EE 2004 Lab 3 Superposition and Thevenin Rev 1_2
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ECE2004 Fundamentals of Electric Circuits ECE2004 Fundamentals of Electronics I 1
Lab 3 Rev 1.2 1 10/3/2022 © NYU Tandon School of Engineering
Lab #3 DC Circuits and Network Theorems I.
Overview The experiments outlined in this lab will test the basic properties of resistive circuits that were discussed theoretically during lectures. The major objects experimenting with the concepts of Superposition, Source Transformation and finding the Thevenin equivalent of a circuit. II.
Experimental Procedure Equipment List ±
Tektronix CDM250 Digital Multimeter (DMM) (for voltage and resistance measurements) ±
Fluke 8010A Digital Multimeter (DMM) (as an ammeter) ±
Keysight U8031A Triple Output DC Power Supply (as current source) ±
Tektronix CPS250 Power Supply (as voltage source) ±
Banana to Alligator Clip, Red (quantity 3) ±
Banana to Alligator Clip, Black (quantity 3) ±
Breadboard ±
220 Ω, 5%, ½ watt resistor ±
470 Ω, 5%, ½ watt resistor
±
1 kΩ, 5%, ½ watt resistor (quantity 2)
±
2.2 kΩ, 5%, ½ watt resistor
±
4.7 kΩ, 5%, ½ watt resistor
±
Resistance Decade Box, 1 Ω to 10 M Ω Resistance Range, 1% Accuracy, AEMC BR07
A.
Measuring a Circuit with Two Independent Sources 1.
Configuring U8031A
Power Supply and BK Precision 8540 Electronic Load The circuit under test will be driven with two independent sources, one 5V source and one 20 mA source. Fig. 1 shows the block diagram of the circuit under test and two sources. The 5V voltage source will be supplied by one of the channels from the Keysight U8031A Triple Output DC Power Supply. The 20 mA current source will be created by the series combination of the BK Precision 8540 Electronic Load connected to another channel of the DC power supply.
Figure 1 Circuit for testing Superposition
ECE2004 Fundamentals of Electric Circuits ECE2004 Fundamentals of Electronics I 2
Lab 3 Rev 1.2 1 10/3/2022 © NYU Tandon School of Engineering
Setting the U8031A power supply “Output 1” Voltage A.
Using the [POWER] switch, turn OFF the U8031A power supply. B.
Press and hold [All On/Off]
when powering on the unit. Continue holding until dOnE
is displayed. This operation sets the unit back to factory default. C.
Set the limits: a.
Press [1]
, press [Display Limit]
, Press [Voltage/Current]
. While “V” is blinking, adjust the voltage to 30V (maximum). Press [Voltage/Current]
, “A” will be blinking, adjust current to 0.5 A (500 mA maximum). b.
Press [Voltage/Current]
until “A” and “V” are no longer blinking. This will ensure that the settings for “Output 1” are not accidentally changed. c.
Press [Display Limit]
to return to meter mode (
Limit
turns off). Setting BK Precision 8540 Electronic Load Output Current A.
Enable the key sound (beep
). a.
Press the blue shift key. If you hear an audible beep press the shift key again and then skip down to step two. b.
Now press the view key to enter the setup mode. You should now see OCP displayed at the top left corner of the display. c.
Press the view key two more times. You should now see beep displayed and under it you’ll see that it indicates that the beep is off. d.
Use the knob to change the beep from off to on. e.
Now press the view key three more times to exit the setup mode. B.
Enter Current Control (CC) mode.
a.
Press the mode key until the LED under CC mode is enabled.
C.
Display the CC set value a.
Press the view key unti
l the LEDs for “Set” and “W” are enabled.
b.
The value on the upper left hand corner of the display should read “0.000”. If not, then adjust the value to “0.000”. This can be accomplished by using the left arrow, right arrow, and knob. 2.
Connecting the Electronic Load to the Voltage Source Fig. 2(a) shows an ideal 20 mA current source. Fig. 2(b) shows the wiring diagram for creating a constant current generator by connecting the electronic load the voltage source. As shown in Fig. 2(b), connect the positive
terminal from DC Power Supply “Output 1” to the positive
terminal to the electronic load. The negative terminal of the electronic load is the positive side of a current source.
ECE2004 Fundamentals of Electric Circuits ECE2004 Fundamentals of Electronics I 3
Lab 3 Rev 1.2 1 10/3/2022 © NYU Tandon School of Engineering
Figure 2(a) Ideal 20 mA current source; (b) current source using an electronic load and a voltage source 1)
Set the output current. a.
Turn on the power supply by pressing [Output 1 On/Off]
. b.
Adjust the current to 20 mA (0.020) on the Electronic load. Press the “On/Off” key on the Electronic load to enable the output terminals.
c.
Check the operation of the constant current generator by placing a 220-ohm resistor across the current source terminals, also include a DMM configured as an ammeter as shown in Fig. 3. What is the current measured by the ammeter? Using another DMM, measure and record the voltage across the 220-ohm resistor? Calculate
the true resistance using Ohm’s law (R=V/I), i
s your calculation within the 5% tolerance of the 220-ohm resistor? Figure 3 Circuit for verifying constant current source operation 3.
Assemble the Circuit with Two Independent Sources Using the DMM, measure the resistance for all your resistors listed on Table 1. Calculate the percent error from the expected value (printed on the resistors using the color bands). Are your measured values within the tolerance for each resistor? In your lab report, comment on the measured value relative to the expected.
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ECE2004 Fundamentals of Electric Circuits ECE2004 Fundamentals of Electronics I 4
Lab 3 Rev 1.2 1 10/3/2022 © NYU Tandon School of Engineering
Table 1 Expected and Measured Resistance Reference Expected Resistance (ohm) Measured Resistance (ohm) % Tolerance = (exp.-meas.)/exp. X100 R3 470 R1 1K R2 2.2K R4 1K RL 4.7K Turn OFF both power supplies. Wire the circuit onto a breadboard as shown in Fig. 4, carefully assemble the circuit as to not mix up the two 1 kohm resistors (R1 and R4). Turn ON the 20 mA current source first. Turn ON the +5V source. Measure the three node voltages and record on Table 2. Calculate the current flowing in the load resistor, I
L
, enter on Table 2. Read the ammeter, record the measured current flowing into the circuit from the I
S
source, record on Table 3. Figure 4 Complete Test Circuit Table 2 Measured Node Voltages and Load Current (
I
L
) Parameter Measurement Units V
A
V V
B
V V
C
V I
L
= (
V
B
-
V
A
)/
R
L
mA Table 3 Measured Source Current, I
S
Ideal Source Current Measured I
S
(mA) 20mA
ECE2004 Fundamentals of Electric Circuits ECE2004 Fundamentals of Electronics I 5
Lab 3 Rev 1.2 1 10/3/2022 © NYU Tandon School of Engineering
In your lab report, calculate the ideal node voltages using Nodal, or Mesh, analysis. For your calculation, use the recorded resistor values from Table 1 and the measured current from Table 3. Compare your calculated node voltages and I
L
to those values on Table 2. Discuss any discrepancies. 4.
Superposition In this section, you will apply the principal of Superposition to your lab circuit to verify that the sum of the two measured circuits is equal to the node voltages measured on Table 2 above. A.
Voltage Source Only (Superposition #1) Turn OFF the current source and disconnect the wire from the ammeter as shown in Fig. 5. You should recall that making a current source zero is equivalent to an open. Measure the node voltages and record on Table 4 under the “Super #1” column. Also calculate the load current, I
L
, and record on Table 4. Figure 5 Superposition #1 test circuit B.
Current Source Only (Superposition #2) Turn OFF the channel for the voltage source and place a short across it’s terminals as shown in Fig. 6. Reconnect the current source and turn back ON. Measure the node voltages and load current and record on Table 4 under the “Super #2” column.
ECE2004 Fundamentals of Electric Circuits ECE2004 Fundamentals of Electronics I 6
Lab 3 Rev 1.2 1 10/3/2022 © NYU Tandon School of Engineering
Figure 6 Test circuit #2 for superposition Complete Table 4 by adding the values on the Super #1 and Super #2 columns. In your lab report, compare the original values, on Table 2, to the “Add” values on Table 4. Does this experiment show the principal of superposition? Explain any discrepancies.
Table 4 Measured Node Voltages and Load Current (IL) for Superposition Parameter Super #1 Super #2 Add V
A
(V) V
B
(V) V
C (V) I
L
(mA) = (
V
B
-
V
A
)/
R
L
5.
Source Transformation In this section, you will apply the principal of source transformation to the independent current source and its parallel resistor R4. Using source transformation, calculate the equivalent voltage source (
V
EQ
) and equivalent series resistor (
R
EQ
). Use the measured values from the ammeter for current and the R4 resistor for the parallel resistor. Fill in Table 5 with your calculated values. Table 5 Measured Node Voltages and Load Current (
I
L
) Equivalent Parameter Calculated Value Units Voltage Source (
V
EQ = Ammeter/R4) V Series Resistor (
R
EQ
= R4) Ω Turn OFF both DC supplies. Disconnect the current source and R4. Remove the ammeter. Reset the U8031A power supply back to constant voltage mode (CV) by repeating the following Reset procedure.
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ECE2004 Fundamentals of Electric Circuits ECE2004 Fundamentals of Electronics I 7
Lab 3 Rev 1.2 1 10/3/2022 © NYU Tandon School of Engineering
1.
Using the [POWER] switch, turn OFF the U8031A power supply. 2.
Press and hold [All On/Off]
when powering on the unit. Continue holding until dOnE
is displayed. This operation sets the unit back to factory default and “CV” mode Connect the equivalent source transformation elements as shown in Fig. 7. The U8031A supply will be used as V
EQ
. Turn ON both supplies and set U8031A to V
EQ
determined on Table 5 above. Using the DMM, measure the three node voltage and calculate I
L
, enter these values on Table 6. In your report, compare these values to the values measured in the original circuit (Fig. 4
/Table 2
). Did the source transformation change any of the node voltages and/or I
L
? Discuss in your lab report. Figure 7 Source Transformation equivalent circuit Table 6 Measured Node Voltages and Load Current (IL) using Source Transformation Parameter Measurement Units V
A
V V
B
V V
C
V I
L
= (
V
B
-
V
A
)/
R
L
mA 6.
Thevenin Equivalent In this section, you will determine the Thevenin Equivalent circuit attached to the load resistor R
L
. Thevenin equivalent calculations are made in four steps; 1) remove the load resistance, 2) measure the open circuit voltage, 3) make all independent sources zero, 4) determine the equivalent resistance, R
TH
, across the open terminals. For this part of the experiment, you will follow the same procedure. A.
Determine V
OC
= V
TH
Disconnect R
L
, and using a DMM, measure V
OC
across the open terminals (also referred here as V
B
-
V
A
). Record V
OC
on Table 7. Fig. 8 shows the circuit to be measured.
ECE2004 Fundamentals of Electric Circuits ECE2004 Fundamentals of Electronics I 8
Lab 3 Rev 1.2 1 10/3/2022 © NYU Tandon School of Engineering
Figure 8 Circuit for measuring Thevenin parameter, V
OC
B.
Determine R
TH
Turn OFF the channels for both voltage sources and place a short across both, as shown in Fig. 9. Using a DMM, measure the resistance, R
TH
, across the open terminals and record the resistance measurement on Table 7. Figure 9 Circuit for measuring Thevenin parameter, R
TH
Table 7 Measured Thevenin Parameters Parameter Measurement Units V
OC
(V) = V
TH
V R
TH
(ohm) Ω C.
Replace circuit with Thevenin Equivalent
In this last section, you will replace the circuit with its Thevenin equivalent and measure the voltage and current across R
L
. The load resistor, R
L
, is the original 4.7 k
Ω.
Configure the equivalent circuit shown in Fig. 10 using the Decade Resistance Box for R
TH
and one voltage source (DC Power Supply) for V
TH
. Set the Decade Resistance Box to the value of R
TH
listed on Table 7 above. Set the DC voltage to V
TH
. Using a DMM, measure the load voltage, V
L
, and knowing the true resistance for R
L
, calculate I
L
. Place these values on Table 8. In your report, compare these values to the load voltage and load current found in the Fig. 7
/Table 6
.
ECE2004 Fundamentals of Electric Circuits ECE2004 Fundamentals of Electronics I 9
Lab 3 Rev 1.2 1 10/3/2022 © NYU Tandon School of Engineering
Figure 10 Circuit for measuring load parameters with Thevenin equivalent Table 8 Measured load parameters using Thevenin Equivalent Parameter Measurement Units V
L
V I
L
= V
L
/ R
L
mA
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