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EE 22100 Electrical Engineering Laboratory I Spring 2023 Lab Report Experiment #4 Superposition Instructor: Muhammad Irfan Name: Christian Chu Yang Date: 3/18/2023

Purpose: To determine whether or not certain circuits follow the law of superposition Objective: The goal of this lab is to test the linear elements such as resistors, capacitors and diodes in the circuits and see if they satisfy the superposition principles. Procedure: Superposition with resistors: To determine if superposition principle holds we tried with a circuit containing several resistors and 2 DC input voltage sources as shown in figure1 Figure1: resistor circuit with 2 DC voltage sources

For the first scenario, we set V1=4 and V2=0 by shorting the V2 source as shown in figure 1a, and then we measure the Vout1 which is the node between the two 22k ohm resistors and the 10k ohm resistor with the Digital Multimeter. For the second scenario we set the V1=0 and V2=8 by shorting the V1 source as shown in figure 1b. Then we measure the Vout2 which is the node between the two 22k ohm resistors and the 10k ohm resistor with the Digital Multimeter Figure 1a: first scenario

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Figure 1b: second scenario Measured(v ) Calculated(v ) Error(% ) Vout1 0.7 0.708 1.129 Vout2 -2.0521 -2.057 0.23821 V(total ) -1.3511 -1.3505 0.0444 Table 1: measured and calculated values for circuit 1 Data analysis: In order to calculate the output voltage, the circuit was simplified using parallel and series resistors and then we got the current and individual currents R(total) = (22kΩ + 10kΩ)// (22kΩ // 10kΩ) = 29.619kΩ I(22kΩ) = 8v/29.619kΩ = 0.27mA V(10kΩ) = 8v – (22kΩ x 0.27mA) = 8v- 5.94v = 2.057v Since polarity was switched, the final answer should have a negative value Superposition with capacitors: In this part of the lab we will investigate superposition using one capacitor and a resistor, including 2 sources (DC and AC) as shown in figure 2. First, we short the V2 (AC) source and set V1(DC) = 4v as shown in figure 2a, and then we measure the Vout1 which is the node between the 10kΩ resistor and the 0,1u capacitor with the Digital Multimeter. For the second scenario we set the V1(DC) =0 by shorting the V1 source and set V2(AC) = with an offset of 0,

amplitude of 1vpp and frequency of 10kHz as shown in figure 2b. Then we measure the Vout2 which is the node between the 10kΩ resistor and the 0,1u capacitor with the oscilloscope. Figure2: circuit used for superposition principle with a capacitor

Figure2a: first scenario for capacitor circuit Figure2b: second scenario for capacitor circuit

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Figure 2c: AC +DC oscilloscope measurement for capacitor Figure 2d: Matlab graphs from capacitor circuit

Measured( v) Calculated( v) Error( %) Vout1(D C) 3.99 4 0.2499 Vout2(A C) 2.08 2 3.846 V(total) 2.51 2 4 Table2: measured and calculated values for circuit 2 Superposition with Diodes: In this final part of the lab we will test the superposition principle with a diode. Diodes allow current to flow one way but not the other. We will be using two resistors and 2 DC sources as shown in figure 3. For the first scenario we will set V1=4 and V2=0 ass shown in figure 3a, we use the oscilloscope to measure the values with scale settings, then we save images and data using LabViewVI. We repeat the same step for the second scenario but we set V1=0 and V1=4 as shown in figure 3b

Figure 3: circuit used for superposition principle with a diode Figure 3a: first scenario for diode circuit Figure 3b: second scenario for diode circuit With the diode facing downwards, we get that V1=0.641 and V2=0.747 with a Vtotal of 0.68. We repeat the same process as mentioned before except that we put the diode facing upwards. Once we do this, we get V1=2.00 and V2=1.98 with a Vtotal of 3.992. As we can see the superposition principle holds for when the diode is facing upwards. Conclusion:

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From this experiment we could verify that superposition principle holds for linear circuits such as the resistor one and the capacitor one. In the other hand, the diode circuit didn’t follow the principle except as for when the equation was in the reverse bias case which supported the superposition principle References:  Electrical Engineering Laboratory I, CCNY Department of Electrical Engineering, New York, NY Spring 2016