Introduction to Circuit Analysis
Overview
In this lesson we will
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Introduce a very high level view of electricity
Introduce voltage and current
Several major and common electronic components
Examine some of the basic rules of electronics
Explore some simple circuits
Getting Started
We analyze circuits for several reasons
•
Understand how they work
•
Learn how to design from other people’s work
•
Debug our own designs
•
Troubleshoot circuit or system that may have failed
Observe these are same reasons we analyze a system in any field
Chemistry
Mechanical engineering
Civil engineering
Computing science
Physics
Any other field of science
We learning to solve problems
We’ll start with some of the
•
Basic terms
• Components
Then see what we can do with them
The Terms
Three of the fundamental items in electronics
•
Circuit
•
Current
•
Voltage
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Electronics is based upon
Controlled movement of electric charge
From one place to another
9 Path that the charge follows as it moves is called the circuit
This path is made up of
•
Electronic components
•
Wires
Wires connect components together
9 Amount of charge that moves through circuit in specified time
Called current
From physics we know
If we raise stone above earth’s surface against gravity
Work stored as potential energy
If we have two charges
Decrease separation between them
Work stored in system as electric potential energy
9 We define electric potential energy - voltage
Work required to move a charge
From infinity to reference point
Simple analogy for electric circuit
Called water analogy
Consider closed circuit of pipes as in city water system as in following figure
Water flows
From
Source of higher pressure
Through
Pipes
To
Place of lower pressure
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Current flows
From
Source of higher potential
Through
Wires
To
Place of lower potential
Called ground
Tank in drawing
Represents source of higher pressure
Battery in electric circuit
Represents equivalent source
In circuit called potential or voltage
Pipes in drawing
Provide path for water to flow
Wires in electric circuit
Provide path for current to flow
Water in drawing
Represents flow of material through pipes
Current in electric circuit
Represents flow of charge through wires
The Components
Have seen that electric circuit
•
Closed path
•
With things connected by wire
Basic things in electric circuit
Fall into two categories
9 Sources
9 Components
Basic Sources
Sources provide energy to circuit
Enable components to do work
Without sources
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Electric circuit would be of little use
Without source of water
Pipes would serve no purpose
Sources come in two major flavours
•
Voltage sources
Provide voltage – like a battery
•
Current sources
Provide current – like water flowing from a melting glacier
Voltage Source
Value of electric potential
Called volts or voltage
Voltage labeled by letter V
Sometimes lower case v
Electronic symbol for voltage source
Represented by
Circle
Shown in left hand figure
Battery
Shown in right hand figure
Plus sign (+) shows
Positive terminal
Terminal of higher potential
Minus sign (-) shows
Negative terminal
Terminal of lower potential
Current Source
Value of current
Called amperes or amps
Represents amount of charge moved per time
Charge labeled by letter Q
Sometimes by lower case q
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Relationship between current charge and time
Given as
i=
ΔQ
Δt
Current labeled by letter I
Sometimes lower case i
Electronic symbol for current source
Represented by
Circle containing arrow in adjacent figure
Circle is the source
Arrow (↑) shows
Direction of current flow
Ground
Ground refers to reference point in electrical circuit
Other voltages within circuit
Measured with respect to ground
Ground also known as earth
Signal
Ground
Several different electronic symbols for ground
Illustrated in accompanying figure
Components
A First Look
To start will consider three basic components
9 Resistor
9 Capacitor
9 Inductor
Certainly are many many others
Returning to water analogy momentarily
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Chassis
Ground
Earth
Ground
Resistor
Resistor labeled by letter R
Value of resistor
Called resistance
Measured in ohms
Behaviour somewhat like going from ¾” pipe to ½” pipe and back
Smaller pipe restricts flow of water
Resistor restricts flow of current
Electronic symbol for resistor given in adjacent figure
Relationship between voltage current and resistance
Given by following two equations
i=
V = RI
V
R
Equation on left
Fundamental electrical engineering relationship
Known as Ohm’s Law
Capacitor
Capacitor labeled by letter C
Value of capacitor
Called capacitance
Measured in farads
Somewhat like a cistern
Small container for holding water
Capacitor stores electric charge
Electronic symbol for capacitor given in adjacent figure
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Relationship between voltage current and capacitance
Given by following two equations
Given in two forms
First set in differential form
V=
1
C
∑ ΔQ
i =C
ΔV
Δt
Second integral and derivative form
V=
1
idt
C
∫
i =C
dV
dt
Inductor
Inductor labeled by letter L
Value of inductor
Called inductance
Measured in henrys
Somewhat like a cistern on a rooftop
Stores energy
Inductor stores electric energy
Electronic symbol for capacitor given in adjacent figure
Relationship between voltage current and inductance
Given by following two equations
Given in two forms
First set in differential form
V =L
Δi
Δt
i=
i
L
∑ ΔV
Second integral and derivative form
V =L
di
dt
i=
i
dV
L∫
The Next Look
Let’s now look at several additional useful components
9 Switches
9 LED
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Switches
Let’s start with switches
Switch is mechanical device
Are several types of switches
Switches often classified by
Number of poles and the number of throws they have
A pole is a lever arm
Provides a contact between two electrical terminals
A throw is a contact in which the switch can be positioned
Example
SPST
o DIP – Dual Inline Package – switch
Is a single-pole single-throw (SPST) switch
Its single arm
Makes contact in one position
Does not make contact in the other
When contact made – closed
Current can flow through switch
SPDT
ƒ A lock switch
The CAP LOCK key in old keyboards
Actually locks in
o Two-position lever-arm switch
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Considered a single-pole double-throw (SPDT) switches
The single arm is making contact in either position
DPST – DPDT
Several other configurations
Illustrated in next diagram
Can use switch to generate input
Connect the switch as shown in following figure
Observe that we have a pull-up resistor shown
Such a resistor is used to ensure
Never have an open input
Nothing connected to circuit input when switch open
Vcc
10K
circuit input
Switch Closed - Logic 0
Switch Open - Logic 1
Figure 10
DIP Switch with Pull-Up Resistor
LED
Now look device we can use to show circuit output
LED is an acronym for a Light-Emitting Diode.
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Is a semiconductor device that emits light (much like a light bulb) when
Voltage applied at the anode (+) is larger than
Voltage applied at the cathode (-)
Under such conditions, a current will flow from the anode to the cathode
Can regulate amount of current flowing through device
By connecting a current-limiting resistor in series
Value used is usually 330 ohm
LED and resistor shown in figure
Vcc
330 ohms
+
Driving an LED
Getting to Work
Let’s now see how we can put sources and components together
We need some basic rules first
In accompanying drawing we have
1. Two pieces of wire connected together
Small black dot symbolizes connection
Called node
2. Two currents i1 and i2
i1 going into node and i2 going out
3. First rule i1 and i2 must be equal
Current cannot disappear going into the node or be created by node
Second rule extends the first and so on
1. Three pieces of wire connected together
2. Two currents i1 and i2
i1 going into node and i2 and i3 going out
3. Second rule i1 must equal i2 + i3
Current still cannot disappear going into the node or be created by node
Third rule
1. Voltage measured from high to low potential
2. High considered positive and low considered negative
3. Interpreted as drop in voltage thus (-)
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Fourth rule coming up shortly
Let’s now take a look at components
Components and Circuits
As we noted earlier
Circuit made up of wires and components
Let’s start with simple circuit
We have resister and two wires
We show current i1
Coming in to circuit at terminal A
Going through resistor R1
Leaving the circuit on terminal B
Let’s believe in a little bit of magic for now
Let’s not worry about where i1 comes from nor where it goes
From Ohm’s law we have
V1 = R1 • I1
That is
Voltage drop V1 across resistor
Given by value of resistor multiplied by current through it
While not shown
Assume bottom side of resistor is (-)
Now let’s add some more parts
In the circuit we have
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1. Wire connected between A and left hand side of R1
2. Right hand side of R1 connected to wire which is connected in turn to top of
R2.
3. Bottom of R2 connected to wire which is connected in turn to B.
4. The two resistors are connected in series with each other.
Following the path from A through two resistors we have
V1 = R1 • I1
Then
V1 = R1 • I1
Total from A to B
V1 + V2
Finally
V1 + V2 = R1 • I1 + R2 • I1
= (R1 + R2 ) • I1
From this circuit we can see several things
1. We see that two resistors connected in series add
Can generalize to n resistors
Thus
For n resistors connected in series
n −1
Req =
∑R
i
i =0
2. Voltage drops across two resistors added
Fourth rule
1. Voltage drops in series add
Let’s now take our first circuit and extend it a bit
From our earlier work we know
Cannot consume or create current going into or out of node
Therefore we know that
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i1 = I2 + I3
=
=
V1 V1
+
R1 R2
(R1 + R2 ) • V1
R1R2
V1 =
R1R2
(R1 + R2 )
• i1
The two resistors are connected in parallel
We see from the equation above
Their equivalent resistance given by
Req =
R1R2
(R1 + R2 )
As we did for resistors in series
Can extend relationship to many resistors
Numerator
Will be product of all the resistors
Denominator
Will be sum of all the resistors
Sources
Let’s revisit sources briefly – we’ll begin with voltage sources
Voltage
Series
Let’s start with two voltage sources connected in series
What happens if we connect two different voltage sources in parallel
For the following circuit
+
+
+ V1
V
+ V2
V
+
Veq
-
-
-
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For our case
There is no voltage drop across the wires
So starting from the (-) terminal on the left hand side
1. We have a voltage rise (- to +) of V volts
2. Turning the corner we have a voltage drop of V1
3. Followed by a second voltage drop of V2 to take us back to
where we started
We now have
V - V1 - V2 = 0
Thus we see
V = V1 - V2
The values of the two voltage sources added together
Let’s try a different configuration
Now we have
For this circuit we have
V + V1 + V2 = 0
Thus we see
V = - ( V1 + V2 )
For this circuit we have
V - V1 + V2 = 0
Thus we see
V = ( V1 - V2 )
For this circuit we have
V + V1 - V2 = 0
Thus we see
V = V2 - V1
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Current
Parallel
Let’s start with two current sources connected in parallel
What happens if we connect two different current sources in series
For the following circuit
We know that current cant vanish or be created at a node
So
I = I1 + I2
We see then that
Current sources in parallel add as voltage sources did in series
Summary and Review of Objectives
At this time you should have a general understanding of
Voltage and current
Voltage and current sources
How they behave when connected in series or parallel
The basic electronic components
Resistors, Capacitors, Inductors
Switches, LEDs
Simple circuits with
Voltage sources
Current sources
Resistors connected in series or parallel
Ohm’s law
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