ECE 35 Lab 3

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Jan 9, 2024

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ECE 35 Lab 3 Name 1 Huizhuo gan Name 2 Linh Nguyen In this lab you will simulate, build, and observe circuits in order to study superposition and Thevenin/Norton equivalent circuits. Part A: Superposition in linear circuits Do not simulate or build this circuit before reading the following questions. In the circuit below, how would the polarity and magnitude of the output voltage change if you reverse the polarity of the voltage source (V2) and change the direction of current source (I1)? Hint: The effect of each source on the output voltage can be analyzed using the following expression: 𝑉 = 𝑎 × 𝑉 2 + 𝑏 × 𝐼 1 , in which “a” is the effect of 𝑉 2 and “b” is the effect of 𝐼 1 on the output. Write your hypothesis here: The magnitude of the output voltage will change into the . 𝑉 = ? * 𝑉2 +− ? * 𝐼1 Do you expect the same change if you change the polarity or the direction of only one source? Yes.

What is the impact of the location of the ground on the measured value of V out ? If you move the ground to another place, the value of the Vout will be changed. Now run the simulation in PSpice and test your hypotheses. Were your expectations correct? If not, explain why. Our expectation is partially correct. The voltage turns into -V so it means that a and b turns into -a and -b. Show your results to a TA before continuing to the next part.

Part B: Finding the Thevenin equivalent circuit Do not simulate or build this circuit before reading the following explanation. In this linear circuit, the values of R2 and R3 are not given. You will be asked to find the thevenin equivalent circuit between A and B (without R L ) and show that this 0 One way to find the Thevenin parameters of a linear circuit is by attaching a variable load (a variable resistance) to the A and B terminals and vary the load (R L ) resistance value. For each value of R L , the value of i L (the current through R L ) and (the voltage across R L ) 𝑉 𝐿 can be measured. For linear circuits, these data points should lie on a line (see the figure below). Values of V th , I N , and R th can be read directly from the graph as shown. Please note that if you choose to plot V L vs I L , the slope will be equal to -R th .

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Now build the circuit. A TA will give you two resistors to use as R2 and R3. It doesn’t matter which one you use for R2 or R3. Using the 10K potentiometer as. R L , measure V L , i L , and R L for 5 different values of R L . Make sure that V L and i L are measured over a large spectrum of R L values. Write an equation below that relates V L and i L to V th and R th . Use your gathered data to calculate what the parameters of the Thevenin equivalent model are and write them below. Plot the recorded data in Excel and fit a straight line to it. Use the equation of that line to find the V th and R th parameters. Write your recorded data and the calculated V th and R th values here: Add a picture of your plotted data below. Looking at plotted data, what is the minimum number of measurements you could have taken to find an estimate of V th and R th ?

Now, plot the power dissipated by the load vs load resistance using your recorded data. For what value of the load resistance is the power maximized? Is this what you expected? Now, use a 1k Ω resistor as R L and measure the V L and i L . Record your measurements below. Build the Thevenin equivalent circuit using the V th and R th you found, connect a 1k Ω load resistor to the equivalent circuit, and measure the V L and i L . Record your measurements below. Show your results to a TA before continuing to the next part.

Part C : Using the circuit theorems in linear circuits Do not simulate or build this circuit yet. In the following linear circuit, how would the voltage across R L change if you multiply the value of V 1 , V 2 and V 3 by 2 (without changing the load resistor)? Note that this circuit has three positive voltage sources. What linear circuit theorem can you make use of to take measurements of this circuit without having to build it using all three sources? Now build the circuit with V 1 = 8V, V 2 = 4V, V 3 = 2V and 5k Ω as the load resistor. Measure V AB for these voltage source values, then measure V AB for V 1 = 16V, V 2 = 8V and V 3 = 4V. Record your measurements for each case below.

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Now, set V 1 = 8V, V 2 = 4V, V 3 = 2V and use a 10 k potentiometer as the load resistor. Change the Ω resistance of the potentiometer until the output voltage across the load is half of the open circuit voltage. What is the value of this resistance and how is it related to the Thevenin equivalent resistance? Show your results to a TA before continuing to the next part.

Part D: Thevenin equivalent circuits with dependent source Analytically calculate the open circuit voltage and short circuit current in the following circuit assuming that R L is a load (remove R L to find V oc and i sc ). Now, simulate the circuit and find the values of V oc and i sc . Compare your calculated values to the simulated values. Show your results to a TA before turning in the lab. Remember to sign out and turn in this lab document on Canvas for BOTH lab partners.