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Contents
Introduction
2
Equipment & Component List
3
Digital Multimeters
4
Instek GOS-622G Oscilloscope
6
Elenco XK-700 Electronic Trainer
12
The Oscilloscope
Project 1
Measuring Amplitude & Voltage
19
Project 2
Measuring Period & Frequency
21
Project 3
Instantaneous Voltage & RMS Values
23
Project 4
Additional Input Modes & Operations
26
Project 5
Advanced Measurement Techniques
29
Project 6
Forward & Reverse Bias Diode
31
Project 7
Half-Wave Rectifiers
33
Project 8
Full-Wave Bridge Rectifiers
35
Project 9
Inductive Kick
37
Project 10
Inductors in Series & Parallel
39
Project 11
Relationship of XL to Inductance & Frequency
40
Project 12
Relationships in Series RL Circuits
41
Project 13
Relationships in Parallel RL Circuits
43
Project 14
RC Time Constants
45
Project 15
Capacitance in Series & Parallel
50
Project 16
Relationship of XC to Capacitance & Frequency
52
Project 17
Relationships in Series RC Circuits
54
Project 18
Relationships in Parallel RC Circuits
56
Project 19
Relationships of XL & XC to Frequency
58
Project 20
Circuit Characteristics when XL is equal to XC
59
Project 21
Bandwidth Related to Q
61
Project 22
Circuit Characteristics when XL is equal to XC
65
Project 23
Bandwidth Related to Q
68
Diodes & Rectifiers
Inductance
Capacitance
Series Resonance
Parallel Resonance
Formulas
70
Instructor Sign Off Sheet
73
June 2008
Introduction
This lab book is designed for students who have completed the first Concepts of Electronics course and
have a good foundational understanding of Ohm’s Law principles as well as the rules of series, parallel
and combination circuits in resistive loads.
This course introduces alternating current and the relationships of resistive inductive and capacitive
loads. Since alternating current waveforms are much more complex than direct current, an
oscilloscope will be used to observe these waveforms. The oscilloscope used in this course is the
Instek model GOS-622G.
This lab book provides hands-on experiences to reinforce the electronic theory learned in this course.
Most of the projects in this book promote understanding of the intended points made by performing
calculations and making electrical measurements. The results are then compared and conclusions are
drawn at optimum times during the projects.
The projects in this lab manual are designed to help students develop and improve their abilities to:
•
•
•
•
Follow instructions carefully,
Make accurate measurements and calculations,
Analyze technical data appropriately,
Draw logical conclusions from their observations and calculations.
When performing each lab experiment, make sure the meter and test instruments are set to the correct
function and range to ensure accurate readings. There are also many calculations and measurements
in these lab projects that will require rounding of decimal points. To ensure a correct answer, make
sure each number is rounded to the nearest hundredth (two decimal places). For example, if an
answer calculates to 3.457 mA, the correct answer would be 3.46 mA. If an answer calculates to
21.3523 kΩ, the correct answer would be 21.35 kΩ. If the answer is a whole number or if the
hundredths place is a zero, the extra zeros do not need to be added. For example, an answer of 10
volts does not need to be written as 10.00 V.
The answers must also be written in metric prefix form with the correct unit label. For example, an
answer of 11270 Ω should be written as 11.27 kΩ. An answer of .482 A should be written as 482 mA,
etc.
For your convenience, the Ohm’s Law formulas along with many other formulas used in this course
have been added toward the back of this lab manual. Also included is an instructor sign-off sheet.
Have your instructor initial and date this sheet in the appropriate location when the corresponding
project is correct and complete. This will help both you and your instructor track your progress
throughout the experiments.
2
Equipment
•
Elenco XK-700 electrical trainer
•
Multi-range digital multi-meter (DMM)
•
Instek GOS-622G dual trace oscilloscope
•
Stopwatch
•
Breadboard jumper wires
Components
•
Diode, 1N4002, 1 amp (4)
•
Resistors
•
•
o
100 Ω, carbon film, 1 watt, 5% tolerance (2)
o
1 kΩ, carbon film, 1 watt, 5% tolerance
o
3.3 kΩ, carbon film, 1 watt, 5% tolerance
o
4.7 kΩ, carbon film, 1 watt, 5% tolerance
o
10 kΩ, carbon film, 1 watt, 5% tolerance
o
18 kΩ, carbon film, 1 watt, 5% tolerance
o
27 kΩ, carbon film, 1 watt, 5% tolerance
o
680 kΩ, carbon film, 1 watt, 5% tolerance
o
10 MΩ, carbon film, 1 watt, 5% tolerance
Capacitors
o
0.1µF, ceramic disc, 50V (2)
o
1.0µF, electrolytic, non-polarized, 50V (2)
o
47µF, electrolytic, non-polarized, 50V
Inductors
o
100 mH, D.C.R. 150 Ω (2)
o
1.5 H, iron core, filter choke
3
Digital Multimeters
Resistance Function
Ranges from 200Ω to
200MΩ
ON / OFF power switch
Continuity / Diode Test
Function
Transistor Test Function
DC Current Function
Ranges from 2mA to
20A.
DC Voltage Function
Ranges from 200mV
to 1000V DC
AC Current Function
Ranges from 2mA to
20A.
AC Voltage Function
Ranges from 200mV
to 700V AC
Capacitance Function
Ranges from 2nF to
200µF
“V, Ω” jack
Use this jack for the red
test lead when measuring
voltage or resistance.
“A” jack
Use this jack for the red test
lead when measuring current
from 200mA to 20A
“mA” jack
Use this jack for the red
test lead when measuring
current from 0 to 200mA.
“COM” jack
Use this jack for the
black test lead.
Figure P-1
Multimeters are very useful test instruments. By operating a multi-position switch on the meter they can
be quickly and easily set to be used as a voltmeter, an ammeter or an ohmmeter. Some meters have
additional features used to measure capacitance and frequency as well. They have several settings
called “ranges” for each type of meter and the choice of either alternating or direct current
measurements.
Voltmeter
To test for voltage, first determine whether the application you're testing uses AC or DC voltage. Then
set the dial to the appropriate function and plug the red test lead into the correct jack used to measure
voltage.
Like all test procedures, when testing voltage, set the meter to the range just higher than the expected
voltage and decrement it down as needed to increase the accuracy of the reading. If you don't know
the expected range, set the range to the highest one available. Take the black test lead and place it on
the negative polarity point of the circuit you want to measure. The red test lead will go on the more
positive polarity point. When measuring voltage, the test leads of the meter must always be connected
in parallel or “across” the component or circuit to be measured as in Figure P-2 on the next page.
4
Voltmeter leads connected in parallel
with resistor being measured.
Power
Supply
6.00
V
6V
A
mA COM VΩ
Figure P-2
Ammeter
To measure current, break the circuit where you want to take the reading. Set the meter to AC or DC
current depending on the source being tested. Plug the test lead into the correct jack to measure the
expected current.
Note: Most meters have a separate jack that needs to be used to measure current from 0 to 200mA
and from 200mA to 10A or sometimes 20A.
Insert the meter in series or “in line” with the circuit to be measured by placing the red test lead on the
positive polarity point and the black lead on the negative polarity point (see Figure P-3). Similar to the
voltage, the correct current range needs to be selected. Start by selecting the next range higher than
the expected reading. If the meter ever reads “0” when an actual reading should be present, check the
fuse for the 200mA port.
Ammeter leads connected in series
with the circuit being measured.
Power
Supply
12.00
12V
mA
A
mA COM VΩ
Figure P-3
Ohmmeter
To test for resistance, first remove the power from the circuit component to be tested. This prevents
the meter from becoming damaged by the source. After ensuring that all power is off, set the dial to the
resistance function. Select the appropriate range on the dial. Remove the component to be measured
from the circuit (This prevents false readings from any other components in the circuit). Make sure the
test leads are plugged into the correct jack to measure resistance. Connect your test leads to the
component and take the reading.
It's important that you have good contact between the test leads and the component being tested. Dirt,
oil and poor test lead connection can undesirably alter resistance readings.
Remove power from the circuit prior
to taking resistance measurement.
1000
Ω
A
Figure P-4
mA COM VΩ
5
Instek GOS-622G Oscilloscope
Front Panel Controls
16
4
9 15
12 14 17 22
21 23
31
29
30
32
25
27
26
28
36 1
2
3
34
33
7
6
5
8
11 10 13 18 35 19 20
24
Figure P-5
Cathode Ray Tube (CRT) Controls:
INTEN
Controls the brightness of the trace.
(1)
FOCUS
Allows for focusing of the trace to the sharpest image.
(2)
TRACE ROTATION
Potentiometer for aligning the horizontal trace in parallel with the grid lines.
(3)
CRT SCREEN
For viewing waveform.
(4)
Vertical Axis Controls:
(5)
CH 1
(6)
(7)
AC-DC-GND
VOLTS/DIV
(8)
VARIABLE
(9)
(10)
POSITION
CH 2
(11)
(12)
AC-DC-GND
VOLTS/DIV
(13)
VARIABLE
(14)
(15)
POSITION
MODE
(16)
(17)
CHOP
CH 2 INV
Vertical input terminal for Channel 1. When in X-Y operation, X-axis input
terminal.
Selects connection mode between Channel 1 input signal and vertical amplifier.
Selects the Channel 1 vertical axis sensitivity from 1mV/DIV to 5V/DIV in 12
ranges.
Fine adjustment of Channel 1 vertical axis sensitivity. When in CAL position,
sensitivity is calibrated to the indicated value.
Vertical position control of Channel 1 trace.
Vertical input terminal for Channel 2. When in X-Y operation, Y-axis input
terminal.
Selects connection mode between Channel 2 input signal and vertical amplifier.
Selects the Channel 2 vertical axis sensitivity from 1mV/DIV to 5V/DIV in 12
ranges
Fine adjustment of Channel 2 vertical axis sensitivity. When in CAL position,
sensitivity is calibrated to the indicated value.
Vertical position control of Channel 2 trace.
Selects operation of CH 1 and CH2
CH 1
The oscilloscope operates as a single-channel instrument using CH 1.
CH 2
The oscilloscope operates as a single-channel instrument using CH 2.
DUAL The oscilloscope operates as a dual-channel instrument using both CH
1 and CH 2. CHOP/ALT are automatically changed by the TIME/DIV
setting.
ADD
The oscilloscope displays the algebraic sum of the two signals.
Allows for the two traces to be displayed in the CHOP mode at all ranges.
The oscilloscope displays the algebraic difference of the two signals when in
ADD mode.
6
Horizontal Axis Controls:
(18)
TIME/DIV
(19)
SWP. UNCAL
(20)
SWP. VAR
(21)
(22)
(23)
POSITION
X 10 MAG
X-Y
Trigger Controls:
(24)
EXT TRIG
(25)
SOURCE
(26)
TRIG. ALT
(27)
COUPLING
(28)
SLOPE
Selects the rate at which the waveform is displayed across the CRT screen
(sweep speed).
When pushed in, the sweep time can be made slower using the SWP.VAR
control (20) by a factor of ≥2.5 of the indicated value. When not pushed in, the
indicated values are calibrated.
Vernier control of sweep time. Allows horizontal time scale to be set in between
the discrete TIME/DIV settings. The indicated values are calibrated when the
SWP. UNCAL (19) button is not pushed in.
Horizontal positioning control of the trace.
When button is pushed in, a magnification of 10 occurs on the horizontal scale.
X-Y operation is enabled when pressed.
When in X-Y mode, time is no longer measured on the X axis. The X axis
represents the CH 1 input and the Y axis represents the CH 2 input.
Input terminal is used in common for external triggering a signal. To use this
terminal, set SOURCE switch (25) to the EXT position.
On this setting, a better-conditioned signal can be used to trigger the scope while
observing a relatively weak signal.
Selects the internal triggering source signal.
CH1
When the VERT MODE switch (15) is set to DUAL or ADD, selects CH
(X-Y)
1 for the internal triggering source signal. When in X-Y mode, select
CH 1 for the X-axis signal.
CH 2
When the VERT MODE switch (15) is set to DUAL or ADD, selects CH
2 for the internal triggering source signal.
LINE
Selects the AC power line frequency signal as the triggering signal.
EXT
The external signal applied through EXT TRIG input terminal (24) is
used for the external triggering source signal. When in the X-Y mode,
the X-axis operates with the external sweep signal.
When the VERT MODE switch (15) is set to DUAL or ADD, and the SOURCE
switch (25) is selected at CH 1 or CH 2, with the engagement of the TRIG. ALT
switch (26), CH1 and CH 2 will be alternately selected for the internal triggering
source signal.
Selects the coupling of the triggering signal to the trigger circuit in accordance with
the characteristics of the measured signal.
AC
This coupling is for AC triggering which is used most commonly. As the
triggering signal is applied to the trigger circuit through an AC coupling
circuit, stable triggering can be attained without being affected by the
DC component of the input signal. The low-range cutoff is 10-Hz.
HF REJ
(High frequency rejection) The triggering signal is fed to the trigger
circuit through an AC coupling circuit and a low pass filter (approx. 50kHz). The higher frequencies are rejected and only the lower
frequencies are applied to the trigger circuit. (Useful for noise reduction)
TV
Useful for observation of TV video signals. The triggering signal is AC
coupled and fed through the triggering circuit to the TV sync separator
circuit. The separator circuit picks off the sync signal, which is used to
trigger the sweep. Thus the video signal can be displayed stably.
Being linked to the TIME/DIV switch, the sweep speed is switched for
TV-V and TV-H as follows:
TV-V: 0.5s – 0.1ms
TV-H: 50µs – 0.1µs
DC
The triggering signal is DC-coupled to the trigger circuit. This mode is
used when triggering is desired with the DC component of the triggering
signal or when a signal with very low frequency or a signal with a large
duty cycle ratio is needed to be displayed.
Selects the polarity of the triggering signal.
+
Triggering occurs as the triggering signal crosses the triggering level in
a positive-going direction.
–
Triggering occurs as the triggering signal crosses the triggering level in
a negative-going direction.
7
(29)
LEVEL
Displays a stationary waveform and sets a start point for the waveform. The trigger
level changes in the positive direction when the control knob is turned clockwise,
and it changes in the negative direction as the knob is turned counter-clockwise.
(30)
LOCK
(31)
HOLDOFF
(32)
TRIGGER MODE
When the LEVEL LOCK switch is engaged, the triggering level is automatically
maintained within the amplitude of the triggering signal, and stable triggering is
made without requiring level adjustment (although jitter may not be suppressed
when in the ALT mode).
Used when the signal waveform is complex and stable triggering cannot be attained
with the LEVEL knob alone.
Selects the desired trigger mode.
AUTO
NORM
Others:
(33)
POWER
(34)
(35)
(36)
POWER
GND
CAL
When no triggering signal is applied or when triggering signal is less
than 50-Hz, sweep runs in the free run mode.
When no triggering signal is applied, sweep is in a steady state and the
trace is blanked out. Used primarily for observation of a signal ≤ 50-Hz.
Main power switch of the instrument. When this switch is turned on, the LED (34) is
also turned on.
LED indicating oscilloscope power is turned on.
Ground terminal of oscilloscope main frame.
This terminal delivers the calibration voltage of 2-VP-P, 1-kHz, positive square wave.
The output is 2kΩ.
8
Instek GOS-622G Oscilloscope
Basic Operation
Before applying power to the oscilloscope, ensure the instrument switch settings and controls are set to
the default settings according to the table below.
Control
No.
POWER
INTEN
FOCUS
VERT MODE
CHOP
CH 2 INV
VERT POSITION
VOLTS/DIV
VARIABLE
AC-DC-GND
SOURCE
(33)
(1)
(2)
(15)
(16)
(17)
(9), (14)
(7), (12)
(8), (13)
(6), (11)
(25)
Setting
OFF
Mid-position
Mid-position
CH 1
Released
Released
Mid-position
0.5 V/DIV
CAL (clockwise)
GND
Set to CH 1
Control
COUPLING
SLOPE
TRIG ALT
LEVEL LOCK
HOLDOFF
TRIGGER MODE
TIME/DIV
SWP. UNCAL
HORIZ. POSITION
X10 MAG
X-Y
No.
(27)
(28)
(26)
(30)
(31)
(32)
(18)
(19)
(21)
(22)
(23)
Setting
AC
+
Released
Pushed in
MIN (c-clockwise)
AUTO
0.5 mS/DIV
Released
Mid-position
Released
Released
After the switches and controls are set to the default settings, connect the power cord to the AC line
outlet and continue as follows.
1. Engage the POWER switch (33) and make sure the power LED (34) is turned on. A trace
should appear on the CRT screen (4) in about 20 seconds. If no trace appears after one
minute, double check the switch and control settings.
2. Adjust the trace with the appropriate brightness and sharpness with the INTEN (1) and FOCUS
(2) controls.
NOTE: Set the intensity only bright enough to legibly see a trace. Setting the trace
intensity too high for a long period of time could cause permanent damage to the CRT
screen.
3. Align the trace with the horizontal center line of the grid by adjusting the CH 1 POSITION (9)
control and TRACE ROTATION (3) control (adjustable by screwdriver).
4. Align the begining of the trace with the left-most vertical grid line on the CRT screen by
adjusting the HORIZ. POSITION (21) control.
5. Connect a probe to the CH 1 INPUT terminal (5). Make sure the slide switch on the probe is set
to the “X1” position.
6. Connect the probe tip to the CAL (36) terminal.
7. Set the CH 1 AC-DC-GND (6) switch to AC and release the
GND. A square waveform similar to the one shown in Figure
P-6 should now be displayed on the CRT screen (The vertical
lines of a square wave may be invisible on your screen but
you should still be able to view the peaks and valleys of the
waveform).
Since the CH 1 VOLTS/DIV (7) is set to 0.5 V/DIV, we can
determine the peak to peak voltage of the waveform. Each
vertical grid square or division represents 0.5 V. Since the
peak to peak waveform is approximately 4 divisions from top
to bottom our peak to peak voltage is 2 volts (0.5-V x 4 divisions = 2-VP-P).
Figure P-6
8. Now change the CH 1 VOLTS/DIV (7) setting to 0.1 V/DIV, and set the switch on the Channel 1
probe to X10. You should now be viewing a square wave that is approximately 2 vertical grid
squares (divisions) high. By turning on the probe’s X10 switch, a multiplier of 10 is introduced
into the waveform’s vertical calculation. The peak to peak voltage of the waveform can then be
9
found by taking the CH 1 VOLTS/DIV setting times a multiplier of 10, times the number of
divisions of the waveform (0.1 x 10 x 2 = 2-VP-P).
The X10 setting on the probe is mainly used for increasing the number of voltage ranges the
oscilloscope is capable of measuring, therefore making it a more versatile instrument. It also
allows for viewing waveforms with higher voltage and amplitude that may otherwise be very
difficult to observe.
9. The next step will be to determine the frequency of the waveform.
Frequency is equal to the reciprocal of the period, or the length of
time needed to complete one waveform cycle. With the TIME/DIV
(18) set to 0.5-mS/DIV, the waveform cycle is approximately 2
horizontal divisions in length. The period can then be found by
taking the TIME/DIV setting times the number of divisions for one
cycle (0.5-mS x 2 = 1-mS). The reciprocal of the 1-mS period will
then be the frequency of the waveform (1/.001-S = 1000-Hz).
One cycle
10. Now change the TIME/DIV (18) setting from 0.5-mS/DIV to 0.1Figure P-7
mS/DIV. By changing the time base to a shorter length of time for
each division, the waveform, in a sense will appear “stretched out”. This allows for a more
accurate frequency measurement.
Each division is separated by 5 smaller divisions indicated as graticule marks on the middle
vertical and horizontal grid lines. Each of these marks represents 0.2 of a whole division. For
example, if one complete cycle of the waveform being measured is just short of 10 divisions by
an amount of one graticule mark, then you would use the value of 9.8
{(9.8 divisions) x (0.1-ms/DIV) = 0.98-mS period}. The reciprocal of the 0.98-mS period would
then be 1020-Hz. A more accurate reading of the same input waveform from step 9.
NOTE: For precision and ease of measuring it is common practice to move and align the
waveform with the vertical and horizontal graticule marks on the CRT screen. This is done by
turning the VERT POSITION (9), (14) and the HORIZ POSITION (21) controls.
Just as the vertical scale has an X10 setting directly on the probes, the horizontal scale has the
X10 MAG (22) switch that can be used the same way to magnify the amount of time per division
by 10 times. Although usually not used as often as the vertical magnifier, the X10 MAG can be
used to examine waveforms with extremely low frequencies.
11. Set the TIME/DIV (18) back to 0.5-mS/DIV.
12. Set the VERT MODE (15) switch to CH2 and align the trace with the horizontal center line of the
grid by adjusting the CH2 POSITION (14) control.
13. Connect a second probe to the CH2 INPUT terminal (10).
14. Connect the probe tip to the CAL (36) terminal so both CH1 and CH2 probes are connected.
15. Set the CH2 VOLTS/DIV (12) control to 0.1 V/DIV and select X10 on the CH 2 probe.
16. Set the CH2 AC-DC-GND (11) switch to AC and release the GND. You should now see the
same square wave signal as before, the only difference being the input is now on CH2 instead
of CH1.
17. Set the VERT MODE (15) switch to DUAL. You should now be able
to see the waveforms of both CH1 and CH2 as shown in Figure P-8.
You are able to move the waveform of each channel by using the
corresponding CH1 or CH2 VERT POSITION (9), (14) controls.
The DUAL channel mode is very useful for comparing two different
waveforms and to observe such characteristics as phase, voltage,
and frequency relationships between the two waveforms. Obviously
in order for an accurate voltage or amplitude reading, both CH1 and
CH2 must be set to the same VOLTS/DIV.
Figure P-8
10
18. Set the VERT MODE (15) switch to ADD. The ADD mode displays the sum of CH1 and CH2
input signals. As you can see the sum of the two 2-VP-P signals is now displayed as a 4-VP-P
square wave. When using the ADD mode, it is important that both CH1 and CH2 be set to the
same VOLTS/DIV.
The ADD mode is mostly used in conjunction with the CH2 INV (17) switch. The CH2 INV
switch inverts the polarity of the CH2 input only. This allows subtractions to be used (CH1
minus CH2) and ungrounded voltage drops in a circuit to be determined. For example, in most
cases the oscilloscope’s ground is connected to the signal generator’s ground through the
wiring of the power cables and the building’s receptacle plugs. This restricts the oscilloscope to
test only across grounded components.
If we look at Figure P-9, typically the oscilloscope ground would
be connected to the circuit ground at point C so all of the
voltage measurements will be taken with respect to that point.
VA
The measurements can then be taken across R2 by placing the
probe at point B or for total circuit voltage at point A. The
oscilloscope cannot, however measure from point A with
respect to point B since the oscilloscope ground and the circuit
ground are essentially the same point. Doing so could result in
shorting R2 thereby giving inaccurate voltage readings. To
then find the voltage drop at R1, the oscilloscope would
essentially subtract the voltage drop (B to C) from the voltage (A to C).
A
R1
B
R2
C
Figure P-9
11
The Elenco XK-700 Electronic Trainer
This guide will explain the basic operations and features of the Elenco electronic trainer that you will be
using for the majority of the lab experiments in this course. Please take a few minutes to read through
this guide and study the illustrations so you will become familiar with the different functions of this
trainer.
In this user guide you will identify the five main sections of the trainer. You will also learn the purpose
and the function of each section.
The five sections of this trainer are listed below. See Figure P-10 for a pictorial diagram of the trainer.
1.
2.
3.
4.
5.
Power supply section
Variable resistance section
Function generator
Digital section
Breadboard section
Variable Resistance
Section
Function / Signal
Generator
Power Supply
Section
Digital
Section
Breadboard Section
Figure P-10
12
Power Supply
The Elenco trainer has several built in DC power supplies to satisfy most electronic design needs.
The two variable DC power supplies produce up to +20 volts and -20 volts at 500 milliamps. Below 15v
the available current is over 1 amp.
Three fixed power supplies produce +12vdc, -12vdc, or +5vdc at 1 amp each.
All of the power supplies are regulated to within 150 millivolts. In other words, if you increase the
current draw from no load to 500 milliamps, the voltage will change less than 150 millivolts.
Variable negative voltage
control Varies negative
voltage from 0 to -20v at
indicated output terminal.
Ground
-12VDC fixed
voltage
Variable positive voltage
control Varies positive
voltage from 0 to 20v at
indicated output terminal.
+12VDC fixed
voltage
Power output terminals
This provides 30VAC center
tapped at 15VAC. This also
provides the output terminal
for positive and negative
variable voltages.
On – Off switch
Allows power to be applied
to all outputs. Switch will
light when on.
+5VDC fixed
voltage
Fuse holder
1.25A 250V
Figure 1
Figure 1
Figure P-11
A variety of different voltages are
available at the power output terminals.
Because the Elenco trainer uses both the
+20v and -20v adjustable voltage
controls, a combined voltage of up to
40vdc is possible. (See Figure P-12)
0 to +20vdc
0 to 40vdc
DC Voltmeter
0 to +20vdc
Ground
0 to -20vdc
0 to -20vdc
DC Voltmeter
DC Voltmeter
Figure P-12
13
30VAC
The power supply section’s output terminal block
also allows for the stepped down AC voltage to be
used direct from the center tapped transformer.
The transformer provides a voltage of 30VAC
from line to line or 15VAC from either line to the
center tapped ground (See Figure P-13).
AC Voltmeter
15VAC
AC Voltmeter
WARNING:
Do not short the 15 VAC output to ground!
Step Down
Transformer
120VAC
Figure P-13
Variable resistance section
The Elenco trainer has two built in variable resistors or “potentiometers” that are available to use for
certain lab experiments. The values of the variable resistors are 1k ohm and 100k ohm max. Taking a
resistance measurement from one side of the terminal block to the other will give the full value of the
resistor (1k ohm or 100k ohm) regardless of the position of the knob. If you take a measurement from
either end of the terminal block to the middle wiper connection, you will get a variable value that will
change with respect to the position of the knob. (See Figure P-15)
1k ohm potentiometer
100k ohm potentiometer
Full 1k ohm
Ohmmeter
0 to 1k ohm
Ohmmeter
1k terminal block
100k terminal block
Figure P-14
1kΩ potentiometer
Figure P-15
14
Function / Signal Generator
The included function generator is capable of producing sine, square and triangle waveforms. The
frequency of this generator is variable from one hertz to over 100,000 hertz in the following five ranges:
10-Hz, 100-Hz, 1-kHz, 10-kHz and 100-kHz. A fine adjustment control makes for easy selection of any
frequency between these ranges. The output voltage amplitude is variable between 0 and 15-VP-P.
The output of the function generator may be taken from the terminal marked “FREQ” with respect to a
ground terminal in the power supply section.
Waveform Selection
Use to select square,
triangle or sine
waveforms.
Frequency Range Selector
Selects 5 frequency ranges
from 10 to 100,000 hertz.
Signal Output Terminal
Terminal provides
connection point for
output signal (with
respect to ground).
Fine Frequency Control
Allows easy selection of
desired function generator
frequency.
Amplitude Control
Controls the voltage
amplitude of the
waveform. 0 – 15VP-P
DC Offset Control
Controls the DC level of the
generator output. DC may be
varied + 10V from zero level.
Figure P-16
Internal Impedance
Every function generator has internal impedance that must be considered when measuring certain
values in the AC circuit. This internal impedance can act as an immeasurable voltage divider and can
slightly skew the measured values of the circuit.
You may notice as you progress through these lab exercises that some measurements to not exactly
match up to their corresponding calculations. Although this can be caused by many different variables
such as meter inaccuracy or tolerance of components, the internal impedance of the generator is one
factor that is sometimes overlooked. To better understand how the internal impedance can affect a
circuit, see Figure P-17.
Function Generator
RS
R1
R2
In Figure P-17, RS represents the internal impedance of
the generator. As you can see, the internal impedance
acts as a resistor in series with the circuit and can
therefore create an undesired voltage drop in the circuit.
In order to eliminate as much error as possible it is very
important that the load resistors (R1 & R2) are relatively
large in resistive value as compared with RS.
On the next page you will determine the internal
impedance of your function generator. This should give
you an idea of how this will affect your circuit values.
Figure P-17
15
Find the Internal Impedance of the Function Generator
1. Connect the red lead of the DMM to the generator output (FREQ terminal) and the black test lead to
ground (GND).
2. Set the open circuit or “no-load” voltage to 6-VRMS.
3. Once the open circuit voltage is set, connect the circuit as shown in Figure P-18 using the 1-kΩ
variable resistor on the Elenco trainer.
4. Connect the voltmeter across the load
and adjust the variable resistor until
the voltage equals half the open
circuit voltage or 3-VRMS.
5. Disconnect the power from the circuit
and measure the resistance of the
variable resistor with an ohmmeter.
The resistance measured should be
very close to the internal impedance
of the generator.
4.00 V
Voltmeter
8-VRMS
What is the internal impedance of the
function generator (ZSource) on your
Elenco trainer?
1-kΩ variable
resistor terminal
Figure P-18
ZSource = _____________________
Digital Section
The digital section of the trainer consists of two “no bounce” logic switches, 8 LED indicator lamps, 8
data switches and a clock generator. The clock generator output is a 5V pulsating square wave. The
frequency of the pulsations can be adjusted with the frequency range selector and fine frequency
control in the function generator section.
Clock Generator Output Terminal
Provides connection point for
pulsating clock signal (5VP-P).
Input Terminal for LED Indicators
“A” input terminal corresponds with
“A” LED etc.
Data Switches
Supplies output
of 5V or 0V
depending on
position.
Logic Switches
No bounce
switches
Logic Switch Output Terminals
Output terminals for corresponding switches
Data Switch Output Terminals
Output terminals for corresponding switches
Figure P-19
16
Breadboard Section
The Elenco trainer is equipped with two breadboards containing a total of 1660 tie points including 6
independent bus lines.
Figure P-20
The board is made of plastic with a matrix of holes. Wires and component leads can be pushed into
the holes to make appropriate connections. Each “hole” on the board contains a metal spring contact.
When a wire or component lead is pushed down into the hole an electrical connection is made with that
hole’s spring contact.
The breadboards provide an interconnection between certain holes on the board using metallic “bus”
connections made underneath the surface. The holes are internally connected so that each 50 hole
horizontal bus line is independent from the other and each small 5 hole vertical bus line is also
connected independently. Figure P-21 shows the internal connections of the holes on the breadboard.
Vertical bus line
Horizontal bus line
Figure P-21
Because of the built-in interconnections and the typical circuit board layout, some of the following
techniques are commonly used when working with a breadboard.
•
•
•
•
A jumper wire can be used to connect the positive source lead to one of the horizontal buss
lines marked with a “plus” (+) sign.
Another jumper wire can be used to connect the negative source lead or GND to one of the
horizontal buss lines marked with a “minus” (-) symbol.
A short jumper wire can then be used to connect each horizontal source connection row to the
appropriate point(s) in the circuit on the vertical bus line portion of the board.
When connecting component leads, plug one lead of a component into a vertical column hole
and the other lead of the component into another vertical column hole in a separate bus line.
Connect the component, spaced as necessary for the size of the component.
17
Figures P-22 & P-23 are sample series and parallel circuit connections using a breadboard. These are
just a small sample of the many different methods and combinations for connecting circuits using
breadboards. These examples are shown using the positive variable voltage supply.
(a)
Variable
0 to +20vdc
Ground
Variable
0 to -20vdc
R3
560Ω
(b)
+
VA
Sample series circuit layout
(a) Pictorial Diagram
(b) Schematic Diagram
680Ω
_
R2
470Ω
R1
Figure P-22
(a)
Variable
0 to +20vdc
Ground
Variable
0 to -20vdc
(b)
+
VA
Sample parallel circuit layout
(a) Pictorial Diagram
(b) Schematic Diagram
−
R1
470Ω
R2
560Ω
R3
680Ω
Figure
P-23
Power
18
The Oscilloscope
Measuring Amplitude & Voltage
Project Objectives:
•
To provide practice using an oscilloscope to measure peak to peak voltage and amplitude of a
sine wave.
Items Needed:
- Elenco electronics Trainer
- Digital muti-meter
- Oscilloscope
- Jumper Wires
NOTE: In order to complete the lab projects in this book it is very important that you understand the
basics of how an oscilloscope operates. If you are using an Instek GOS-622G or similar model, be
sure to complete the tutorial beginning on page 9 of this lab book prior to working on the lab
projects. If you are using a different oscilloscope to complete these projects, make sure you read
and completely understand the owner’s manual that came with your instrument.
It is also very important that you know the default switch and control settings that would allow you to
accurately observe a waveform. Occasionally the projects in this lab book will refer to the default
control settings found on page 9 of this book. If you are not using the Instek model GOS-622G,
make sure you are familiar with the controls and the default settings of your oscilloscope.
Experiment
1. Insert a jumper wire into the FREQ output terminal found in the analog section of the Elenco
trainer.
2. Insert a second jumper wire into the GND terminal in the power supply section of the trainer.
3. Connect a probe to the channel 1 input of the oscilloscope. Connect the probe tip to the output
(FREQ) wire. Connect the ground clip lead of the channel 1 probe to the GND jumper wire.
4. Make sure the oscilloscope controls are set to the default setting as shown on page 9 of this
book. Also make sure the switch on the channel 1 probe is set to X10.
5. Turn on the power switch to the oscilloscope and use the vertical and horizontal position
controls to align the trace with the center horizontal grid line.
6. Make sure the WAVEFORM control on the Elenco trainer is set to “sine wave”. Apply power to
the trainer and set the CH1 AC-DC-GND switch to AC (release ground switch).
7. Adjust the frequency from the Elenco trainer with the COURSE
FREQ and FINE ADJUST controls found in the function generator
section of the Elenco trainer. Adjust until a waveform with two
complete cycles fills the oscilloscope CRT screen (see Figure 1-1).
If a waveform does not exist or if the height of the waveform is
very short, try increasing the AMPLITUDE control.
8. Set the CH1 VOLTS/DIV setting to 0.1V/DIV. Adjust the amplitude
from the Elenco trainer until you get a peak to peak waveform of 6
vertical divisions (grid lines) high.
Figure 1-1
The peak to peak voltage can now be calculated. Multiply the
CH1 VOLTS/DIV setting times the number of divisions from the positive peak to the negative
peak of the waveform. _________ VOLTS/DIV x _________ divisions = _________
19
The result then needs to be multiplied by 10 since the CH1 probe is set to X10.
What is the peak to peak voltage of the waveform? ________________ VP-P.
This means the peak voltage or amplitude must be ________________ Vpeak and the RMS
or effective voltage must equal ________________ VRMS. (VRMS = Vpeak x 0.707)
Since voltmeters read AC voltage in RMS values, we can confirm this calculation.
9. Use a voltmeter set for AC volts to measure the voltage from the generator. Compare the result
with the calculated RMS value in the previous step.
Voltmeter reads ________________ V.
10. Keep the frequency set so two complete waveform cycles are showing on the oscilloscope CRT
screen (as in Figure 1-1). Set the CH1 VOLTS/DIV setting for each example below and make
sure the switch on the CH1 probe is set to X10. Set the peak to peak waveform to the specified
number of vertical divisions using the AMPLITUDE control on the Elenco trainer. Draw each
waveform and indicate the peak voltage or “amplitude” of the waveform. Be sure the voltage
level is accurate on your drawing. Do not use a voltmeter for this portion of the exercise.
You can easily read the waveform by moving it using the CH1 vertical position control on the
oscilloscope.
VOLTS/DIV = 0.5V/DIV
3 divisions peak to peak
VOLTS/DIV = 50mV/DIV
7 divisions peak to peak
VOLTS/DIV = 0.1V/DIV
4.5 divisions peak to peak
Voltage = ________ Vpeak
Voltage = ________ Vpeak
Voltage = ________ Vpeak
11. Set each waveform to read the given amplitude for each example. Draw the waveform and
indicate the VOLTS/DIV setting that was used. Make sure the X10 setting on the CH1 probe is
used. Do not use a voltmeter.
Amplitude = 2.5 Vpeak
Amplitude = 5 Vpeak
Amplitude = 400 mVpeak
VOLTS/DIV = _________
VOLTS/DIV = _________
VOLTS/DIV = _________
20
The Oscilloscope
Measuring Period & Frequency
Project Objectives:
•
To provide practice using an oscilloscope to measure the period and frequency of a waveform.
Items Needed:
- Elenco electronics Trainer
- Oscilloscope
- Jumper Wires
NOTE: Before beginning this lab project, make sure the oscilloscope is set according to the default
switch and control settings found in the table on page 9 of this book.
Experiment
1. Connect the CH1 oscilloscope probe across the FREQ and GND terminals on the Elenco trainer
and set the WAVEFORM for a sine wave.
2. Apply power to both the oscilloscope and the function generator. Align the trace in a manner
that it begins with the left-most vertical grid line and is in line with the horizontal center grid line.
Set the time base (TIME/DIV) to 1mS/DIV and the CH1 VOLTS/DIV to 0.1V/DIV.
3. Set the CH1 AC-DC-GND switch to AC (release the ground switch). If a sine wave does not
appear, try increasing the AMPLITUDE on the function generator. If a waveform still does not
appear, double check the default oscilloscope settings on page 9.
4. Using the COURSE FREQ and FINE ADJUST controls on the
function generator, adjust the signal to obtain a sine wave cycle
that is 7 horizontal divisions in length. Your oscilloscope CRT
screen should resemble Figure 2-1 (disregarding the vertical
aspect of the waveform).
7 divisions
The period or the amount of time to complete one cycle of the
waveform can now be determined. The TIME/DIV is set to
1mS/DIV and the cycle is 7 divisions in length, the period will be
the product of the two or 7mS.
The times 10 magnifier is not put into consideration in the case
Figure 2-1
with this example. This is because the horizontal X10 MAG
switch is not actuated in accordance with the oscilloscope default control settings.
Since frequency is the reciprocal of the period, ( f = 1 ) the frequency can now be
period
determined.
What is the frequency of this waveform? __________________
What would the frequency be if one cycle was 10 divisions in length? __________________
What would the frequency be if one cycle was 5 divisions in length? ___________________
5. Just as the frequency can be determined from the reciprocal of the period, the period can also
1
be determined from the reciprocal of the frequency ( period = f ).
For example, set the frequency to a 1-kHz signal. In order to accomplish this, we first need to
find the period. The reciprocal of 1000-Hz is 1mS. This means that it takes 1mS to complete
one full cycle of the waveform.
21
The easiest method to display this particular waveform would be
to divide the 1mS period by 10 since there are 10 horizontal
divisions on an oscilloscope. The TIME/DIV setting would then
be 0.1 mS/division and one complete cycle would be showing on
the oscilloscope screen stretching across all 10 divisions as
shown in Figure 2-2.
Unfortunately this is not so simple with every frequency value.
Take 60-Hz for example. The reciprocal of 60 equals a period of
16.67mS. Divide 16.67mS by ten since there are ten horizontal
divisions on the oscilloscope screen. Since a TIME/DIV setting
of 1.667mS does not exist, the next highest selection must be
used. In this case it would be the 2mS/division setting.
Figure 2-2
Since each horizontal division represents 2mS, the frequency of
the waveform would need to be adjusted so the length of one
complete cycle would stretch 8.33 divisions on the screen. The
waveform should look similar to Figure 3 (Disregarding the
vertical aspect of the waveform at this time).
6. Adjust the amplitude and VOLTS/DIV setting for a peak to peak
waveform of 6 vertical divisions. Use the COURSE FREQ and
Figure 2-3
FINE ADJUST controls to configure the horizontal length of each
waveform according to the period given in each example below. Draw each waveform, record
the frequency and indicate the TIME/DIV setting used.
You can move the waveform for easier reading by using the horizontal position control on the
oscilloscope.
Period = 2 mS
Period = 0.5 mS
Period = 8 mS
Frequency = _________
Frequency = _________
Frequency = _________
TIME/DIV = _________
TIME/DIV = _________
TIME/DIV = _________
7. Keep the peak to peak waveform set at 6 divisions. Adjust the waveform for the frequency
given. Draw each waveform and record the period.
Frequency = 200 Hz
Frequency = 1.6 kHz
Frequency = 400 Hz
Period = ____________
Period = ____________
Period = ____________
TIME/DIV = __________
TIME/DIV = __________
TIME/DIV = __________
22
The Oscilloscope
Instantaneous Voltage & RMS Values
Project Objectives:
•
•
To use an oscilloscope to measure the instantaneous and RMS voltage values of a sine wave
and verify through calculations.
To compare the accuracy of voltage measurement with an oscilloscope and a DMM with various
frequencies applied.
Items Needed:
- Elenco Electronics Trainer
- Digital multi-meter
- Oscilloscope
- Jumper Wires
NOTE: Before beginning this lab project, make sure the oscilloscope is set according to the default
switch and control settings found in the table on page 9 of this book.
Experiment 1 – Instantaneous Sine Wave Values
1. Connect the CH1 oscilloscope probe across the FREQ and GND terminals on the Elenco trainer
and set the WAVEFORM for a sine wave.
2. Set the CH1 VOLTS/DIV to 0.1V/DIV and make sure the
switch on the CH1 probe is set to X10.
3. Set the TIME/DIV to 0.1mS/DIV and adjust the frequency
to obtain a cycle length of 8 divisions.
What is the frequency of the waveform? ___________
4. Adjust the AMPLITUDE for a peak to peak waveform
stretching 8 vertical divisions. Draw the waveform in
Figure 3-1.
Figure 3-1
5. From the screen, measure the voltage at each 0.1 mS
interval and record “Measured Voltage” column in the
table below.
How many degrees does each 0.1mS division represent? ___________________
What is the peak voltage value of the waveform? _________________________
time (ms)
degree of rotation
Measured Voltage
Computed Voltage
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
6. Use the formula (E(INST) = E(PEAK) x SIN∠θ) to calculate the instantaneous voltage at every 0.1
mS division. Enter the calculated results into the table and verify each measurement.
23
7. Using a voltmeter set for AC volts, measure the output of the generator and compare the result
to the instantaneous voltage at 45 degrees.
Generator output = ____________________ VAC. Since voltmeters measure RMS values
and the SIN of 45 degrees is 0.707, measuring the waveform at 45 degrees on an oscilloscope
should be relatively close to the RMS or effective value of generator output.
Using this method to find the instantaneous voltage of a sine wave in 45 degree increments is
simple if the waveform cycle is exactly 8 horizontal divisions in length. Unfortunately not every
frequency can be set to an 8 division cycle.
8. Set the TIME/DIV to 0.5mS/DIV and change the frequency from
the generator to 200 Hz. Change the CH1 VOLTS/DIV to
0.2V/DIV and set the voltage to 12 VP-P. Sketch the waveform
as Figure 3-2.
A frequency of 200 Hz on the 0.5mS/DIV setting will result in a
waveform 10 divisions in length. In order to accurately
determine the instantaneous voltage values of a waveform in
increments of 45 degrees, the waveform will need to be 8
horizontal divisions in length. This can be done by using the
SWP.VAR. control in the horizontal section of the oscilloscope.
Figure 3-2
9. Depress the SWP. UNCAL button to unlock the variable sweep (SWP.VAR.) control and adjust
the variable sweep until the waveform is 8 divisions in length. If you are not sure of the location
of these controls on your oscilloscope, refer to the front panel controls diagram and description
on page 6.
Once you have a waveform measuring 6 VPEAK and stretching 8 divisions in length, use the
oscilloscope to measure the instantaneous voltage readings at every 45 degree increment and
record in the table below. Use the formula given in step 6 to calculate the instantaneous voltage
values and compare the results with the measured values.
time (ms)
degree of rotation
Measured Voltage
Computed Voltage
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
10. Release the SWP. UNCAL control!!!
Using the variable sweep control is very useful to measure instantaneous voltage values of a
sine wave but will distort the frequency and period of the waveform. It is recommended to lock
out the SWP.VAR control by releasing the SWP. UNCAL during normal measuring conditions.
Leaving the variable sweep control in an “un-calibrated” state may cause frequency and period
readings to be inaccurate.
The vertical sections also have a variable voltage control VAR. which is useful in dual-trace
mode for setting the peak voltage of two waveforms equal to easily observe phase relationships
between the two waveforms. Similar to the SWP.VAR, when used, the voltage aspect of the
waveform will be inaccurate. Therefore the VAR. control should be set clockwise to the CAL.
position when measuring voltage.
24
Experiment 2 – Voltmeter Response to Frequency
In the previous experiment an oscilloscope was used to determine the RMS value of a sine
wave’s voltage. One reason you might want to do this is convenience. If a signal is already
displayed on the screen, a reading can be taken without connecting a voltmeter.
A more fundamental reason for using an oscilloscope to measure RMS voltage has to do with
the frequency of the signal being measured. The frequency ranges on most digital meters are
very limited. For example, many DMMs can only measure to several kHz. Some of the higher
quality DMMs however, can measure to much higher frequencies.
Oscilloscopes can usually measure a much broader range of frequencies. Even inexpensive
oscilloscopes can usually measure waveforms in the tens of MHz while top of the line
instruments can measure in the hundreds of MHz even to the GHz range.
With this experiment we will compare the ability of the oscilloscope and digital multi-meter to
measure voltage at different frequencies.
1. Connect the CH1 probe across the FREQ output of the signal generator. Adjust the generator
to a 100-Hz sine wave with a 12-VP-P (6VPEAK) voltage.
2. Calculate the RMS voltage and record in the table below for each frequency.
3. Using the digital multi-meter, measure and record the RMS voltage of the waveform. Repeat for
the other frequencies indicated in the table.
Frequency
Peak Voltage
100 Hz
6 VPEAK
1000 Hz
6 VPEAK
10,000 Hz
6 VPEAK
15,000 Hz
6 VPEAK
20,000 Hz
6 VPEAK
50,000 Hz
6 VPEAK
100,000 Hz
6 VPEAK
Calculated RMS
DMM reading
What conclusions can you draw from this data?
________________________________________________________________
________________________________________________________________
________________________________________________________________
The Oscilloscope
Additional Input Modes & Operations
25
Project Objectives:
•
•
To practice using an oscilloscope to measure and compare two different waveforms at the same
time in dual trace mode.
To practice using an oscilloscope to add two input signals and measure ungrounded
components in a series circuit.
Items Needed:
- Elenco Electronics Trainer
- Digital multi-meter
- 1 µF Capacitor
- Oscilloscope
- Jumper wires
- Resistors
4.7kΩ, 10kΩ, 18kΩ, 27kΩ
Once again, before starting this lab project, be sure the oscilloscope is set according to the default
switch and control settings found in the table on page 9 of this book.
Experiment 1 – Dual Trace Mode
1. Align both CH1 and CH2 traces with the horizontal center grid line on the CRT screen. You can
switch to CH2 by selecting CH2 with the MODE switch.
2. Connect the circuit as shown in Figure 4-1. Use the left and center terminal on the 1kΩ variable
resistor located in the variable resistor section on the Elenco trainer. Turn the knob of the
variable resistor to the full counter-clockwise position.
VA
8-VP-P
2-kHz
R1
1kΩ
rheostat
R2
4.7kΩ
CH1
CH2
GND
Figure 4-1
3. Connect the CH1 probe across the function generator output and set the generator for a 8-VP-P,
2-kHz sine wave using the 50 µS/DIV horizontal time base setting.
4. Connect the CH2 probe tip between R1 and R2 and set the oscilloscope MODE switch to DUAL.
Make sure the CH2 VOLTS/DIV is set the same as CH1.
Both probe switches should also be set to X10.
The dual trace mode permits multiple waveforms to be
viewed at the same time. In this case, only one trace is
visible because R1 is currently set at minimum or zero
ohms, therefore no voltage drop exists across R1 and the
two probes are essentially measuring the same point.
5. Turn the knob for R1 to the full clockwise position and
sketch the waveforms as Figure 4-2. Label each
waveform as CH1 and CH2.
Since R1 and R2 are both resistive loads, their voltage
drops will always be in phase with each other. In other
words, the two waveforms will intersect the 0V
centerline of the screen at the same point.
Figure 4-2
26
Figure 4-3
6. Remove power from the power supply and replace R2 with a 1µF capacitor. Set the CH2 probe
to X1 and connect it across the capacitor. Apply power to the circuit. Sketch the waveforms as
Figure 4-3. Once again, label each waveform as CH1 and CH2.
As you will learn later in this course, resistive and capacitive loads “are out of phase”. This can
be determined because both waveforms do not intersect each other at the (0V) horizontal
centerline of the screen.
The amount of phase angle shift between two waveforms can be determined by the divisions
separating the two waveforms. For example, if the waveform cycle on the CH1 input stretches
the full 10 divisions and there are 360 angular degrees per cycle, then each division would
represent 36 angular degrees.
What is the phase shift (in degrees) between the two waveforms? ____________________
Experiment 2 – Differential Measurements
Considering Figure 4-4, suppose you want to measure the voltage
across R1 using an oscilloscope. At first, you might try connecting
the scope like a voltmeter by attaching the probe tip to point “a” and
the ground clip to point “b”. In most cases however, this will not
work. If the oscilloscope ground and the generator ground are not
isolated from each other, then R2 will be shorted by the ground clip
on the probe. If the leads are reversed so that the ground clip is at
point “a” and the probe tip is at point “b” then the entire source
output is shorted to ground. The best way to measure ungrounded
components in a circuit is by using differential measurements.
a
Source
R1
b
R2
c
Figure 4-4
Refer to Figure 4-5. CH1 measures the total source voltage from point “a” to ground at point “c”
while CH2 measures across R2 from point “b” to ground at point “c”. The oscilloscope has an
“ADD/INVERT” mode which permits a display of CH1 minus CH2. The result on the screen would
then be the signal voltage from point “a” to point “b” or VR1.
a
Source
R1
b
CH1
R2
CH2
GND
c
Figure 4-5
NOTE: The Elenco trainers used in this course have an internal ground which is isolated from the
line ground. Because of this, the ground clip on the oscilloscope probes will not short the circuit as
indicated above (as long as the oscilloscope is used in single channel mode). Most signal
generators and oscilloscope grounds will not be isolated. Using differential measurements is
therefore the preferred method for measuring ungrounded circuit
a
components.
1. Connect the circuit shown in Figure 4-6.
R1
2. Connect the CH1 probe tip to point “a” and connect the CH2 input
probe to point “b”. Clip the ground lead of both probes to the
circuit ground at point “c”. Make sure both probes are set to X10.
18kΩ
6-VP-P
1 kHz
b
R2
10kΩ
3. Set the source (CH1) to 6-VP-P with a 1-kHz frequency.
c
Figure 4-6
27
What is the peak voltage of CH1? _______________
What is the peak voltage of CH2? _______________
Since CH1 is measuring the full source voltage and CH2 is measuring the voltage drop across
R2, the voltage drop across R1 can be determined by subtracting the CH2 voltage value from the
CH1 value.
What is the calculated voltage drop across R1? _______________
4. Leave the circuit connected and set the MODE switch to “ADD”.
As you can see the ADD mode adds both CH1 and CH2 input signals. With both channels
added, the oscilloscope should be showing a sine wave with a peak voltage slightly over 4 volts.
The ADD mode is most often used with the CH2 INV switch. The CH2 INV switch inverts the
waveform on the CH2 input only. This allows for a differential measurement of CH1 minus CH2
and would be equivalent to the voltage drop across R1.
5. Press the CH2 INV switch and record the peak voltage of the waveform. Compare the result to
the calculated R1 voltage drop in step 3.
What is the measured voltage drop across R1? _______________
Differential measurements can also be used with larger circuits containing more than just two
voltage drops.
6. Add a 27kΩ resistor R3 in series with the circuit so your circuit
resembles Figure 4-7.
a
R1
18kΩ
7. Before applying power to the circuit, calculate and record the
“peak” voltage drops across the three resistances.
Peak V1 calculated = _______________
6-VP-P
1 kHz
R2
10kΩ
c
Peak V2 calculated = _______________
R3
27kΩ
Peak V3 calculated = _______________
8. Use the ADD mode with the CH2 INV switch to measure the
“peak” voltage drop across each resistor. Keep the ground clip for
both input probes attached to ground at point “d”.
b
d
Figure 4-7
Measure V1 by connecting the CH1 probe to point “a” and CH2 to point “b”.
Peak V1 measured = _______________
Measure V2 by connecting the CH1 probe to point “b” and CH2 to point “c”.
Peak V2 measured = _______________
Measure V3 by connecting the CH1 probe to point “c” and CH2 to point “d”.
Peak V3 measured = _______________
The Oscilloscope
Advanced Measurement Techniques
Project Objectives:
28
•
•
To practice using an oscilloscope to measure superimposed ac and dc voltages.
To practice using an oscilloscope to indirectly measure current using a current sensing resistor.
Items Needed:
- Elenco electronics Trainer
- Digital multi-meter
- Oscilloscope
- Jumper wires
- Resistors
100Ω, 1k, 3.3k, 4.7k, 10k, 18k
Make sure the oscilloscope is set according to the default switch and control settings.
Experiment 1 – Superimposed AC and DC
Thus far in this course the focus has been on using the “AC” position of the AC-DC-GND vertical
coupling switch. The “AC” position is best for keeping the display centered and showing only the
AC or time varying aspects of a signal. The AC setting however, blocks all DC information so there
is no way of knowing if the AC signal is superimposed with a DC voltage. In other words, if the
vertical coupling is set to AC rather than DC you will not know if there is a DC offset along with the
AC signal. The AC setting is mainly used for observing the frequency of signal or when observation
of only the AC portion of the circuit is required.
In order for the oscilloscope to “block out” the DC voltage, the AC setting places a capacitor in
series with the oscilloscope input. This can lead to possible distortions of the displayed waveform.
For example, observe a 20Hz waveform in both the AC and DC switch positions. What differences
do you see?__________________________________________________________
__________________________________________________________________
We will now experiment with the effect of superimposed AC and DC signals using the DC OFFSET
control found in the Function Generator section of the Elenco trainer.
1. Center the CH1 trace if necessary and establish a 2VP-P sine wave with a 1kHz frequency. Use
the 50mV/DIV setting and 0.1mS/DIV for the time base.
2. Set the vertical coupling (AC-DC-GND) to DC. Turn the DC OFFSET control on the generator
until the waveform is centered 2 divisions above the horizontal center line on the screen.
3. Use a DMM on its DC volts setting to measure the input to the oscilloscope and record the
value, then change the DMM to its AC volts setting and repeat the measurement.
DC input voltage = ________________
AC input voltage = ________________
Sketch the waveform as Figure 5-1 then change the
coupling to AC and sketch the waveform on the same
grid. Label each waveform as DC or AC coupling.
How did the vertical shift compare to the dc value
measured on the DMM? _____________________
______________________________________
______________________________________
______________________________________
Experiment 2 – Measuring Current with an
Oscilloscope
Figure 5-1
ILoad
ET
RLoad
29
Figure 5-2
If we consider Figure 5-2, the load current (ILoad) is determined by Ohm’s Law (ELoad / RLoad) where
“ELoad” is the RMS value of the source voltage and “ILoad” is the RMS value of the load current. An
oscilloscope can indirectly measure this load current by adding a current sensing resistor (RS) in series
with the circuit as shown in Figure 5-3. The voltage can then be measured across the sensing resistor
using an oscilloscope, converted to RMS, and then computed as ILoad = VS / RS. This method will be
fairly accurate as long as RS is very small compared to RLoad.
1. Using an ohmmeter, accurately measure and record the resistance of the 100-Ω sensing
resistor and the 4.7-kΩ RLoad.
Measured
RS =
ILoad
ET
RLoad
4.7kΩ
RS = 100Ω
CH1
CH2
GND
Figure 5-3
_________________
Measured RLoad = _________________
2. Connect the circuit in Figure 5-3. Use the CH1 probe to set the generator to a 6-VP-P, 100-Hz
sine wave.
3. Use the CH2 probe to measure the peak voltage across the sensing resistor. Convert the peak
voltage to RMS and record the value in the space below.
Measured VS = _________________ (RMS)
4. Use Ohm’s Law to determine the RMS value of the load current (ILoad = VS / RS)
Indirectly measured ILoad = _________________ (RMS)
5. Break the circuit and insert a DMM set for AC mA. Measure and record the circuit current.
Compare the result to the indirect method of measuring in step 4.
Reminder – When measuring current, ammeters must be connected in series so all the circuit
current flows through the meter.
Directly Measured ILoad = _________________ (RMS)
6. Replace the one resistor RLoad of Figure 5-3 with the entire
network of resistors in Figure 5-4. Repeat steps 1-5 using the
oscilloscope to indirectly measure ILoad and compare with the
direct measurement using the DMM.
1kΩ
18kΩ
10kΩ
Indirectly measured ILoad = _________________ (RMS)
Directly Measured ILoad = _________________ (RMS)
How do the results compare? _____________________
_________________________________________
3.3kΩ
4.7kΩ
Replaces only RLoad
Figure 5-4
_________________________________________
Diodes & Rectifiers
Forward and Reverse Bias Diode
30
Project Objectives:
•
To demonstrate how a forward and reverse bias diode can control the current of a dc circuit.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- 1k Ω resistor
-Diode 1amp
Experiment
1. Without applying power, measure the diode with a DMM set to the
diode test position (
). Connect the negative lead of the meter to
the cathode and the positive lead to the anode. With the meter
connected in this configuration you will be measuring the forward
voltage of the diode.
Anode
Cathode
Figure 6-1
Forward voltage of the diode: Vforward = ___________________ V.
2. Swap the meter leads connected to the diode so the negative lead is connected to the anode
and the positive lead is connected to the cathode. With this configuration you will be measuring
the reverse voltage of the diode.
Reverse voltage of the diode: Vreverse = ___________________ V.
When testing a good diode with the diode tester on a DMM, you should get a voltage reading of
approximately 0.6 – 0.75 V when connected to read the forward voltage of the diode. When
reading the reverse voltage, you should not get a
reading on the meter.
3. Connect the circuit in Figure 6-2 use the positive dc
variable supply on your Elenco trainer to apply 5 volts to
the circuit.
+
–
VA
R
1 kΩ
VR
The resistor is in the circuit to monitor current. Since this
Figure 6-2
is a 1kΩ resistor, the voltage drop across the resistor will
be approximately the same value of current in the circuit
measured in milliamperes. For example, if you measured 15 volts across the resistor, through
the use of Ohm’s Law the current in the circuit will then be 15mA. Use this method to determine
the circuit current by measuring VR with a DMM.
IT = ___________________ mA (approximately)
What is the voltage drop across the forward-biased diode? ___________________ V.
4. Remove power from the circuit and flip the diode around so the cathode will now be connected
to the positive side of the voltage source and the anode will be connected to the 1kΩ resistor.
5. Apply 5 volts to the circuit. Determine the circuit current using the same method as in step 3.
IT = ___________________ mA
What is the voltage drop across the reverse-biased diode? ___________________ V.
For the reverse-biased condition, is the diode acting like an open or a short? _____________
6. Remove power from the circuit and turn the diode around once more so that it is forward-biased.
Set VA in steps as indicated and record the current and diode voltage drop at each step.
VA = 0.25 V:
IT = ___________________ mA VD = ___________________ V
31
VA = 0.5 V:
IT = ___________________ mA VD = ___________________ V
VA = 1 V:
IT = ___________________ mA VD = ___________________ V
VA = 2 V:
IT = ___________________ mA VD = ___________________ V
VA = 4 V:
IT = ___________________ mA VD = ___________________ V
VA = 10 V:
IT = ___________________ mA VD = ___________________ V
Once the applied voltage reached a certain level of forward biasing, did the voltage drop across
the diode increase, decrease or stay about the same as compared to the change in the applied
voltage?
________________________________________________________________
This experiment verifies that a diode will conduct when current flows in one direction but not the
other. Will a diode conduct when the anode is positive or negative with respect to the cathode?
________________________________________________________________
What would happen if an AC current were applied to a diode?
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
Diodes & Rectifiers
Half-Wave Rectifiers
32
Project Objectives:
•
To demonstrate the characteristics of a half-wave rectifier and the effects of capacitor filtering.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Oscilloscope
- DMM
-10k Ω resistor
-Diode 1amp
- Capacitors
0.1 µF, 1 µF
Experiment
D1
1. Connect the circuit in Figure 7-1.
2. Set the function generator to a 100 Hz sine wave with a
peak voltage of 6 VAC.
AC
RL
10kΩ
DCoutput
What is the RMS input voltage? ________________
Sketch two complete cycles of the input waveform in the
space provided as Figure 7-2.
Figure 7-1
Which VOLTS/DIV setting was used?
_____________________________________
Which TIME/DIV setting was used?
_____________________________________
3. Using a DMM, measure the output in both AC and DC volts.
ACoutput = _________________________
DCoutput = _________________________
Figure 7-2
4. Connect the oscilloscope across RL. Sketch two complete cycles of the new waveform as
Figure 7-3 and record the peak voltage reading. Make sure the oscilloscope channel being
used is set for “DC” coupling (AC-DC-GND switch).
Vpeak = ________________________________
Why is the peak voltage of the rectified waveform slightly
less than the applied 6 V in step 2?
_____________________________________
_____________________________________
_____________________________________
_____________________________________
Figure 7-3
5. Make sure the function generator is set to a frequency of 100-Hz and an amplitude of 6 Vpeak.
Connect the 0.1 µF capacitor in parallel to the 10 kΩ resistor.
Using a DMM, measure the new DC output voltage.
DCoutput = _____________________
33
Sketch two complete cycles of the new waveform as
Figure 7-4 with the 0.1 µF capacitor added to the circuit.
Capacitors can be used in a variety of electronic
applications. In the case with this lab experiment a
capacitor is being used as an electronic filter to smooth
out the ripple from the DC output.
Figure 7-4
When the current reaches the peak in the dc output the
capacitor becomes fully charged. When the supply current
drops below the capacitor charge level, the capacitor will
begin to discharge. This helps smooth out the dc ripple.
Obviously different sized capacitors will act as better filters
than others.
What would happen if the capacitor currently in the circuit were replaced with a larger one?
________________________________________________________________
________________________________________________________________
6. Replace the 0.1 µF capacitor with a 1.0 µF capacitor.
Use a DMM to measure the new DC output voltage.
DCoutput = _____________________
Sketch two complete cycles of the new waveform as
Figure 7-5 with the 1.0 µF capacitor added to the circuit.
Was your prediction in step 5 proven by adding a larger
capacitor across the load? ___________________
List two advantages of adding a filter to a rectifier circuit.
_____________________________________
_____________________________________
Figure 7-5
_____________________________________
34
Diodes & Rectifiers
Full-Wave Bridge Rectifiers
Project Objectives:
•
To demonstrate the characteristics of a full-wave bridge rectifier and the effects of capacitor
filtering.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Oscilloscope
- DMM
-10k Ω resistor
-Diode 1amp (4)
- Capacitor, 1.0 µF (2)
Experiment
AC
D4
D3
D1
D2
R1
10 kΩ
DC out
CH1
CH2
GND
Figure 8-1
1. Connect the circuit in Figure 8-1.
2. Set the function generator to a 100 Hz sine wave with a peak
voltage of 6 VPEAK.
What is the RMS input voltage? ____________
Sketch two cycles of the input waveform as Figure 8-2.
Which VOLTS/DIV setting was used? ________________
Which TIME/DIV setting was used? _________________
3. Using a DMM, measure the DC output voltage.
Figure 8-2
DCoutput = ________________________
If you notice, the load (R1) is not connected to ground. In most cases this prevents an
oscilloscope to be used to measure directly across the load with a single input channel. This is
because the oscilloscope ground and the generator ground are usually tied together. A direct
measurement of the output would then essentially short out one of the diodes.
This can be overcome, however by using both input channels
on the oscilloscope and performing a differential
measurement.
4. Connect the oscilloscope as shown in Figure 8-1. Set the
vertical MODE switch to ADD and perform a differential
measurement between CH1 and CH2 by pressing the CH2
INV switch. Sketch two complete cycles of the waveform as
Figure 8-3 and record the peak voltage reading.
Vpeak = ________________________________
Figure 8-3
35
Why is the peak of the rectified waveform approximately 1.4 volts less than the peak of the
applied voltage instead of 0.7 volts as in half-wave rectifiers?
________________________________________________________________
________________________________________________________________
5. Connect two 1.0 µF capacitors in parallel to the 10 kΩ resistor. See Figure 8-4.
Using a DMM, measure the new DC output voltage.
AC
D4
D3
D1
D2
DCoutput = _____________________
R1
10 kΩ
C1
1 µF
C2
1 µF
DC out
Figure 8-4
In the space provided in Figure 8-5, sketch two complete
cycles of the new waveform with the 1.0 µF capacitors
added to the circuit.
As you can see, capacitor filtering will smooth the DC output
signal reducing or eliminating the ripple. The smoothed
output of the rectifier can then be used to power sensitive
electronic equipment whereas the non-filtered output is
unsuitable.
Figure 8-5
36
Inductance
Inductive Kick
Project Objective:
•
To measure the inductive “kick” voltage of an RL circuit using an oscilloscope.
Items Needed:
- Electronics Trainer
- Jumper Wires
- 1.5 H inductor (iron core)
- Oscilloscope
- DMM
- 1kΩ Resistor
In this lab project we will attempt to measure the inductive “kick” that results from interrupting
the current through an inductor.
Experiment
1. Measure the DC resistance of the 1.5-H inductor.
P
Rl measures ________________.
2. Construct Figure 9-1 and connect the oscilloscope
probe across R1. Apply 15Vdc to the circuit.
Rl
15V
R1
1kΩ
DC
The inductive kick that we want to measure will be
a negative voltage spike that last for only 1 - 2
milliseconds. In order to best read the spike with
the oscilloscope, it is recommended that the scope
time base and sweep be set so that the trace
slowly moves across the screen. 0.1 - 0.5 sec/division should be fine.
L
1.5H
Figure 9-1
3. Set the “VOLTS/DIV” on the scope to 5. Make sure the switch on the test probe is set to X10.
4. In order to measure the voltage spike, current needs to be abruptly removed from the circuit.
While watching the trace on the scope, disconnect the circuit at point “P” by removing a jumper
wire from the power supply to the breadboard RL circuit. You may need to do this several times
in order to get an accurate reading on the spike. The trace intensity can also be increased as
needed but only to the amount of brightness that is needed for reading the voltage spike.
Record the voltage of the spike below. Remember to multiply the scope reading by ten since
the X10 probe is being used.
Voltage spike measured = ________________.
The spike occurs because the instant the power is disconnected, the magnetic field collapses
which induces a voltage in the coil. This causes a great deal of energy to be released in a very
short amount of time.
U
s
i
n
g
IT
Rl
R1
DC
IT
+
I1
Figure 9-2A
IL
IT
DC
R1
IT
―
Rl
―
+
Figure 9-2B
Figure 9-2A shows a similar circuit in a steady state before the power is disconnected. Notice
the polarity of the inductor along with the current flow.
37
When the current flow to the inductor is interrupted as in Figure 9-2B, the magnetic field
collapses. This collapse causes a change in polarity of the inductor. The inductor will then
attempt to maintain the same current as when the circuit was in a steady state. This current will
pass through R1 for a very short length of time. The amplitude of the voltage spike will depend
on the ratio of resistance of R1 to Rl.
5. Use circuit analysis to calculate the current through the inductor before the power supply was
interrupted.
IL steady state current = ___________________.
6. Immediately after the current source is interrupted, the current must remain the same for a short
length of time through the remainder of the circuit. Using Ohm’s Law and the current calculated
in step 5, calculate the amplitude of the voltage spike at R1. Compare your result to the
measured voltage in step 4.
R1 voltage spike calculated = ___________________.
It is easy to see how by abruptly breaking the current through a large inductor such as motor or
coil, a voltage into the thousands of volts can be created. Even small inductances in electronic
systems can create enough voltage to cause problems if circuit protection devices are not used.
In most cases these voltage spikes are undesirable but they can be controlled through proper
circuit design. One example of a regular use of inductive kick is the ignition system on most
automobiles. Here, the primary winding of the ignition coil is interrupted at the appropriate time
by a control circuit to create the spark needed at each spark plug.
38
Inductance
Inductors in Series and Parallel
Project Objectives:
•
To demonstrate through circuit measurements that series and parallel connected inductances
are analyzed in the same manner as series and parallel connected resistances.
Items Needed:
- Electronics Trainer
- Jumper Wires
- DMM
- Oscilloscope
- 100 mH inductor (2)
- 100 Ω resistor
Experiment
In this exercise we will be recording the AC circuit current with a single inductor, then two inductors
in series, and finally two inductors in parallel. The effects of total inductance will be illustrated by
connecting two coils in series and in parallel.
1. Measure the resistance of the two 100-mH inductors that will be used in this project. Record the
results below.
Resistance of L1 = _________________.
Resistance of L2 = _________________.
2. Connect the circuit shown in Figure 10-1. Set the source
voltage to 8-VP-P and the frequency to 2-kHz.
What is the RMS value of the source voltage?
Source voltage = ___________________ RMS
3. If VA were DC, what would the current be through this
L1 = 100mH
VA
8-VP-P
2- kHz
R1
100Ω
circuit? _________________.
4. Measure the RMS voltage drop across R1 (V1) and calculate
the current.
V1 = _______________. IT = _______________.
Figure 10-1
Why is the current a lower value than if DC were applied?
________________________________________________________________
________________________________________________________________
5. Insert the second inductor (L2) in series with the circuit. Make sure the source is still set to 8-VPP, 2-kHz. Measure V1 and calculate the current.
V1 = _______________. IT = _______________.
Was the current higher or lower with two inductors in series? _______________.
We can conclude that inductors connected in series add similar to resistors connected in series.
6. Configure the circuit so L2 is in parallel with L1 and R1 is in series with the main current line.
Measure V1 and calculate the current.
V1 = _______________. IT = _______________.
Was the current higher or lower with two inductors in parallel? _______________.
We can conclude that inductors connected in parallel add like resistors connected in parallel.
39
Inductance
Relationship of XL to Inductance and Frequency
Project Objectives:
•
To verify the XL formula and the direct relationship of inductive reactance to both inductance and
frequency by measuring circuit parameter changes associated with the changes in inductance
and frequency.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope
- 100 mH inductor (2)
- Resistor 1-kΩ
Experiment
1. Connect the circuit shown in Figure 11-1.
2. Set the function generator to a frequency of 1-kHz and set
VA to 3-VRMS. Measure the voltage across the resistor (VR)
and the voltage across the inductor (VL).
VR = _______________
VL = _______________
L1
100mH
VA
3-VRMS
1-kHz
R1
1kΩ
3. Using the known values for the resistor, calculate the circuit
current and XL using Ohm’s Law. (XL = VL/I).
IT = _______________
XL = _______________
Figure 11-1
4. Now calculate XL using the XL formula. (XL = 2πfL). Compare the result to the Ohm’s Law
method in step 3.
XL = _______________________________
5. Insert a second 100-mH inductor (L2) in series with L1 and R1. Make sure the VA and frequency
remain the same. Measure VR, calculate IT, measure the voltage across the total inductance of
L1 and L2, then calculate XL total using Ohm’s Law.
VR = __________________
IT = __________________
VL = __________________
XL = __________________
What happened to XL when the value of inductance in the circuit was doubled? __________
________________________________________________________________
Is XL directly or inversely proportional to the amount of inductance? __________________
6. Remove L2 and configure the circuit to once again resemble Figure 11-1. Make sure the
source still measures 3-VRMS. Change the frequency to 2-kHz. Repeat the measurements and
calculations used in the previous steps.
VR = __________________
IT = __________________
VL = __________________
XL = __________________
Compare the result of XL in this step to the result of XL in steps 3 and 4. What happened to XL
when the frequency of the circuit was doubled? ________________________________
________________________________________________________________
Is XL directly or inversely proportional to frequency? _____________________________
40
Inductance
Relationships in Series RL Circuits
Project Objectives:
•
•
•
To observe key electrical relationships in a series RL circuit.
To demonstrate that simple DC analysis techniques cannot be used to determine AC circuit
parameters containing inductive reactance due to out-of-phase elements.
To determine the value of inductance in a series RL circuit.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope
- 100 mH inductor
- Resistor 1-kΩ
Experiment
1. Measure the resistance of the 1kΩ resistor.
R measured = ________________ Ω
L
100mH
2. Connect the circuit shown in Figure 12-1.
3. Set the function generator to a frequency of 2-kHz and set the
source to 12-VP-P. Measure the RMS values of VA, VR, and VL.
12-VP-P
2-kHz
VA = _____________________ RMS
R
1kΩ
VR = _____________________ RMS
VL = _____________________ RMS
Figure 12-1
Does VR plus VL equal the applied voltage? __________
Why? ___________________________________________________________
4. Use the following vector addition formula to find the sum of VR and VL. VT = VR2 + VL2
VT calculated = _______________.
All things considered, is this relatively close to the measured value of VA? __________
5. Calculate the following: IT from (VR / R); XL from (VL / IT); and Z from (VT / IT).
IT = ________________
XL = ________________ Z = ________________
Does Z equal the arithmetic sum of R and XL? ________. We may conclude that since VA is
not equal to VR + VL and Z is not equal to R + XL, these values must be the result of two vectors
out of phase.
6. Use the vector formula (Pythagorean Theorem) to
calculate Z and compare the result to the calculated Z
in step 4. Add the measured resistance of L to R
before making the calculation.
Z calculated = _____________________
7. In the space provided to the right, draw a vector
diagram using the voltage values measured in step 2.
8. Use the vector diagram along with trigonometry to
determine the phase angle.
∠θ = ______________________________
41
9. Use a dual-trace oscilloscope to perform a phase comparison of VA and IT. Since the circuit
current is in phase with the resistor voltage, the resistor voltage can be used to represent the
circuit current. Connect CH2 of the oscilloscope across the resistor and CH1 across VA as
shown in Figure 12-2.
Set the source to CH1 and mode to “Dual Trace”. Measure the phase difference between the
two traces. Remember, a complete cycle is 360 degrees.
VA
4-VRMS
2-kHz
L
100mH
R
1kΩ
CH1
CH2
GND
Figure 12-2
∠θ measured = _________________________
Does this oscilloscope phase measurement reasonably
agree with the calculated phase angle
performed in step 7? ______________________
10. Draw both of the waveforms you see in the dual-trace
mode as Figure 12-3. Label each waveform (IT and VA).
According to your results, does the IL lead or lag VL?
____________________________________
Figure 12-3
When the value of inductive reactance and the frequency of the circuit are known, the value of
inductance in the circuit can be determined by using the following formula: L =
XL
2π f
11. Determine the circuit inductance using the calculated XL value in step 5. Compare the result to
the marked inductance rating on the component.
L = ______________________.
This method of determining inductance in a circuit can be extremely useful. If the frequency in
a circuit is known, a simple current measurement and an inductor voltage drop measurement is
all the information required to determine the value of inductance in the circuit.
42
Inductance
Relationships in Parallel RL Circuits
Project Objectives:
•
•
To observe key electrical relationships in parallel RL circuits.
To demonstrate that simple DC analysis techniques cannot be used to determine AC circuit
parameters containing inductive reactance due to out-of-phase elements.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope (Dual Trace)
- 100 mH inductor
- Resistors, 1kΩ
Experiment
1. Connect the circuit in Figure 13-1.
2. Set the function generator to a frequency of 2-kHz and
the source voltage to 12-VP-P. Measure the following
RMS voltages.
VA
4-VRMS
2kHz
VA = ________________________ RMS
VR = ________________________ RMS
R
1kΩ
L
100mH
VL = ________________________ RMS
The voltage across each component should be the
Figure 13-1
same and equal to VA. This verifies that the voltage
across the resistor is in phase with the voltage across the inductor in a parallel RL circuit.
3. Measure the total current and each individual branch current. Record your results below.
NOTE: Remember to break the circuit and insert the ammeter in series with the component(s)
to be measured. Also, check to make sure the meter lead is plugged into the mA port and the
function is set for AAC.
IT = _________________ IR = _________________ IL = _________________
Does the total current equal the arithmetic sum of the branch currents? _______________
Why? ___________________________________________________________
_______________________________________________________________
Use vector addition to find the sum of IR and IL. ( IT =
IR2 + IL2 )
IT calculated = ______________. Is this relatively
close to the measured IT? ______________
4. In the space provided, draw a vector diagram using the
current values measured in step 3.
Use the vector diagram along with trigonometry to
determine the phase angle.
∠θ = ___________________________________
5. Find Z by (VA / IT) and XL by (VL / IL).
Z = ________________ XL = _______________
43
If we were to calculate Z by the known values of R and XL, could we use the exact same
method(s) as calculating total parallel resistances in a DC circuit? ____________________
Explain your answer: _________________________________________________
________________________________________________________________
________________________________________________________________
6. Determine the value of inductance in the circuit by using the following formula:
XL
L = 2π f
Compare the calculated value to the 100mH rating of the component.
Calculated inductor value = ___________________
44
Capacitance
RC Time Constants
Project Objectives:
•
•
To demonstrate the charging and discharging characteristics of a capacitor.
To observe that a capacitor takes five time constants to change from one set voltage to another.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Capacitor 47 µF (non-polarized)
- Resistors, 680kΩ, 1kΩ
- Stopwatch
Experiment 1 – Charging Characteristics
1. Construct the circuit shown in Figure 14-1. Use the variable
DC power supply as the source but make sure no power is
applied to the circuit at this point.
47 µF
2. Take a DC voltage reading across the capacitor to make
sure it is fully discharged. If a voltage reading is present,
connect a 1kΩ resistor in parallel to the resistor until the
meter reads 0 volts.
680 kΩ
3. Making sure there is an open connection between points A
and B, set the applied voltage to 20 VDC.
A
B
Figure 14-1
4. Connect the voltmeter across the 680kΩ resistor and set the meter to the 20 VDC range.
5. Close the open connection between points A and B and immediately begin recording the
voltage in 5 second increments for the first 20 seconds, 10 second increments until 1 minute
and then 20 second increments until 3 minutes have passed. Record your results in the
“Resistor Voltage” row of the table below.
In order to find the charge voltage of the capacitor, the resistor voltage needs to be subtracted
from the applied 20 volts. Record these calculations in the row labeled “Capacitor Voltage”.
Time
0.05
0.10
0.15
0.20
0.30
0.40
0.50
1.00
1.20
1.40
2.00
2.20
2.40
3.00
Resistor
Voltage
Capacitor
Voltage
6. Use the measured capacitor voltage values and plot them on Graph G1 on the following page.
Use a straight edge to connect the measurement points.
Is this graph linear or exponential? _______________________________
The charging current eventually charged the capacitor to a voltage equal to (VA, VR) _______.
Was the current maximum at the beginning or end of the charge time? _________________
At the first instant of charge time, the voltage across the resistor was equal to (VA, VC) ______.
At the end of the charge time, the voltage across the resistor was ______ volts. The voltage
across the capacitor is equal to VA.
45
46
7. The time that a capacitor needs to charge can be divided into 5 time constants. During each
time constant the voltage increases by 63.2% of the maximum remaining voltage. For example,
if the applied voltage were 100V, the voltage after the first time constant would be 63.2% of
100V or 63.2V. The second time constant would be 63.2% of the remaining voltage. To find the
remaining voltage we need to subtract the voltage after the first time constant from the applied
voltage. 100V – 63.2V = 36.8V. The remaining 36.8V then needs to be multiplied by 63.2%.
36.8V x .632 = 23.26V. We then add the 23.26V to the voltage after the first time constant.
63.2V + 23.26V = 86.46V. The voltage after the second time constant would be 86.46V. The
remaining 3 time constants can then be calculated using the same method.
Using the previous example above as a reference, calculate the voltage after each time
constant. Use 20 volts for your applied voltage.
VCALC after Time Constant 1 = ___________________
VCALC after Time Constant 2 = ___________________
VCALC after Time Constant 3 = ___________________
VCALC after Time Constant 4 = ___________________
VCALC after Time Constant 5 = ___________________
8. To calculate the length of time for one time constant we need to use the formula (t = R x C)
t = time for one time constant in seconds
R = resistance in ohms
C = capacitance in farads
What is the length of each time constant in this circuit? __________________________
9. Using your calculation for the time constant length, mark the location of each time constant on
the graph you created in step 6.
10. Record the approximate voltage after each time constant according to the graph.
VMEAS after Time Constant 1 = ___________________
VMEAS after Time Constant 2 = ___________________
VMEAS after Time Constant 3 = ___________________
VMEAS after Time Constant 4 = ___________________
VMEAS after Time Constant 5 = ___________________
Do these numbers coincide with the calculations in step 7. ________________________
List 3 reasons why the measured values may not perfectly match the calculated values.
1. ______________________________________________________________
2. ______________________________________________________________
3. ______________________________________________________________
47
Experiment 2 – Discharging Characteristics
1. Turn the power supply off and disconnect all wires from the
power supply to the circuit components. Connect a
voltmeter across the 680 kΩ resistor and set the range for
20 VDC.
2. Insert a jumper wire across the same connection points the
power supply was connected in Experiment 1 and
immediately begin recording the voltage in 5 second
increments for the first 20 seconds, 10 second increments
until 1 minute and then 20 second increments until 3
minutes have passed. Record your results in the
“Capacitor Discharge Voltage” row of the table below.
Time
0.05
0.10
0.15
0.20
0.30
0.40
0.50
1.00
1.20
47 µF
jumper wire
680 kΩ
Figure 14-2
1.40
2.00
2.20
2.40
3.00
Capacitor
Discharge
Voltage
3. Use the measured capacitor discharge voltage values and plot them on Graph G2 on the next
page. Use a straight edge to connect the measurement points.
Is this graph linear or exponential? _______________________________
Did the capacitor take the same time to discharge through the resistor as it did to charge?
____________. At the end of the discharge time VC = __________; VR = __________.
48
49
Capacitance
Capacitance in Series and Parallel
Project Objectives:
•
To demonstrate that capacitors in series add similar to resistances in parallel and capacitors in
parallel add similar to resistances in series.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Capacitors 2 - 1.0 µF
- Resistors 10MΩ, 1kΩ
- Stopwatch
Experiment
1. Construct the circuit shown in Figure 15-1. Use the
variable DC power supply as the source but make sure
no power is applied to the circuit at this point.
C1
1 µF
2. Make sure an open connection exists between points
a and b. Verify the capacitor is fully discharged by
touching the capacitor leads across a 1kΩ resistor. Set
the applied voltage to 20-VDC.
3. Set the voltmeter for the 20-VDC range and connect it
across the resistor as shown in Figure 15-1.
R
10MΩ
a
b
V
Figure 15-1
4. At the same time, close the circuit between points A & B and use a stopwatch to begin timing
the length of capacitor charge time. Stop timing when the resistor voltage reaches 100mV.
Make three different attempts at timing the capacitor charge time. Make sure the power supply
is disconnected and the capacitor is discharged through the 1kΩ resistor between each attempt.
After recording the time for all three attempts, record the average charge time of the capacitor.
NOTE: All three attempts should be within several seconds of each other. If one of the
readings is too far off, omit it when calculating the average.
Charge time attempt #1 = ______________ seconds.
Charge time attempt #2 = ______________ seconds.
Charge time attempt #3 = ______________ seconds.
Average charge time = ________________ seconds
5. Disconnect the power supply from the circuit. Completely
discharge the capacitor through the 1kΩ resistor. Insert a
second 1.0 µF capacitor (C2) in series with C1 as shown
in Figure 15-2. Repeat step 4.
C1
1 µF
C2
1 µF
Charge time attempt #1 = ______________ seconds.
R
10MΩ
Charge time attempt #2 = ______________ seconds.
Charge time attempt #3 = ______________ seconds.
Average charge time = ________________ seconds
a
V
b
Figure 15-2
Did the capacitor charge time increase or decrease from the result in step 4? _____________
When multiple capacitors are connected in series, an effect occurs that is similar to increasing
the distance between the plates of a single capacitor.
50
This causes the total circuit capacitance to (increase, decrease) _____________________
Since the new RC time is approximately (double, half) __________________ the length of
time as with a single capacitor and the resistance has not changed, it can be concluded that the
new total capacitance is ____________ µF. Our observations conclude that capacitors in
series add similar to resistors in ______________________.
6. Disconnect the power supply from the circuit.
Completely discharge the capacitors through the 1kΩ
resistor. Remove C2 and connect it in parallel with C1.
Configure the circuit so the 10MΩ resistor is connected
in series with the two parallel capacitors as shown in
Figure 15-3. Once again, repeat step 4.
C2
1 µF
C1
1 µF
R
10MΩ
Charge time attempt #1 = ______________ seconds.
V
Charge time attempt #2 = ______________ seconds.
Charge time attempt #3 = ______________ seconds.
a
b
Figure 15-3
Average charge time = ________________ seconds
The charge time is now approximately (double, half) __________________ the time
recorded in step 4.
When capacitors are connected in parallel, an effect of increasing the plate area of a single
capacitor occurs.
This causes the total circuit capacitance to (increase, decrease) _____________________
The total capacitance of C1 and C2 in parallel is (double, half) __________________ the
capacitance of C1 alone and the new value of capacitance in the circuit would be _______ µF.
In conclusion, capacitors in parallel add like resistors in __________________.
51
Capacitance
Relationship of XC to Capacitance and Frequency
Project Objectives:
•
To verify the XC formula and the inverse relationship of capacitive reactance to both capacitance
and frequency by measuring the circuit parameter changes associated with the changes in
capacitance and frequency.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope
- Resistor 18 kΩ
- Capacitors 0.1µF, 1.0 µF
Experiment
1. Measure and record the resistance value of the 18kΩ resistor.
R measured = _______________________
2. Connect the circuit shown in Figure 16-1
3. Set the function generator to a frequency of 100-Hz and
set VA to 12-VP-P. Measure the RMS source voltage, the
voltage across the resistor (VR) and the voltage across
the capacitor (VC).
C
0.1µF
VA
12-VP-P
100 Hz
R
18 kΩ
VA = __________________________ RMS
VR = __________________________ RMS
Figure 16-1
VC = __________________________ RMS
4. Calculate the circuit current using the known values of R.
Calculate XC using Ohm’s Law (XC = VC / I).
IT = ___________________ XC = ___________________
5. Calculate XC by using the XC formula.
Compare to the value of XC in step 3.
XC = ______________________________
6. Change C to a 1.0 µF capacitor and find the values as in steps 2 and 3.
VR = __________________________ RMS
VC = __________________________ RMS
IT = ___________________ XC = ___________________
Calculate XC using the XC formula as in step 4.
XC = __________________________
What happened to XC when the value of capacitance was increased? ________________
_______________________________________________________________
The value of capacitance increased by approximately ten times. The XC of the 1.0 µF capacitor
was approximately (ten times, one-tenth) ________________ the XC of the 0.1 µF
capacitor. Is XC directly or inversely proportional to capacitance? ___________________
52
7. Keep the 1.0-µF capacitor in the circuit and the source set at 12-VP-P. Change the frequency to
200-Hz. Repeat the measurements and calculations used in the previous steps.
VR = __________________________ RMS
VC = __________________________ RMS
IT = ___________________ XC = ___________________
Calculate XC using the XC formula as in step 6.
XC = __________________________
Is the XC with 200-Hz approximately double or half the value it was with the 100-Hz applied in
step 4? _________________________________________________________
8. Keep the frequency set at 200-Hz and change C back to a 0.1-µF capacitor. Repeat the
measurements and calculations used in the previous steps.
VR = __________________________ RMS
VC = __________________________ RMS
IT = ___________________ XC = ___________________
Calculate XC using the XC formula as in step 6.
XC = __________________________
Is the XC of the 0.1-µF capacitor at 200-Hz about one-half that at 100-Hz in step 4? _______
Is XC directly or inversely proportional to frequency? ____________________________
List two reasons why the XC calculated using Ohm’s Law and the XC calculated using the
capacitive reactance formula may be slightly different.
1. _____________________________________________________________
_____________________________________________________________
2. _____________________________________________________________
_____________________________________________________________
53
Capacitance
Relationships in Series RC Circuits
Project Objectives:
•
•
•
To observe key electrical relationships in a series RC circuit.
To demonstrate that simple DC analysis techniques cannot be used to determine AC circuit
parameters containing capacitive reactance due to out-of-phase elements.
To determine the value of capacitance in a series RC circuit.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope (Dual Trace)
- Resistor 18 kΩ
- Capacitor 0.1µF
Experiment
1. Measure the resistance of the 18kΩ resistor.
R measured = ________________ Ω
2. Connect the circuit shown in Figure 17-1.
3. Set the generator to voltage 12VP-P and the frequency to 100Hz. Measure the RMS values of VA, VR and VC.
VA = _____________________ RMS
12-VP-P
100 Hz
VR = _____________________ RMS
R
18 kΩ
VC = _____________________ RMS
Does the sum of VR and VC equal VA? ______________.
C
0.1 µF
Figure 17-1
This is because VR and VC are not in phase with each other. Arithmetic addition cannot be
used. Vector addition must be used instead to add the two phases together.
4. Use the following vector addition formula to find the sum of VR and VC VT = VR2 + VC2
VT calculated = _______________. Is this reasonably close to the value of VA in step 2 all
factors considered? ________
5. Calculate the following: IT from (VR / R); XC from (VC / IT); and Z from (VT / IT).
IT = ________________ XC = ________________ Z = ________________
Does Z equal the arithmetic sum of R and XC? ________. We may conclude that since VA is
not equal to VR + VC and Z is not equal to R + XC, these
values must be the result of two vectors out of phase.
6. Use the vector formula (Pythagorean Theorem) to calculate
Z. Compare the result to the calculated Z in step 4.
Z calculated = ________________________
7. In the space provided to the right, draw a vector diagram
using the voltages from step 2.
8. Use the vector diagram along with trigonometry to
determine the phase angle.
∠θ = _______________________________
54
9. Use a dual-trace oscilloscope to perform a phase comparison of VA and circuit current. Since
the circuit current is in phase with the resistor voltage, the resistor voltage can be used to
represent the circuit current. Connect CH2 of the oscilloscope across the resistor and CH1
across VA as shown in Figure 17-2.
Set the source to CH1 and mode to “Dual Trace”. Measure the phase difference between the
two traces.
VA
12-VP-P
100 Hz
C
0.1µF
R
18 kΩ
CH1
CH2
GND
Figure 17-2
∠θ measured = _________________________
Does this oscilloscope phase measurement reasonably agree with the calculated phase angle
performed in step 7? _______________________
10. Draw both of the waveforms you see in the dual-trace
mode as Figure 17-3. Label each waveform (IT and VA).
As you may recall, the circuit current is being
represented by the voltage across the resistor.
According to your results, does the IC lead or lag
VC? ______________________________
When the value of capacitive reactance and the
frequency are known, the value of capacitance
1
in the circuit can be determined using the following formula: C = 2π f X
C
Figure 17-3
11. Determine the circuit capacitance using the calculated XC in step 4. Compare the result to the
specified capacitance rating of the component.
C = ____________________________
Just as the inductance in a circuit can be determined by performing a few simple measurements
and calculations, the capacitance in a circuit can be determined in a similar way. The circuit
frequency, current, and capacitor voltage drop are all the information required to determine the
circuit capacitance.
55
Capacitance
Relationships in Parallel RC Circuits
Project Objectives:
•
•
To observe key electrical relationships in a parallel RC circuit.
To demonstrate that simple DC analysis techniques cannot be used to determine AC circuit
parameters containing capacitive reactance due to out-of-phase elements.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope (Dual Trace)
- Resistor - 1kΩ
- Capacitor 0.1µF
Experiment
1. Connect the circuit in Figure 18-1.
2. Set the function generator to a frequency of 1-kHz and
the source voltage to 8-VP-P. Measure the following
RMS voltages.
8-VP-P
1-kHz
VA = ________________________ RMS
R2
1kΩ
C
0.1µF
VR = ________________________ RMS
VC = ________________________ RMS
Figure 18-1
Does VR equal VC? ______________________
Is VR in phase or out of phase with VC?_____________________________________
3. Measure and record the total circuit current and the current through each parallel branch.
Remember to break the circuit and insert the meter in series with the component(s) being
measured.
IT = _________________ IR = _________________ IC = _________________
Does the total current equal the arithmetic sum of the branch currents? _______________
Why? ___________________________________________________________
_______________________________________________________________
Use vector addition to find the sum of IR and IC. ( IT =
IR2 + IC
)
IT calculated = ______________. Is this close to the
measured value in step 3? ___________________
4. In the space provided to the right, draw a vector diagram
using the current values obtained in step 3.
Use the vector diagram along with trigonometry to
determine the phase angle.
∠θ = ___________________________________
If the frequency was decreased, would ∠θ increase,
decrease, or stay the same? ___________________
56
5. Find Z by (VA / IT) and XC by (VC / IC).
Z = ________________________ XC = _______________________
If we were to calculate Z by the known values of R and XC, could we use the same
method(s) as calculating total parallel resistances in a DC circuit? ____________________
Explain your answer: _________________________________________________
________________________________________________________________
________________________________________________________________
6. In order to calculate Z in a resistive/reactive parallel circuit we need to use a formula that
employs a combination of the Pythagorean Theorem and the reciprocal formula for calculating
parallel resistances. The formula shown below can be used.
Z =
1
( )+( )
1
R
2
1
XC
2
Using the formula above, calculate Z from R and XC. Compare to the value of Z in step 5.
Z calculated = _____________________.
1
7. Determine the value of capacitance in the circuit by using the following formula: C = 2π f X
C
Compare the calculated value to the 0.1µF rating of the capacitor.
Calculated capacitor value = ___________________
57
Series Resonance
Relationships of XL and XC to Frequency
Project Objectives:
•
To verify the direct and inverse relationships of XL and XC to frequency when the frequency of
the applied signal is changed.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope
- 100 mH inductor
- 100 Ω Resistor
- 0.1 µF Capacitor
Experiment
1. Connect the circuit in Figure 19-1.
2. Set the source voltage to 8-VP-P and the frequency to 1-kHz.
Measure the RMS values of VA, VR, VL and VC. Calculate IT
using the measured values of R. Calculate XL and XC using
Ohm’s Law.
VA = _______________
VR = _______________
VL = _______________
VC = _______________
IT = _______________
XL = _______________
XC = _______________
C
0.1µF
8-VP-P
1-kHz
L
100mH
R
100Ω
Figure 19-1
3. Change the frequency to 2-kHz. Reset the source to 8-VP-P. Once again, measure the RMS
values of VA, VR, VL and VC and calculate IT, XL and XC.
VA = _______________
VR = _______________
VL = _______________
VC = _______________
IT = _______________
XL = _______________
XC = _______________
When the frequency was doubled, XL (doubled, halved, stayed the same) _______________
and XC (doubled, halved, stayed the same) ___________________________________
Is XL directly or inversely proportional to frequency? _____________________________
Is XC directly or inversely proportional to frequency? _____________________________
When an AC circuit contains both inductance and capacitance, a frequency must exist where XL
and XC become resonant and completely cancel each other out. In this circuit would the
resonant frequency be higher or lower than the 2-kHz setting? ______________________
58
Series Resonance
Circuit Characteristics When XL is equal to XC
Project Objectives:
•
•
To demonstrate the effects of a circuit set at a frequency where XL = XC.
To show the resistive effects of a series RLC circuit at resonance.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope
- 100 mH inductor
- 100 Ω Resistor
- 0.1 µF Capacitor
NOTE: The function generator on the Elenco trainer has a large amount of internal impedance as
compared to the resonant impedance of the circuit in this project. This internal impedance acts as
an un-measurable voltage divider in the circuit and may slightly distort the waveform or cause the
source voltage to appear to change as the frequency is adjusted closer to resonance. This change
in source voltage will not affect the outcome of the lab project.
Experiment
1. Connect the circuit in Figure 20-1. Set VA at 8-VP-P, 1.2 kHz.
2. Connect the voltmeter to measure VR and slowly adjust the
frequency from the signal generator until VR is at its highest
value. Measure and record VR, VL and VC. Calculate IT from
the measured values of R then calculate XL and XC.
VR = ________________ IT = ________________
L
100mH
8-VP-P
1.2 kHz
VL = ________________ XL = ________________
R
100Ω
VC = ________________ XC = ________________
What is the approximate frequency of the altered sine wave?
C
0.1µF
Figure 20-1
Approximate frequency = _______________________
Since the voltage across the inductor (leads, lags) _____________ the current by
approximately 90 degrees and the voltage across the capacitor (leads, lags) _____________
the current by about 90 degrees, then VL and VC are close to 180 degrees out of phase with
each other. Since the current is the same throughout a series circuit we can conclude that XL
and XC are vectorally opposite and are equal at a resonant frequency. This means that they
cancel out each other’s effects on total impedance.
Assuming XL and XC are perfectly equal and opposite, would the circuit current be in phase with
the applied voltage? ______________
3. Change the frequency to 2 kHz. Measure VL and VC and determine whether the circuit is acting
more inductive or capacitive.
VL = ___________________ VC = ___________________
Is the circuit now acting like an RL or RC circuit? _____________
IT now (leads, lags) _____________ VA by an angle between 0 and 90 degrees; thus the
circuit is (inductive, capacitive) _________________________
59
4. Now change the frequency to 1 kHz. Measure VL and VC and determine whether the circuit is
acting more inductive or capacitive.
VL = ___________________ VC = ___________________
Is the circuit now acting like an RL or RC circuit? _____________
IT now (leads, lags) _____________ VA by an angle between 0 and 90 degrees; thus the
circuit is (inductive, capacitive) _________________________
We may conclude that at a resonant frequency where XL = XC, the series circuit essentially
acts as a pure ________________________ circuit.
At frequencies above resonance, a series RLC circuit will act as a(n) _____________ circuit.
At frequencies below resonance, a series RLC circuit will act as a(n) _____________ circuit.
At a resonant frequency, is Z higher or lower than it would be at any other frequency? Why?
________________________________________________________________
________________________________________________________________
60
Series Resonance
Bandwidth Related to Q
Project Objectives:
•
•
To determine the bandwidth of a series RLC circuit.
To verify that the bandwidth is narrower with higher quality circuit components and wider with
lower quality circuit components.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope
- Inductors, 1.5H, 100mH
- Resistors, 100Ω, 1kΩ
- 0.1 µF Capacitor
Experiment 1
1. Set the generator to an RMS voltage of 3-V and the frequency
to 500-Hz. Make sure no load is connected when setting the
source voltage.
L
1.5 H
2. Connect the circuit in Figure 21-1.
3-VRMS
500-Hz
3. Measure across VR and set the frequency for resonance
(maximum VR). Measure VL, and VC. Calculate IT at resonance
using the measured values of R.
VR = _________________
C
0.1 µF
R
100 Ω
IT = _________________
VL = _________________ VC = _________________
Figure 21-1
Measure the frequency at resonance. Remember, frequency is
the reciprocal of the period.
Approximate frequency = _________________________
The total circuit Q can be determined by the following formula: Q =
VL
VA
What is the approximate Q of this circuit? (Use the “no load” 3-VRMS for VA) ______________
fR
Use the following formula to calculate bandwidth: Bandwidth =
Q
Bandwidth = ________________________
If the current decreased to 70.7% of IMAX what would be the approximate value of the current?
_______________________. What would VR equal? ________________________
Bandwidth in a series resonant circuit is defined as the difference between the two frequencies,
one above and one below resonance at which the circuit current is 70.7% of the maximum
current which occurs at resonance.
4. Adjust the frequency above resonance where VR equals 70.7% of maximum VR. Record this
frequency then adjust the frequency below resonance until VR once again equals 70.7% of
maximum VR. Record this frequency and then determine the measured bandwidth from the
difference of the two frequencies recorded.
f above resonance where VR is at 70.7% = ___________________________________
f below resonance where VR is at 70.7% = ___________________________________
Measured Bandwidth = ________________________________________________
This measured bandwidth should resonably compare with the calculated bandwidth in step 3.
61
5. Change the 100Ω resistor to a 1kΩ resistor and repeat the steps above.
VR = ____________________
IT = ____________________
VL = ____________________ VC = ____________________
Resonant frequency = _________________________________
Q = ______________ Calculated Bandwidth = ______________
f above resonance where VR is at 70.7% = ____________________
f below resonance where VR is at 70.7% = ____________________
Measured Bandwidth = ________________________________
What happens to the Q of a circuit when the resistance becomes larger?
________________________________________________________________
________________________________________________________________
What happens to the bandwidth of a circuit when the Q becomes larger?
________________________________________________________________
________________________________________________________________
62
Experiment 2
1. Connect the circuit shown in Figure 21-2. Set the “open
circuit” source for an RMS value of 3-V and the frequency to
1-kHz. Make a “frequency run” to enable graphing the circuit
current versus frequency. Measure and record VR in
increments of 100-Hz starting at 1-kHz and ending at 2.5-kHz.
Calculate the circuit current for each increment by (VR / R) and
record in the table below.
2. Use the current values from the table to create a graph on the
following page. Label the following points on the graph: (1)
The approximate resonant frequency, (2) the circuit’s
bandwidth points which are 0.707 x current value at
resonance.
Frequency
VR
L
100 mH
3-VRMS
1-kHz
C
0.1 µF
R
100 Ω
Figure 21-2
IT
1.0 kHz
1.1 kHz
1.2 kHz
1.3 kHz
1.4 kHz
1.5 kHz
1.6 kHz
1.7 kHz
1.8 kHz
1.9 kHz
2.0 kHz
2.1 kHz
2.2 kHz
2.3 kHz
2.4 kHz
2.5 kHz
63
Bandwidth, IT versus Frequency
6.0
5.0
Current in mA
4.0
3.0
2.0
1.0
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
Frequency in kHz
64
Parallel Resonance
Circuit Characteristics When XL is equal to XC
Project Objectives:
•
•
To demonstrate the effects of a parallel RLC circuit when set at a frequency where XL = XC.
To show the resistive effects of a parallel RLC circuit at resonance.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope
- 100 mH inductor
- 0.1 µF Capacitor
- Resistors 100 Ω (2), 1 kΩ
Experiment
A
1. Set the “no-load” generator source to 5-VRMS and the
frequency to 1-kHz.
2. Connect the circuit in Figure 22-1
3. Connect a voltmeter across R1 and adjust the circuit
frequency until the voltage across R1 is minimum.
Record VR1 and measure the frequency.
VR1 = _______________________________
frequency = __________________________
4. Measure and record the voltage from point A to point
B (VA-B). Calculate IT from VR1. Measure VR2 and
calculate IC. Measure VR3 and Calculate IL.
L
100 mH
C
0.1 µF
R3
100 Ω
R2
100 Ω
R1
1 kΩ
B
Figure 22-1
VA-B = ________________________
IT = _________________________
VR2 = ________________________
IC = _________________________
VR3 = ________________________
IL = _________________________
With V1 set to the minimum voltage, are IC and IL close to being equal? ________________
In theory, due to the canceling effects of the capacitive and inductive currents in a parallel
resonant circuit, the total circuit current should be equal to zero and the total circuit impedance
should be infinitely high. In practical circuits, however, impedance (Z) is maximum at resonance
XL
and circuit current (IT) is therefore minimum. This is due to the quality (Q) of the circuit. Q =
R
5. Calculate the impedance of only the parallel portion of the circuit using the IT and VA-B values
from step 4.
Z = _________________________
Use the XC formula to find the XC of the capacitor at the resonant frequency.
XC =
1
2πfC
XC = _________________________
Use the XL formula to find the XL of the capacitor at the resonant frequency.
XL = 2πfL
XL = _________________________
Notice that Z is greater than either branch’s opposition to current. This differs to a purely
resistive parallel circuit where Z would be less than the lowest value resistive branch.
65
6. Use a dual-trace oscilloscope to perform a phase comparison. Since the voltage across R1 is in
phase with the circuit current, VR1 can be used to represent the circuit current. Connect CH1 of
the oscilloscope across the source and CH2 across R1 as shown in Figure 22-2.
A
L
100 mH
C
0.1 µF
CH1
R1
1 kΩ
CH2
R3
100 Ω
R2
100 Ω
B
Figure 22-2
Set the source to CH1 and mode to “Dual Trace”.
Make sure the VOLTS/DIV settings are the same for
both channels. Draw and label both waveforms at
resonance (VA and IT).
Are the two waveforms in phase or out of phase?
___________________________________
7. Keep the same circuit but change the frequency to 2
kHz. Measure V2 and V3. Calculate IC and IL.
V2 = ______________ IC = ______________
V3 = ______________ IL = ______________
Waveforms at Resonance
The circuit at this frequency is acting equivalent to an (RL, RC) circuit? _________________
Therefore, when a frequency is above the resonant frequency, a parallel RLC circuit will act
(resistive, inductive, capacitive) _________________. This differs from a series RLC
circuit, which above resonance acts (resistive, inductive, capacitive) _________________.
Using the same oscilloscope connections and
settings in step 5, draw and label both the VA and the
IT waveforms when the frequency is set above the
resonant frequency.
Are the two waveforms in phase or out of phase?
___________________________________
Is the circuit current leading or lagging the voltage?
___________________________________
8. Now change the frequency to 1 kHz which is well
below the resonant frequency. Measure V2 and V3.
Calculate IC and IL.
Waveforms above Resonance
66
V2 = _________________________ IC = _________________________
V3 = _________________________ IL = _________________________
The circuit at this frequency is acting equivalent to an (RL, RC) circuit? _________________
Therefore, when a frequency is below the resonant frequency, a parallel RLC circuit will act
(resistive, inductive, capacitive) _________________. This differs from a series RLC
circuit, which above resonance acts (resistive, inductive, capacitive) _________________.
Once again, use the same oscilloscope connections
and settings in step 5. Draw and label the VA and the
IT waveforms when the frequency is set below the
resonant frequency.
Are the two waveforms in phase or out of phase?
___________________________________
Is the circuit current leading or lagging the voltage?
___________________________________
Waveforms below Resonance
67
Parallel Resonance
Bandwidth Related to Q
Project Objectives:
•
•
To determine the bandwidth of a parallel RLC circuit.
To note how Q and Z are changed when a shunt resistance is added to a circuit.
Items Needed:
- Electronics Trainer
- Jumper Wires
- Digital multi-meter
- Oscilloscope
- 100 mH inductor
- 0.1 µF Capacitor
- Resistors, 100Ω (2), 18kΩ
Experiment
A
1. Set the “no-load” source from the generator to 5-VRMS and
the frequency to 1-kHz.
2. Connect the circuit in Figure 23-1
3. Measure the voltage across R1 and adjust the circuit
frequency until VR1 is minimum and the circuit is at
resonance. Record VR1 and measure the approximate
resonant frequency.
VR1 = _______________________________
Resonant frequency = ___________________
4. Measure and record the voltage from point A to point B
(VA-B). Calculate IT from VR1. Measure VR2 and calculate IC.
C
0.1 µF
L
100 mH
R2
R1 100Ω
100Ω
B
Figure 23-1
VA-B = ________________________
IT = _________________________
VR2 = ________________________
IC = _________________________
What is the Q of this circuit? (IC / IT) _______________
5. Calculate the impedance of the parallel portion of the circuit by dividing VA-B by IT.
Z = __________________________
If the impedance above decreased to 70.7% what would be its approximate value?
ZMAX x 0.707 = _______________________
What would IT equal if VA-B were divided by the decreased value of Z?
IT = _______________________
Similar to the bandwidth in a series resonant circuit, bandwidth in a parallel resonant circuit can
be determined by computing the frequency on both sides of resonance where the impedance is
70.7% of its maximum value. The low frequency must then be subtracted from the high value.
6. Find the two frequencies at which Z = 70.7% of ZMAX by indirectly measuring IT with the
oscilloscope at R1. Increase or decrease the frequency as necessary until the voltage drop
across R1 matches the IT value determined in step 5. One frequency will be above the resonant
frequency and the other will be below.
Frequency above resonance where Z is at 70.7% = _____________________________
Frequency below resonance where Z is at 70.7% = _____________________________
68
Determine the bandwidth from fhigh - flow
Bandwidth = __________________________
Use the bandwidth formula (Bandwidth = fR/Q) to determine the bandwidth. Use the resonant
frequency along with the value of Q computed in step 4 to find the answer.
Bandwidth = __________________________
This calculated bandwidth should resonably compare with the measured value, however this
could be slightly inaccurate due to circuit resistances and the internal impedance of the
generator among other factors.
7. Connect an 18 kΩ resistor in parallel with the circuit (between points A and B). Repeat the
procedures in steps 3 through 6 to determine the bandwidth. Be sure to once again set V1 for
minimum.
V1 = _______________ IT = ________________ VA-B = _______________
Calculate Z of the parallel portion of the circuit by dividing VA-B by IT.
Z = ___________________
What will the total circuit current be at the two frequencies when Z = 70.7% of ZMAX?
Current when Z is 70.7% of ZMAX = _________________________________________
Find the two frequencies, one above and one below resonance at which Z = 70.7% of ZMAX by
measuring IT (VR1).
f above resonance where IT is at 70.7% = ____________________________________
f below resonance where IT is at 70.7% = ____________________________________
Determine the bandwidth from fhigh - flow
Bandwidth = __________________________
Is the bandwidth with the 18-kΩ shunt wider or narrower than without it? _______________
Does this mean that the Q of the circuit increased or decreased? ____________________
69
Formulas
Ohm’s Law
ExI
I2 x R
E
I
P
I
E
R
P
R
E
R
IxR
XL = 2 π f L
R
P
I
E
Peak to Peak = Peak x 2
Peak = Peak to Peak / 2
Peak = RMS x 1.414
RMS = Peak x 0.707
Average = Peak x 0.637
Average = RMS x 0.9
Frequency =
Period =
Inductance & Inductive Reactance
XL
L=
2π f
I
PxR
P
I
EINST = EPEAK sin ∠θ
EPEAK = EINST / sin ∠θ
sin ∠θ = EINST / EPEAK
E
P
E
P I
R E
E
P
AC sine wave formulas
XL
f=
2π L
RL Series Circuits
ET =
VA =
ER2 + EL2
P2 + VARsL2
Z = R2 + XL2
Capacitance & Capacitive Reactance
RC Series Circuits
1
1
1
XC =
C=
f=
2πfC
2 π f XC
2 π C XC
ET =
VA =
ER2 + EC2
P2 + VARsC2
Z = R2 + XC2
1
Period
1
Frequency
RL Parallel Circuits
IT = IR2 + IL2
VA =
Z=
P2 + VARsL2
1
() ( )
1
R
2
1
+
XL
2
RC Parallel Circuits
IT = IR2 + IC2
VA =
Z=
P2 + VARsC2
1
() ( )
1
R
2
1
+
XC
2
RLC Circuits
fR =
1
2 π LC
Bandwidth =
fR
Q
(fR = frequency at resonance)
70
Notes:
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Notes:
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72
Instructor Sign-off sheet
Project
Student Name:
Lab Project Description
Project 1
Measuring Amplitude & Voltage
Project 2
Measuring Period & Frequency
Project 3
Instantaneous Voltage & RMS Values
Project 4
Additional Input Modes & Operations
Project 5
Advanced Measurement Techniques
Project 6
Forward & Reverse Bias Diode
Project 7
Half-Wave Rectifiers
Project 8
Full-Wave Bridge Rectifiers
Project 9
Inductive Kick
Project 10
Inductors in Series & Parallel
Project 11
Relationship of XL to Inductance & Frequency
Project 12
Relationships in Series RL Circuits
Project 13
Relationships in Parallel RL Circuits
Project 14
RC Time Constants
Project 15
Capacitance in Series & Parallel
Project 16
Relationship of XC to Capacitance & Frequency
Project 17
Relationships in Series RC Circuits
Project 18
Relationships in Parallel RC Circuits
Project 19
Relationships of XL & XC to Frequency
Project 20
Series, Circuit Characteristics when XL is equal to XC
Project 21
Series, Bandwidth Related to Q
Project 22
Parallel, Circuit Characteristics when XL is equal to XC
Project 23
Parallel, Bandwidth Related to Q
Instructor Initial
Date
73