
First use Pythagorean theorem to calculate the unknown value of Z and the
scientific function ATN (tan-1) to determine the phase angle.
It will be found that where values for capacitive reactance are small in
relation to R the resultant impedance will almost equal the circuit resistance.
The overall circuit impedance can never be less than R. This is proved by
observing the relationship between the sides of the right angle triangle.
RCL SERIES: Series RL Phase Angle.
Here we find the circuit impedance and the effect on the resultant phase
angle for a series RL circuit. When the inductor reactance XL and the
resistor value are known. The previous comments relating to an RC circuit
triangle still apply.
From the right angle triangle, the 'hypotenuse' represents the total circuit
impedance Z. The value of R is shown as the triangle 'base or adjacent'.
Therefore, the 'height or opposite' will represent the inductive reactance XL.
The phase angle is dependent on the relationship between values of R and
XL. First use Pythagorean theorem to calculate the unknown value of XL
and the scientific function tan-1 to determine the resultant phase angle.
Note that as this is an inductive circuit the phase angle is always positive,
which is exactly opposite to that for a capacitive circuit.
RCL SERIES: Using Sin and Cos Trigonometric Functions.
Using the Sin and Cos trigonometric functions the individual voltages across
the resistor and inductor can easily be found. Similarly for the RC
configuration.
Here the voltage developed or applied across the circuit is known along with
its resultant phase angle, which in practice will be determined by the relative
values of R and XL.
The calculations are based on the relationships of a right-angled triangle.
From the graph it can be seen that VL leads VR by 90°.
The resultant voltage phase angle will move towards the greater value of VR
at 0° or VL at +90°. This is shown graphically as a right angle triangle.
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RCL PARALLEL: RC Parallel Circuit.
Interactive Content!
Currents IR and IC are 90° out of phase and cannot be added directly. The
total current or resultant will depend upon the resistance of R and the
reactance (AC resistance) of C.
As the reactance of C falls relative to the resistance of R, so more current
flows in the capacitor branch and the resultant phase angle increases towards
+90°.
RCL PARALLEL: RL Parallel Circuit.
The current through L will lag the applied voltage and resistor current by
90°. IL is limited by its reactance (XL) at the applied frequency. XL
becomes larger with increasing frequency.
The calculations show that as the current IL is decreased relative to IR so the
resultant phase angle will get smaller and approaches zero degrees.
As the relative value of XL is reduced compared to that of the resistor (R),
so the inductor conducts a greater proportion of the current and the resultant
phase angle becomes larger, approaching 90° where the resistor ceases to
have any significant effect.
The negative phase angle indicates a lagging or inductive circuit.
RCL PARALLEL: RCL Parallel Circuit.
An RCL parallel circuit produces a resultant current which is a combination
of IR and the difference between IC and IL. The effective total current is
found using the phasor diagram. It will be seen that IR is at the base of a
right angle triangle and IL minus IC or IC minus IL forming the
perpendicular.
The hypotenuse is the amplitude of the resultant current. The phase is found
by measuring or calculating the angle ø.
To calculate the resultant use the Pythagorean theorem. IC and IL are 180°
out of phase or flowing in opposite directions and will therefore cancel. The
resultant current is the difference between the two.
The tan-1 scientific calculator function will return the phase angle.
RCL PARALLEL: RCL Waveforms.
Connecting a resistor, a capacitor and inductor in parallel produces the
individual voltage and current relationships as shown. The voltage will be
common across R, C and L.
Current IR is in phase with V. Currents IC and IL flowing in the capacitor
reactance Xc and through inductor XL will be ±90° to the applied voltage
and at 180° out of phase to each other, and will therefore partially cancel or
completely if they are equal.
To charge a capacitor and develop a voltage across it, current first needs to
flow into the capacitor. This is explained by the leading current waveform
and an easy way to remember 'lag and lead'. An inductor on the other hand
will resist the current flow caused by an opposing magnetic flux. Current
therefore lags or is behind the voltage for the inductor.
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CAPACITANCE: Capacitor Charging.
Interactive Content!
Connecting a capacitor in series with a resistor across a steady DC supply
causes the capacitor to eventually become charged to a voltage equal to the
battery. The time it takes is determined by the resistor and capacitor values.
Normally the capacitor is considered to be charged when the voltage reaches
63% of the supply voltage. This takes a period of time equal to C × R in
seconds.
The reason for the exponential waveform shape is that when the capacitor is
uncharged it is effectively a short circuit and a relatively high current flows,
determined mostly by the value of R. As the capacitor charges a voltage is
developed across it which opposes or subtracts from the applied voltage (V).
As V - VC decreases and VC approaches V, the charging current tends
towards zero. It takes a period of approximately five time constants for C to
become fully charged (or discharged).
CAPACITANCE: Capacitor Discharging.
With the switch contacts set between a-b, the capacitor will eventually
become fully charged. The internal resistance of the battery which is small,
will be the only limitation on the charging current. However, this topic is
more concerned with capacitor discharge. Place the switch in the b-c
position and the circuit consists of a fully charged capacitor with a resistor
connected in parallel.
Current will begin to flow, thereby discharging the capacitor. The time it
takes will depend upon how large the capacitance is and how small the
resistance is.
Time constant is again R × C, but this time it is the period it takes for the
fully charged capacitor to discharge to 37% of the fully charged state. 37% is
the result of subtracting 63% from 100%.
Note the discharge is rapid at first owing to the high current flow and then
progressively slows as the capacitor charge becomes exhausted and the
voltage developed across it falls.
CAPACITANCE: Capacitor Charge & Discharge Cycle.
A capacitor is a device able to store an electric charge. In its simplest form it
consists of two metal plates separated by an insulator called a dielectric. A
charge is stored across the plates by closing switch S1, negative (surplus)
electrons are forced onto one plate and an electron (deficiency) is caused on
the other as electrons are attracted away by the battery (+ve).
Reverse the battery and the capacitor charges in the opposite direction.
On closing S1, current will flow limited only by R1 to charge the capacitor.
As the charging waveform shows the current flow is rapid at first, but
gradually reduces as the capacitor becomes fully charged, whereby current
flow eventually ceases.
On opening S1 the capacitor charge remains. Closing S2 begins the process
of discharge via R2, rapid at first, then gradually slowing. The values of R1,
R2 and the capacitance of C will determine how long the charge/discharge
process takes.
CAPACITANCE: Calculating Capacitor Value.
Capacitor values are determined by three factors. Plate area; distance
between the plates and dielectric type. To obtain a larger capacitance, either
increase the plate area or bring the plates closer together.
A variable capacitance can be made by changing the dielectric, for example
sliding a mica sheet from between the two plates, the mica dielectric is then
replaced by air in the space between, which has a different dielectric
constant to that of the mica, previously present.
If the capacitor has more than two plates multiply the plate area by the
number of plates -1. The minus one is because there is always one less space
between the plates than the number of plates.
The Toolbox has a further calculation that enable you to change the number
of plates.
CAPACITANCE: Calculating Capacitor Charge.
The Coulomb is used to measure electrical quantity. It is the amount of
electricity delivered in one second by a current of 1 ampere. The larger the
capacitor the more energy it will store, which is measured in Joules.
One Joule of energy is when 1 ampere is made to flow through a resistor of 1
Ohm for one second. I is the average current delivered during the period of
charge.
CAPACITANCE: Capacitor Charging Waveforms.
As switches S1 and S2 are alternately opened and closed C charges via R1
and discharges via R2. As R1 = R2 the charge and discharge times will be
the same.
Initially IC flows through R1, as the charge builds up the voltage is reduced
across R1 and C charges more slowly. Hence the exponential waveforms.
One time constant is calculated to be 63% VC or 37% of IC.
It takes approximately five time constants for the capacitor to fully charge or
discharge. The R, C time constant can be lengthened by increasing the
values of the resistors and/or the capacitor.
CAPACITANCE: Calculating RC Time Constant.
The instant switch S is closed a current will flow via the resistor to charge
the capacitor. The charge time will depend upon the values of the resistor
and capacitor.
The time constant of R and C is normally calculated to be at 63% of full
charge, where it takes approximately 5 time constants to reach full charge.
We can find the voltage across the capacitor at any given time by measuring
the rate of charge at that point. When t1 equals one fifth of the total charge
time the voltage developed across C will be 63% of the battery voltage.
The initial charging current can be calculated from Ohm's Law. Note that I
falls exponentially as an increasing proportion of the voltage is developed
across C.
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CAPACITORS: Capacitor Reactance.
Interactive Content!
Capacitive reactance is the opposition to the applied voltage change. The
symbol Xc is used and expressed in Ohms.
Capacitive reactance decreases with increasing frequency and is therefore
inversely proportional to the capacitance. This relationship between
frequency and capacitive reactance is opposite to that for an inductor.
The graph shows an accurate representation of the capacitor reactance over a
typical range of frequencies. This is included to enable the response curve to
be plotted. For very low frequencies the reactance will be extremely high,
effectively open-circuit. For increasing frequency the capacitor reactance
falls, exponentially.
This is opposite to the effect on an inductor, where the inductive reactance
increases with applied frequency in a straight line.
CAPACITORS: Capacitors in Series.
Connecting capacitors in series has the same effect as increasing the distance
between the plates on a single device, thereby lowering the total capacitance.
This is proved by the fact that the series combination charges more rapidly
than any single capacitor. For the series circuit the combined capacitance
will always be smaller than the lowest value.
Capacitors connected in this way can be used to make an AC voltage divider
and so the working voltage of any individual capacitor could be less than the
peak supply potential. This can be an advantage if a device with the correct
maximum working voltage is not to hand. Ensure polarised capacitors are
always connected correctly, i.e. all in the same direction across the supply.
To calculate individual voltage drops multiply the reactance of each
capacitor by the series current to find that developed between each junction.
Voltages will be inversely proportional to each capacitors value.
The circuit current is determined using Ohm's Law, by dividing the applied
voltage by the total series reactance (AC resistance). Adding the individual
voltage drops will always equal the applied voltage.
CAPACITORS: Capacitors in Parallel.
Connecting capacitors in parallel increases the total plate area and therefore
their combined capacitance will be the individual capacitance's added
together.
The applied voltage is present equally across C1, C2 and C3.
Each capacitor provides a branch through which the current divides
proportionally to the capacitor reactance, at the applied frequency. Larger
values of capacitor will take more current as their reactance will be lower.
The branch currents when added together will equal the total current.
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INDUCTANCE: Storing Energy in an Inductor.
Interactive Content!
Connect a battery across an inductor and a current will be made to flow
through the coil winding. As the current changes (builds-up) energy is stored
in the coil as a magnetic flux the density of which is dependent upon the
amount of current flowing, determined by R1. A magnetic field exists only
whilst a current is flowing in an inductor. When the current ceases to flow,
the field collapses.
If S1 is opened and S2 closed, the energy produced by the collapsing field
will be dissipated in R2. The rate of collapse can cause a very large voltage
spike to occur which other circuits need to be protected from. This safety
measure is usually in the form of a reverse biased (commutating) diode
connected across the coil which conducts on the reverse voltage.
The rate of current change will determine the back-EMF (reverse voltage)
developed across L. This can reach extremely high levels (thousands of
volts) and should be controlled. The faster switch S1 is opened and S2 is
closed and the lower the value of R2 then the higher the back-EMF.
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INDUCTANCE: Calculating an Induced Voltage.
Unit of inductance is the Henry, (symbol L). Inductance of one Henry =
1Volt of induced EMF from a changing current of 1Amp per second. I1 and
I2 represent two values of current.
The difference between I1 and I2 is the current change. 100mA to 150mA =
50mA. Similarly 0mA to 50mA equals 50mA. It is the amount of current
change in a given period of t. Confirm your result by working the calculation
in reverse.
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INDUCTANCE: Calculating Inductive Energy.
When current flows, energy will be stored in L, as a magnetic field. The
energy absorbed is measured in Joules.
When the field collapses the stored energy is released as power to a resistive
circuit, determined by the formula for 'average power'.
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INDUCTANCE: Inductive Circuit Waveforms.
On closing S1, IL will gradually increase through L. It cannot reach its
maximum value instantly as the magnetic field previously built up in L
opposes the current flow.
At the same time the voltage across L reduces towards zero. Opening S1 and
closing S2 provides a current path as the magnetic field collapses and stored
energy is dissipated in R2.
A time constant for the LR circuit is calculated to be at 63% of IL or when
VL has reduced by 63%. The process of the magnetic field building up in L
and collapsing is repeated as the switches are alternately opened and closed.
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INDUCTANCE: Calculating RL Time Constant.
On closing switch S1 current will flow from the battery via the resistor to
build up a magnetic field within L.
The time taken to reach the coil saturation point is determined by the values
of R and L. The time constant is calculated to be 63% of the 'Steady State'
current, which takes approximately 5 time constants to complete.
We can find the current flowing in the coil at any given time by calculating it
at that point in the waveform. When t1 equals one fifth of the total saturation
time the current in L will be 63% of the maximum current.
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INDUCTORS: Inductive Reactance.
Interactive Content!
The opposition to current change in an inductor is called reactance and given
the symbol XL (AC resistance) and expressed in Ohms. The back-EMF
generated opposes the applied current change.
Whilst capacitors inhibit the flow of direct current and allow the passage of
alternating currents, inductors exploit the opposite effect, they resist AC and
allow DC to pass through. Therefore, inductors have a low reactance (AC
resistance) at low frequencies which increases as the frequency is increased.
Compare the graph waveforms for capacitive and inductive reactance, the
Xc gives an exponential waveform and XL is a straight line.
You will see the effect of combining capacitive and inductive reactance
when we look at tuned circuits.
Inductive reactance is proportional to the applied voltage frequency.
Applying AC Ohm's Law using XL in place of R and will prove that as the
frequency is increased so the current decreases.
INDUCTORS: Inductors in Series.
The total inductance of the series inductor connection is the sum of L1 + L2
+ L3. The current I flows through each value of L; the individual voltages
V1, V2 and V3 will depend upon reactive values of L1, L2 and L3 at the
applied AC voltage frequency.
One way to increase the inductance of a coil is by winding on more turns to
the coil former, which in turn increases the voltage developed across that
winding.
INDUCTORS: Inductors in Parallel.
Calculations for inductors connected in parallel can be made as if they were
resistors. Their combined inductance reduces as each new value is added.
Individual branch currents will be inversely proportional to each value of
inductance.
Branch currents are calculated using Ohm's Law, replacing resistance by the
reactance of the combined or individual inductors at the applied frequency.
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IMPEDANCE: RC Series Impedance.
Interactive Content!
Impedance is the sum of resistance and reactance in an AC circuit, it is
measured in Ohms and given the symbol Z. Impedance can be used in place
of resistance when calculating AC using Ohm's Law on reactive circuits.
The voltages developed across R and C (Xc) cannot be added directly as the
voltage across C is at 90° to that across R.
The impedance triangle can be a useful method to graphically find the
impedance Z.
The resultant impedance phase angle will be determined by the relative
values of R and Xc. With the angle becoming greater as the reactance of the
capacitor to the applied frequency increases.
A lagging (-) phase angle indicates a capacitive circuit.
IMPEDANCE: RL Series Impedance.
The impedance of any series circuit can never be lower than the fixed value
of R or the circuit resistance. The reactance (XL) is however, frequency
dependent. It increases with frequency. Voltages developed across R and XL
will be at 90° and therefore cannot be added directly.
The impedance phase angle will approach 90° as the relative value of XL is
increased to that of R.
Since XL (and Xc) react to changes in frequency it will be seen that altering
the component value produces not only a change in phase angle, but also
effects the circuit impedance.
IMPEDANCE: RCL Series Impedance.
The RCL series circuit is a combination of the RC and RL series circuits.
The voltages developed across Xc and XL will be in 180° phase opposition
and cancel.
A positive resultant phase angle means the circuit is behaving inductively
with the current lagging the applied voltage. A negative resultant angle and
the current will lead the voltage as is the case for a predominantly capacitive
circuit.
IMPEDANCE: R.C Parallel Impedance.
The parallel RC circuit is an alternating current divider, V being common to
R and C. Individual branch currents will depend upon relative values of R,
and Xc at the applied frequency.
IR and IC at 90° cannot be added directly and so Pythagoras' theorem is
applied.
As for two resistors in parallel the circuit impedance will always be lower
than R or Xc. The impedance phase angle will be dependent upon IR and IC
relationship.
IMPEDANCE: R.L Parallel Impedance.
The current through L will lag IR by 90°. The resultant negative phase angle
will depend upon the relative values of R and XL. Dividing the applied
voltage by Z will determine the total current.
There cannot be a direct addition of IR and IL because of their 90° phase
angle.
The formula is derived from that for resistors in parallel.
As the circuit is inductive the phase angle will be negative.
IMPEDANCE: RCL Parallel Impedance.
The RCL parallel circuit can be considered as two reactance's, Xc and XL
where the currents are in phase opposition, in parallel with a resistor.
Impedance Z is V / resultant I.
Impedance phase angle is calculated from the difference between IL and IC
divided by IR.
IMPEDANCE: Conductance, Susceptance and Admittance.
AC calculations using Conductance, Susceptance and Admittance can
sometimes be an easier method of finding a circuit impedance. Compare the
calculations yourself to the RC parallel impedance topic.
The SI unit of measurement for Conductance, Susceptance and Admittance
is the Siemen, and is given the symbol S. An element has a conductance of
one siemen when it has an electrical resistance of one Ohm.
Admittance (Y) can be visualised as the current flowing into an AC circuit
divided by the supply voltage i.e. the circuit impedance (Z) and is therefore
the reciprocal of Z.
When found in complex number calculations, admittance can be resolved
where conductance (G) forms the real r number part, and susceptance (B) is
the imaginary part or ±j. The two having a ±90° phasor relationship.
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RADIO AND COMMUNICATION: AM Radio Transmitter Block
Diagram.
Interactive Content!
AM is an abbreviation for Amplitude Modulation. The AM radio transmitter
is the collection of circuits that generate the electromagnetic waves that
convey our messages to receivers. The simple diagram contains all the
blocks necessary to make this happen. Beginning with the input as a tiny
signal from the microphone this is first amplified and then mixed with the
output from the Variable Frequency Oscillator (VFO). This combined
voltage signal must then be amplified and sent as much more powerful
signal with an output impedance suitably matched to drive the antenna.
The output is always a sine wave with a constant frequency for that
transmission, called a carrier. Onto this is modulated our audio signal. The
purpose of the carrier is to provide a means of transferring audio frequency
signals which by themselves do not radiate as electromagnetic waves,
whereas the higher frequency of the carrier does, extremely effectively.
There are several methods of modulating this carrier, but for now we will
only consider amplitude modulation. This means the carrier frequency
remains constant, but the mixed audio signal causes this to be varied in
amplitude. This is the loudness of the received speech. The frequency of the
audio signal continually varies as we speak and this shows as longer or
shorter duration of the modulation envelope, where higher speech
frequencies cause the modulation to occur much faster than lower
frequencies.
Microphone is a device that outputs electrical energy from input sound
energy.
The force of the speech causes a transducer i.e. moving coil or crystal to
output a small voltage that varies in both amplitude and frequency in direct
relation to the level and frequency of the speech.
The output from the microphone is at a very low level, no more than a volt
in amplitude.
The audio amplifier increases that amplitude to a sufficient level suitable for
modulating the carrier waveform. A low pass audio filter is required as part
of this circuit to severely limit any frequencies above 3kHz. This narrow
range of audio frequencies is sufficient for intelligible speech.
The modulator has two inputs, one the carrier which is a sine wave of
relatively high frequency (1 to 500MHz) and generated by the Variable
Frequency Oscillator and the other the amplified audio (speech) signal.
The modulator is a circuit that outputs a signal that is a combination of the
two. This means the high frequency carrier now includes the audio
information (having a ride).
Variable Frequency Oscillator is a frequency generator and produces a
carrier at the desired wavelength for transmitted signal, between 1MHz and
500MHz. It's always a pure sine wave. Any errors here mean the signal
transmitted could fall outside the allocated radio bands. In practice this
method of an amplitude modulated output is not actually used, because it is
extremely inefficient, but forms basis of all radio transmissions and so its
important to understand the principle of using one carrier to transport the
wanted audio signal to the receiver(s) antenna.
It is extremely important that the output frequency, which is continuously
variable by the user controls, once selected remains stable and various
methods are used to ensure this. These range from switched crystal
oscillators to digital frequency synthesisers. Accurate calibration of the VFO
is an important part of using your rig. This is one area of the transceiver
circuit where the difference between the budget and top of the range rigs will
be clearly identified.
The input i.e. output from the modulator (audio modulated carrier) will
usually be a voltage waveform with very little current (fairly high
impedance), however the signal for driving the antenna must contain
electrical power, most likely a low voltage with lots of current (low
impedance), depending upon the design of the power amplifier.
Radio Frequency (RF) amplifier is similar to an audio amplifier where a
small voltage drives the cone of a heavy loudspeaker via a powerful
amplifier capable of developing lots of watts, except in this case its at a
much higher RF (Radio Frequency). To limit the transmitter output to those
frequencies in the desired transmission band, a low pass filter is
incorporated, thereby cutting off any frequencies outside those permitted.
Transmitter Antenna provides the electromagnetic interface between your rig
and the outside world. To be effective it has to be designed to match the
output impedance of the transmitter to maximise on the efficiency of the
power output and also physically constructed so as not cause obstructions or
interference with other electrical equipment.
This is greatly simplified here, but helps to explain the operation of an
antenna. When transmitting, consider the antenna as a transformer operating
at a high frequency. The current changes in the carrier sine wave will cause a
'magnetic' field to build up around the dipole that will radiate outwards. This
magnetic radiation can be picked up by ferrite rod aerials tuned to the same
frequency as the ferrite provides an easy path for the magnetic flux which is
then converted to a weak voltage input signal at the receiver through the
aerial coil winding. The voltage (electrical) fluctuations will be similarly
collected by any tuned dipole. An antenna tuned to the same frequency will
cause tiny currents to travel down the feeder to the RF input stages of the
receiver, thereby developing the voltage input signals, which are then
amplified and demodulated.
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RADIO AND COMMUNICATION: AM Radio Receiver Block
Diagram.
The purpose of our simple amplitude modulated signal receiver is collect the
extremely weak transmitted signal at the desired frequency, to detect the
audio component of the signal, remove the unwanted carrier and amplify the
audio to a sufficient level of power for driving the loudspeaker.
The block diagram shown contains all the component parts necessary for the
practical reception of signals, but in this simplified form has lots of
limitations and is included here to introduce the basics of signal reception.
The radio signal, consisting of a modulated high frequency carrier will be
picked up by the antenna tuned by the length of its dipole to the frequency
range of the required transmission band.
This is conducted by the cable, coax or twin feeder to prevent pickup of
interference to the input of the RF amplifier. At this point there will be a
wide range of signals present that fall within the band.
This block has two functions, first to select just the one desired carrier
frequency from all those present at the dipole and secondly as far as possible
reject all others (selectivity). This is the function of tuning.
Next it has to amplify the very weak signal received (modulated carrier) to a
sufficient level to drive the demodulation circuits.
The demodulator has to recover the original audio signal by removing the
carrier.
See Simple AM Diode Detector for a full explanation.
Audio Amplifier is identical to any home audio amplifier. It simply accepts
an audio signal (speech) and raises its power sufficiently to drive a
loudspeaker. If the transmitted radio signals are limited to just speech, say
3kHz bandwidth this does not have to be of particularly high quality
amplifier, nevertheless should output the audio with clarity, no additional
distortion or noise. Loudspeaker converts electrical energy to sound waves,
exactly the opposite to the workings of a microphone.
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RADIO AND COMMUNICATION: Main Types of Antenna.
HALF WAVE DIPOLE. The simplest antenna systems consist of nothing
more than a piece of wire strung between two points with a connection of
either coax or twin feeder made to the centre. The length however is
important and is measured to be half the wavelength of the transmitter output
frequency. The principle of operation forms the basis on which all other
designs are made and will be discussed more fully in the next topic. Move
the slider to see the required dipole length for each type. Full calculations for
any frequency or wavelength conversions are discussed later.
YAGI ARRAY. A television receiver aerial is a yagi array. It consists of a
dipole to which the download connection is made, behind which is the
reflector and in front a number of directors. Adding the reflector, which is
around 1/8 of a wavelength behind and 5% longer than the dipole collects
any signal from the direction of the transmitter and reflects it back to the
receiving element the dipole. Directors successively decrease in length by
about 5% and again with a 1/8 wavelength spacing in front. The more
directors present the more directional and the greater the antenna gain.
QUARTER WAVE GROUND PLANE. The bit sticking up is one half of a
dipole the other half is like a mirror image formed by the ground plane
which could be a flat copper disk, but works just as well with four simple
quarter wavelength radials. For practical reasons of antenna length this type
is restricted to use at the higher frequencies with shorter wavelengths.
FIVE-EIGHTHS WHIP. This device has a loading coil at the base between
the antenna and the coax. This effectively makes the length of the antenna
three quarters of a wavelength long providing a 50 Ohms impedance match
to the transmitter output. Again for practical reasons of length these are used
at VHF only.
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RADIO AND COMMUNICATION: Antenna Current and Voltage
Distribution.
A dipole is an inductor tuned to an ideal frequency determined by its length
i.e. half a wavelength where the standing current and voltage will be
distributed as shown. In the centre there will be maximum current decreasing
to zero at either end. Note this is in the same direction, shown as positive.
The voltage as for any inductor will be delayed by 90° and will be in a
positive direction at one end and negative at the other. Note these waveforms
are each half of a full cycle.
Along the length of the dipole the impedance is determined by the
amplitudes of the voltage and current and calculated by the application of
Ohm's Law (there are no reactive elements to consider). A connection made
at any point along the length of the dipole will require a suitable impedance
match.
Using the typical figures given the impedance can be calculated. Note: we
are using instantaneous values and in practice these could be continually
changing in amplitude during a period of speech or data, depending upon the
method of transmission.
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RADIO AND COMMUNICATION: Simple Communications System.
An essential part of communications equipment is the conversion of
information which is understood by ourselves to a form which can be carried
from one place to another, i.e. transmitted.
The two circuits used to carry out this operation are called a modulator and
demodulator respectively and the process of conversion at the transmitter is
known as signal encoding. For a simple radio system this is just a matter of
converting the audio or modulating frequency to a much higher radio
frequency making it suitable for transmitting. Alternatively, when a fibre
optic cable is the transmitting medium the signal would need to be to
converted into pulses of light, or to two discreet ±voltage levels for transfer
between computer terminals via the RS232 interface.
At the receiving end, any high frequency carrier previously added, or voltage
level changes made will have to be converted back (decoded), leaving the
information exactly as it was before entering the encoder/modulator at the
transmitter. Take note of the order that the information is transmitted and
received, i.e. first in first out.
The underscore character is included to make the space between the
transmitted space words visible.
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RADIO AND COMMUNICATION: Morse Code Communication
System.
Morse code is one of the most efficient methods of transmitting information
from A to B and is one reason it is still used today. However, with modern
communications equipment its no longer regarded as the only international
emergency signal. It's still retained by amateur radio enthusiasts as an
effective way for long distance communication. The senders key, pulses the
carrier sine wave ON or OFF enabling a sounder (buzzer) at the other end.
A representation of a Morse code practice oscillator serves to demonstrate an
internal communications system. The output-receiving device being
separated by a length of cable.
A duplicate system connected in the reverse direction would enable what is
called a duplex system, i.e. simultaneous communication both ways.
The oscillator is built around a 555 Timer integrated circuit connected as
astable oscillator that when enabled gives a continuous output square wave.
Pressing the key, which is normally open, activates the device via the logic
inverter and generates a sound output (buzz), the duration of which would
depend upon a DOT or a DASH being transmitted.
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RADIO AND COMMUNICATION: Measuring Wavelength.
The properties of frequency and wavelength cannot be separated, where one
is as a result of the other. Wavelength is represented by the Greek symbol
Lambda, and is the distance travelled throughout one complete waveform or
cycle. To measure wavelength the start point can be anywhere during the
sine wave, but the end point must always be the same position on the next
cycle.
Radio waves travel at the speed of light which is 300,000,000 metres per
second. Therefore, dividing the wavelength into this figure returns the
frequency in cycles per second, called Hertz (Hz) signal.
For the radio transmission of information from one point to another, three
things are required, a transmitter, an intervening medium (the air, copper or
fibre optic cable) and the receiver. The transmitter will consist of apparatus
capable of producing energy in the form of high frequency alternating
current, which is delivered to a transmitting aerial. Nearly all this energy
surging in the connecting wire to the aerial will be dissipated in the form of
electromagnetic waves, or vibrations in the surrounding medium called the
Ether.
These radiated waves will travel through the Ether and reach the receiving
aerial that must be situated within the desired reception area. A tiny
electrical current will be induced in the aerial circuit that is the same shape
as that fed to the transmitting aerial. This received information is then
amplified (to use a modern term, conditioned) as necessary to produce either
the corresponding sound in a loudspeaker or maybe digital pulse waveforms
for processing within a computer. The basic principle of transmitting and
receiving has never changed from the very early work done by Marconi
around the turn of the last century.
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RADIO AND COMMUNICATION: Wavelength to Frequency.
The frequency of a voltage or current waveform is the number of complete
cycles occurring during one second, measured in Hertz (Hz). The waveforms
f1, f2 and f3 each double in frequency and are demonstrated by counting the
number of complete cycles during time period, t1 to t2. Wavelength is
measured in metres and is the length of one complete cycle.
As the frequency is increased the wavelength of the signal inevitably
becomes shorter.
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RADIO AND COMMUNICATION: Amplitude Modulation.
Amplitude modulation is the simplest method of converting audio
information into a form suitable for transmission. Shown here as an audio
sine wave.
In order to transmit the signal the lower audio frequency must be combined
with a much higher carrier frequency, of say around 1MHz or greater. The
amplitude modulated carrier is transmitted through space and shown in the
lower diagram.
The result of this combination is a carrier frequency, plus two side-band
frequencies. One each side of the carrier removed by ± the modulating
frequency. The bandwidth of the transmitted signal is twice the modulating
frequency. The depth of modulation is how much of the carrier is modulated;
this is the loudness of the output or amplitude of the sine wave. The
modulation % varies from 0 for an unmodulated carrier to 100% where the
full depth of the carrier is used. Over modulating will lead to distortion and
the generation of unwanted signals caused by using non linear part of the
modulator.
At the receiver the carrier is removed using a simple diode rectifier type of
detector, leaving the original audio signal. Amplitude Modulation is used by
long, medium and short wave radio. But it is prone to interference and the
available bandwidth limits the maximum audio frequency that can be
transmitted. Frequency Modulation FM is the accepted method for domestic
VHF radio. Radio Amateurs for example use a modified form of Amplitude
Modulation, called single sideband, where the carrier and one of the side
bands is removed before transmission only to be reinserted at the receiver.
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RADIO AND COMMUNICATION: Frequency Modulation.
Frequency modulation, known as FM is currently used to provide the best
quality national radio coverage, it's also adopted by radio amateurs as one of
their methods for transmitting audio frequency signals around the world. The
main advantages being, absence of distortion and a clean noise free signal.
The transmitter modulator or encoder uses the pure carrier frequency to
represent zero amplitude of the audio signal. Positive audio amplitudes
increase the carrier frequency and negative amplitudes reduce it. The overall
speed at which this occurs is a measure of the transmitted audio frequency.
The bandwidth required at the transmitter is dependent on the maximum
audio modulation frequency and the amount of carrier deviation designed
into the system.
Peak Frequency Deviation, is the maximum amount by which the frequency
may vary and the Modulation Index is a guide to the number of practical
sidebands and directly affects the required signal bandwidth.
The UK FM radio transmissions have a peak carrier deviation of 75kHz and
a maximum audio frequency of 15KHz thereby enabling hi-fi quality sound
to be transmitted. Amateur Radio enthusiasts typically use much lower
figures of a maximum audio frequency of 3kHz and a peak deviation of
5kHz.
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RADIO AND COMMUNICATION: Simple AM Diode Detector.
The simplest of all radio receivers is based on a circuit that used to be known
as a crystal set where the crystal is now replaced by a germanium diode to
detect the incoming signal. The signal (electro-magnetic wave) is picked up
on a long wire antenna (aerial), which induces a very small current in the
series tuned acceptor circuit C1, L1. The resonate frequency of the parallel
circuit L1; C2 is made adjustable enabling tuning of the available stations.
As L1 and C2 will only resonate at a single station frequency, all others will
be rejected as the circuit will have a low impedance outside a band of
frequencies around the tuning point.
Presented to the anode of the diode will be a modulated carrier wave (see the
topic on amplitude modulation). A germanium diode is used as it requires
less than 0.2V to become forward biased and the signal amplitude at this
point is no more than a few hundred millivolts, which is insufficient to
forward bias a silicon diode. The diode removes one half of the carrier wave
and its modulation as it only conducts on the positive half cycle.
Capacitor C3 is chosen to have a low reactance (AC resistance) at the carrier
frequency and therefore removes it. The remaining audio frequency
modulating signal is then available across the headphones or ear piece
having sufficient energy content to move the transducer thereby enabling
audible sound to be heard.
An alternative, ferrite rod aerial will be found in a portable transistor radio
and forms part of the aerial input tuning circuit. The tiny magnetic part of
the radiation generated by a radio transmitter is encouraged to flow through
the ferrite rod and induces a minute current into the coil winding. Adding a
small variable capacitor in parallel with the ferrite rod coil produces a very
simple tuned circuit that can be tuned to select any one of the many
incoming radio frequencies.
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RADIO AND COMMUNICATION: FM Demodulator.
L1/C1 and L2(centre tapped)/C2 are the last IF transformer. At resonance the
voltage and currents around this circuit will be in phase. Note this whole
circuit is balanced about 0V where C4, C5, R1 and R2 form a bridge circuit.
Across this bridge is developed the audio output signal. At centre (zero
audio signal) of the FM deviation VL3 will be at 90° to both L2V1 and
L2V2 due the relationship of the transformer windings, D1 and D2 will be
biased equally and C6 will be charged by I, R1 and R2 will have identical
voltages across them and will cancel, for zero audio amplitude.
As the carrier deviates from the IF tuned frequency, circuit L2/C2 will
become either capacitive or inductive upsetting the balanced phase
relationship between L2V1 and L2V2. The result vectors VAB and VAC will
vary in amplitude, no longer completely cancelling. Diodes D2 and D2
rectify VAB and VAC charging C4 and C5, their product appearing across
C7.
C6 is quite large as it acts to limit (smooth out) carrier amplitude variations.
To appreciate what is happening, move the slider to simulate the deviations
that occur in the Frequency Modulated signal. You will see the amplitude
changing in response to carrier deviations. How quickly this happens is
determined by the audio frequency.
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RADIO AND COMMUNICATION: Signal Multiplexer.
Multiplexing means mixing together. This example shows how two signal
sources A and B are alternately switched before transmitting just one
character at a time. To recover the messages (return to their original
character sequence) requires the receiver to also switch back to A and B
channels.
The problem here is one of synchronising the switches which could be
situated a great distance apart.
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RADIO AND COMMUNICATION: Fibre Optic Communications.
Fibre optics are now used more-and-more to replace the traditional copper
connecting cables. The best example being in the distribution of cable
television. The advantages are low cost and the capability of carrying
hundreds of signals down a single glass fibre at any one time.
In this simple example the LED, R1 and S1 are operating as a simple
transmitter sending a beam of light through the fibre optic link, activated by
pressing S1. A photo-diode (PD) acts as the receiver. As the light falls onto
PD its reverse bias conditions change to make its resistance lower.
The gate voltage of the Field Effect Transistor rises as it is pulled up by the
low resistance of PD, thus causing its drain voltage to fall due to the
increased current now flowing in R3. This lower voltage appears on the base
of the PNP transistor making it conduct heavily, which in turn pulls the
collector voltage towards the supply rail, thereby sounding the buzzer.
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TUNED CIRCUITS: Tuned Circuit at Resonance.
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Circuit resonance forms the basis of tuning. A series or parallel tuned circuit
will resonate when the reactance's of C and L are equal. The reactance of a
capacitor falls exponentially with increasing frequency whilst for an inductor
it increases in a straight line.
At resonance the series circuit will present a low impedance to the applied
signal, and the parallel circuit having a high impedance.
TUNED CIRCUITS: Series Circuit at Resonance.
All series RCL circuits have a natural frequency at which they will resonate
determined by the values of C and L, presenting a low impedance Z to the
applied signal. The point of resonance is determined by reactance's of C and
L being equal and their opposing voltages cancelling.
The impedance of the series circuit at resonance can never be lower than R.
At all other frequencies the impedance will be high. This configuration is
known as an acceptor circuit.
It can be seen that by altering the values of C and L the frequency of
resonance changes, the individual component reactances remaining equal.
This is the principle of tuning or better described as frequency selection.
TUNED CIRCUITS: Parallel Circuit at Resonance.
The parallel tuned circuit is also known as a rejector. It has high impedance
Z at resonance and low impedance at all other frequencies. Ignoring the
effect of R by making it a very high value, say more than 100MOhms and it
will be seen that at resonance this circuit will have extremely high rejection
impedance. The impedance will however, always be less then the value of R,
because it is a parallel circuit.
At resonance the values of capacitive reactance Xc and inductive reactance
XL will cancel as they are in 180° phase opposition.
TUNED CIRCUITS: Finding the Q of a Tuned Circuit.
The Q of a series tuned circuit is the magnification factor of the applied
signal. At resonance XL and Xc will have equal reactance's. Q is calculated
by dividing XL by the series loss resistance R.
Since R acts as a damping resistor on the frequency response, increasing R
in relation to XL reduces the magnification of the circuit and thereby
increases the circuit bandwidth f1 - f2.
TUNED CIRCUITS: Tuned Circuit Bandwidth.
High Q series tuned circuits have sharp response curves, peaking at the
frequency of resonance. Bandwidth is the range of frequencies close to f
before falling off either side of the response curve. Bandwidth is measured at
0.707 (70.7%) of the peak. The larger the bandwidth the lower Q will be and
the flatter the response curve. Try changing the value of R.
The Plot Window vertical scale shows a relative value of current flowing
through a series circuit at frequencies around the resonate frequency. The
amplitude falls away sharply either side of the peak for low values of R.
Remember the series tuned circuit will have a low impedance at resonance.
Therefore, the current flowing through C, L and R can be found by dividing
the impedance Z into the applied voltage across the circuit. The value of R
has a damping effect which in turn reduces the value of Q, thereby
increasing the bandwidth, but at the expense of the circuit gain.
TUNED CIRCUITS: Coupling Tuned Circuits.
Mutual inductance occurs when the changing current (AC) in one coil L1
(primary) induces a current to flow in the other L2 (secondary). An EMF of
one Volt is induced in L2 due to the current in L1 changing at a rate of one
Ampere per second. When the mutual inductance will be one Henry.
TUNED CIRCUITS: Selectivity.
Cin will have a low reactance (AC resistance) at frequencies f1 - f3 of the
input signal. Frequencies close to f1 signal will be shorted to ground by the
low impedance path of the series acceptor circuit, leaving f2 and f3 present
at the input of the parallel rejector which is tuned to reject those around f3
frequency, the value of Cout is chosen to present a low reactance path to the
required frequency f2.
Overall the purpose of the circuit is to remove frequencies either side of f2.
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ATTENUATORS: Attenuation.
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An attenuator is a simple circuit constructed entirely from resistors. The
purpose of which is to reduce a signal level equally across all those
frequencies present. This differs from a filter circuit, which allows a
particular group of frequencies to pass through and attenuates others.
For the moment we are only interested in the input and output voltages to
determine the degree of attenuation (measured in decibels as a ratio between
the two voltages). An input of 10V and an output of 5V would be a loss of
-6dB. Similarly, an input of 20V and an output of 10V would also have an
attenuation or loss of -6dB.
The other consideration for attenuators is the input and output impedance,
which may or may not be equal. This is important to ensure that there is a
correct match between circuits for the maximum transfer of power. We will
be introducing this feature later.
ATTENUATORS: Cascading Amplifiers and Attenuators.
The reverse of attenuation is amplification. We can also measure the gain of
an amplifier in dB. Therefore this topic applies equally to amplifiers and
attenuators where the output of one stage forms the input to the next.
Overall amplification or attenuation can be found by adding the individual
stage gains measured in decibels. Input/output ratios are referred to as gain
or loss in dB.
To calculate the stage output voltage the gain (dB) is first divided by 20
(voltage calculation, see previous topic). It is then necessary to find the antilog of the gain/loss that was previously expressed in logarithmic form.
The stage output voltage is then the input voltage multiplied by the stage
gain. The overall output voltage could also be found by first adding the stage
gains in decibels and applying the formula as for a single stage between the
input and the final output.
ATTENUATORS: Symmetrical T Attenuator.
The symmetrical attenuator is a resistor network which will reduce the input
by N (as a voltage ratio) and maintain the correct source and load resistance
match, i.e. 1kOhms looking into the attenuator, with an equal 1kOhms
impedance output to the next stage.
The symmetrical attenuator is chosen when its necessary to introduce a
signal reduction into an existing circuit, where the design has already
determined a requirement for an equal input and output impedance.
A good example would be to reduce the input signal to prevent overloading
for a Television or Radio aerial system where both the aerial and the tuner
have a designed input impedance of 50 or 75ohms.
It is normal practice to measure attenuation in dB's (decibels). The numerical
variable N is the anti-log of the amount of attenuation in decibels. As shown
there are two ways to approach this topic. Firstly, to calculate the resistor
values for the desired attenuation or secondly to determine the amount of
attenuation for a particular set of resistor values.
ATTENUATORS: Asymmetrical T Attenuator.
When the source impedance and load impedance's are unequal the attenuator
type is referred to as 'asymmetrical' or unbalanced.
First it is necessary to calculate the anti-log of the attenuation N (gain ratio)
this is then inserted into the calculations to find R1, R2 and R3. Note R2 is
calculated first which is then subtracted from the values determined for R1
and R3, where the different source and load impedance's are accounted for.
Impedance is normally recognised by the symbol Z.
ATTENUATORS: Symmetrical pi Attenuator.
The symmetrical pi attenuator is a further example of a circuit with matching
input and output impedance's.
ATTENUATORS: Asymmetrical pi Attenuator.
Apart from the configuration of the three resistors the asymmetrical pi
attenuator has the same characteristics as the asymmetrical T type.
To make the calculations easier to follow two temporary variables S and P
are used which are determined by the values of the source and load
impedance's. When calculating, the order of the arithmetic rules must be
followed, where the content of the brackets is carried out first.
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PASSIVE FILTERS: RC Low Pass Passive Filter.
Interactive Content!
Typical examples of filter circuits are used for AC smoothing in a power
supply , separating the frequencies within a loudspeaker enclosure, i.e bass
treble and mid range or the signal processing in a radio or television receiver.
Filters act as an electronic gateway by allowing some frequencies to pass
whilst others are rejected.
A low pass filter has a pass band situated below fc which is the cut-off
frequency. Frequencies above this point being gradually attenuated. At fc the
reactance of C will equal the series resistance, thus forming a voltage divider
network. At frequencies below fc the reactance of C will be high and a
greater part of the input will be available as output.
For frequencies greater than fc, Xc falls relative to R thereby reducing Vout.
Filter response is expressed in decibels as the output is relative to the input,
using the formula for voltage.
PASSIVE FILTERS: RC High Pass Passive Filter.
The pass band is always measured at the -3dB point on the amplitude scale.
As the reactance curve of a capacitor is exponential it's usual to show
frequency on a logarithmic scale. This enables a very wide frequency range
to be observed, with the added advantage of clearly seeing the slope or rate
of attenuation, often referred to as roll-off.
A high pass passive filter can be constructed by reversing the positions of R
and C for a low pass type , where the reactance of C now forms the upper
section of the voltage divider circuit. With the exception of the formula for
Vout, the calculations are the same.
As we shall show it is possible to build wide band filters by combining the
low pass and the high pass filters. However, for narrow band acceptor
circuits a simpler solution exists, using the series resonant filter.
PASSIVE FILTERS: Band Pass Passive Filter.
The series resonant filter has a minimum impedance Z at resonance.
Therefore maximum current will flow at this point where nearly all the input
voltage will be developed across the resistor. At resonance the reactance of
the capacitor and inductor will cancel as they are in 180° phase opposition.
We are ignoring any voltage which would normally be dropped across the
coil DC resistance.
The width of the frequency pass band (bandwidth) will be a function of the
circuit Q factor. This is largely dependent upon the value of the resistance.
As with all filters the output is measured at the -3dB point on the response
curve. A series band stop or rejector circuit can be constructed by reversing
the positions of R with C and L, where the output is measured across C and
L series combination.
PASSIVE FILTERS: Band Stop Passive Filter.
The band stop filter circuit is often known as a notch. Its purpose is to
remove a narrow band of frequencies from those present. Often these circuits
have a high Q and therefore narrow bandwidth, which enables rejection of
just that specified range. The attenuation rate is still -20dB per frequency
decade (equal to 6dB per octave, or doubling of frequency) which in some
circumstances may not be sharp enough.
As with all filters the rate of attenuation can be improved by cascading,
where the output of one provides the input to the next. The overall result is
then -40dB or -60dB rejection per frequency decade.
All inductors contain DC resistance which is a result of the coil winding. We
normally ignore it in our calculations. However, in this example it needs to
be considered, as there will be an amount of signal developed across it. The
lower Rwnd can be made the better the rejection at the resonate frequency.
The bandwidth and Q values for the circuit are found as for the band pass
filter.
PASSIVE FILTERS: Wide Band Passive Filter.
Where a large range of frequencies are to be selected (or rejected), a wide
band filter is used. This is simply a low pass filter that rejects frequencies
above the upper cut-off point. The selected band of lower frequencies is then
used as the input to the high pass filter where all frequencies below the lower
cut-off point are attenuated.
The pass band is the difference between the two cut-off points at -3dB rolloff.
In this example you determine the lower frequency and the pass band. For
simplicity only, the same resistor values are used for both filters, but
capacitor values are calculated to produce the lower and upper cut-off points.
Another solution might be to take the central frequency of the pass band and
then work the upper and lower cut-off points from there, as a ± frequency
above and below the middle of the pass band.
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ACTIVE FILTERS: RC Low Pass Buffer Active Filter.
Interactive Content!
Active filters differ from passive types as they comprise both active and
passive components. The active part, which can be a transistor or in this case
an Op-Amp provides gain or attenuation only at the frequencies in the pass
band.
This example uses an amplifier configured as a buffer circuit with a gain of
1. The filter response is -20dB per frequency decade, the same as for the
passive type. The difference being that this design would not be affected by
the next stage loading (input impedance), owing to the buffer amplifier.
R1 and C1 form the low pass filter circuit, the output of which is connected
to the non-inverting input to the Op-Amp. From the Op-Amp theory you will
recall that there is virtually zero voltage across the Op-Amp inputs, also
negligible input current, therefore, only a very small current flows through
Rf, which means the voltage across C1 is almost identical to Vout.
By reversing the positions of R1 and C1 and the circuit can be changed into
a high pass filter.
ACTIVE FILTERS: RC Low Pass Active Filter.
Constructing low frequency 'passive filters' often requires the use of
inductors which may have to be of a very large value at the operating
frequency. They are also both expensive and bulky. The same low frequency
cut-off points can be determined more efficiently using active filters, where
inductors are rarely used owing to the DC resistance of the coil.
The simple circuit shown has a roll-off of -20dB per decade. To achieve
steeper slopes the circuits can be cascaded.
The formulae given demonstrates the calculations, where the parallel
impedance R2, C2 forms the feedback path, which in conjunction with R1
determine the circuit gain, symbol Av.
At frequencies above fc the reactance of C2 will significantly lower and be
in parallel with R2, thereby resulting in a gradually reducing overall
impedance as the frequency increases. This attenuates the output by reducing
the Op-Amp gain. For frequencies below fc, C2 will present a high
impedance and Av will largely be as a result of the R2, R1 resistor network.
ACTIVE FILTERS: RC High Pass Active Filter.
By rearranging the feedback resistor R2 with R1 and C1 a high pass active
filter can be constructed. The cut-off frequency is determined by the
reactance of C1 in series with R1 and the voltage gain by the ratio of the
input impedance R1, C1 and the feedback resistor R2.
The impedance of the series combination of R1, C1 will be low for
frequencies above fc, therefore the gain of the operational amplifier will
increase. Below fc the high value of the series impedance will reduce the
gain thereby rejecting those frequencies below fc.
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OSCILLATORS: Positive Feedback.
Interactive Content!
Positive feedback occurs when a portion of an output signal is fed back to
the input in the same phase. (Feedback is normally expressed as a ratio,
however using the term Feedback % makes the calculations easier to
follow).
The input signal is reinforced by the positive feedback and results in the
output increasing still further. Under most circumstances, i.e. audio
amplifiers this is undesirable. An example is the familiar 'howl around'
which occurs when a microphone is placed too close to the output speaker in
a P.A. system. However, the consequence is exploited to achieve oscillation.
To examine the effect modify the default values slightly and monitor the
input and output amplitudes. Feedback amounts are normally only a few percent, just sufficient to maintain oscillation. The overall stage gain is then set
to just compensate for circuit losses.
Note that this is exactly the opposite to the calculation for negative feedback,
with only a minor modification required to the formula to achieve the
opposite effect. The feedback signal must be exactly in phase with the input
or some cancellation will occur.
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OSCILLATORS: RF Variable Frequency Oscillator.
RF Variable frequency Oscillators are required to generate the sine wave
carrier frequency, usually between I and 500MHz. As for any oscillator
positive feedback is required which is in phase with the transistor output to
generate the sine wave output. The base collector junction for a common
emitter transistor having a 180° phase inversion. Bipolar transistors or FETs
are used as RF frequencies are beyond the range of operational amplifiers.
The winding of L2 is arranged to allow a further 180° reversal. The output is
therefore regenerative producing positive feedback. The amplitude of the
feedback signal is just sufficient to maintain oscillation and to make up for
circuit losses.
Output frequency is determined by the resonate frequency of L1, C1 (user
front panel control). Sine wave generators are normally reserved for radio
frequencies (RF) as the values of the inductor and or capacitor forming the
tuned circuit can become very large at low frequencies making construction
impractical. At high frequencies stray capacitance can cause instability.
Component lead inductance and positioning can affect the output frequency,
where its important to remain within, say the Amateur Radio bands.
In addition to good circuit design and close tolerance components a stable
power supply is required. It will also be necessary to screen the oscillator to
prevent the pickup of stray signals or had capacitance and to ensure that any
circuits i.e. power or output transformers are positioned as far away as
possible.
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OSCILLATORS: Phase Shift Oscillator.
The phase shift oscillator uses an RC ladder network to produce the 180°
phase reversal. This is added to the normal transistor phase change to enable
360° positive feedback. Ideally each stage should each add 60°, but the
calculation shows this to differ slightly.
In practice each stage component values and input/output voltages will not
all be equal due to tolerance variations. R3 is in parallel with the transistor
input resistance.
Text books always quote the attenuation rate in the ladder network to be -29,
which is a ratio of Vin to Vout. Therefore the amount of feedback ß to
compensate should be slightly greater than this to maintain circuit
oscillation.
Oscillators constructed in this way normally have a fixed frequency as any
adjustment would necessitate the same changes being made to all three
capacitors and the associated resistors at the same time. Otherwise the ideal
60° phase cascading would not be maintained.
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OSCILLATORS: Wien Bridge Oscillator.
The Wien bridge oscillator comprises an AC voltage divider circuit to
provide positive feedback. R1, R2 and C1, C2 having equal values. The
amount of feedback ß is determined by the reactive value of the capacitors
C1,C2 within the overall impedance of the voltage divider. This circuit will
produce a sinewave output at a fixed frequency.
The gain of the oscillator is largely as a result of the negative feedback
developed across R4.
To show the effect on frequencies other than that of resonance click on
Change Freq. and force values around the natural frequency. It will be seen
that maximum feedback amplitude occurs around the natural frequency
falling off above and below. The 0° phase angle is only true at the resonate
frequency. For all other frequencies there will be a phase shift due to the
relative values of R and Xc.
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OSCILLATORS: Astable Multivibrator.
The astable multivibrator is an oscillator which produces two square
waveform outputs, the second of which has a 180° phase reversal. The
oscillator is free running, generating a continuous output. The frequency is
determined by the values of R1,C1 and R2,C2.
When the values of R1,R2 and C1,C2 are equal the output is a square
waveform. Changing the relative values of the resistors and capacitors alters
the mark (t1) and space (t2) ratios.
Oscillation is a result of each transistor becoming saturated, whilst the other
is cut-off due to the charge developed across the capacitors. As the opposite
collector voltage switches between 0V and 6V the corresponding Vbe is
forced low, cutting off that transistor, making its collector volts rise, thereby
charging the opposite capacitor.
This forces a change of TR1,TR2 ON/OFF states. An action which is
regenerative resulting in very fast action producing the square wave outputs.
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OSCILLATORS: Unijunction Transistor.
The unijunction transistor (UJT) consists of a piece of n type silicon
semiconductor with connections B1, B2 at each end. A third terminal E
(emitter) is connected via a PN junction part way along the semiconductor
bar. The equivalent circuit shows this as two series resistors where the
position of the emitter forms the 'intrinsic stand off ratio' parameter. This is
determined during manufacture and quoted in the data books.
With a low voltage on the emitter the PN junction is reverse biased and IB2
can be calculated from Ohm's Law.
As the emitter voltage rises above Vd + VRB1, the PN junction becomes
forward biased. The diode shown in the equivalent circuit conducts heavily
(VEpeak is the voltage required for PN junction to become forward biased)
causing the voltage between the E and B1 to fall rapidly, generating a
negative resistance over the bottom section of the semiconductor bar. This
causes the emitter current to also increase rapidly, an effect that is exploited
when constructing a relaxation oscillator.
The device therefore has two stable states. UJTs are less common nowadays
as Operational Amplifiers connected as voltage comparators offer a better
solution.
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OSCILLATORS: UJT Oscillator.
The most common application of the UJT oscillator is as a pulse generator
(called a relaxation oscillator) for the control of an SCR (Thyristor) power
supply. At switch-on C1 begins to charge exponentially via R1 with a time
constant determined by R1 × C1 seconds. As the critical VEpeak voltage is
reached the UJT PN junction becomes forward biased, which conducts
heavily thereby removing the charge developed across C1.
This rapidly changing emitter current causes the voltage across Rout to rise
sharply. A condition, which remains until the charge on C1, falls to the
VEB1 saturation point on the UJT characteristic curve. The PN junction is
then reverse biased and the output voltage across Rout falls rapidly as the
process is repeated. Generating an output square waveform at a frequency
determined by R1,C1.
A similar low value resistor in the B2 lead would produce an anti-phase
square wave output. When this device is used as part of a SCR control
circuit VBB is taken from the rectified positive half cycle of the AC mains.
Adjusting the value of R1 changes the timing period that the UJT is biased
on during this half cycle, thereby the period the SCR is allowed to conduct,
which in turn controls the charge time on the power supply smoothing
capacitors.
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CIRCUIT THEOREMS: Superposition Theorem 1.
Interactive Content!
When a circuit has multiple sources of voltage the current flowing at any one
point will be a sum of the currents from each source and each power supply
will act like a short circuit on another power supply. In this example the R3
current is made up of electrons from both batteries. Each battery contribution
will depend on the source voltage and the associated resistor values.
Applying the Superposition theorem means we consider the each half of the
circuit as if it is supplied from one source, i.e. V1 with V2 shorted and then
V2 with V1 shorted. The potential difference across R3 will be a sum of
these quite separate calculations.
The effect of shorting out the battery is to place the resistor on that side of
the circuit in parallel with R3. Remember their combined value will always
be lower than the smallest one. The voltages Va and Vb at the potential
divider junctions are then calculated and added. This is the resultant voltage
across R3.
Circuit currents can be found by applying Ohm's Law.
CIRCUIT THEOREMS: Superposition Theorem 2.
The Superposition theorem is now used to determine the potential difference
(PD) across a conductor with an impedance of 5ohms supplied by two
generators each with its own internal resistance. The PD across R is
calculated twice as before by shorting out the opposite generator.
The generator internal resistance must remain in circuit when its associated
generator is shorted.
Consider the circuit first with the voltages opposing where the resultant
current through the cable is the difference between the potentials at either
end. Current will be flowing in both directions.
Reversing V2 causes the voltages to add around the circuit. All the current
will flow in the same direction. Calculations are as before except now the
two resultant voltages are now added to find that developed across the cable.
Try taking R1 out of circuit by making it a very high value, say 15Mohms.
You now have a simple series circuit. Ohm's Law will prove your
calculations.
CIRCUIT THEOREMS: Constant Voltage Source.
A constant voltage source is defined as an AC or DC supply or generator
with an ideal zero impedance connected in series with a very low value
series resistance Rs.
The generator should be able to maintain its output voltage regardless of the
amount of current drawn from it. Lead-Acid (motor car) and Ni-Cad
rechargeable batteries and the AC mains supply approach this ideal zero
impedance supply.
Choosing a design where the value of Rs is small compared to Rload will
help to maintain a constant voltage output. In practice if the load were short
circuited then all the voltage would be developed across Rs.
When designing your circuit the current supplied by the generator should be
sufficient to develop a voltage across the load which is close to that supplied
by the generator, i.e. make Rs volts as small as possible. The greater the ratio
of the voltages across the two resistors the more stable the load voltage.
CIRCUIT THEOREMS: Constant Current Generator.
The ideal constant current generator can deliver a constant current to the
load, where the voltage is whatever is required to sustain that current. This
circuit is a current divider which splits the current in a ratio which which is
inversely proportional to the values of Rp and Rload, i.e the smaller the
value of resistance the greater the current that flows.
When the load is removed all the available current flows through Rp. As the
load current increases so the current in Rp is reduced.
If you have a current generator which develops a certain voltage across Rp
with the load disconnected. That is the value of an equivalent voltage source
where the series resistance Rs should equal Rp.
CIRCUIT THEOREMS: Thévenin's Theorem 1.
The Thévenin theorem is used to produce an equivalent circuit which
consists of a source voltage and a series resistance only. With this example it
may help if you think of a battery or generator as a very low impedance
source, just a few Ohms, which is the internal resistance.
We have chosen this example so you can compare the results with the
voltage divider topics which use Ohm's Law to find the circuit parameters.
Here we want to find the loaded output voltage. Make a note of the unloaded
output voltage of the simple voltage divider; this is our source voltage. Next
produce an equivalent circuit by shorting the input terminals and calculate
the resistance R1 || R2.
The load current will flow from the source voltage through the equivalent
series resistance causing a voltage drop across it (this is found by Ohm's
Law where V = I × R). Subtract this voltage from the source voltage and we
have the Thévenin equivalent voltage.
CIRCUIT THEOREMS: Thévenin's Theorem 2.
Again we are aiming to reduce our circuit to a source voltage and a series
resistance. Note that this time we are not concerned with the output load.
Thévenin voltage and resistance will remain the same irrespective of load
variations. Any changes in the load requirements are reflected in the PD
developed across RTH.
The advantage of this approach is that the source voltage only needs to be
found once, whereas using Ohm's Law requires a completely new set of
calculations for each change in the load requirements.
The procedure is as before. Find the voltage at the junction of Rs and R1,
disregarding the load. This is the Thévenin equivalent voltage VTH. Next
short the generator inputs leaving the internal resistance (Rs) in circuit.
Calculate the Thévenin RTH. Rs and R1 are in parallel and as R2 is also in
circuit its resistance must be included.
Ohm's Law can now be applied across the load to find the current, resistance
or power dissipated in the output circuit.
CIRCUIT THEOREMS: Norton's Theorem.
Norton's theorem enables a resistor or impedance network to be replaced by
a single generator or DC source with a parallel resistance. This results in a
constant current generator where the source current always remains the same
irrespective of load variations.
To explain this circuit we combine both Thévenin and Norton theorems.
The Norton current In is calculated by shorting the output terminals (cd),
thereby placing R3 in parallel with R2. The load voltage will depend upon
Rload power demands, but the current supplied will remain constant, any
variations taking place by the current in Rn.
Rn and Rload are in parallel and so act as a current divider. With Rload open
circuit all the generator current flows in Rn. Shorting Rload and all the
available current bypasses Rn. Therefore Rn current = In - load current
requirements, providing current stabilisation. Change the value of Rload and
monitor In, you will note it never changes, which can be confirmed by the
calculations.
CIRCUIT THEOREMS: Maximum Power Transfer.
To ensure the greatest possible transfer of power from a voltage source to the
load, RL must be matched to the value of the internal resistance of the
source Rs.
This is shown by graphing the power delivered to the load against possible
values of RL, using the formula I² × RLoad
Obtaining the maximum transfer of power is inefficient as half the available
power is lost across Rs and must therefore be dissipated within the power
supply. However, in communications systems where the source impedance is
relatively high, impedance or resistance matching is essential.
A typical example might be in ensuring the impedance of a antenna exactly
matches the output impedance of the transmitter for maximum signal
transmission, but more importantly to avoid signal reflections back down the
cable which could destroy the transmitter output circuits.
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COMPLEX NUMBERS: Polar to Rectangular Number Conversion.
Interactive Content!
Equations used in electronics are frequently written in 'polar form' to
mathematically represent the amplitude of an AC signal with its
corresponding phase angle.
A complementary method is in 'rectangular form', which then enables these
values to be drawn as phasors. This is often referred to as j notation.
Real numbers (± r) appear on the horizontal axis. Imaginary numbers (± j)
on the vertical axis. Positive phase angles are anti-clockwise. Negative phase
angles clockwise. Beginning at the +r or 3 O'clock position as 0°.
COMPLEX NUMBERS: Rectangular to Polar Form.
When complex numbers are written in rectangular form, the values they
actually represent are not always immediately obvious. Whereas in polar
form it is easy to visualise the amplitude and the phase angle. Which is one
reason why its useful to be able to convert from one to the other.
The length of the vector line can be made to represent voltage, current or
impedance within an AC circuit, along with the resultant phase angle.
Conversion is based on the trigonometric relationships for the right angle
triangle.
COMPLEX NUMBERS: Rectangular Addition.
Rectangular addition may be used to combine two out-of-phase voltage or
current amplitudes.
The resultant value and its phase angle can be produced simply by finding
the sum of the 'real' numbers and the sum of the 'imaginary' numbers and
plotting the result as new values on the r and j axis.
To find the answer in polar form, use the rectangular to polar conversion
formulae, previously shown.
COMPLEX NUMBERS: Rectangular Subtraction.
Complex number subtraction is carried out by subtracting the 'real' parts and
the 'imaginary' parts to produce a new resultant and phase angle.
Complex numbers are used for calculating, out-of-phase voltages and
currents which cannot be added or subtracted directly.
Impedance can also be shown as a complex number, where resultant RC or
RL voltages are at opposing phase angles.
COMPLEX NUMBERS: Complex Number Multiplication.
Multiplication of complex numbers can be made easier by first converting
the two rectangular numbers into their equivalent polar form.
Here the two amplitudes A and B are multiplied together and their phase
angles added.
Conversion of the resultant back to rectangular form can then be carried out.
COMPLEX NUMBERS: Complex Number Division.
To divide two complex numbers convert each into its polar form and divide
the amplitudes A and B, then subtract the phase angles.
COMPLEX NUMBERS: RC Series in Complex Form.
Current will flow through both components developing an in-phase voltage
across R. The voltage across C will lag I by 90°. The amplitude of the
resultant or applied voltage can be found by applying Ohm's Law across the
circuit impedance.
The phasor diagram shows the relationship between V, Vr and Vc. Note that
as Vc lags Vr this is shown using j notation as -jVc.
Represented in polar form we have the applied voltage and the resultant
phase angle across the circuit. Whereas in rectangular form the resultant
voltage is shown as r,-j on account of the lagging voltage across C.
COMPLEX NUMBERS: Circuit Values from Complex Numbers.
A complex number is a value with magnitude and phase which may be
written in either polar or rectangular form.
Mostly you will find complex numbers in AC calculations written using the
rectangular form as j notation where the real part of the number represents
voltages, or currents which are in phase, in this case those developed around
R. The imaginary or j part will refer to the reactive part of the circuit, either
capacitive or inductive.
Here you can explore both aspects of j notation by making the value for the
imaginary part, positive or negative. Note that when the imaginary value is
negative this will apply to a capacitive reactance where the voltage lags the
current. Similarly for inductance the voltage will lead the current.
We already know the applied voltage and its frequency. From the complex
number we can determine the resistor value and the circuit reactance,
whether it's capacitive or inductive. Impedance, current, power etc, can then
all be found.
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DC POWER: DC Power V and I.
Interactive Content!
Power is the work done when electrons flow through a circuit.
In a good conductor there are lots of free electrons and so little power is
consumed. However, when resistance is present, work has to be done to
release sufficient electrons for the required current to flow. This generates
heat as wasted energy.
By combining Ohm's Law and the formula for finding circuit power P then
twelve resulting equations can be developed.
Select the appropriate formula to determine the power rating of a resistor in
a DC circuit.
DC POWER: DC Power I and R.
Power is the work done when electrons flow through a circuit.
In a good conductor there are lots of free electrons and so little power is
consumed. However, when resistance is present, work has to be done to
release sufficient electrons for the required current to flow. This generates
heat as wasted energy.
By combining Ohm's Law and the formula for finding circuit power P then
twelve resulting equations can be developed.
Select the appropriate formula to determine the power rating of a resistor in
a DC circuit.
DC POWER: DC Power V and R.
Power is the work done when electrons flow through a circuit.
In a good conductor there are lots of free electrons and so little power is
consumed. However, when resistance is present, work has to be done to
release sufficient electrons for the required current to flow. This generates
heat as wasted energy.
By combining Ohm's Law and the formula for finding circuit power P then
twelve resulting equations can be developed.
Select the appropriate formula to determine the power rating of a resistor in
a DC circuit.
DC POWER: Series Resistor Power.
For the series DC circuit the current is common for all values of R. Using the
power formula P = I² Rn. The individual rating for each resistor can be
found.
Added together the resistor power ratings will equal the total power of the
circuit.
Note the wattage (power) rating is proportional to the resistor value, i.e.
increasing resistance generates more heat as a greater voltage is developed
across it, even though the current remains the same.
DC POWER: Parallel Resistor Power.
In the parallel connection each resistor will have the same voltage developed
across it. The power dissipated in R1, R2 and R3 can be found from the
formula given, where the voltage and resistance are known. The total power
consumed by the circuit will be the sum of the individual resistor power
factors.
Increasing an individual resistor value will reduce that branch current and
therefore reduce the individual resistor power dissipated or wasted heat
generated.
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AC POWER: Amplifier Power Gain/Loss.
Interactive Content!
A power amplifier is designed to supply energy to an external load which is
usually of a low impedance and therefore requires a power supply which is
able to deliver sufficient current to meet this demand.
Power gain or loss is measured in decibels, which is a logarithmic ratio. It is
useful to remember that ± 3dB is a doubling or halving of power.
AC POWER: Power Levels Expressed in Decibels.
Power when expressed in decibels tells us something about the relationship
between two levels, where the actual values need not concern us. For
example an amplifier with an input power of .5W and an output power of
1W will have a power gain of 3dB. Similarly an amplifier input of 5W and
an output of 10W is still +3dB gain. Decibels represent a ratio between the
two values.
Taking the default values as an example. It can be seen that the power output
is 10,000 times greater than the input. Converting this to its logarithmic
equivalent makes the subsequent maths easier as it enables the logarithmic
values to be simply added or subtracted, when calculating the overall gain of
an amplifier comprising several stages. The logarithmic ratio of the default
input is 4.00, make a note of the number of noughts in the power gain result
above. Next reduce the power input to 0.1mW and compare; also increase it
to 10mW. The results should make logarithmic ratios easier to understand.
This logarithmic ratio is also associated with our ears, this means we hear
extremely small noises and those thousands of times louder with equal
clarity. This logarithmic ratio is given the term Bel. However, these units are
too large for most practical purposes and so are divided by ten and expressed
in decibels.
Note that logarithms can be used with base values other than 10. Natural
logarithms for example have a base e, where e = 2.71828. Therefore, ensure
your scientific calculator is switched to the correct mode. Decibels only
relate to power ratios and cannot be applied to voltages and currents, unless
of course the amplifier input and output impedances are the same and the
values will then represent power levels.
AC POWER: RC Series Power.
In theory the energy stored in the capacitor during the positive half cycle is
returned during the negative half. Therefore true power is that dissipated by
the resistor. Found from I ² × R.
Reactive power is the rate at which a capacitor stores energy. This is not lost,
as it is returned during the following half cycle.
Apparent power is the resultant of the proportion of true and reactive power
determined by the values of resistance and capacitive reactance. Which is the
same as I² multiplied by the circuit impedance. See RC Series Impedance
topic.
To find the capacitive reactance the frequency is required (See Capacitor
Reactance). VR and VC are developed at 90° across R and C by the current
I, circuit resistance and capacitor reactance. VR and VC are found using AC
Ohm's Law.
AC POWER: RL Series Power.
Energy is stored in an inductor as a magnetic field, which is formed as the
current builds up. The inductor does not consume reactive power as it is
returned to the circuit during current decay.
True power is that developed by the current flow in R.
Apparent power is a result of the relationship between R and XL and the
amount of current flowing in the circuit.
AC POWER: Capacitance Reactive Power.
As current flows to charge a capacitor the voltage lags by 90 degrees. Power
is a product of the applied voltage and the current through Xc (capacitive
reactance) where power is developed twice for each charging cycle as
current flows into and out of the circuit.
The result is a power sine wave at twice the charging frequency. Reactive
Power is measured in Va's (volt-amperes).
AC POWER: Inductance Reactive Power.
When the applied voltage reaches its peak value, current begins to flow in
the inductor.
The inductors reactive power is measured in Va's (volts-amperes). Note that
when calculating the power curve instantaneous values, a positive value
multiplied by a positive is positive, also negative times a negative is positive.
Whereas positive × negative is negative.
AC POWER: Power Factor Correction.
Often AC circuits are required to drive inductive loads which consist of
transformers, electric motors, loudspeakers etc. This inductive component
introduces a current lag (-phase angle) to that of the supply voltage. The
objective of the Power Factor calculation is to minimise the wasted energy
of such a circuit, by counteracting this lag. The useful or true power of the
circuit can be measured directly by a Wattmeter. This is basically a
combination of an ammeter and a voltmeter, which displays the product of
the voltage and current.
By adding a capacitor across the parallel RL circuit we can introduce a
compensating current IC into the circuit which is in 180° phase opposition to
IL. Ideally we are looking for a power factor of 1.
To understand the circuit, begin with the default values given and note the
true power indicated by the wattmeter and the current IT taken from the
supply. Change the value of the compensating capacitor value slightly to
alter the calculated power factor. Note that the supply current increases
inversely to the power factor improvement, while the true power (the useful
part) remains unchanged.
Maximising the efficiency of this type of circuit means smaller connecting
cables can be used for the same amount of work output. Power factor
improvement is particularly applicable to heavy engineering, where a modest
increase in circuit efficiency can result in large cost savings.
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SILICON CONTROLLED RECTIFIER: Basic SCR Operation.
Interactive Content!
The SCR Silicon Controlled Rectifier is also known as a Thyristor. This
device is a diode that has to be triggered into conduction, once holding
current flows the gate pulse can be removed and it will continue to conduct.
The only way to switch the SCR off is by removing the anode voltage,
thereby stopping the holding current. SCRs are able to handle very large
currents making them ideal for power supply applications.
The operation of the SCR can best be explained by connecting together a
PNP and an NPN transistor as shown. When TR2 is made to conduct by
placing a positive trigger voltage on its Gate the collector current flows
through TR1 base which is forward biased, causing TR1 to conduct heavily.
This in turn provides the base drive for TR2 which continues to flow even
when the gate trigger voltage is removed. The only way to stop this
regenerative conduction is to either remove the Anode potential or make the
Cathode voltage higher than that on the Anode (reverse biasing).
SILICON CONTROLLED RECTIFIER: Simple Alarm Latch.
The circuit shown uses the SCR in simple a burglar alarm arrangement.
Once the alarm has been triggered then it should only be able to be reset by
the owner and not by giving the burglar the opportunity to turn it off, which I
am sure they would prefer!
Re-setting the broken alarm protective loop has no effect. The LED
continues to light to show the circuit has been tampered with.
SILICON CONTROLLED RECTIFIER: Time Delay SCR Switch.
This application replaces the loop alarm with a resistor capacitor network
thereby providing timing before activation.
Suppose the circuit were arranged to cause the gate to be triggered only
when the capacitor reaches 63% of its full charge, equivalent to a time of CR
seconds. Once this point is reached the RC network has no further effect and
the LED remains lit.
One application for a similar circuit could be as a photographic dark room
timer. The device can only be reset by the user. Making R1 a variable
resistance could provide varying timer periods.
Resetting the SCR also removes the charge on the capacitor ready for next
time. By replacing R1 and C1 with very large values, long periods before the
device activates could be achieved. Whilst this simple circuit will work in
practice a full discharge path should be included for C1. At present the
charge can only leak away through R1 and D1 via SCR1 whilst it is still
conducting, i.e. from peak charge down to the SCR1 trigger point.
SILICON CONTROLLED RECTIFIER: SCR Phase Control.
In the conducting state the SCR operates as a half wave rectifier. It is usual
practice to add a protection diode D1 in series to remove the mains negative
half cycle. This circuit is connected as a power controller, where the SCR
conduction (ON) time is determined by the value of the Load. For low value
loads, requiring more current a greater proportion of the positive half cycle
of the mains is used to deliver power.
As the load demands get smaller the gating pulse is made to occur later
thereby reducing the available output power. When the mains cycle swings
in a negative direction the SCR is switched off as the holding current is
removed.
This is a dynamic circuit as the timing of the gating pulse is determined by
the load requirements. Its frequency of operation is 50Hz as the trigger
control will activate on each positive going half cycle.
SILICON CONTROLLED RECTIFIER: Triac and Diac.
Using just one half cycle of the mains AC waveform, limits the SCR
controlled power circuit to a maximum of 50% of the available power. This
can be overcome by employing a Triac which comprises of two SCRs
connected in inverse parallel with a common gate terminal. A voltage pulse
applied to the gate causes the Triac to conduct on each half cycle. The device
being automatically turned off as the mains crosses its zero line. This type of
circuit could be used as a lamp dimmer or electric drill speed controller.
A Diac is commonly used to conduct the gate pulses. Made up of two Zener
diodes, with a 32Volt rating, connected in inverse parallel. A Diac will
conduct equally on both halves of the mains cycle when its break-over
voltage is exceeded and become non-conducting as the mains amplitude
reduces to zero.
The capacitor will commence charging at the beginning of both positive and
negative halves of the mains cycle. The rate of charge is controlled by the
adjustment of R1. Note the time constant of R1, C1. Where one half of the
UK 50Hz mains has a duration 10ms.
As the voltage across C1 reaches the Diac break-over voltage, it conducts,
placing a pulse of the correct polarity on the Triac gate, from which point the
Triac also conducts for the remainder of the waveform half cycle. As the
mains cycle reduces towards its zero crossover level it automatically
discharges C1 ready for a repeat sequence of the opposite polarity.
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POWER SUPPLY: Half Wave Rectifier.
Interactive Content!
Positive half cycles greater than 0.6V cause the diode D1 to conduct and
current flows into the load, also charging C1. During the negative half cycles
the diode is cut-off, and C1 discharges via RL. Until the next positive pulse
arrives.
One way of increasing the reserve charge stored in C1 is to use a larger
capacitance value. This reduces the ripple voltage as there is more energy
stored to supply the circuit during off peak periods. Rs limits the diode
forward current, especially during switch-on.
The effect of poor smoothing of the voltage peaks can be shown by giving
C1 a low value, say 25µF.
There are just two main considerations when selecting a rectifier diode for a
particular application. The current flow, both steady and peak values where a
smoothing capacitor, for example might need to be initially charged and the
Peak Inverse Voltage (PIV). This is the maximum instantaneous voltage that
the device can withstand when connected in the reverse direction. If the
diode design value is exceeded then the device will break down due to an
avalanche effect. This is the same principle as for a zener diode, but this time
it will not recover and the diode will be destroyed, most probably inflicting
some additional circuit damage.
POWER SUPPLY: Full Wave Bridge Rectifier.
The input to the full wave rectifier is a sine wave at 50Hz (mains frequency).
However, due to the diode configuration the rectifier gives output current on
both positive and negative half cycles which is 100Hz.
C1 is therefore charged twice during each cycle giving it less time to
discharge, thereby reducing the unwanted ripple voltage and providing a
smoother voltage output.
POWER SUPPLY: Zener Diode Characteristics.
When forward biased, i.e. anode positive to cathode the Zener diode behaves
much the same as any other p.n. device. However, where they differ is the
ability to recover (normal diodes are permanently destroyed) from a reverse
p.n. junction breakdown, which occurs when excessive voltages are
connected in the reverse direction, cathode positive anode negative.
Zener diode voltages can be precisely defined during manufacture, which if
exceeded cause the reverse leakage current to rapidly increase as the
covalent electron bonds are fractured, owing to a large electric field
appearing across the depletion layer. Typical breakdown voltages are from
2.7V to 100V.
Low voltage diodes breakdown due to this 'Zener' action, but for higher
voltage devices which have a much wider depletion layer, the breakdown is
caused by an avalanche effect. This is where ruptured bonds allow free
electrons to collide with other bonded electrons with sufficient energy to
dislodge them, resulting in a further increase in electron movement, this
effect is cumulative therefore the term avalanche.
Because of this cumulative action, higher voltage devices have a much
sharper knee region on the response curve.
POWER SUPPLY: Zener Diode Voltage Regulation.
Zener diodes exploit the reverse biased breakdown voltage of a PN junction.
Any diode will do this if the maximum rated reverse voltage is exceeded and
will usually result in its destruction.
Zener diodes are manufactured to breakdown and then recover at very
precise voltages. This makes them the obvious choice for power supply
regulation. In this simple circuit the voltage output can never be more than
the Zener diode rated voltage.
If the load current connected to the output is excessive, the voltage can be
pulled below the Zener voltage by the voltage dropped across the series
resistor and so this circuit is only able to provide 'over-voltage' regulation.
POWER SUPPLY: Zener Diode Series Resistor.
The series resistor provides a voltage drop from Vin to Vload. The load
current and the Zener current are added to find the total circuit current,
which flows through R1 as Iin.
For our calculations we just need to find the voltage to be dropped across
R1, which is difference between the supply voltage and Zener design
voltage. Ohm's Law is then applied to determine the value of the series
resistor.
POWER SUPPLY: Zener Diode Current.
When the Zener diode is in action, that is compensating for changes in load
current, it acts as a variable current device. The calculations prove that
within certain limits, changes in load current have no effect on supply
current, where the Zener current accounts for the difference.
The Zener current is the total current - the load current.
The value of R1 must be high enough to protect ZD1 when coping in a 'no
load' condition, where it carries the maximum current. Also R1 must be of
low enough value to be able to supply maximum load current without the
load voltage falling below the Zener voltage. These are all circuit design
considerations.
POWER SUPPLY: Zener Diode Power Rating.
The Zener diode when connected as a 'shunt regulator' will provide a stable
output voltage for changes in load current.
Without ZD1 present the junction R1/Rload voltage rises as load current
reduces.
Including ZD1 in circuit and this voltage rise increases the diodes reverse
bias causing a greater Zener current to flow. This opposes the voltage
increase thereby stabilising the output voltage.
POWER SUPPLY: Transformer Turns Ratio.
The transformer considered here is for a 'mains supply' connection. The UK
mains are around 250V, which is much too high for practical applications,
especially transistor circuits. The main purpose of the transformer is to step
down this voltage to a more convenient level. There are also step-up types
available which can be seen by making the secondary output voltage greater
than that of the primary.
The output voltage depends on the relationship or ratio of the number of
turns on the primary which is connected to the mains, and the secondary or
equipment end. The turns-per-volt of the primary is a design factor, and
relates to impedance and current requirements of the circuit. Input a range of
voltages to see the effect on the input, output turns ratio.
A further role of the transformer, and in some instances of more importance,
is to provide electrical safety isolation. The secondary winding is isolated
from the direct mains AC voltage by the insulation between the coil
windings.
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VOLTAGE REGULATION: Fixed Voltage Regulator.
Interactive Content!
When exploring the Zener diode, an example of a simple power supply was
used to provide voltage stabilisation independent of load current variation.
This is fine when current demands are low; however, a fixed voltage
regulator is a much better way.
These devices which are available in a range of both positive and negative
fixed output voltages contain not only a form of Zener diode regulation, but
also short circuit or over current and thermal overload protection. But more
important they are much easier to use.
Firstly, determine the stabilised voltage from one of the standard packages.
Provide a rectified DC supply (some degree of ripple being present is
acceptable) and then connect the common point to the zero volts line.
Note. There is a requirement for some 'overhead voltage', for example 8V 5V = 3V. In some cases this 'overhead' can be several times larger than the
regulator voltage, but it may mean the need for a larger heat sinking
arrangement as the voltage dropped between input and output will be
dissipated as power loss across the device.
VOLTAGE REGULATION: Variable Voltage Regulator.
This example shows a variable voltage stabilised regulator. The output
voltage is determined by the relationship between the values of R1 and RV1,
which form a voltage divider circuit. R1 is fixed to develop a reference
voltage (produced by the regulator) across it of 1.25V.
Adjustment of RV1 changes the voltage upon which the reference volts sits
(added to). Raising or lowering of this voltage adjusts the stabilised output
potential.
As the reference voltage Vref remains constant, stabilisation is achieved.
Replacing RV1 with one or more Zener diodes connected in series is another
way of obtaining a fixed stabilised non-standard output voltage using this
device.
Note. The unstabilised input voltage must be greater than the maximum
output voltage required to provide some 'overhead'.
VOLTAGE REGULATION: Regulated Power Supply.
T4 base current determines the overall DC operating conditions of this
regulator, pre-setting T2 base voltage and T1 current. The 0.6V between the
base and emitter of T4 provides a stable voltage reference point irrespective
of output voltage changes. T1, T2 are connected as a Darlington pair to
provide high current output.
T3 is for excessive load current protection. Currents greater than about
1Amp bias T3 into conduction due to the increased voltage drop across R4,
thereby reducing T1 base drive via T2. Try adjusting the load to a value of
10ohms.
Output voltage stabilisation is provided by the feedback path and 180° phase
reversal through T4. Increased load current demand normally pulls down the
supply voltage. This reduces T4 base bias, raising T2 base voltage; thereby
driving T1 harder on to supply the increased current.
A reduction in load requirements biases off T2, T1 due to the increased
current through R1, R2 as T4 conducts more due to increased base current.
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19 12047 9.3821
MAGNETISM: Attraction and Repulsion.
Interactive Content!
By placing two bar magnets (magnetic iron) end to end they either attract or
repel one another.
A bar magnet is referred to as a permanent magnet because it retains its
magnetic properties. Around each magnet there exists a magnetic flux which
when brought into the range of a similar field will cause the two bodies to be
either attracted or repelled. When positioned to attract, the result is that of
one long magnet where the path of the flux is directed through both magnets.
The strength of a magnet (flux, unit Weber) may be expressed by the number
of lines of force leaving the N pole and entering the S. Flux density varies
around the magnet but is concentrated at the poles and is the number of lines
of force passing through an area of 1sq cm. Here the unit of measurement is
the tesla, symbol (T) where one tesla is a density of one Weber of magnetic
flux per square metre.
The physical size of a magnet is not related to its magnetic strength, this
depends upon the flux density.
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MAGNETISM: Magnetic Field of a Straight Conductor.
For this experiment iron filings are first sprinkled on a card and randomly
arranged by tapping the card. If a piece of straight wire is connected as
shown across a DC supply, a current will flow when closing the switch. The
direction of current is for conventional current, i.e. from positive to negative
which magnetises the filings, giving each a N and S pole, as for a compass
needle.
Concentric circles are formed due to the magnetic field around the
conductor.
The direction of the lines of force is determined by the current direction,
using the right-hand screw rule. Tightening a screw represents the current
flowing down through the card making the field clockwise. Reverse the
current and the field is now in the opposite direction, as if the screw were
inserted from below.
Flux density is greatest close to the wire and reduces towards the outer edges
if the card.
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MAGNETISM: Magnetic Field of a Single Coil.
Remembering the right-hand-screw rule we can now develop this topic
further by examining the effect on the magnetic flux pattern of a coil.
Note, you are viewing the coil through one single loop. With the battery
connected one way round the current flows up through the card forming an
anti-clockwise pattern of filings and then down through the card clockwise.
Changeover the current direction by reversing the battery and the flux
pattern is now in the opposite direction.
The central arrow on the diagram indicates the direction of flux. Adding
more turns to the coil makes the field inside the coil winding stronger, as the
flux becomes concentrated in a small area. In a multi-turn coil this flux
concentration can be improved by winding the coil on a bar of magnetic
material, i.e. ferrite or soft iron which provides a path for the flux.
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MAGNETISM: Electro-magnet.
An electro-magnet can be constructed by winding a coil of wire around a
piece of ferrous material, i.e. soft iron.
This is often called a 'solenoid'. When the switch is closed current flows in
the winding causing a magnetic field around the coil, thereby magnetising
the soft iron core. Increasing the current through the winding or adding more
turns to the coil can improve the strength of the electro-magnet. Magnetic
saturation of the core will eventually occur.
The direction of the magnetic flux determines which end of the core is North
and which is South. Reversing the direction of current through the coil will
change this.
An example of the use of an electro-magnet in electronics is as a relay
switch. Or as an electrically operated crane, whereby the magnetic field
generated is used to lift, say, a car body and drop it by switching off the
energising current. Winding the coils onto a horseshoe shaped magnet brings
the poles closer together thereby concentrating their magnetic force around a
smaller area.
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MAGNETISM: A Closed Magnetic Circuit.
A magnetic circuit is the path of the magnetic field. The diagram shows a
permanent magnet where the poles are connected via three pieces of soft
iron. The closed magnetic flux path is therefore continuous. All the magnetic
effect is enclosed within this path, with little detected outside.
The reluctance of the iron is the resistance of the material to magnetic flux.
Iron is a good magnetic conductor, providing a path of lowest resistance.
The second diagram is one found in transformers. Current through the coil
replaces the permanent magnet and can be determined from the formulae
given. The type of core material determines the strength of the field.
Permeability is the ratio of the magnetic flux density to the magnetic force
producing it.
In an electric circuit current is due to the existence of an electromotive force.
Similarly, in a magnetic circuit flux is due to a magnetmotive force (m.m.f.)
and proportional to the current and number of turns. The constant of 1.257
converts m.m.f. to the equivalent SI unit (ampere-turns).
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MAGNETISM: Magnetic Circuit with an Air Gap.
We now introduce an air gap in the magnetic circuit. Air or non-magnetic
materials have a very high 'reluctance' compared to iron, requiring that its
path be kept as short as possible. In practice this air gap could enclose a
moving coil as part of an electric motor or analogue meter movement.
The presence of the air gap considerably increases the number of ampereturns required to produce a given value of flux lines.
Compare the amount of current required to produce the same number of
lines with a core of the same dimensions, with or without the presence of the
air gap by referring back to the previous closed magnetic circuit topic. Note:
the length of the path must always include the width of the air gap.
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MAGNETISM: Force on a Conductor in a Magnetic Field.
A conductor is positioned inside a magnetic field created by two opposing
permanent magnet poles. With current switched off there is no influence on
the permanent magnetic field.
A current flow sets up a series of concentric lines of force around the
conductor in a clockwise direction. The effect is a crowded magnetic field
above the conductor as the field is reinforced and a less dense field below as
the flux in the lower part of the conductor and the N to S field is in
opposition.
As the lines of force try to shorten the path above the conductor from N to S
this exerts a mechanical force on the upper part of the conductor pushing it
in a downward direction. If the magnet poles or the current were reversed the
resultant direction would be upward.
The force imposed on the conductor can be calculated as shown.
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MAGNETISM: Permanent Magnet Induction.
Generating an EMF (electromotive force) with a permanent magnet and a
coil of wire. Shown is a circuit consisting of a coil of wire with a current
meter connected across it. This meter is zero centring and will deflect in
either way depending upon the current direction.
As the magnet is inserted the lines of force link with the turns in the coil.
The meter will only deflect whilst the magnet is in motion and will return to
zero when stationary. Moving the magnet in and out causes an EMF to be
induced in the coil, which can be increased by moving the magnet faster.
As the magnet is moved towards the coil the induced current will cause a
force which opposes that movement, similar to two N or S poles of
permanent magnets. On removal of the magnet a force will be felt as an
opposite attraction of the fields takes place.
The induced EMF will increase in proportion to the number of turns on the
coil, with the direction of current determined as before.
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MAGNETISM: Electro-magnetic Induction.
By replacing the permanent magnet with an electro-magnet (a coil with an
iron core) then electro-magnetic induction can be made to take place. If the
current in the primary coil (electro-magnet) is constant, i.e. DC then no
meter movement will be detected. However, a changing current, either by
increasing or decreasing will cause a current to be induced into the
secondary or outer coil.
Once the increasing current reaches maximum then no further change is
taking place and the field collapses.
When the primary current is 'growing' the magnetic field is expanding across
the secondary winding, an EMF will be induced in the outer coil in a
direction which will oppose the change, i.e. of reverse polarity.
The field caused by this induced EMF will try to oppose the change; that is it
will attempt to continue the original direction of the flux. It is in this way an
EMF can be made to flow in one coil by the changing current in another and
is the principle of the transformer.
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MAGNETISM: Self Induction and Back EMF
When a current is made to flow through a coil it is found that the voltage
developed across the coil does not change immediately. This is caused by a
magnetic field that is produced around the coil that induces an EMF into the
coil, which opposes the growth in main current. This is called a back-EMF
and works in opposition to the applied voltage.
When the current reaches a steady state there is no further change in the lines
of force and the back-EMF falls to zero. If the main current is reduced there
is again a change in the flux and an EMF is induced. This time it's in a
direction which tries to maintain the main current, slowing down its decline.
Back-EMF potentials can become extremely high. This is mostly as a result
of the speed of change in the current direction. Try reducing the period of
change whilst maintaining the other circuit conditions. Protection needs to
be included in circuit design using large inductors to prevent the destruction
of sensitive components from this high reverse voltage.
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ELECTRICAL MACHINES: A Simple AC EMF Generator.
Interactive Content!
A simple generator can be constructed by rotating a coil of one turn between
the poles of two permanent opposing magnets, alternatively this could be the
ends of a horseshoe magnet. As the coil is rotated, (called an armature)
around the X - X axis, an EMF will be induced which appears across the
load resistor 'Rload'.
The example shows two conductors the active length is that which is under
the influence of the magnetic flux. Note the connection to the slip rings
which develop an AC waveform.
When the two conductors in the diagram are vertical the induced EMF is
zero. As they are rotated clockwise a maximum positive EMF will result as
the conductor cuts the magnetic flux. There is a sinusoidal fall in EMF as the
second reversed vertical position is approached which then increases in the
negative direction, thereby completing one revolution.
The output EMF and the frequency will depend largely on the speed of
rotation (velocity) as the flux density and dimensions of the coil will remain
fixed in a practical application.
ELECTRICAL MACHINES: Generating a Greater EMF Output.
A generator consisting of just one turn would be of little practical value in
terms of providing a useful voltage. However, it greatly simplifies the
explanation of the generator action.
We have seen that the EMF output can be raised by speeding up the velocity
at which the flux lines are cut by the conductor. But as previously mentioned
for an AC generator this also changes the frequency of output.
The preferred method of increasing the power delivery of the generator is to
increase the number of turns on the armature. The calculations are included
to demonstrate this principle. Remember that for each turn the conductor
crosses the flux path twice. Also it is assumed here that the entire coil is
within the influence of the flux path.
All the flux will be linked with the coil during a one quarter revolution of the
armature, i.e. any change through 90°.
ELECTRICAL MACHINES: Generator with DC Output.
This machine is called a unidirectional generator (dynamo). The output of
which is a series of EMF pulses, all in the same positive direction. Resulting
in an average EMF developed across the load resistor. The smoothness of
this output could be improved by increasing the number of coils, thereby
providing many more pulses within each revolution.
This is not the same as adding more turns to a single coil, which would
increase the EMF output.
The difference between this DC generator and the previous AC machine is in
the connections to the armature coil, where a commutator is now used.
The single coil is connected to two copper segments by carbon brushes. As
before the output EMF is as a result of the coil cutting across the lines of
magnetic flux. With any inductive machine an EMF will only be generated
whilst the lines of flux are being cut. Stop the rotation at any angle and the
output falls to zero.
ELECTRICAL MACHINES: DC Motor and Speed Control.
The construction of a DC motor and a DC generator are the same. To run as
a motor the generator load is swapped to a current source (battery). Here we
have added field coils to the pole pieces to produce the magnetic field.
Connecting a variable resistor in series with these coils and controlling the
magnetic flux at the poles is one method of changing the motor speed.
However, this example uses the Back-EMF voltage.
An electric motor is designed to develop a certain number of revolutions
'rpm' under specified conditions and load. Relative speed is therefore
calculated against these design parameters. If you input the running
parameters to those for the motor design and then adjust the motor series
resistance you will be able to see a change in motor speed.
If the battery were connected directly across the armature coil a heavy
current would destroy it, therefore the voltage needs to be applied gradually.
As the speed builds up the armature conductors are cutting the flux produced
by the field winding, generating a Back-EMF in opposition to the supply
voltage, limiting the flow of armature current.
The value of the series resistor can now be reduced safely allowing more
current to flow which gradually speeds up the motor. A DC motor will reach
a stable operating speed when the back-emf of the armature and the
frictional losses balance the input power.
ELECTRICAL MACHINES: Stepper Motor.
Stepper motors are found in many electronics products, computer printers
are a typical example where the paper and print head are accurately moved
by incremental positioning. The stepper driver requires just four pulses sent
in a particular sequence to move the rotor in either direction.
The speed of changing the pulses determines the motor speed. The rotor is
made from soft iron and provides a path for the flux across the pair of
electro-magnetic coils.
Follow the sequence of pulses which energise each pair of coils. You will see
that four of the poles are magnetised at any one time. This is to ensure the
rotation is in the correct direction. Logic 1 on a transistor base causes
collector current to flow in that pair of coils.
Normally all the control logic for a stepper motor is contained in a dedicated
IC that produces the correct sequence of pulses from a clock and direction
select pins. An alternative approach is to use the output of a micro-controller
if a particular action or sequence is required.
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TRANSFORMERS: Transformer Alternating Voltages and Currents.
Interactive Content!
Most power supplies are based on a step-down AC voltage derived from a
mains-transformer. These, like most components are available to suit every
conceivable application. Choosing a suitable supply rail voltage and
therefore transformer winding ratio's for your project can save expense on
having to reduce surplus overhead voltage elsewhere i.e. through dropping
resistors or voltage regulators, which in turn then become hot as energy is
wasted, requiring the use of heat sinks.
An ideal transformer as shown here will have an efficiency of 100%. There
will be no losses in the flux linking between the primary and secondary
windings. In practice this is not so, nevertheless high levels of efficiency can
be found.
Any alternating current changes made in the primary winding will be
reflected in the secondary. Transformers can be step-up where N2 > N1 or
step-down N2 < N1.
As the flux (dotted line) is common to both primary and secondary an
induced EMF per turn will be the same for both windings. Once this is found
then all other calculations follow. Note the current and voltage relationships
between the primary and secondary. Where for a step-up transformer the
ratio of primary to secondary current is inversely proportional to the turns
ratio.
The power dissipated in the load will be reflected back to the input (primary)
circuit, i.e. the power input must at least equal to that consumed by the load.
TRANSFORMERS: Input Impedance.
A transformer makes an ideal impedance matching device. However, there
are more efficient, less expensive ways of achieving the same result using
transistors. The main advantage of using a transformer is to provide an
electrically safe isolated output.
An unloaded transformer secondary winding will make the primary
impedance very high. To see this, give the load a high value of say,
10Mohms (open-circuit) by making I2 very small. Gradually increase I2 and
note the transformer primary impedance falls.
Whilst the number of turns normally reflects the voltage output, either as a
step-up or step-down arrangement, we can also use the transformer to
achieve maximum current transfer between two previously unmatched
impedances.
For example: we wish to supply a current of 10Amps at 25V from a circuit
with an output impedance of 2.5kOhms. Determine the transformation ratio.
A typical transformer of conventional design with a rating of say, '12VA' will
give an indication as to the maximum loading that can be placed across the
secondary output winding.
For example, a 12V secondary with a maximum current of 1A which is 12V
× 1A = 12VA. Another of the same physical size might be 40V with a
maximum current of 300mA; this again equals 40Volts × 0.3A = 12VA.
Mains transformers frequently have two secondary windings thereby
enabling full wave rectification where both positive and negative supplies
can be derived by connecting the windings in series with a centre tap at 0V.
TRANSFORMERS: Maximum Power Transfer.
An ideal AC source will comprise the generator voltage and its associated
internal resistance. For the maximum transfer of power, i.e. minimise losses;
any load Rload must equal the source internal resistance. Even so the power
delivered is only half of that produced by the generator. The other half is lost
across the internal resistance.
In a practical situation Rload will rarely be the same as the generator internal
resistance, hence the need to interface the two with a matching transformer.
This impedance match can be achieved by adjusting the transformer turns
ratio to compensate for the amount of mismatch. As far as the generator is
concerned the value of the load now looks like its own internal resistance.
Ignoring any other circuit losses, maximum power is transferred to the load
when the load resistance and the generator internal resistance have the same
value.
You can determine which winding is the primary and which the secondary
by looking at the windings. As it's a mains step-down type, the higher
voltage mains will require more turns and thinner wire as it conducts less
current. The secondary is required to supply more current and so its most
likely the winding will be thicker and need less turns as the voltage output is
that much lower.
TRANSFORMERS: Auto Transformer.
An auto transformer is a transformer in which part of the winding is
common to both the primary and secondary. The number of turns on the
upper part is N1 - N2 where N is the number of turns. The electrical
specification of an autotransformer is usually determined by its rating, which
is measured in VA volt-amperes. This is a product of voltage and current of
the transformer, i.e. apparent power.
The auto transformer can be connected either way round to provide either a
step-up or step-down function.
The advantage of this type of transformer is a cost saving owing to the
smaller amount of copper used in the windings. The disadvantage is there is
no electrical isolation between input and output as the same current flows in
both circuits.
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THREE PHASE SYSTEMS: 3-phase Generation of EMF.
Interactive Content!
Most UK domestic consumers are fed from a 240V AC single phase supply.
As we have seen this can be generated by rotating a single turn coil between
two permanent magnet poles. The waveform shows that a single rotation of
the coil through 180° produces the familiar sinusoidal waveform.
An alternative source of a single phase 240V can be found by tapping off a
3-phase national grid supply as we shall now explore.
When three coils are placed 120° out of phase to each other and rotated
together they produce a 3-phase supply.
By convention these are coloured Red, Yellow and Blue with a fourth
conductor, coloured black as a neutral connection. 3-phase supplies are used
for national electricity distribution. Smaller conductors can be used, thereby
saving copper. The three EMF's produced are all at the same amplitude, but
displaced by 120°.
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THREE PHASE SYSTEMS: Balanced Star Generator.
Where a 3-phase generator provides a balanced output and the loads
connected to each phase are identical then the calculation of voltage and
current for, say the red phase can be applied equally to the other two phases.
Voltages Vr, Vy and Vb are called phase voltages and are the potential
difference developed between phases Vry, Vbr and Vyb line voltages.
The UK electricity supply has a line voltage of 415V between any two
phases and 240V phase voltage to the neutral line.
A 3-phase generator windings are normally connected in a star configuration
where each limb voltage and current are 120° apart.
As the individual currents in a balanced system added together come to zero
the neutral line is often omitted when only a line voltage is required.
However, for the distribution of a 240V domestic supply four wires are used.
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THREE PHASE SYSTEMS: Adding a 3-phase Balanced Star Load.
Connected to the output of a 3-phase generator, will be either three single
phases as used for a domestic mains supply, or line voltages to a 3-phase
load. Shown here is a balanced load where all three output voltages and
currents are identical in amplitude, but 120° out of phase to each other. For
clarity only the 'red phase' calculations are shown, those for blue and yellow
connections are identical.
Individual phase voltages and currents are calculated as shown by applying
Ohm's Law.
Power dissipated in each resistor limb of the load is a product of the phase
voltages and currents. Total power required from the generator is a sum of
the individual powers dissipated in each resistor.
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THREE PHASE SYSTEMS: Unbalanced 3-phase Star Load.
So far we have looked at 3-phase systems where the load is the same across
all phases. We now consider this as an unbalanced load. An example might
be where 240V single-phase heaters are connected to a 415V 3-phase supply.
Some could be switched on and dissipating heat, where others are switched
off. Determine the individual phase currents and the total current.
The sum of the currents will flow in the common neutral connection as In.
To find In it is necessary to compensate for the 120° phase differences.
Using trigonometry the instantaneous values are found for each of the three
phase angles and added to produce the real and imaginary complex number
components. Applying Pythagorean Theorem calculates the equivalent
magnitude of current in the neutral conductor.
3-phase loads can be resistance, capacitance, inductance, impedance or any
combination. All that is necessary to make your calculations is to find the
equivalent reactance (AC resistance) and consider the load as you would a
resistor.
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THREE PHASE SYSTEMS: 3-phase Balanced Delta Load.
A Delta configuration is an alternative to the 'star' 3-phase connection. Note
there is no neutral line. The voltage between any pair of lines is equal to the
phase voltage of the generator. The line currents are comprised of the one
flowing into the load and that flowing from the load where the actual current
is the addition of the two.
Also the line current is the phasor difference between two phase currents.
As the phase and line voltages and currents are identical for each phase then
calculations are shown for the red phase only. The other two are implied
unless it's for an unbalanced system.
Three-phase loads can be designed as either a star or delta configuration,
whereas generators are normally restricted to the star mode.
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THREE PHASE SYSTEMS: Star and Delta Transformations.
A 3-phase load may be in either a star or delta configuration. However, to
change from one to the other requires the resistor values to be recalculated.
This is to ensure that the impedance between any two of the line conductors
remains the same and therefore consumes the same amount of power.
The circuit Z or impedance for the limbs of either configuration could
comprise capacitance, inductance, resistance or a combination of all three.
But could easily be replaced by resistor values only.
To prove the equivalence of the circuits, give Z1, Z2 and Z3 in the star
circuit an equal impedance, say 65ohms. The equivalent delta impedance
will be 195ohms. Now go back and input these values into both the balanced
star and delta load topics and compare the line currents, having selected an
appropriate line voltage of around 200V.
From these results you can calculate that the power dissipated in each circuit
is the same. Remember P = I² × R.
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THREE PHASE SYSTEMS: Displaying a Phasor Output.
Within this short introduction to the principles of 3-phase systems its not
possible to explore how all the various phase angles are derived in a
complex circuit consisting of resistance, capacitance and inductance.
Where the line voltages and phase loads present an equal impedance to the
generator then the phase voltages and currents, and power consumed will be
equal.
Introducing reactive components into the circuit which themselves have 90°
phase difference between the voltage and current further complicates the
equation. Furthermore as the currents within the limbs of the three phase's
change, cancellation will take place as currents in any single conductor can
be flowing in both directions simultaneously.
Despite all this it is possible to make reliable calculations of what is
happening in a 3-phase circuit. For this reason the operation of a 3-phase
system is frequently shown using a phasor diagram, which shows
graphically the resultant current amplitudes and their respective phase
angles.
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ENERGY TRANSFER AND COST: Electrical Charge.
Interactive Content!
Electrical charge is measured in coulombs and given the symbol Q. It is a
product of current (amps) flowing in a given period of time (seconds). This
doesn't have to be a stored charge, it could equally be the energy consumed
by an electric heater over the same period of time.
Shown is a simple circuit to charge a battery pack made up of both series
and parallel combinations of cells. As it's an enclosed unit it can be
considered as just one battery. Note we are not concerned with the battery
voltage as this is determined by the internal combination of cells (around
1.2V each), nor the amount of current that can be drawn from a fully charged
battery.
Batteries are normally purchased with a designed capacity measured in Ah
(Amperes-per-hour). A fully charged 200Ah battery can deliver 100 Amps
for two hours or one amp for 200 hours.
Subject to the limitations of the battery construction, batteries can be
charged at very high currents for short periods of time, or for very long
periods at tiny currents known as trickle charging.
ENERGY TRANSFER AND COST: Electrical Energy and Tariff.
Energy is the ability to do work and so if a circuit power is measured in
watts and the time in seconds then the units of energy are watt-seconds or
joules.
It will be seen from the calculations that we first need to determine the
power rating of the circuit and then for how long that power is consumed.
This example shows an electric heating element, but it could equally be a
light bulb or any other circuit or apparatus connected to an electricity supply.
One reason for the measurement of energy is to enable a charge to be made
for the amount used. This is simply the number of units consumed multiplied
by the unit price.
Electricity supply companies provide a range of tariffs to enable customers
to choose the charging method which is the most economical for their needs.
Government taxes i.e. VAT, will also have to be applied, and these may
include additional energy levies.
ENERGY TRANSFER AND COST: Measuring Electrical Energy.
Electrical power can be measured directly using a device called a wattmeter.
This is a combination of an ammeter and a voltmeter and provides an output
in watts or kilowatts, depending upon its application. Note there is a series
coil to pickup the current and a parallel voltage coil to measure the voltage
across the load.
To obtain a measure of the total energy used we must however, include time,
which multiplied by the power delivered gives an output in kWh.
Finally to enable the energy consumed to be understood by a non-technical
person i.e. meter reader or consumer and processed, the final output is
converted to units of electricity as discussed in the previous topic.
ENERGY TRANSFER AND COST: Electrical Energy for Heating
Water.
One of the most costly uses of electrical energy is in heating water, both in
domestic and industrial use where it is often converted to steam to drive
machinery and other processes.
For the most efficient transfer of heat from an electrical element i.e. in a
kettle it should be immersed in the water where the maximum surface area is
exposed to the liquid.
A unit of heat is the quantity required to raise the temperature of the mass of
water through 1°C. Water has the highest known specific heat and for most
calculations can be assumed to be unity. The unit of 'specific heat capacity'
symbol (c) is the joule and the constant 4200J/kg/°C applies to water. Other
materials and liquids will have different values. We can therefore apply the
theory and calculate the electrical energy required to raise the temperature of
water by any given amount.
Heating water can never be 100% efficient, but with recent improvements in
lagging methods and the use of plastics which have poor heat conductive
properties much greater efficiencies can be achieved in modern energy
saving systems.
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ATOMIC STRUCTURES: Hydrogen Atom.
Interactive Content!
All matter is made up of a three dimensional lattice of atoms. An atom
consists of a central core called the nucleus containing protons and neutrons
around which orbit one or more electrons. Atoms are extremely small and
millions of them are required to make up the smallest humanly visible
object.
The simplest atom is that of the Hydrogen element which has just one proton
and one orbiting electron. The number of electrons in orbit determines the
type of material. The electron orbit is referred to as a shell. Each is given a
letter K - N.
Electrons carry a negative (-) charge, whereas protons are positively (+)
charged. An atom in its neutral state has an equal number of electrons to
protons where the positive and negative charges cancel to achieve an
electrical balance.
However, should an electron be forced to leave its orbit the atom takes on a
positive charge and will therefore try to attract a negative electron from a
neighbouring atom to regain its neutral state. The atom, which has just had
its outer electron, pulled away in turn takes on a positive charge causing an
electrical movement from one atom to another. This is the principle of
current or electron flow. The direction of movement is determined by
applied potential polarity.
ATOMIC STRUCTURES: Electron Shells.
The structure of an atom is often represented as a series of concentric circles
called 'shells'. In the following examples each shell is identified by the letters
K to N and a number representing the number of electrons in orbit for that
type of material.
There will be an equal number of protons in the atom nucleus to maintain an
electrical balance, i.e. neutral state.
The electrons are held in place by the electrostatic attraction of the positive
protons and the negative electron charges. The electrons in the outer shells
or orbits are held less firmly because they are further away and it is these
which contribute to a flow of electron current being easily attracted away by
the positive potential of say, a battery.
ATOMIC STRUCTURES: Carbon Atom.
An electric current is the result of a 'free electron' movement towards a
positive voltage potential within a conductor. To understand what is
happening it is necessary to have an appreciation of the physical structure of
the various elements that make up electronic materials.
Carbon is a non-metallic element, but a carbon rod is a good conductor of
electricity. It is also known as graphite. Some types of resistors are
constructed of carbon where the composition of the material determines the
electrical resistance.
In electronics we are only concerned with the electrons in the outer orbit and
so the diagram can be greatly simplified to show just those called 'valence
electrons'. This will make things much easier for us when we go on to
explore semiconductor theory.
ATOMIC STRUCTURES: Silicon Atom.
Silicon is a non metallic element with a crystalline structure and is used in
the manufacture of glass, which is a good insulator as there are no free
electrons available to enable the silicon to conduct electricity.
However, Silicon forms the basis of 'silicon semiconductors', where an
extremely small impurity element is added to the crystal which either
provides additional free electrons or creates a small electron deficiency.
If the added impurity introduces additional free electrons then current flow
will be due to electron movement. Similarly if the impurity creates an
electron deficiency then the current flow is determines through the
movement of holes (absence of an electron). This principle is fundamental to
your understanding of how diodes and transistors work and will be fully
explored later.
ATOMIC STRUCTURES: Copper Atom.
Copper is a very good conductor of an electric current, which is also
inexpensive, thereby enabling it to be used extensively for flexible electric
cables and for the conducting tracks on a printed circuit board. The single
electron in the outer shell is easily attracted away from the parent atom to
contribute to current flow.
The binding of the electrons in the outer shell of good conductors is so weak
they are sometimes called 'free electrons' and can be made to move around
by external influences, by heat or electromagnetic radiation from other
components for example which can cause electrical noise.
Being able to influence the electron flow within a conductor is actually put
to good use within a transformer where the windings are tightly coupled and
the voltage across the primary induces a voltage across the secondary
proportional to the primary to secondary turns ratio.
ATOMIC STRUCTURES: Germanium Atom.
Germanium is a metallic element. However, due to its structure the outer
electrons are not easily released, which makes it a poor conductor. It's used
in the manufacture of germanium semiconductors (now largely superseded
by silicon devices) where impurity atoms are added to either provide
additional free electrons or to create an electron deficiency depending upon
the semi-conductor type ('N' or 'P' type).
Germanium semiconductors (diodes) are still found in some radio detection
circuits where their lower forward bias voltage (0.2V) can be an advantage
when demodulating very small amplitude signals.
One disadvantage of germanium semi-conductors is they produce an
increase in current carriers with increasing temperature, making them less
stable than silicon devices. This means they are more prone to 'thermal
runaway' as increases in temperature cause a corresponding increase in
current carriers, thereby producing more heat and so it goes on.
Unless suitable protection circuits are included, i.e. negative feedback, then
thermal runaway could eventually result in the destruction of the device due
to overheating.
ATOMIC STRUCTURES: Silicon Crystal Covalent Bonds.
The atoms in both silicon and germanium crystals are packed together so
closely that their valence electrons actually move around in the path of
neighbouring atoms. This produces a covalent bond or linking between two
adjacent atoms. Note that each atom still only has four valence electrons, but
appears to have eight. Therefore, a silicon or germanium crystal will have
four neighbours, which are arranged in a three-dimensional structure, but
shown here as two-dimensional.
Remember that an atom is always trying to establish a neutral potential and
so these additional circling electrons upset this equilibrium, the result being
any two adjacent atoms attract and repel the pair of electrons with equal and
opposite force and it is this tension that holds the structure together in a
crystal formation, producing a solid piece of material.
The dotted lines on the diagram are simply to indicate the path around which
the electron travels as it is shared by two adjacent atoms. Also shown is an
alternative two-dimensional representation of covalent bonds, which should
make the actual electron pairing a little clearer.
Both silicon and germanium at absolute zero temperature (-273°C) will
become perfect insulators as there ceases to be any free electrons when all
become paired in their respective covalent bonds. However, at room
temperature these bonds get broken, whereby some of the electrons break
away from their valence shell, generating electrical noise. It is the controlled
creation of free electrons in the material that makes semi-conduction
possible.
ATOMIC STRUCTURES: P-type and N-type materials.
A pure silicon crystal, which by itself is a good insulator, forms the basis of
the majority of semiconductors used in electronics and microelectronics. To
increase the electrical conductivity of the base material requires combining
an impurity that has either an additional electron to make N-type or an
electron deficiency for P-type in the outer valence shell and is called doping.
Conduction is by holes (absence of an electron) in P-type semiconductor
material or through electron movement in that for N-type.
An N-type requires a tiny amount of a pentavalent material (five electron
valence shell). This could be phosphorus or arsenic or antimony as each has
the extra electron required in the outer shell. The fifth electrons are called
'free electrons' and are the majority carriers (where holes are minority
carriers) and are the ones that contribute mostly to current flow through the
now impure silicon. The additional pentavelent atom is also known as a
donor atom because of the additional electron.
The P-type semiconductor material has a shortfall of electrons through the
inclusion of an impurity such as indium, boron or aluminium which are
known as trivalent, as they have just three electrons in their valence shell.
Therefore the conduction is by means of the movement of holes as the
majority carriers and electrons as minority. Here the additional atom is called
an acceptor atom because it is able to take up one of the free electrons
through the process of recombination.
Applying voltage across a piece of N-type or P-type material and the
majority and minority current carriers are attracted by the opposing positive
and negative potentials. A piece of doped semiconductor material is of little
use as it is in effect a resistance, it is not until the two types are fused
together that it makes up semiconductor device.
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DIODE THEORY: The PN Junction Diode Characteristics.
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Semiconductor diodes commonly known as rectifiers allow a relatively high
current to flow in one direction only, owing to a forward resistance of only a
few ohms, whilst having a high resistance to current when connected in
reverse.
To enable this action a semiconductor junction is formed by joining together
two pieces of material, one doped as a p-type, having a deficiency of
electrons called (+) holes (trivalent), the other n-type, having an excess of (-)
electrons (pentavalent). At the point where p and n type materials come
together, some electron/hole recombining takes place across the junction.
This forms a neutral region with very few free electrons or holes, therefore
very few current carriers.
Note the use of the term 'ion' to describe a positively or negatively charged
atom. Negatively charged have an additional electron (donor atoms having
five electrons in their valance shell) and positively charged atoms have a
deficiency of electronics (where the donor impurity has only three in outer
shell). Therefore n-type and p-type.
Because of this shortage of current carriers, the area either side of the PN
junction acts as a poor insulator (semi-conduction), a bit like an ordinary
resistor. By applying a forward bias voltage i.e. the p-type connection to
battery (+), this region can be made to contract, thereby taking on a forward
resistance of only a few ohms. This enables a high current to flow. Apply the
battery in the opposite direction as a reverse bias and the junction expands
forming an extremely high resistance.
The I, V curve shows a typical forward and reverse bias arrangement for a
PN junction diode and will be explored fully as we proceed.
DIODE THEORY: Simple Diode Circuit.
This simple diode circuit demonstrates the effect of connecting a diode in a
forward or reverse biased condition. Also shown are a number of alternative
symbols found in electronic circuits.
On forward biasing the diode, anode (a) positive to the cathode (k) the lamp
will light as the forward resistance is low, typically < 100ohms. In the
reverse biased direction the diode resistance is high (several Mohms) and the
lamp is extinguished, as it is starved of current.
The cathode end is normally indicated by a band around the diode. The
cathode is easy to remember by writing Kathode and reverse the 'K' where
the arrow indicates the direction of conventional current flow i.e. positive to
negative.
DIODE THEORY: Forward Biased PN Junction.
On connecting the battery +V to the p-type material the junction is forward
biased. Negative electrons will cross to the p-region attracted by the battery
(+) potential and positive holes will move into the n-region, similarly
attracted by the negative battery potential.
It takes a potential of about 0.6V to overcome the junction barrier of a
silicon diode, (germanium types require less at approximately 0.25V),
thereafter a large increase in current +I flows owing to the low forward
resistance of the diode.
See how the resistance of the diode is high for low bias voltages below the
knee of the curve and then takes on a linear characteristic throughout the
upward part of the slope. This topic is developed further later. See Finding
the Diode Forward Resistance.
DIODE THEORY: Reverse Biased PN Junction.
Reverse biasing the junction expands the PN region, and makes the junction
develop a high electrical resistance.
When connecting a battery as shown, positive (+) to the n-type material,
increasing the reverse bias causes the mobile carriers (positive holes and
negative electrons) to be repelled as the negative battery terminal attracts the
holes and the positive battery terminal attracts the electrons. Simply, it pulls
the two types of current carriers apart preventing them recombining.
A reverse biased junction can develop a resistance of many millions of
Ohms. As there is a shortage of mobile current carriers.
Try inputting a range of values up to 50V and note there is a dramatic
increase in current above the reverse breakdown voltage of 40V, due to the
much lower diode resistance.
DIODE THEORY: Finding the Diode Forward Resistance.
Before we consider the characteristics of a diode, first note that a resistance
produces a linear or straight line curve, where the current varies in direct
proportion to the increase or decrease in the voltage across it. See the Ohm's
law topic.
A diode or any PN junction has a non-linear relationship between the current
and voltage. This means the resistance of the device varies throughout the
path of the curve. There are two straight portions one horizontal leading up
to the knee after which the curve rises steeply in a vertical direction.
To graphically find the diode resistance at any given point the formula is
applied using voltage and current values. Simply adjust the voltage and
current or X-Y coordinates to select a place on the curve and apply Ohm's
law.
Along the horizontal portion the resistance will be higher as the change in
current is tiny for a relatively large change in voltage. Moving around the
knee of the curve and the resistance becomes less before reducing
substantially as you enter the straight vertical line at 0.7V, after which the
resistance will be low and remain constant.
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DIODE APPLICATIONS: Light Emitting Diode 1.
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The Light Emitting Diode LED, is a PN junction diode that will emit light
when forward biased, that is when current flows from its anode to the
cathode. When selecting an LED for a particular application it should be
remembered it's a visible indicator and so both brightness level, especially
during daylight and the viewing angle need to be considered.
The forward voltage drop can be between 1.6V and 2V depending upon the
device type. The more forward current the brighter the light output. In this
application the logic inverter places 0V or 5V on the cathode that turns the
LED ON or OFF. The series resistor R1 determines the forward current.
Normally a flat on the base of the LED identifies the cathode or the cathode
is the shortest leg.
A range of high quality bright LED's are available to the constructor with
red, green and yellow with diffused lens in 2 sizes 3mm and 5mm. The
optical construction ensures that they give a good visible light output, low
drive current and fast response time. LED's are also suitable for pulsed
operation the frequency and mark space ratio of, which will effect the visible
light output as for a proportion of the time the device, will be switched off.
The viewing angle is usually around 80° to 120°. The recommended forward
current is 10 to 20mA, the more current the brighter the output.
Fixed 5V and 12V types are now often used. These LED's are particularly
applicable to logic circuits as they include an internal resistor, designed to
operate directly from five or 12Volts, greatly simplifying circuit design.
Making good logic level indicators. The easiest way to confirm you have
this type is to measure the forward resistance; it will always be higher than
normal type owing to the value of the series resistor. If in doubt you should
always check as replacing with a normal type will cause excessive current to
flow, which will destroy the LED and possibly other components feeding the
circuit.
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DIODE APPLICATIONS: Light Emitting Diode 2.
Most light emitting diodes require a series resistor for current limiting,
where the maximum potential between the anode and cathode should be no
more than 2Volts. Light emitting diodes consist of a P.N. junction that emits
light due to the recombination of excess electron-hole pairs when it is
forward biased. Where the amount of light emitted is proportional to the
number of excess minority current carriers, which in turn is a result of the
bias current determined by the supply voltage and series resistor values.
In this demonstration the LED is connected in series with the current
limiting resistor. The purpose of the resistor is to limit the forward current to
a safe level to avoid destroying the diode. When the LED is forward biased
it develops approximately 1.9V across the PN junction. To calculate the
resistor value, subtract 1.9 from the supply or battery voltage and apply
Ohm's Law.
The forward current should not be allowed to exceed around 20mA for full
brightness. If in doubt consult the data books or component catalogues.
If you are driving an LED from an AC supply, a standard rectifier diode
should be connected in series with the LED to limit the reverse voltage on
the negative half of the AC waveform. LEDs have a very low maximum
reverse voltage, 5V is typical and the device will be destroyed if this is
exceeded.
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DIODE APPLICATIONS: Opto Coupler.
In a semiconductor material the current carriers (electrons) can be excited by
the application of heat or light. The opto-coupler consists of an LED in an
enclosed package with a transistor without a base connection.
When the diode is made to conduct the light within the package causes the
transistor also to conduct through the movement of the carriers in the
transistor base region. Note the phase reversal of the pulses and the use of a
logic inverter in this instance to provide the drive ON/OFF voltage.
LEDs can operate in the infrared part of the visible spectrum and are found
in optical communications. These devices are mostly used in conjunction
with a photodiode (detector), connected in reverse bias mode where the
small current flowing through it is made to vary proportional to the amount
of light falling on the PN junction, the output of which needs to be amplified
for it to be of practical use.
Opto-couplers are used in analogue applications and have breakdown
voltages between input and output of several thousand volts, making them
ideal for electrical isolation purposes.
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DIODE APPLICATIONS: Seven Segment Light Emitting Diode.
Light emitting diodes can be connected together as an array and are available
packaged for specific functions. Here we demonstrate a 'seven segment'
device frequently found as part of a numerical display. Single digits displays
can be stacked to indicate longer numbers
These devices produce a bright visual indicator with a number count from 0
to 9 and usually include a decimal point. Most common are types with single
or double digit although up to four digit displays are available. In addition,
devices that can output alphanumeric characters, these require more
individual LED's to make up the character. By combining both, upper and
lower case characters, it is possible to display HEX characters that use 0-9
and A-F as valid characters.
To keep the number of pins on the LED package to a minimum it is usual to
internally strap together either the diode anodes or cathodes. Unless a special
LED driver chip is used each diode must be fed via a current limiting
resistor, calculated as for a single LED. Using a single resistor connected to
either the common anode or cathode pin is bad practice as it will cause the
overall level of illumination to change as the supply voltage falls depending
upon how many of the individual LEDs are activated.
The main disadvantage of the LED display is they can consume very high
currents, as each LED requires around 10 - 20mA for a reasonable light
output. Pulsed techniques are often used to make the display appear on all
the time due to the persistence of vision of the human eye.
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DIODE APPLICATIONS: Relay Protection Diode.
Diodes form a useful function in protecting against large voltage spikes
which are often developed as a result of the back-EMF generated in
inductive circuits.
Observe the effect on the oscilloscope display when disconnecting the diode.
This very large pulse could destroy transistors or integrated circuits if not
limited to a safe level through clamping.
As the pulse is negative going the diode needs to be connected as shown.
When the relay coil is de-energised the back-EMF voltage forward biases
the diode, this effectively absorbs the energy as it acts as a short circuit
across the inductive load.
It is therefore necessary to ensure the diode power rating is sufficient to
dissipate this energy without itself being damaged.
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TRANSISTOR THEORY: NPN Transistor Construction.
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There are two bipolar transistor types, NPN and PNP. Bipolar is the
description given to a transistor, which uses both electrons and holes
(absence of electrons), as current carriers. The operating conditions are
considered for the more popular NPN type, which consists of two PN
junctions fused together to form one continuous piece of semiconductor
material, with the connections as shown.
Note the emitter arrow direction in the transistor symbol, this indicates the
direction of base emitter conventional current flow.
A transistor can be represented as two back-to-back diodes. The applied
voltage polarities show the base-emitter junction to be a forward biased
diode (low resistance path), whereas the collector-base is reverse biased
(high resistance path).
Connecting two diodes as shown will not perform the action of a transistor
as the junctions must be fused together. In practice the piece of
semiconductor is made extremely small with the base region measured as
just a few microns in width. This is to enable electrons to pass from the
emitter to the collector (current flow), attracted by the higher collector
potential.
TRANSISTOR THEORY: NPN Transistor Principle.
The NPN transistor consists of two PN junctions. By increasing the base
emitter junction forward bias voltage, it forces electrons to cross into the
base region.
As the base is only about one micron thick, electrons are easily attracted by
the higher positive collector potential and continue as collector current. Base
current thereby controlling the collector current.
Note: The transistor in this example has a fixed gain or multiplication factor
of 50. For the common emitter circuit its symbol is hFE. This value will be
found in transistor data books, and will vary between different transistor
types and is determined during manufacture.
TRANSISTOR THEORY: Transistor Configurations.
Shown here are three connection configurations for a transistor. Each has a
particular purpose. The 'common emitter' will have a medium input and
output impedance measured in kOhms. It has a signal inversion between the
base and collector. This is the usual arrangement for a simple amplifier. The
'common base' configuration has a gain of less than 1. The input impedance
is low and output high making it ideal as a matching circuit. There is no
signal phase inversion.
The 'common collector' or 'emitter follower' has a high input impedance and
low output. Again it's used for impedance matching. The output signal
follows the input with no phase inversion.
The current gain of a transistor hFE, hFB and hFC (note the common
connection E, B and C) is determined by the manufacturer. A typical figure
could range from 50 to 1000.
TRANSISTOR THEORY: DC Operating Conditions.
The collector current will be 100 times the base current. If the base current is
excessive (Rb low value) or the collector load resistor too large the collector
voltage will, in theory be pulled below zero volts. In practice the transistor
has saturated.
Your aim in circuit design is to choose values for Rb and Rc to make Vc
(collector voltage) about half the combined battery voltage under these DC
conditions.
The batteries can be considered to be in series and will set up the transistor
DC bias voltages. The base voltage will be clamped at 0.6V due to the action
of the base/emitter junction. Rb will determine the base current, which if
increased will cause a greater amount of collector current to flow and the
collector voltage to fall.
The emitter carries both IB and IC.
TRANSISTOR THEORY: Transistor Switch.
When used as a current switch the transistor will be forced to operate in
either of two states. Fully ON and conducting the maximum collector current
or OFF where ideally no current flows at all.
By increasing the base current the transistor can be made to saturate, where
maximum IC (collector current) will flow, and collector volts will fall to a
low value (that developed across the ON resistance), determined by Rc.
Open the switch, collector volts rise to the applied voltage less the transistor
leakage current × Rc.
The transistor is then either saturated or cut-off and therefore operates as a
current switch.
TRANSISTOR THEORY: Simple Signal Amplifier.
The common emitter transistor will amplify the small input AC voltage,
thereby causing collector current to flow in R2. The output voltage change
(input volts × Av) is as a result of the alternating collector current in R2. The
output signal voltage is at 180° phase inversion to that at the input.
Over driving the input (>100mV) will cause the output voltage to be cut-off
to ±6V as the collector current saturates on the positive waveform excursion
and clipping occurs on the negative.
The AC current gain (hfe) in this configuration is close to the DC current
gain (hFE) and is the AC collector current divided by the AC base current.
Normally peak-to-peak AC values are used in this calculation.
The base bias voltage is derived from the current flowing in R1, which is in
series with the base emitter (diode). For a silicon transistor this can never be
more than 0.6V and so any input greater than this will result in a distorted
output.
TRANSISTOR THEORY: DC Transistor Amplifier.
To ensure the quiescent (no signal) transistor collector current is correct,
thereby avoiding signal distortion due to clipping or saturation, the transistor
DC bias conditions must first be set. The collector voltage VC in this
configuration is chosen to be two thirds of the supply rail Vcc.
RC and RE are calculated to have a 2 : 1 value ratio. To ensure the stability
of the base voltage, the current in R2 is made approximately 10 times the
base current IB. R1 carries current IR2 plus IB. Therefore IR1 = IB × 11.
From just two circuit parameters the supply voltage and the transistor emitter
current, all the other component values can be determined by carrying out a
few simple calculations.
If you look at any text book example of a common emitter amplifier the
component values will all have the same basic relationship, thereby applying
the formulae to other transistor circuits is straightforward.
TRANSISTOR THEORY: AC Transistor Amplifier.
Capacitors Cin and Cout provide DC isolation. To AC the capacitors are
considered to be short circuits. However, in practice they will have some
reactance (AC resistance) at the input frequency as the calculated figures
show.
As far as the signal is concerned reactance of CE will be in parallel with RE
and grounds the emitter to AC, thereby removing the signal emitter feedback
which would otherwise oppose changes in input signal.
As we shall see this alters the slope of the effective AC load line from that of
the DC, thereby changing the AC stage gain from that calculated for the
purely DC bias conditions.
TRANSISTOR THEORY: Two Port Transistor Model.
The diagram represents a transistor amplifier model. Parameters used to
measure transistor-operating conditions are given the symbol h (meaning
hybrid), as they contain a mixture of both voltage and current. Note that for
hi and hf the output is considered a short circuit for AC signals, and for ho
and hr the input is open circuit to AC.
The h-parameter symbol is normally followed by a subscript character,
which denotes the transistor configuration, for example hie (i)nput resistance
for a common (e)mitter. (f)orward transfer, (o)output and (r)everse transfer.
Subscript is (c) i.e. hfc, means 'emitter follower' or 'common collector'
configuration. Similarly hib denotes input in a 'common base' configuration.
Lower case letters mean the circuit is being analysed for AC conditions.
To determine the input resistance, or how the circuit appears to the previous
output stage AC Ohm's Law is applied. Output resistance is found in the
same way, however, here we use its reciprocal value called 'Conductance'.
(Symbol G and measured in units called Siemens).
AC current gain is a ratio of the current in the input to output circuit. The
reverse transfer voltage ratio will be considered further when analysing the
equivalent circuit.
TRANSISTOR THEORY: Hybrid Circuit for Common Emitter
Configuration.
In the upper diagram each of the four h-parameters are shown along with
their relationship to the equivalent transistor circuit. The h-parameters are
determined using the calculations in the previous 2-Port Model. Voltage
'hreVce' is fed back from the output and appears in series with the input
resistance as a voltage source.
The two overlapping circles represent a current generator the value of which
is the input current Ib times the transistor signal current gain hfe.
Because the value of the reverse transfer voltage ratio hre is small and the
output resistance represented by hoe is high, they can be ignored, thereby
simplifying the equivalent circuit.
At this stage we have not yet considered the effect of any external
components.
TRANSISTOR THEORY: Equivalent NPN Transistor Circuit.
The equivalent common emitter circuit is shown for the schematic diagram
above. Note the absence of any reference to the capacitors. Capacitors
represent short circuits to AC signals. Therefore, Cin and Cout are ignored.
The emitter bypass capacitor Ce effectively shorts out Re by taking the
emitter to ground potential as far as the signal is concerned.
There will also be a large capacitance associated with the power supply
which to AC means the supply rails are connected together.
Circuit 'input resistance' is calculated using the parallel resistor formula as
the values of R1, R2 and the transistor input resistance are all in parallel. On
the output side the actual collector load will be Rout in parallel with RL.
This is given the symbol R'L.
The current gain is a result of the hfe value of the transistor and the
relationship between the values for R'L and RL.
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BIPOLAR TRANSISTOR: Signal Clipping.
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The 'emitter follower' transistor configuration has no output phase reversal.
C1 providing DC isolation from the previous stage.
To ensure the output signal not distorted the transistor has to be correctly DC
biased or set-up. Its importance is demonstrated here. R1 and R2 determine
the quiescent (no signal) transistor base voltage. The emitter will always be
0.6V less than the base voltage.
To faithfully reproduce (distortion free) the input signal at the output without
transistor clipping requires the emitter to be biased to about 5.4V, therefore
the base voltage needs to be set to 6V by choosing equal values for R1 and
R2.
The incoming AC signal will add to or cancel this standing DC bias
condition. When a test meter is applied it will show the average of the
excursions, which is the same as the DC voltage. An oscilloscope on the
other hand will follow the voltage changes and display the AC waveform. To
observe the effect of clipping or saturation, reverse the default values of R1
and R2.
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BIPOLAR TRANSISTOR: DC Load Line.
The DC load line is a graphical representation of the DC conditions of the
transistor circuit (bias range) and is used to arrive at the correct operating
point to ensure there is no distortion of the output signal.
The DC operating point is found by selecting the correct base biasing
conditions for a no signal input.
For class A output, point Q is the ideal bias voltage setting. Biased to p1 the
transistor would be saturated maximum current flowing for the selected
resistor values, RC and RE. VCE being zero. At p2 the transistor is cut off
with only leakage current flowing.
Note the calculation is made using the voltage between the collector and
emitter VCE.
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BIPOLAR TRANSISTOR: AC Load Line.
The slope of the AC load line is calculated as change in mA/V (mA per volt)
and is steeper than the derived for the DC conditions.
Capacitors are considered to be short circuit to AC signals, therefore the
emitter of our transistor amplifier circuit is grounded to AC which means the
AC load line is calculated using RC only. As the collector current changes so
does the output voltage by an amount expressed in mA/V.
The gain of the amplifier increases to AC signals, as the negative feedback
due to the emitter resistor is no longer present due to the effect of shorting of
the cathode bypass capacitor.
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BIPOLAR TRANSISTOR: AC Current Gain.
The practical result of the 'load line' can be seen when AC signals are
applied. Changes in input current cause the collector current to change, the
amount of which is determined by the transistor current gain (hfe).
The current gain for a typical small signal transistor would range from 50 to
200 and is determined by the manufacturer. Within the same batch of
transistors of the same type, hfe values can vary widely. This needs to be
taken into account when designing transistor circuits; one way is to include
emitter resistors, which introduce an element of DC voltage feedback into
the circuit.
The AC output voltage swing can be calculated by multiplying the collector
current Ic by the value of RL. Larger values of the collector load resistor will
therefore provide greater voltage output peak-to-peak values. The maximum
output signal swing, before signal clipping takes place is limited by the value
of Vcc.
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BIPOLAR TRANSISTOR: Push Pull Output Stage.
This example of a push-pull output stage uses both NPN and PNP transistor
types. The NPN transistor requires the base voltage to be more positive than
the emitter to enable conduction and for the PNP type the base is made more
negative than the emitter before it can begin to conduct.
The transistor collectors are connected to the (+) and (-) supply rails and the
emitters to zero volts via the loudspeaker speech coil.
A positive signal transition makes the top NPN transistor conduct causing a
current to flow in one direction through the loudspeaker coil. As this signal
reverses in the negative direction the PNP transistor conducts enabling an
opposite current to flow through the loudspeaker.
Each transistor providing an equal and opposite current flow. Thereby the
changing input signal results in the reproduction of a sine wave loudspeaker
current. The maximum power output is calculated using the formula shown.
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BIPOLAR TRANSISTOR: Crossover Distortion.
One common problem experienced with the push-pull output stage is that of
crossover distortion, where the output current switches from one output
transistor to the other during the non linear portion of the transfer curve.
This is overcome by providing a small bias voltage (slightly greater than
0.6V) which forces both transistors to conduct during this output transition
by moving the operating point away from the non-linear part of the curve.
To forward bias each transistor, resistors RA, RB and RC make TR1 base
positive and TR2 base negative with respect to their emitters which are held
close to 0V by the low speaker coil resistance.
This small bias voltage causes a permanent quiescent collector current to
flow. RA and RC may be adjustable to enable the base voltages to be set for
minimum quiescent current before distortion. In addition RB could be
replaced by series diodes to produce the required voltage drops. This has the
added advantage of compensating for temperature changes in the output
transistors.
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BIPOLAR TRANSISTOR: Power Output Stage.
Transistor output stages are generally referred to as power amplifiers. This is
because they tend to operate at high current levels and therefore consume
power. They also generate wasted heat and care should be taken during
design to maximise efficiency which is rarely very high, at the same time
ensure the transistor operates within the device parameters.
The typical power transistor specification (i.e. maximum operating limits)
provides design guidelines.
DC power is the total power used by the amplifier from input to output. AC
power is the power available to the output load, in this case the loudspeaker.
The power dissipated in the transistor P(tot)Watts (mostly in the collector
region as heat) must not be exceeded and therefore a suitable heat sink
should be fitted.
See the power curve for the range of VCE and IC values. Quiescent biasing
conditions for a class A amplifier should be around half the Vcc point, which
means that even under no signal conditions a fairly high mean level of
current will always flow. The alternating input signal causes IC to deviate
about this point. HFE is the current gain of the device and along with FT, the
maximum operating frequency, is fixed by the manufacturer.
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BIPOLAR TRANSISTOR: Two Stage Amplifier.
There are a number of reasons why it is appropriate to use more than one
stage of amplification. The two most common are to take advantage of the
various configurations when matching the inputs and outputs to the
preceding or the following stages and where the gain required might cause
instability or distortion of the signal if just a single transistor were used.
Sometimes amplifiers are cascaded not only to achieve maximum overall
gain, but to cover the desired frequency response, where each stage is
designed to handle a particular group of frequencies. This is more suited to
RF (Radio Frequency) amplifiers and is common in television and radio
receivers.
Often amplifier gains are calculated in decibels (dB), however, when
designing a simple audio amplifier its more useful to think in terms of
voltage amplitude as this is what would be measured using an oscilloscope.
No matter how many stages of amplification are used there are still
limitations on the amplitude of the final output which is governed largely by
the supply voltage where it will clip excessive voltage excursions.
The calculations are straightforward the stage gains are just multiplied
together. To find out more about determining amplifier gains select the
'Attenuators' topic.
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BIPOLAR TRANSISTOR: Cascading Transistor Amplifiers.
When two or more stages of amplification are used, the circuit analysis must
take into account the whole of the combined stages. In this case the circuit
conditions around TR1 will have some effect on the operation of TR2, and
the loading of TR2 will similarly influence TR1.
Begin by familiarising yourself with the circuit operation and change the
values of TR1 collector load and TR2 emitter resistors. The first stage has
phase inversion and contributes all the circuit gain. TR2 is an emitter
follower with a gain of less than one, but has the advantage of a low output
impedance. Compare this with the output impedance of TR1, which is
relatively high.
The collector load RL of TR1 is made up of Rc in parallel with the input
impedance of TR2 which in turn is determined in part by the value of the
emitter resistor along with the current gain hfc of TR2. To begin the analysis
it's often convenient to start with the output stage and work back.
Follow through the mathematics using a calculator to confirm the results.
Note the analysis uses transistor h parameters. These are explained in the
<Transistor Theory: Two Port Transistor Model> topic.
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BIPOLAR TRANSISTOR: Calculating Coupling Capacitor Values.
Consider this simple AC amplifier as comprising two high pass filters
sandwiching the transistor amplifying device. For our purposes we will look
at this circuit in isolation, but in practice, whenever the response or electrical
conditions are considered the circuits driving and loading will also have
some influence.
You will see that we have added a very large smoothing capacitor, this
represents our supply impedance and at audio frequencies will be extremely
low, in fact less than an Ohm. This means that for our calculations the supply
rail and the zero are effectively connected together. Also as the transistor is
forward biased the base and emitter are shorted.
Redrawing the input circuit, Cin now forms a potential divider with the
parallel combination of R1|R2|Re. If we aim to make the reactance (AC
resistance) of Cin equal to the parallel resistor combination there will be a
signal reduction of 50% at the transistor base through the voltage divider.
Increase the value of Cin and its reactance will reduce relative to the parallel
resistors and more of the signal will be made available at the transistor base.
Ideally we should be aiming for a Cin to have a reactance of about 10% of
the input impedance which is typically less than 10k for this circuit and so a
reactance of 1k would be acceptable.
The output circuit is also a voltage divider where ideally the reactance of
Cout should be low compared with the resistance of the collector load. To
the AC signal the top end of Rc is grounded. Note Cout becomes Cin of the
next stage. Actual circuit measurements using test equipment may require
these values to be modified to give the desired frequency response, but it's a
useful starting point. Top end frequency limits are determined by stray
capacitance and transistor parameters etc.
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TRANSISTOR CONFIGURATIONS: Emitter Follower Configuration.
Interactive Content!
The diagram shows a simple Emitter Follower circuit, where owing to the
transistor base-emitter junction, the emitter voltage will always be 0.6V
below the base voltage. Because of the low value emitter resistor the circuit
is able to supply high currents without upsetting the biasing caused by
changes in the emitter voltage.
Other practical uses of this circuit are for impedance matching, where the
base circuit has a high input impedance and the emitter a low output
impedance. Thereby, enabling larger current loads to be driven than for a
common emitter configuration.
There is no phase inversion between the base and emitter of a transistor, as
the base is made more positive, increasing current flows between the emitter
and collector, therefore there is a larger voltage developed across the emitter
resistor and the emitter volts rise.
TRANSISTOR CONFIGURATIONS: Input Impedance.
The emitter or output impedance is largely determined by the value of the
emitter resistor which normally has a low value of less than 1kOhms.
The input impedance can then be calculated. (hFE) is the signal current gain
of the device and is set at the time of manufacture and therefore cannot be
changed. If you require a higher current gain select a device with a higher
hFE, it's not quite that simple but need not concern us here.
To find the input impedance multiply the current gain + 1 by the value of the
emitter resistor whereby it will be observed that there is a considerable
difference between the calculated input and output impedance's.
The transistor input impedance is effectively in parallel with the previous
stage or source impedance. But because the transistor input impedance is so
much higher it has little or no loading effect across the resistor 'Rsource'.
TRANSISTOR CONFIGURATIONS: Transistor Biasing Voltage.
It is important that the correct biasing conditions are set-up for the transistor
base circuit if the input waveform is not to become distorted or clipped.
Here we can show the result of incorrect biasing. Adjust the transistor base
bias voltage to ensure the output waveform is reproduced exactly as the
input. In this example a bias voltage between 2.2V and 3V is within the safe
operating region. Biasing the transistor outside these limits will result in a
distorted output due to clipping or transistor saturation.
An emitter follower configuration has been chosen to demonstrate the
principle because the waveforms are in phase. The same effect would occur
if the output were taken from the collector, but would be phase reversed.
Applying a large signal input causes the transistor to saturate as it conducts
heavily, and the voltage developed across the emitter resistor is theoretically
greater then Vcc.
TRANSISTOR CONFIGURATIONS: Shifting the DC Bias Level.
We know from our 'transistor theory' that AC waveforms are superimposed
on a DC bias level. The AC waveform pulls this standing voltage up and
down producing an output waveform. Change the switch positions and you
will observe the output is level shifted between the transistor base and
emitter.
For these diagrams the sine waveform is not distorted, however, if the bias
voltage is incorrectly set then the clipping shown on the previous topic
occurs.
Signal clipping is caused by the transistor saturating, sometimes called
bottoming, where the output voltage is pulled so low that there is not enough
voltage 'headroom' for the reproduction of the sine wave, consequently the
bottoms are chopped off.
The other is when the tops are cut-off, caused by the transistor not having
enough forward bias or the DC output voltage is too close to the supply rail
for a full output waveform swing.
TRANSISTOR CONFIGURATIONS: Common Emitter Amplifier.
The common emitter amplifier is the easiest to understand. It has a high
voltage gain, but requires the correct DC conditions to be set-up using base
bias resistors.
From this point all other voltages can be calculated. The only other
consideration is to ensure that the collector voltage is set to a value which
allows a faithful reproduction of the output waveform without clipping.
Select base resistor values to produce 1.25V at their junction and a collector
voltage about half the supply voltage, i.e. 6V. The output waveform can then
safely have a peak output of about 5V without introducing distortion.
TRANSISTOR CONFIGURATIONS: Bias and Stabilisation.
Establishing the correct transistor biasing conditions not only sets the DC
operating point, but is important in providing stability for temperature and
differences in actual device parameters spreads. You should note that hFE
and VBE parameters do not normally change for an individual device, but do
vary, even between those from the same batch.
hFE (current amplification factor) values are quoted in component
catalogues as 'typical'. Close tolerance devices can be obtained for particular
applications, but in the main differences in current gain can be overcome
through suitable biasing.
There are three methods of biasing shown. Voltage biasing with emitter
feedback is the most common for class A amplifiers and as you will see from
the graph provides the most stable conditions. For collector to base biasing,
an increase in IE through a variation in the individual transistor gain
decreases the base voltage as the transistor collector volts falls, this action
turns off the base emitter junction thereby bringing IE back to the design
current. Simple current biasing does no more than provide the DC base bias
voltage.
The graph values for IE are plotted across the range permissible. You can
compare the calculated emitter currents IE from the same point on the
horizontal scale for the three biasing methods.
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ACTIVE TRANSISTOR CIRCUITS: LDR Pull Up, Pull Down Circuit.
Interactive Content!
Both the circuits here exploit the effect of pulling up or down voltages at the
junction of a voltage divider resistive network.
The LDR has high dark resistance that falls to a low value when brightly lit.
Therefore, the LDR can be considered as a switch under these two
conditions.
However, there will also be varying levels of brightness between darkness
and bright light and this will cause the voltage output to range from almost
the maximum supply to nearly zero as the LDR resistance changes.
The voltage divider current can be calculated from the formula shown.
Should there be a load connected at the junction it would be effectively
placed in parallel with the lower resistance. See loading a voltage divider
topic.
ACTIVE TRANSISTOR CIRCUITS: Thermistor Pull Up, Pull Down
Circuit.
LDRs are light dependent resistors, thermistors are temperature dependent.
The calculations remain as before but this time changes in temperature need
to be considered.
A typical device might have a resistance at 25°C of 4.7kOhms. By
increasing the temperature the resistance falls to around 150ohms (negative
temperature coefficient NTC).
There are also thermistor devices, which operate, in the opposite direction,
i.e. resistance goes up with temperature increase (positive temperature
coefficient PTC).
ACTIVE TRANSISTOR CIRCUITS: Light Operated Transistor
Switch.
A further application of the LDR is when biasing an NPN bipolar transistor.
The value of R1 needs to be calculated to ensure the transistor bias is correct
for the range of light levels applied. Otherwise the transistor could be forced
permanently ON or OFF.
ACTIVE TRANSISTOR CIRCUITS: Light Dependent Resistor and
Relay Circuit.
To ensure the correct voltage threshold is applied to the transistor, which in
turn drives the relay, a variable resistor is placed in the lower part of the
divider.
The transistor on-off range can then be manually adjusted. Resistor R2 is
included to avoid overdriving or saturating the transistor.
Assuming it requires a junction voltage of 2.5V to switch on the transistor,
the calculations will show the correct setting for VR1.
ACTIVE TRANSISTOR CIRCUITS: Thermistor Controlled Switch.
The final application in this section is for thermostatic control, is essentially
the same as the previous example except that VR1 and the active element are
transposed.
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FIELD EFFECT TRANSISTORS: Basic N Channel FET.
Interactive Content!
JFET is short for 'Junction-Gate Field Effect Transistor' normally referred to
as FETs. FETs are controlled by an electric field (voltage) as opposed to an
electric current as is the case for a bi-polar transistor. The channel is made of
n-type material and the gate p-type. Their operation is very similar to that of
a thermionic valve.
As the gate voltage is made more negative (gate to channel junction is
reverse biased) the depletion region widens. This is an area where positive
holes are filled with negative electrons, thereby removing the current carriers
through cancellation. Note the shape of the depletion region, tapering is
caused by the voltage drop along the channel, where the width will be
greater closer to the drain due to the greater reverse bias.
As VGG is made more negative a point is reached when ID ceases to flow,
known as 'pinch off'. By holding VGG at 0V, then current through the device
can be controlled by voltage VDD. Behaving as fixed value resistor. Having
a reverse biased input means the input impedance is extremely high. Its this
high impedance that can destroy the device if static charges come in contact
with an unprotected device.
Also available are p-type FETs where the channel is made of p type
semiconductor material. Voltages for this device are simply a reversal of
those for the n-type. Also available are IGFETS, insulated gate field effect
transistors, called MOSFETS, these have an insulated gate just a few
microns thick, between the channel and the gate. This reduces any leakage
current, thereby increasing the input impedance even more up to hundreds of
megohms.
FIELD EFFECT TRANSISTORS: Basic MOSFET Transistor.
MOSFET stands for Metal-Oxide-Semiconductor Field Effect Transistor.
The n channel is normally made very thin and insulated from the gate
electrode forming a small capacitor.
On connecting VDD between the channel and the substrate it forms a PN
junction which is reverse biased. Current can then flow between the 'source'
and 'drain' through the channel which is n-type material.
Making the gate positive with respect to the source and the effective width
of the channel is made greater (enhanced) so more current flows.
This is called the 'enhancement' mode. By making the gate negative with
respect to the source and its in 'depletion' mode and the effective width of
the channel is reduced (depleted) thereby restricting current flow.
FIELD EFFECT TRANSISTORS: FET Negative Biasing.
As with a bipolar transistor the field effect type has to be biased to produce a
standing DC voltage on the drain which is normally around half the VDD
potential. Applying a negative voltage to the gate is one method. In this
example -1.05V would be ideal. The negative voltage repels the electrons in
the gate area of the channel and increases the depletion region.
Incorrect biasing will result in the AC signal at the collector becoming
distorted as the transistor is saturated or clipped by being driven too hard,
causing the drain volts to fall to nearly zero or to be clipped as the electron
flow is cut-off and the drain volts rise.
The AC signal is connected to the gate via the coupling capacitor where its
positive and negative voltage excursions reinforce or cancel the depletion
region previously set up by the bias gate voltage and vary the channel
current.
The amplified AC signal appearing as alternating VD output across RL.
FIELD EFFECT TRANSISTORS: FET Automatic Biasing.
The FET can be DC biased automatically. Where RS provides the bias
voltage to take the source to a more positive potential than the gate. Owing
to the very high input impedance of the FET there will be negligible current
flowing into the gate.
To demonstrate the principle, assume a 100µV across RG (in practice its
almost zero). Comparing or subtracting the gate voltage from the source
voltage will produce a difference voltage. Because the source is at a higher
potential the gate will effectively be negative. The condition required for
automatic negative biasing. This is exactly the same principle as used for
Valves and grid biasing.
However, there is a reduction in signal gain as the source resistor generates
negative feedback which opposes the gate voltage change. The addition of
the source de-coupling capacitor CS provides a low impedance path to the
AC signal, thereby shorting out RS to the signal. This restores the gain to its
original level for the AC component.
FIELD EFFECT TRANSISTORS: Depletion / Enhancement MOSFET.
The Depletion / Enhancement MOSFET has a standing or quiescent current
flowing determined by the value of RL when 0V are applied to the gate.
Increasing or decreasing this bias (gate to source voltage VGS) above and
below zero volts will cause this quiescent DC current to change.
Depletion mode current reduces ID whereas in the enhancement mode the
gate voltage will increase the amount of ID flowing.
The application of an AC signal voltage to the gate causes ID to swing about
the quiescent current operating point. When VGS = 0V positive half cycles
increase drain current (enhancement), negative half cycles reduce it
(depletion).
FIELD EFFECT TRANSISTORS: Enhancement MOSFET.
The Enhancement type of MOSFET is normally biased to the middle of the
linear part of the curve by a fixed DC positive voltage from the junction of
R1 and R2.
Applying a signal to the gate via the input capacitor will cause the gate
voltage to swing about the fixed bias point. Thereby changing the drain
current ID.
Amplification is through the increased AC voltage swing caused by ID
flowing through RL. The value of RL determines the gain. As ID is
increased so the voltage VD falls. There is a 180° phase change between the
gate and the drain.
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BASIC OPERATIONAL AMPLIFIERS: Inverting Op-Amp.
Interactive Content!
The inverting Op-Amp is the most commonly found configuration. The
output has a 180° phase inversion of the input.
Amplifier stage gain is determined by dividing Rf by Rin. Multiply the
amplitude of the input by the gain (Av) to find the output amplitude. This
can be as peak, peak-to-peak or RMS. value, whichever the input is
measured as, even DC levels.
Note the input connection is made to the (-) terminal, signifying it is used as
an inverting amplifier. The negative sign of the output voltage also denotes
the phase inversion.
Negative signs in electronics do not always mean a negative voltage or
current. Usually it's just to show that measurement is opposite to a positive
value. For current this would mean it is flowing in the opposite direction.
BASIC OPERATIONAL AMPLIFIERS: Non-Inverting Op-Amp 1.
This is an example of a Non-Inverting Op-Amp. Note the input is to the (+)
terminal indicating that the output will be in the same phase as the input.
Negative feed back is applied in the usual way.
The gain calculation however, is slightly different, the reason will be
explained later.
BASIC OPERATIONAL AMPLIFIERS: Non-Inverting Op-Amp 2.
There is no phase inversion between (+) input and the output of the noninverting operational amplifier. Negative feedback is applied to the (-) input.
Remembering there is virtually zero voltage developed across the input
terminals Vin also appears across R1.
The gain is the ratio Rf to R1, which together form a potential divider.
Therefore, Vout = ((Rf + R1) / R1) × Vin. Simplified to, Vout = (Rf / R1 + 1)
× Vin. and that's where the +1 comes from mentioned earlier.
BASIC OPERATIONAL AMPLIFIERS: Dual Supply Op-Amp.
Operational amplifiers are commonly found connected across a dual voltage
supply. The output is then at a zero voltage when there is no input, i.e. the
potential difference between inputs is 0V. Here the (+) non-inverting input is
also held at zero potential by the junction of R1 and R2 which have equal
values.
As VR1 is varied about its central point the output will change to the
opposite state, i.e. negative input, positive output, thereby switching the
diodes D1 and D2. Try inputting ±4V.
The circuit gain is very high owing to the absence of any feedback resistor.
This enables a fast switching action for very small changes of input about
the zero line.
Depending upon the input polarity, output current will either flow into, or,
out of, the Op-amp. This configuration is frequently used in audio amplifiers
as it avoids the need for coupling capacitors, thereby considerably
simplifying circuit design.
BASIC OPERATIONAL AMPLIFIERS: Input Difference Amplifier.
The difference or differential amplifier forms the basis of the operational
amplifier. The device amplifies the difference between the two inputs. If
both inputs are at the same potential the output is unchanged.
In this example the output will sit at about 7.5V when the two inputs each
have an equal potential applied. If the difference is negative the output
voltage rises above 7.5V or if positive the output falls below 7.5V, i.e. phase
inverted output.
The values of R1 to R4 determine the operating conditions of the amplifier.
There is a phase inversion between the base and collector of a transistor but
none between the emitter and the collector. The input voltage to T1 base is
applied in the same phase to the emitter of T2. T2,therefore has a bias
voltage which is the difference between the emitter and base potentials.
This voltage difference varies the current flow through R1 and the voltage
dropped across it. Note: For an excessive input voltage difference, the output
voltage will be 'clamped' by the supply rails.
BASIC OPERATIONAL AMPLIFIERS: Buffer Amplifier.
The buffer Op-Amp is often referred to as a voltage follower. Firstly, note
the input connections to the (+) terminal, which means it is a non-inverting
type of amplifier, i.e. the input and output have the same phase.
Maximum amount of feedback is passed to the inverting input and so the
stage gain is unity or 1.
However, it has another specific purpose and that is to achieve the maximum
transfer of power between two amplifying stages. This requires that the
inputs and outputs have a matching impedance. The buffer stage ensures this
is met. The input is generally considered to have a high impedance and
therefore imposes minimum load on the preceding stage output.
The output has a very low impedance typically of less than 100ohms and is
therefore capable of driving relatively large loads without a reduction in
output signal level.
BASIC OPERATIONAL AMPLIFIERS: Integrator Amplifier.
Replacing the feedback resistor with a capacitor can be a useful way to
generate a Voltage Ramp. (Note the inverted output). The slope of which is
determined by the values of Vin, R and C. Vin supplies the capacitor charge
current, which is limited by R.
The instantaneous output voltage at any point on the slope can be found by
applying the formula.
In theory some very large negative voltages can be generated, but for a
practical circuit the output will be clamped to the zero or negative supply
rail.
BASIC OPERATIONAL AMPLIFIERS: Differential Amplifier.
The differential amplifier, amplifies the voltage difference between the two
inputs. Therefore we need to determine the effective voltage input to the OpAmp. This is found by subtracting one input from the other.
The result could be positive, negative or zero voltage, depending upon the
input relationship. Thereafter, the Op-Amp behaves as a normal inverting
amplifier. The output of which will be a phase inversion of the input
difference.
Note: the equal input resistor and feedback and (+) terminal grounding
resistor values. The stage gain is determined in the normal way.
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OP-AMP THEORY: Inverting Long Tail Pair.
Interactive Content!
The long-tailed pair transistor configuration forms the basis of the
Operational Amplifier. In this example it consists of two NPN transistors
with their emitters connected together and having a common emitter resistor.
The voltage developed across the emitter resistor through either transistor
conducting will be reflected as a change in collector current in the other.
The amplifier has two inputs, inverting and non-inverting, with a single
output.
INVERTING INPUT. A signal applied to the (-) input is phase inverted
between base and collector of T1. Increasing the base current causes the
collector current to also increase, thereby the pulling down the collector
voltage, as a greater voltage is dropped across the collector load resistor R1.
OP-AMP THEORY: Non-Inverting Long Tail Pair.
Following on from the previous topic using the same pair of transistors we
can now look at the second configuration.
NON-INVERTING INPUT. Applying a signal to the (+) input and the
voltage developed at the top of Re follows the T2 base voltage. As there is
no phase change between the emitter and the collector of a transistor the
collector signal of T1 remains in phase with the emitter. T2 acting as an
emitter follower drives T1 from its emitter circuit.
OP-AMP THEORY: Negative Feedback.
Negative feedback is used to reduce the gain of an Operational Amplifier. If
a proportion of the output is fed back to the input in anti-phase, via the
feedback resistor the two signals will cancel and the stage gain is reduced.
The symbol used to indicate the amount of feedback is ß.
Note, as the gain is increased a larger signal will be applied as feedback
eventually cancelling the input completely.
The open-loop gain of an Op-Amp can be large, e.g. multiplied by 100,000
or more is not uncommon. Open loop gain is normally quoted in decibels
(dB) and this can vary between devices. However, when negative feed back
is applied the gain is solely dependant upon the relationship between the
input and feedback resistors and so substituting an OP-Amp for a type with a
different open loop gain will have no effect.
The effects of external temperature changes are also counteracted when the
device is connected in a closed loop configuration. Op-Amps can also be
used in an open loop configuration (no feedback resistor), when processing
digital pulses for example or connected as switching comparators when very
fast changes in output for small input variations are required.
OP-AMP THEORY: Positive Feedback.
Positive feedback results in an increase in output amplitude.
This can be achieved in an Op-Amp circuit by connecting the feedback
resistor to the (+) or non-inverting input. However, positive feedback is
regenerative, which means a greater proportion of the increase in output
amplitude is fed back to the input. This arrangement forms the basis of an
oscillator circuit.
Positive feedback is normally undesirable in amplifiers as it results in
oscillation. Good circuit design will include careful component placement
and the use of negative feedback to prevent this from occurring.
OP-AMP THEORY: Virtual Earth.
As there is a negligible current flow into the Op-Amp (high impedance)
there will be no voltage developed across Rop. Note the (+) non-inverting
input is held at ground potential. Zero volts drop across Rop means the
inverting (-) input must also be at ground or virtual earth. Therefore, any
small input current can only flow through the feedback resistor towards the
low impedance output end.
In other words Rin and Rf are in series between the input and output.
The inverting (-) Op-Amp input is also referred to as a summing point we
will explore this further when looking sum and difference amplifiers.
Basically this means that if more than one input is applied to the (-) input the
combined current from these sources can only flow in Rf since none flows in
Rop. The output amplitude is a result of this input combining of currents.
As the Op-Amp supply sits across the zero line, input voltages can be either
positive or negative the combining current in Rf with be an addition (SUM
or DIFFERENCE) of these currents as those flowing into the virtual earth
point circuit cancel those flowing out. The resulting current flowing in Rf.
OP-AMP THEORY: Gain and Frequency Response.
The graph shows the gain versus frequency response for a typical
operational amplifier. It will be observed that the very high gain is only
available at the expense of higher frequencies or bandwidth limitation.
Therefore, to design an amplifier with a wide signal bandwidth, the gain has
to be sacrificed. Overall increased gain at the higher frequencies can be
achieved through cascading a number of amplifying stages together.
The relationship between the input and feedback resistor values determines
the stage gain and thereby the amplifier frequency response. Note. The
logarithmic scales used to display the very large range of frequencies and
gain.
There are a wide range of different Op-Amps available and so its important
to choose one suitable for the application to take advantage of its improved
or better suited characteristics. The 741 device for example uses bipolar
transistors, which require a higher input current than, an equivalent
MOSFET type, the latter having a much greater input impedance. Some
devices include an input-offset compensation adjustment to set the output to
zero when the both inputs are at the same potential.
Slew rate is another consideration. This is the rate at which the output can
change measured in V/µs. In most student experiments it's not important, but
in higher frequency applications it needs to be taken into account, if signal
distortion is to be minimised.
OP-AMP THEORY: Common Mode Rejection Ratio. CMRR.
Ideally an Op-Amp, which consists of a differential amplifier input circuit as
its front end, should provide an output voltage of zero when both inputs (-)
and (+) have the same potential. However, this is not always possible in
practice, but values close to zero can be achieved for more expensive
devices.
Any signal which appears simultaneously on both inputs is called a 'common
mode signal' and often arise due to the pickup of noise and interference on
the high impedance inputs. The ability of the differential input to suppress
common mode signals is called the 'Common Mode Rejection Ratio' CMRR
and is quoted in decibels.
The higher the CMRR the better, where a typical figure from the data sheets
is around 90 dB. To get the best results select devices with a high open-loop
gain parameter. You can see this by increasing the default Open-Loop Gain
to 1000.
The numerical equivalent value of the CMRR (shown in the calculations
Window) means the wanted input signal is amplified that many times more
than the unwanted common mode signal (interference or noise). A figure of
say 10,000 means the noise is 10,000 times less than the desired signal
which is pretty good for most applications.
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OP-AMP APPLICATIONS: Voltage Oscillator.
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In this circuit we show the Op-Amp connected as an oscillator. In a practical
circuit it would produce a continuous output waveform. R4 provides a
feedback path to the inverted input and R5 to the non-inverted input. C1
begins to charge via R4, the (+) input has a fixed potential of 4V due to the
potential divider R1 and R2 in parallel R3.
As the voltage across C1 rises (producing the upward part of the triangular
wave shape) above 4V the Op-Amp output falls due to the phase inversion.
A triangular waveshape is really a small part (straighter bit at the beginning)
of an exponential waveform which is then amplified.
This discharges C1 (producing the downward part of the triangular
waveform) via R4, towards this now lower potential at the Op-Amp output.
Also the voltage on the (+) input falls as it now has three 100kohm resistors
connected in parallel across its input.
This forces the Op-Amp to conduct for longer by maintaining the potential
difference between the inputs as the (-) falls due to C1 discharging. Note: the
phase inversion between the input and output waveforms.
OP-AMP APPLICATIONS: Schmitt Trigger.
The sensitivity of an operational amplifier can be improved when comparing
two voltages at its inputs by connecting it as a Schmitt Trigger. The device is
then called a Comparator.
Positive feedback is applied to the non-inverting input which re-enforces the
voltage applied to the inverting (-) input. R1, R2 and R3 resistor values
determining the switching or changeover point.
In practice there is a range of input voltages, around the mid bias point that
have no effect on the output state. The inverted input potential must
therefore be above or below this null range to switchover the output. The
LED in this example indicating the output state.
OP-AMP APPLICATIONS: Sinking and Sourcing Output Current.
Current flowing out of or into the output pin of an operational amplifier is
termed sourcing or sinking that current.
Setting VR1 to 4V causes the output to rise to 12V (high gain, no feedback
resistor) and (conventional) current is sourced from this high potential
towards zero volts via R4.
Re-adjusting VR1 to 8V and the output voltage of the Op-Amp falls to a low
value and current is sunk from the higher potential junction of R3 and R4
which is fixed at half the supply voltage by equal value resistors R1 and R2.
OP-AMP APPLICATIONS: Timer Delay Circuit.
The Op-Amp output is the amplified difference between the (-) and (+)
inputs.
The RC time constant is equal to 63% of the capacitors full charge. VR1 is
set to 3.15V (63% supply) and so as the charge on C1 builds it will
eventually place a voltage on the inverted Op-Amp input greater than 3.15V.
When this occurs the previous 5Volt output will fall rapidly due to the high
gain of the circuit, i.e. no feedback resistor.
Up until the (adjustable) threshold point is reached the Darlington transistor
conducts, the lamp lights during C1 charge. As the output voltage falls the
transistor switches off, and the lamp goes-out. That is until the discharging
voltage falls to the threshold point and the lamp is turned on again.
VR1 controls the ON time of the lamp by raising or lowering the threshold
voltage. Pressing S1 starts the timer by enabling C1 to begin charging. If the
threshold voltage is set to 63% of the supply (i.e. 3.15V) the calculation
represents the lamp ON time in seconds.
OP-AMP APPLICATIONS: Light Sensitive Comparator.
Resistor R1 and the LDR form a potential divider network. When bright
light falls on a Light Dependent Resistor its resistance falls to around
1kOhm. In the dark it is very high, greater than 5-10Mohms.
The Op-Amp acts as a comparator with its (+) input set to half the supply
voltage by the variable resistor. The LDR is in a pull-down configuration. In
the dark the potential on the (-) input is high and because there is no
feedback resistor the Op-Amp rapidly changes to the opposite state.
When light falls on the LDR its resistance drops and the (-) input is pulled
down switching over the Op-Amp (comparator). In a practical circuit the
threshold or switch-over point could be controlled by the variable resistor.
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SUM AND DIFFERENCE AMPLIFIERS: Difference Amplifier.
Interactive Content!
The Difference Amplifier (analogue subtractor), gives an output proportional
to the Difference between the input potentials. With equal values for the
input and feedback resistors the gain will be unity or one.
Output phase will be dependent upon the greater of the inverted (-) or noninverted (+) input. By changing the ratio of Rf to R the voltage difference
can be amplified. Note, Rf appears in two places and will have equal values.
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SUM AND DIFFERENCE AMPLIFIERS: Summing Amplifier.
The Summing Amplifier (analogue adder) gives an output which is
proportional to the Sum of the voltage inputs. Current flows through input
resistors R1, R2 and R3 (equal values) determined by V1, V2 and V3.
The currents developed in the input resistors (calculated by Ohm's Law) by
each input voltage are combined at the Summing Point, as this is a virtual
earth current flows in Rf.
The negative sign indicates the output is phase inverted.
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SUM AND DIFFERENCE AMPLIFIERS: Integrator Amplifier.
An operational amplifier integrator may be constructed by replacing the
feedback resistor with a capacitor. The output is as a result of input change
over a specified period of time. Here it is shown as being between t1 and t2.
The time constant for your chosen resistor and capacitor values is also
shown. Which is the time taken to charge C to 63% of a full charge. The full
charge taking approximately five times C × R
The calculation shows the output voltage change over a specified time using
these component values. The slope is the rate of change over a given period.
In theory it is possible generate very high slope voltages, but in practice
these are clamped (limited) by the supply voltage rail. High slope values
indicate a sharply changing output voltage.
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SUM AND DIFFERENCE AMPLIFIERS: Digital to Analogue
Conversion.
The summing amplifier can be used to perform D-to-A (digital to analogue)
conversion. Input resistors are connected in parallel by applying logic 1 to
each switch (analogue switches operated by logic pulses within an IC
package) causing it to close.
As the MSB (most significant bit) resistor has the lowest value it will
contribute a greater proportion of current. Each additional logic 1 lowers the
combined parallel input resistance, thereby changing the ratio of Rf to Rin,
and the amplifier gain.
Whilst this circuit can perform fast D-to-A conversion, it has one major
drawback which is the difficulty in manufacturing the close tolerance
resistor values. Especially when the number of binary bits exceeds eight.
The use of ladder networks as shown in the next topic is a preferred solution.
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SUM AND DIFFERENCE AMPLIFIERS: Digital to Analogue Using a
Resistor Ladder.
The R-2R ladder network D-to-A conversion technique is based on an
integrated circuit AD7524, 8-Bit Buffered multiplying DAC from ANALOG
DEVICES, where its internal circuit requires just two resistor values.
The output from the Op-Amp is dependent upon the current flowing into the
inverting input terminal as a result of the switched combination of resistors.
Calculation of the output voltage from the various series parallel resistor
combinations is not necessary (in fact its extremely complicated), as it can
be found by applying the simple formula shown.
Multiply the reference voltage by the ratio of binary-to-decimal equivalent
data input, to 255 (the maximum binary 8-bit decimal value). Within certain
limits any voltage can be used as a reference. Obviously excessive voltages
will cause a large current to flow. A better solution is to make VREF small
and adjust the Op-Amp gain by the increasing the value of its feedback
resistor.
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ANALOGUE MULTI-METER: Measuring Voltage. (Voltmeter)
Interactive Content!
To enable an analogue meter movement to measure voltages greater than its
designed capability, a resistor needs to be inserted in series to limit the
current flowing through the meter coil, to that which produces a full scale
needle deflection (FSD).
A typical circuit diagram is shown in the lower half of the display which has
four voltage ranges. 1Volt, 10V, 100V and 1kVolt. In practice these would be
switched positions from a single input.
Each of the series resistor values is calculated using the formula shown.
Here you can experiment with not only different voltage ranges, but also
various values for the meter movement.
Suppose you are measuring 50V and using our values for FSD and Ra. You
would select the 100V input. The total circuit resistance would be 999k + 1k
= 1Mohms. Therefore the current would be 50 ÷ 1000,000 = 50µA = half
full scale deflection. Note. The total meter circuit resistance (Rm + Ra)
always equals input voltage range ÷ the current required to give a full scale
needle deflection on the meter.
ANALOGUE MULTI-METER: Measuring Current. (Ammeter)
A typical analogue meter movement will have a full scale current deflection
stated in µA. To enable currents greater than this to be measured 'shunt
resistors' need to be connected in parallel to bypass the meter coil winding.
The value of this shunt resistor can be found from the formula given.
When a current flows through the parallel combination of the coil winding
and the shunt resistor, a voltage will be developed between points A and B.
The coil current can be determined by voltage A, B ÷ the coil resistance and
the shunt current by voltage A, B ÷ shunt resistance. When added they will
equal the measured current I.
To avoid overloading the meter movement maximum current (FSD), changes
in the value of the shunt resistance need to be made by switching to the
appropriate current range.
The value of the shunt resistor is inversely proportional to the current range
selected.
ANALOGUE MULTI-METER: Measuring Resistance. (Ohmmeter)
Before measuring an unknown resistance value, adjustment would be made
to (RV1) to set the meter needle to zero. This is to compensate for battery
ageing. Thereafter, the circuit can be considered to be the same as for
voltage measurement. All that is required is to find the multiplier resistance
values (Rm) for the various Ohm ranges.
The maximum (FSD) current is determined by the meter movement
resistance.
Connecting a test resistor across the input terminals places its unknown
value in series with (Rm) and (Ra). This reduces the current through the
meter, which is reflected on the scale by the needle moving to the left where
the value can be read.
So as not to exceed the maximum FSD for low values of resistance a range
of Rm's values would be connected in series. Also for higher resistance
values, increases in the battery voltage need to be considered. An alternative
and better way of constructing a circuit to measure resistance would be to
use a Wheatstone bridge, which is covered later.
ANALOGUE MULTI-METER: Effect of Meter Loading.
Connecting an analogue meter to measure the potential difference across a
resistive circuit effectively places the resistance of the meter in parallel with
the circuit resistance. A voltage divider circuit is used to demonstrate the
effect.
Analogue meters have a designed sensitivity measured in Ohms/volt. The
higher the value the better the meter, typically 20,000 Ohms/volt for a good
analogue meter.
In practice you would select an appropriate meter range. However, in our
simulation we use the applied DC voltage, as this is the maximum circuit
voltage. Input a range of values for the DC supply and R2. Next change the
meter sensitivity to prove that the higher values place less load on the circuit
and therefore provide a more accurate voltage measurement.
This loading effect can be largely ignored when using a digital meter as the
input resistance is in the region of several Mohms. This is because the test
meter input is usually built around a field effect transistor which by its
nature has a very high input impedance.
ANALOGUE MULTI-METER: Meter Overload Protection.
An analogue meter movement coil consists of a very fine winding of wire
which is easily destroyed by excessive current. For protection two back-back
diodes are connected across the movement.
These clamp excessive voltage excursions to ± 0.6V.The normal operating
voltage developed across the meter for full scale deflection can be calculated
using Ohm's Law. In this case 0.0001 × 1000 = 100mV and providing the
meter is switched to the correct voltage range then this value will not be
exceeded.
The diodes come into operation when the value of Rm is too low for the
voltage being measured. For an AC waveform D1 and D2 will clamp the
positive and negative excursions to 600mV as each diode becomes forward
biased on the alternate waveform half-cycles.
Similarly, ±overloading DC voltage will cause just one diode to conduct. In
practice once 100mV has been exceeded the needle will be hard over on the
scale and so the coil must be sufficiently robust to cope with the excess
current produced by the 500mV overload.
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COMPONENT TESTING: Resistors.
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A resistor has just one parameter to be tested, its value. Other measurements
such as power rating, type etc are manufacturers and circuit design
considerations. The easiest way of checking the component value has to be
direct measurement using a calibrated 'Ohmmeter'. Measuring resistors 'incircuit' should be avoided unless they are of a very low value, as there will
most likely be a number of other resistive paths connected in parallel,
introducing measurement errors.
Applying Ohm's Law will determine the resistance between two circuit
points in circumstances where both the voltage and current can both be
found. A third method is calculating the unknown value against a standard
component. This method is particularly suited when it's necessary to find
matched pairs of resistors. Equal value resistors will develop an equal
voltages.
Providing a component type and size is chosen with adequate safety margins
for working voltage and current then reliable operation can be assumed, they
rarely fail by themselves. Resistors breakdown because they are stressed,
causing them to overheat thereby lowering their value causing more current
to pass which in turn contributes to their destruction. Resistors never become
short circuit, they reduce in value and eventually burn-out.
Typical causes of overheating might be semiconductor short circuit. The
resistor then acts like a fuse becoming open circuit, thereby removing the
voltage supply.
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COMPONENT TESTING: Capacitors.
In theory capacitors do not change in value (electrolytic types can
significantly change with age due to a 'drying out' of the electrolytic paste),
but can develop short-circuits (S/C) or become open circuit (O/C) and so
tests are usually confined to these two conditions. Markings on modern
capacitors cannot normally be accidentally rubbed off, making measuring
unnecessary. Many digital multi-meters now incorporate capacitance ranges.
These work by applying a constant frequency and calculating the component
reactance.
A capacitor S/C can be confirmed by connecting it in series with a resistor
across a fixed voltage. Normally at switch-on the voltage across 'R' should
high gradually reducing to almost zero as the capacitor charges. A
permanent high voltage across 'R' indicates a S/C. Capacitors should be
tested under working voltage conditions, lower voltages might not show a
dielectric breaking down under load.
An oscilloscope incorporates a useful AC test signal for O/C's (The probe
adjustment terminal gives square waveform of a fixed frequency). It should
be noted that some capacitor values will integrate this input and so the
displayed results might not be a perfect square wave. It is nevertheless a
quick and easy way to test for an O/C.
An analogue meter provides a useful indication of the charge and discharge
voltage developed across a capacitor. This test needs a long 'R,C' time
constant. Therefore for low value capacitors increase the value of 'R'.
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COMPONENT TESTING: Diodes.
Diodes can be tested using an analogue multi-meter, set to the ×100 ohm's
range. Digital meters are OK, but owing to their nature are not as good at
giving a comparative visual indication of the diode's condition. Some digital
meters do however, incorporate a special diode test position.
Testing any semiconductor junction requires it to be biased onto the
operating region of its characteristics curve. This is achieved by applying a
voltage of >0.6V for a silicon diode across the device. An analogue meter
when set to the ohm's range has positive DC voltage on the negative lead.
The reason for this is that when the Ohms ranges are selected the meter
needs to provide current, whereas for other measurements the meter takes its
supply from the circuit under test. The voltage reversal ensures the needle
movement is in the same direction for both applications.
The resistance values given are typical for any general purpose diode.
However, examination of the listing in any component catalogue will show a
very wide range from signal diodes to high power rectifiers capable of
carrying several amps, some with very high peak inverse voltages (PIV).
To provide an indication of a diode's condition, particularly for forward,
reverse and leakage resistance it's best to compare readings with a known
good diode.
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COMPONENT TESTING: Silicon Controlled Rectifier.
The Silicon Controlled Rectifier (SCR), often called a 'thyristor' is simply a
diode with a controlling gate terminal. On first connecting the SCR across
the meter prods it appears open circuit, which is correct. Briefly short the
negative terminal (+) of the meter to the gate to simulate a gating pulse and
the device conducts heavily. Once conducting the gate connection can be left
in place or removed, as it has no further effect.
To switch the device to its non-conducting state, remove the anode supply
voltage, the SCR will then unlatch.
SCRs are heavy duty devices and so the above test will not necessarily
highlight a faulty component, or one which breaks down under load. As with
all power rectifiers the most likely fault will be a short or open circuit. An
extensive test means the SCR must be subjected to load conditions.
An ideal solution is to use a motor vehicle battery and headlamp bulb. The
battery has a low voltage and therefore electrically safe, but able to supply
sufficient current to fully load the SCR. Even under these conditions you
should still ensure that the SCR is operated within its designed specification
and if required correct heat-sinks should be fitted.
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COMPONENT TESTING: NPN Transistor.
For testing purposes the bi-polar transistor can be considered as two back-toback PN junctions (diodes), where each may be measured separately as for a
normal diode. The resistance values will be similar, but as there is a much
larger number of transistor types available having a wide range of
characteristics then actual values can differ markedly. The best method is by
comparative measurements against a known good device of the same type.
The test results shown are for an NPN transistor. To carry out the same range
of tests on a PNP device, just reverse the meter probes. With one further test
for a collector-emitter short circuit. A collector emitter open circuit would
mean that both junctions were damaged and would be picked up by the other
individual tests. High resistance or leaky junctions can be extremely difficult
to trace when fault finding, as they lead to unpredictable circuit operation.
A further test is often useful when designing a circuit and that is DC current
gain (HFE). This is quoted in transistor data books, but in practice can vary
and so comparative measurements of collector current ÷ base current will
confirm the device is within specification. Many digital meters include this
test for current gain as a selectable function.
Normally under AC conditions variations in current gain (hfe) between
devices are compensated by incorporating negative feedback loops.
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COMPONENT TESTING: Identifying Transistor Types.
You will find this test much easier to follow if you draw the representative
diode connections for each transistor type and then complete the circuit by
adding the meter connections showing the voltage polarity on the terminals
(remember for most analogue meters the (-) is actually a positive voltage). A
digital meter is not suitable for this test, however many of the more recent
types now incorporate a much more comprehensive transistor tester.
The diode arrows point in the direction of conventional current where the
anode has to be more positive than the cathode for forward bias.
Whilst this test is useful for establishing whether the transistor is NPN or
PNP it doesn't help to find the pin connections, other than which is the base.
In practice for small signal transistors, if the collector and emitter are
reversed, no harm will be done as the biasing resistors will limit the current
through the device.
Providing the transistor number is known then full specifications can be
found in component catalogues or data books. Power transistors and certain
other encapsulations make the connections quite clear, either by bonding the
collector to the case or having a tag which is associated with the emitter pin.
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COMPONENT TESTING: Diode Probe.
In the absence of an oscilloscope a 'diode probe' can provide a useful
indication of the presence, and in certain circumstances measurement of
higher frequency repetitive signals.
This would be particularly appropriate for very high voltage pulses which
could otherwise overload the input of normal test instruments. The AC
ranges on a multi-meter use a similar method for measuring voltages and
currents, except they have full wave rectifiers and inductive smoothing. A
multi-meter is only suitable for low frequency sine waveforms, i.e. 50Hz
mains where the scale indicates RMS values.
The example shown is a triangular or saw tooth waveform. The rectifier
diode conducts on the positively rising waveform charging the capacitor.
During the negative downward part of the waveform the diode is cut-off as
the capacitor charge voltage (diode cathode) is greater than that on the
anode, and the capacitor discharges across the parallel resistance.
The voltmeter will indicate the mean voltage developed across the capacitor
as it continually charges and discharges. Maximum ramp-up periods will
ensure the capacitor remains fully charged, as there is no time allowed for it
to discharge. Similarly a shorter ramp-up period means the capacitor charge
is continually removed over a longer period. The R,C time constant is
important to ensure the voltmeter provides a realistic indication of the
average voltage. In practice there will also be an additional 0.6V dropped
across the diode.
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COMPONENT TESTING: Logic Probe.
A logic probe is an inexpensive piece of test equipment to give a visual
indication of logic states. A simple LED could be used, to check for logic
HIGH, providing the IC output pin can supply the necessary 10-20mA
required. However, using an LED to check for logic LOW could be
misleading. The test point might be at 0V or it could be open circuit, the
resulting output would be the same. The logic probe overcomes this
limitation with the added advantage of not influencing the circuit operation
through loading due it its high input impedance.
The logic probe therefore is a much more reliable option as it indicates true
logic levels, both high and low. The probe does need a connection across the
circuit supply rails. Switches are usually included for testing both TTL and
CMOS logic levels.
The 'pulse' facility is useful to check for the operation of a clock generator
for example. The LED will flash at about 1 second intervals irrespective of
the clock rate. Finally, the memory LED will show if a fast acting pulse has
been detected. Other features sometimes included result in combinations of
the LEDs flashing, i.e. for detecting rising or falling edges of logic pulses.
It should be understood that the HIGH and LOW LEDs will only be fully
illuminated if the logic level remains in that state for a significant period of
time. A train of changing logic levels will result in either or both of the
LEDs being only partially illuminated. Predominately high or low will show
as a greater brightness of that indicator.
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