The George Washington University
School of Engineering and Applied Science
Department of Electrical and Computer Engineering
ECE 11 - LAB
Experiment # 9
Meter Responses, Waveforms and AC Thévenin
Equipments:
Lab Equipment
Equipment Description
Digital Multimeter (DMM)
Keithley Model 175
Function Generator
Tektronix AFG3021B
Digital Oscilloscope
Tektronix TDS460A
Digital Oscilloscope
Instek GOS-620FG
Programmable Automatic RCL Meter
Philips PM6304
BNC T Connector
NONE
BNC Cables
NONE
Banana-to-mini-grabber test leads
NONE
BNC-to-mini-grabber test leads
NONE
Prototype Breadboard
NONE
Table 1.1 – Equipment List
Components:
Kit Part #
Resistor
Resistor
Resistor
Resistor
Capacitor
Capacitor
Capacitor
Inductor
Inductor
Spice Part
Name
R
R
R
R
C
C
C
L
L
Part Description
3.3 kΩ – 470 kΩ Resistors
270  Resistor
270  Resistor
270  Resistor
820 pF Capacitor
0.01 uF Capacitor
0.001 uF Capacitor
1000 uH
10000 uH
Table 1.2– Components list
Symbol Name
(used in schematics
throughout this lab manual)
Rp
R1
R2
R3
C1(in Part I)
C1(in Part II,III)
C2
L1
L2
Objectives:






To use the Oscilloscope to measure the amplitude, frequency and phase of an AC signal
To use the RLC Meter to measure the impedance of resistors, capacitors, and inductors
To create and explain a simple AC impedance model
To determine the Thévenin equivalent of an AC circuit by hand calculation
To find the Thévenin equivalent of an AC circuit by Spice Simulation
To measure the AC Thévenin Voltage, Current, and Impedance
GWU SEAS ECE Department ©2010
ECE 11 – Experiment #9
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Prelab: (Submit electronically prior to lab meeting, also have a printed copy for yourself during lab)
Introduction
AC Thévenin Circuits
The general concepts of AC Thévenin’s and Norton’s theorems are the same as DC Thévenin’s
and Norton’s theorems. The important difference here is that the signals VT , I N , V and I are
phasors,
Z th and Z L are complex numbers representing the source and load impedances.
Finding the Thévenin equivalent of a phasor circuit involves the same process as for DC
resistance circuits, except that we must manipulate complex numbers.
Introduction to the RCL Meter
Fig. 1.1 – RLC Meter (Philips PM6304)
The PM6304 Programmable Automatic RCL meter is used for precise measurements of
resistance, capacitance and inductance. The components to be measured are connected to the
instrument via a separate measurement pad. And the measurement results are displayed o the
LCD.
When measuring, we first connect measurement pad to the connector on the front panel,
Since the equipment is frequency-driven, we need to set the frequency by the button shown in the
right figure
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ECE 11 – Experiment #9
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SPICE Simulation Mini-Tutorial
How to use SPICE to find the AC Voltage and Phase Difference
You start with your desired circuit, like the one in the figure below.
The voltage source’s Part name is VAC. The property: Vdc is the DC offset, Vac is the amplitude.
The part name for capacitor is C.
Create a new simulation, choose “AC Sweep/Noise”, set “Start Frequency” to be required
frequency (10kHz in part 1). And set “End Frequency” to a frequency larger than the “Start
Frequency”, then set Points/Decade to 500.
Before running the simulation, place a “V-probe’s” as shown in the figure above in the areas
where you’d like to see the voltage waveforms at that point in the circuit.
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ECE 11 – Experiment #9
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950mV
900mV
850mV
800mV
10KHz
V(C1:2)
30KHz
50KHz
70KHz
90KHz
Frequency
The voltage value can be seen by turning the cursors on by click the button
in the above
figure. Then you will get a “Probe Cursor” Window as in the below figure. It tells you the voltage
at 10k frequency is 838.088mV, it is the voltage cross Rp.
Now we need to figure out the phase of the voltage. Delete the Voltage Probe.
Then click the button “Pspice”->Markers->Advanced->Phase of Voltage.
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ECE 11 – Experiment #9
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Place that probe in the place as shown in the below picture.
Then run the simulation. The result is shown below.
80.4d
80.0d
79.6d
79.2d
10KHz
VP(C1:2)
30KHz
50KHz
70KHz
90KHz
Frequency
The phase value can be seen by turning the cursors on by click the button
in the above
figure. Then you will get a “Probe Cursor” Window as in the below figure. It tells you the
phase at 10k frequency is 80.351
The voltage across the Rp is 838.088mV /90.351.
How to use SPICE to find the AC Voltage: VTH, IN, and ZTH
For the following circuit, we will need to find VTH, IN (Isc) and ZTH:
GWU SEAS ECE Department ©2010
ECE 11 – Experiment #9
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To find VTH, we disconnect the load (R3), and realize that since no current will flow through L2 or
C2, the Thevenin voltage will be equivalent to the voltage across the cap – C1/inductor- L1 &
resistor (R2) as shown here:
You would then setup an “AC Sweep” simulation (as shown in the last example) and set the “Start
frequency” to 50.39k, the “End Frequency” to 60k, and the Points/Decade to 500.
The green voltage probe will let you plot the voltage across (C1||L1 + R2). Its amplitude will be
the magnitude of the VTH phasor. After running this simulation to get the absolute value of the
VTH, replace the “Voltage” probe with a “Phase of Voltage” probe, you can find out the phase
angle of the VTH phasor.
To find IN (also called: Isc – Ishort-circuit), we would disconnect the load (R3) and short the load
terminals as you see here:
GWU SEAS ECE Department ©2010
ECE 11 – Experiment #9
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For the “AC Sweep” simulation, set the “Start frequency” to 50.39k, the “End Frequency” to 60k,
and the Points/Decade to 500.
Place the “Current“ probe’s as shown in the figure.
Turn the cursors on by click the button
to see the current value.
To find out the phase of the current. Replace the “Current“ probe’s by a “Phase of Current”
probe.
Finally, to find Zth, we use Ohm’s law and divide the two phasors: V/I
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Prelab Problems:
1. AC Circuit Analysis
a) Design a series circuit that has a voltage source (Vs), one capacitor (C1= 820 pF
Capacitor) and one resistor (Rp) connected in series.
b) Draw this test circuit and annotate it as Fig 1.
c) Derive a general equation that will yield the magnitude and phase of a voltage across
Rp. Assume the voltage source Vs = A /_0. Vs is assumed to have a zero
phase=0 because it is the reference voltage. A is the amplitude of Vs.
d) Label this equation - "Equation 1 - Equation for finding Magnitude and Phase of VRp"
e) Substitute the following resistors in for Rp and find the corresponding Magnitude and
Phase of each Rp value given. Rp = 3.3K , 6.8 K, 15 K, 22K, 33K, 47K, 68K, 110K,
220K and 470K Ohms. Use C1 = 820 pF, Voltage source Amplitude =5V and
Frequency= 10 KHz.
f) Repeat step e using SPICE to calculate the phase difference.
g) Put the data in Data Table 1A - "Magnitude/Phase Calculation"
Rp
Magnitude of Rp
Phase of Rp
(hand calculation)
Phase of Rp
(spice calculation)
3.3 K
6.8 K
15 K
22 K
33 K
47 K
68 K
110 K
220 K
470 K
Table 1A – Magnitude/Phase Calculation
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2. AC Thevenin Circuit Analysis
a) Derive general equations to find the Thévenin Voltage (Vth), Thévenin Impedance
(Zth) and Short Circuit Current (Isc) with respect to terminals A and B in the following
figure. Note: R3 is the load resistor.
b) Label the three equations - "Equation 2(a) – Equation for finding Thévenin Voltage
(Vth)”, "Equation 2(b) – Equation for finding Thévenin Impedance (Zth)” and
"Equation 2(c) – Short Circuit Current (Isc)"
c) Use the values for R1, C1, L1, R2 from the component list and your equations to
calculate VTH, ZTH, and ISC. Vs : Vpp=2V @ 50.39 kHz
d) Draw the thevenin equivalent circuit for Fig 2. Label it as Figure 2B - "Thevenin
Equivalent of Figure 2"
e) Build the circuit in SPICE to verify your answers. Keep this circuit file so you can use
it again later during lab
Fig 2 – Circuit to Analyze VTH, ISC, and RTH
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ECE 11 – Experiment #9
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Lab:
Part I - AC Voltage Phase Measurement
a. Set up the function generator to the following specifications.
POWER
1(ON)
WAVEFORM sine wave
FREQ
10 kHz
DTY
50%
AMP
5.0 V
OFS
0V
b. Connect the function generator output through a BNC T to channel 1 of the scope and
connect the other side of the BNC T to a pair of BNC- minigrabber cable.
c. Connect the minigrabber to Vs of Fig 1 which you designed in the prelab.
d. Use another pair of BNC- minigrabber cable to connect the voltage across Rp in Fig 1 to
Channel 2 of the oscilloscope.
e. Set the oscilloscope for dual trace operation. You will see the input signal from the
function generator (on CH1) and the output voltage across Rp of Fig 1 (on CH2) on the
same screen.
f. Put Rp = 3.3 K in the circuit.
g. Measure the magnitude of CH2 (it is the amplitude of Rp) and measure the Phase
difference between the signals on CH1 and CH2.
h. Put the Phase difference values in Data Table 1B - "Phase Difference Measurement"
Repeat steps 7-9 for Rp = 6.8 K, 15 K, 22K, 33K, 47K, 68K, 110K, 220K and 470K
Ohms.
i. Repeat steps e-h using the Analog Oscilloscope
1. Call your GTA over and show how you have setup up your Analog Scope
and how you are calculating the phase difference.
Rp
Magnitude of Rp
Phase difference between
the signals on CH1 and
CH2
(Digital Scope)
Phase difference
between the signals
on CH1 and CH2
(Analog Scope)
3.3 K
6.8 K
15 K
22 K
33 K
47 K
68 K
110 K
220 K
470 K
Table 1B – Phase Difference Measurement
GWU SEAS ECE Department ©2010
ECE 11 – Experiment #9
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Part II - AC Thevenin Analysis w/ Measured Values
In parts II and III, we will build and measure the prelab circuit in figure #2.
a. Use the Philips PM6304 Programmable Automatic RCL Meter to obtain measured values
of R1, R2, R3, C1,C2, L1 and L2. You have to go to the TA room (Room 304) to get the
measurement pad and manual for the PM6304. Record the measured values in Data
Table 2.
1. Your GTA will give you a demonstration on how to use this piece of
equipment before you use it!
b. Update your PSPICE simulation and find Vth, Isc and Zth using measured values of R,
C, L
c. Substitute the measured values of R, C and L in the Equation 2 you derived in prelab to
calculate the Vth, Isc and Zth in Fig 2. Put the results in Data Table 2.
Part III - AC Thevenin Measurement
a. Build the circuit from Fig 2 in the prelab.
b. Measure the Thévenin voltage (Voltage across terminal A and B).
1. Rememeber you cannot use the Oscope to directly measure the voltage across
any component. The Oscope can only measure node-voltages. To recall how to
measure the voltage across a device using an Oscope, see lab #6.
c. Measure Zth (Thévenin impedance) using the RLC meter
1. Disconnect the source from your circuit and short the two wires where the source
used to be
2. Disconnect the load from your circuit
3. Attach the RLC meter and measure the thevenin equivalent
1. Don’t forget the RLC meter is frequency driven, so properly set the
frequency before measuring ZTH.
d. Measure Isc (short circuit current).
e. Write the measured results in Data Table 2.
f. Compare the measured data to the results in Part 2.
Part IV - Lab Writeup:
In the report, discuss the following questions:
a) Why do the measured values have to be used for R, L and C in the Thévenin analysis of
Fig 2?
b) Determine the accuracy of your measurement data in comparison to your calculated
data. What are the percentages of error? Analyze the source(s) of the errors.
c) Why can’t an Oscilloscope measure voltage directly across a device?
GWU SEAS ECE Department ©2010
ECE 11 – Experiment #9
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