Download ECE 3144: Circuit Analysis I

ECE 3144: Circuit Analysis I
Experiment 6
Title:
THEVENIN, NORTON, and SUPERPOSITION
OBJECTIVE: Confirm Thevenin, Norton, and Superposition theorems, and how they simplify circuit analysis.
Discussion: The theorems that we will consider are:
a
Rt
a
=
b
Vt
+
b
Thevenin’s Theorem
a
a
=
b
It
Rt
b
Norton’s Theorem
Superposition: V(out) = sum of individual effects due to internal stimuli, taken one by one with all other stimuli
turned off.
PROCEDURE:
A-1: Connect the circuit as shown by figure 6A-1 on your prototyping breadboard. In this experiment we use three
power supplies, so be efficient with your wiring, use good layout techniques. Because there are variations in these resistance
values, it is recommended that you measure and confirm the values before inserting them into your prototyping motherboard.
3.9kΩ
15kΩ
R1
10kΩ
20kΩ
3kΩ
5.1kΩ
VS1
2kΩ
+
12V
R2
10kΩ
-
6.8kΩ
VS2
+
30kΩ
10kΩ
+
VS3
12V
5V -
Figure 6A-1: Theorem circuit
Warning: Make good use of your motherboard and wiring to be sure that your circuit is accurately connected, because you
will be required to do a MatLab calculation and comparison. And if your answers do not compare favorably, then neither will
your grade. Run a snake check before proceeding to the next step.
A-2. Find the 10kΩ resistance marked above as R1. Measure the voltage across this resistance with your DMM
(DCV setting).
A-3. Now remove resistance R1 and measure the voltage across these two points using your DMM.
You have just measured the Thevenin equivalent voltage Vth.
A-4. Now replace each power supplies with a shorting wire (first disconnect one end of the power supply). Using the
DMM, (Ω setting) measure the resistance between these points.
You have just measured the Thevenin equivalent resistance Rth.
B-1. Restore the circuit of Figure 6A-1.
B-2: Find the resistance marked R2 (value = 10kΩ). Measure the voltage across this resistance
B-3: Remove the resistance R2 and measure the voltage across the two points.
B-4: Replace each power supply with a shorting wire (first disconnect one end of the power supply). Using the DMM
measure the resistance between these two points.
You have now determined Vth and Rth for another site within the circuit.
C-1:
C-2:
C-3:
C-4:
Restore the circuit of Figure 6A-1, which we will now reconfirm using superposition.
Replace VS2 and VS3 each with a shorting wire, and VS1 at its stated voltage. Measure the voltage across R1.
Replace VS1 and VS3 each with a shorting wire, and VS2 at its stated voltage. Measure the voltage across R1.
Replace VS1 and VS2 each with a shorting wire, and VS3 at its stated voltage. Measure the voltage across R1.
C-5: The sum of these three voltages should be almost the same as the value measured under part A-1. If not, run a
snake check and find the reason for the discrepancy before proceeding further.
D-1: Construct the R-2R ladder shown by figure 6D-1. Inputs VA, VB, VC, VD will be taken from the (binary logic)
switches of the MFJ prototyping box. You should have enough resistances in your parts kit to accomplish this circuit.
D-2: Assume that “1” corresponds to switch = high, with output = 5.0V and that “0” indicates that switch = low with
output = 0.0V. You might check one of the logic switches and confirm these values via the DMM.
VA
VB
20kΩ
VC
20kΩ
VD
20kΩ
20kΩ
Vout
10kΩ
10kΩ
10kΩ
20kΩ
GND
20kΩ
GND
Figure 6D-1: Superposition exercise: R-2R ladder
D-3: Measure Vout for each of the following settings:
ABCD = %1000
ABCD = %0100
ABCD = %0010
ABCD = %0001
In making these measurements it is recommended that for best efficiency you should connect the DMM to Vout using bananaalligator cables (and hook-up wire).
When you are through with your measurements on the R-2R ladder, disassemble your circuit and return the extra 20kΩ resistances to the parts/wires drawer for the next person to use.
ANALYSIS:
A. Use Matlab to determine the Thevenin voltage and resistance for part A. Keep in mind that if you make all voltages
sources equal zero and apply a unity current source to the “output” points, then the voltage value will = Rth. Compare to measurements and give percentage error.
B. Use Matlab to determine the Thevenin voltage and resistance for part B. Keep in mind that if you make all voltages
sources equal zero and apply a unity current source to the “output” points, then the voltage value will be equal in value to Rth.
Compare to measurements and give percentage error.
C. Use Matlab to determine voltage across R1 for each of the superposition tests, and compare to your measurements.
D. Analyze the circuit of figure 6D-1 using hand analysis for each of the cases measured, and compare to measurements.
Set up a complete truth table for ABCD = %0000 to ABCD = %1111, with values of Vout as you would expect for each of these
settings. You should see why this circuit is called a binary ladder.
REPORT: This experiment should be written up as a formal report. Pay particular attention to sources of error. Include
your MATLAB input files with your report.