LAB 4
Junchen Liu
Micheal Kyriacou
March 28, 2017

Objective:
The purpose of this experiment is to test the law of superposition with real circuits. And when we c a me across with multiple sources or with complex circuits, the principle of superposition leads to substantial simplifications.

Laboratory :

Superposition with resisters :

S et up the circuit (shown in Figure 1 of the book ) o n protoboard . Measure the output voltage and verify the superposition principle when :
V 1 =4 V, V 2 =0 V and V 1 =0 V, V 2 =-8 V

Superposition with capacitors :

Set up the circuit (shown in Figure 2 of the book ) o n protoboard . Set DC supply to 4V, frequency to 10 kHz, and Amplitude to 1 V pp . Measure the output voltage , save data using oscilloscope, and verify the superposition principle when:
V 1 =4 V, V 2 =0 V and V 1 =0 V, V 2 =1 V pp

Superposition with Diodes :

Set u p the circuit (shown in Figure 3 of the book ) on protoboard . Measure the output voltage , and verify the superposition principle when:
V 1 =4 V, V 2 =0 V and V 1 =0 V, V 2 =4 V

D1

R1
1.0kΩ
R2
1.0kΩ
V2
4 V
V1
4 V
Vout then reverse the direction of the diode and repeat the above steps.
Figure 3 : Circuit to investigate superstition with diodes

Data :

Superposition with resisters:

V out (Measure)
V out 1
V out 2
V out ( Calculated )
Percent Error
-1.3318 V
0.708 V
-2.059 V
-1.351 V
1.42%
The principle of superposition with resistors holds.

Superposition with capacitors:

Vout signal due to both voltage source.

Vout signal due to only DC voltage source.

Vout signal due to only AC voltage source.

36195076200
Matlab graph proves V out = V out 1 + V out 2

If you were to sum the two oscilloscope images that you obtained in part 4 would you get the same trace that you got in part3? Does superposition hold when a circuit has both capacitors and resistors?

Yes, we will get the similar trace when we sum up the 2 of the part 4 oscilloscope images. Superposition holds when the circuit has capacitors and resistors, because the overall output voltage is equal to the output voltage from each voltage source.

Superposition with Diodes:

V out (V)
V out 1 (V)
V out 2 (V)
Original Diode
0.6785
0.67128
0.67135
Reversed Diode
0.67164
0.67164
0.67164

Post lab:

Using the data that you collected in the lab justify whether or not superposition holds for each circuit. If superposition does not hold speculate why?

Superposition holds with circuits shown in Figure 1 and 2, but not the circuit shown in Figure 3, which is because resistors and capacitors are consider linear systems, while diodes are nonlinear, because diode is like a switch, it open and close depends on the voltage across it.

Discussion( Junchen Liu)

This experiment gives me a better idea to the principle of superposition, it is a t heoretical concept that states if a linear system of various independent sources, the output is the sum of each individual outputs. For example, in experiment 1, one can see clearly that the total Vout measured is -1.3318, which is equal to the sum of Vout1 and Vout2. There are three experiments in this lab, we find out the superstition will be hold with both the resistors an d the capacitors. However, superposition with diodes does not hold when t here are diodes in the circuit.