Lab6_RLC

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Wayne State University *

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215

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Electrical Engineering

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Dec 6, 2023

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EECS 215 Laboratory 6 –First and Second Order Circuits L ABORATORY 6 – F IRST AND S ECOND O RDER C IRCUITS Name: Section Number: Submission instructions: Use this document as your lab report template. Fill in the tables below as instructed, save as PDF, and submit the lab report with Gradescope one week after your 2 nd scheduled lab session (this is a 2-week lab). Laboratory 5 – First and Second Order Circuits 1 Parts List 1 1. Introduction and Non-ideal components 1 2. Laboratory: Part One - RC Circuit 2 3. Laboratory: Part Two - RL Circuit 4 4. Laboratory: Part Three - RLC Circuit 6 5. Laboratory: Part Four - RLC Circuit With a Potentiometer (POT) 8 Parts List 1. 68 Ω Resistor 2. 100 Ω Resistor 3. 5k Ω potentiometer 4. 100nF (0.1uF) Capacitor 5. 10nF (10000pF) Capacitor 6. 10mH Inductor 7. 1mH Inductor 1. I NTRODUCTION In this lab you will learn how to build simple first and second order circuits, while using your AD2 to record responses. Using those responses from your WaveForms application, you will then compare this to theory. This lab is designed to be completed in a two week period, so start early! 2. L ABORATORY : P ART O NE - RC C IRCUIT In this part of the lab, you will create a RC circuit, and run a simple square wave test on WaveForms. In order to complete this part of the lab, you will need: Page 1 of 11

EECS 215 Laboratory 6 –First and Second Order Circuits ● 68 Ω Resistor ● 100 nF Capacitor Figure 1: RC Circuit Schematic When building this circuit, place the resistor in series with the capacitor on your breadboard as seen in Figure 1. Then attach your AD2 kit to the circuit using the key shown in Figure 1. We want one of the Oscilloscope probes to measure the output of the circuit created, while the other is measuring the input. In this case, the input of the circuit is the waveform generator from the AD2. Do not forget to attach your 1- and 2- probes to ground (GND). Picture of Circuit {insert here} Save the data as “lab6_data1.csv” and upload it to Canvas. Once our circuit is built: 1. Open WaveForms 2. Open the waveform generator and the oscilloscope 3. We want our waveform generator to have the following parameters: a. Type: Square b. Frequency: 10 kHz c. Period: 100 us d. Amplitude: 1 V e. Offset: 0 , Symmetry: 50% , and Phase: 0% Page 2 of 11

EECS 215 Laboratory 6 –First and Second Order Circuits 4. Now make sure that your Channel 1 and Channel 2 are showing on the oscilloscope, and make sure they have the same range and offset. We want the input and output to be plotted on top of each other to see the effect the circuit has on the voltage output. 5. Once you have everything set up, Run All programs and put a screenshot of the oscilloscope here: Picture of Oscilloscope {insert here} Save the data as “lab6_data2.csv” and upload it to Canvas. 6. Next, solve for the capacitor voltage v C ( t ) as a response to a 1V step function. Type or write in the function in the space below. Next, plot both the measured result and the predicted response using Matlab or Python or any other software that you are comfortable with. Note that you will need to align the time axis so that the two steps line up at t=0 so you can compare the exponential responses. Include your plot below. Explain any differences. Function for V c (t) {insert here} Plot of Predicted and Measured Response {insert here} Explain any differences {insert here} 3. L ABORATORY : P ART T WO - RL C IRCUIT In this part of the lab, you will create a RL circuit, and run a simple square wave test on WaveForms. In order to complete this part of the lab, you will need: ● 68 Ω Resistor ● 10 mH Inductor (with label 103) Figure 2: RL Circuit Schematic When building this circuit, place the resistor in series with the Inductor on your breadboard as seen in Figure 2. Then attach your AD2 kit to the circuit using the key shown Page 3 of 11

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EECS 215 Laboratory 6 –First and Second Order Circuits in Figure 2. We want one of the Oscilloscope probes to measure the output of the circuit created, while the other is measuring the input. In this case, the input of the circuit is the waveform generator from the AD2. Do not forget to attach your 1- and 2- probes to ground (GND). Picture of Circuit {insert here} Save the data as “lab6_data3.csv” and upload it to Canvas. Once our circuit is built: 1. Open WaveForms 2. Open the waveform generator and the oscilloscope 3. We want our waveform generator to have the following parameters: a. Type: Square b. Frequency: 1 kHz c. Period: 1 ms d. Amplitude: 1 V e. Offset: 1 V , Symmetry: 50% , and Phase: 0% 4. Now make sure that your Channel 1 and Channel 2 are showing on the oscilloscope, and make sure they have the same range and offset. We want the input and output to be plotted on top of each other to see the effect the circuit has on the voltage output. 5. Once you have everything set up, Run All programs and put a screenshot of the oscilloscope here: Picture of Oscilloscope {insert here} Save the data as “lab6_data4.csv” and upload it to Canvas. 6. Next, solve for the inductor voltage v L ( t ) as a response to a 1V step function. Type or write in the function in the space below. Next, plot both the measured result and the predicted response using Matlab, Python, or any software you are comfortable with. Note Page 4 of 11

EECS 215 Laboratory 6 –First and Second Order Circuits that you will need to align the time axis so that the two steps line up at t=0 so you can compare the exponential responses. Include your plot below. Explain any differences. Function for V L (t) {insert here} Plot of Predicted and Measured Response {insert here} Explain any differences {insert here} 4. L ABORATORY : P ART T HREE - RLC C IRCUIT In this part of the lab, you will create a RLC circuit, and classify the output as overdamped, under damped, or critically damped. In order to complete this part of the lab, you will need to have: ● 100 Ω Resistor ● 1 mH Inductor (with label 102) ● 10 nF Capacitor (it is a beige ceramic capacitor labeled with 103) Figure 3: RLC Circuit Schematic Page 5 of 11

EECS 215 Laboratory 6 –First and Second Order Circuits As you assemble the board, be sure to place the resistor, inductor, and capacitor in series. Since all the components are in series, it does not matter in which order they are connected, but please build the board like shown in Figure 3 to make debugging easier. Then attach your AD2 kit to the circuit using the key shown in Figure 3. We want one of the Oscilloscope probes to measure the output of the circuit created, while the other is measuring the input. In this case, the input of the circuit is the waveform generator from the AD2. Do not forget to attach your 1- and 2- probes to ground (GND). Picture of Circuit {insert here} Once our circuit is built: 1. Open WaveForms 2. Open the waveform generator and the oscilloscope 3. We want our waveform generator to have the following parameters: a. Type: Square b. Frequency: 5 kHz c. Period: 200 us d. Amplitude: 1 V e. Offset: 0 , Symmetry: 50% , and Phase: 0% 4. Now make sure that your Channel 1 and Channel 2 are showing on the oscilloscope, and make sure they have the same range and offset. We want the input and output to be plotted on top of each other to see the effect the circuit has on the voltage output. 5. Once you have everything set up, Run All programs and put a screenshot of the oscilloscope here: Picture of Oscilloscope {insert here} Save the data as “lab6_data5.csv” and upload it to Canvas. Page 6 of 11

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EECS 215 Laboratory 6 –First and Second Order Circuits 6. Calculate the value of the damping coefficient, , for the series RLC and show your ɑ work: 7. Calculate the value of the natural frequency, ɷ 0 , and show your work: 8. Is the circuit overdamped, critically damped or under-damped? How did you determine this? Use these equations for RLC circuits to determine their properties: ● To find the damping coefficient α = R ( 2 L ) ● To find the resonant frequency ω 0 = 1 √ LC ● To find the damped frequency ω d = √ ω 0 2 − α 2 5. L ABORATORY : P ART F OUR - RLC C IRCUIT W ITH A P OTENTIOMETER (POT) In this part of the lab, you will create a RLC circuit, and manipulate the output to be overdamped, underdamped, and critically damped. In order to complete this part of the lab, you will need to have: ● The circuit from Figure 3 with the 470 Ω resistor replaced with the potentiometer: ? 5 kΩ Potentiometer (POT) When retrofitting the circuit from Figure 3, take the resistor out. Only two legs of the potentiometer need to be used, the middle leg and one end leg. Connect the potentiometer into the circuit using the middle leg and one end leg (it doesn’t matter which end leg). Below is a figure of the style potentiometer we are using. Page 7 of 11

EECS 215 Laboratory 6 –First and Second Order Circuits Figure 4: Wiper Potentiometer The wiper potentiometer is very common. The resistance between terminal 1 and 3 is constant no matter the wiper position. The farther the wiper is from the connected end terminal (1 or 3) the more resistance is seen between pin 2 and that end pin. We want one of the Oscilloscope probes to measure the output of the circuit created, while the other is measuring the input. In this case, the input of the circuit is the waveform generator from the AD2. Do not forget to attach your 1- and 2- probes to ground (GND). Picture of Circuit {insert here} Save the data as “lab6_data6.csv” and upload it to Canvas. Once our circuit is built: 1. Open WaveForms 2. Open the waveform generator and the oscilloscope 3. We want our waveform generator to have the following parameters: a. Type: Square b. Frequency: 1 kHz c. Period: 1 ms d. Amplitude: 2 V e. Offset: 0 , Symmetry: 50% , and Phase: 0% Page 8 of 11

EECS 215 Laboratory 6 –First and Second Order Circuits 4. Now make sure that your Channel 1 and Channel 2 are showing on the oscilloscope, and make sure they have the same range and offset. We want the input and output to be plotted on top of each other to see the effect the circuit has on the voltage output. 5. Once you have everything set up, Run All programs. 6. Once everything is on, we can tune the circuit. Using your small screwdriver, change the poterntiometer’s value by turning the potentiometer’s black wheel. Sweeping the potentiometer from low resistance to high resistance will yield you the overdamped, underdamped, and critically damped phenomena. 7. Tune your potentiometer so that the output is clearly overdamped and provide a picture of your oscilloscope. Picture of Oscilloscope {insert here} Save the data as “lab6_data7.csv” and upload it to Canvas. 8. Remove the potentiometer from the circuit and measure the potentiometer’s resistance. What is the resistance across the middle and end leg? Recalculate the value of the damping coefficient and confirm that the circuit is overdamped. ɑ Value of resistance: Value of alpha: Confirm overdamping: Page 9 of 11

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EECS 215 Laboratory 6 –First and Second Order Circuits 9. Install the potentiometer back into the circuit and adjust its resistance until the circuit is clearly underdamped and provide a picture of your oscilloscope. Picture of Oscilloscope {insert here} Save the data as “lab6_data8.csv” and upload it to Canvas. 10. Remove the potentiometer from the circuit and measure the potentiometer’s resistance. What is the resistance across the middle and end leg? Recalculate the value of the damping coefficient and confirm that the circuit is underdamped. ɑ Value of resistance: Value of alpha (show work): Confirm overdamping (show work): 11. Install the potentiometer back into the circuit and adjust the resistance until the circuit is critically damped. A good way to go about this is to start in the underdamped region of resistance and slowly adjust the resistance until there are virtually no oscillations. Record a picture of your Oscilloscope. Picture of Oscilloscope {insert here} Save the data as “lab6_data9.csv” and upload it to Canvas. Page 10 of 11

EECS 215 Laboratory 6 –First and Second Order Circuits 12. Remove the potentiometer from the circuit and measure the potentiometer’s resistance. Next, calculate the expected value of resistance that will result in critical damping. What is the resistance across the middle and end leg? Recalculate the value of the damping coefficient and confirm that the circuit is critically damped. ɑ Value of resistance: Expected resistance for critical damping (show work): Page 11 of 11