ELE_292_F23_Lab7

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Electrical Engineering

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Dec 6, 2023

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ELE 292 – Linear Systems Lab Lab 7 – The Differentiator and the Fourier Series C1 = 150e-9 R2 = 6.8e6 R1 = 2.2e3 s = 2*np.pi*j D_x = 245.8e-3 H_s = (-s(R2/R1))/(s+(1/(R1*C1)) print(H_s) import numpy as np import matplotlib.pyplot as plt import scipy.signal as sig Collaboraters: Luke Rogers and Ashraf Alnatour Make a report for your laboratory experiment using Jupyter Notebook for submission as usual. Goals: 1) Build the practical (approximation) differentiator that was designed in PreLab. 2) Measure the output when given a sinusoidal input. Infer the phasor of the transfer function. 3) Compare the measured transfer function with the theoretical transfer function of the practical differentiator, and with the theoretical transfer function of the ideal differentiator. 4) Observe the response of the differentiator when given an approximated triangular input. 5) Calculate the output using the phasor method, display the result on the oscilloscope. 6) Observe the response of the differentiator when given a true triangular input. Build the Differentiator you designed for PreLab 1

We are going to test an op amp circuit again this week. Because we are not going to use the Itsybity, we can use a 5V supply. If we wanted, we could connect this to an Arduino Nano because the Nano is a 5V device. In this lab we will simply use Analog Discovery. The drawing below is a reminder of the DIP pin diagram for the MCP6002 op amp. W1 is the positive terminal of Vin (on the circuit schematic above) and W2 is the 2.5V reference connected to Pin 3 of the op amp. The negative terminal of Vin is the ground. Use V+ for the 5V source connected to Pin 8 of the op amp and Pin 4 of the op amp is connected to ground. Observe Vin on Channel 1 and Vout on Channel 2 of the Scope. Set up Wavegen for W1 and W2 Again, we need to use both W1 and W2. W2 is going to be the reference voltage. Use the control similar to what is shown in the figure below to enable W2. When you do you will get two Wavegen windows. 2

Make W1 a 1Hz sine wave with an offset of 2.5V. Make the amplitude 324mV, so the peak-to-peak voltage is 648mV. Make W2 a DC source set to 2.5V. Observe both input and output on Scope at the fundamental frequency On the Scope you should see both the input and output sine waves. You should see an output wave that is phase shifted from the input. Use Analog Discovery to measure Vout on Channel 2. Record the magnitude of Channel 2 and the phase difference between Channel 1 and Channel 2. In your report record the phasor values for Vin and Vout. Because the phasor method tells us that V out = H ( s ) V ¿ , we can determine H(s) from V out V ¿ . Phasors are only valid at one frequency at a time. Because we have set the frequency of Vin to 1Hz, dividing the phasor value of Vout by the phasor value of Vin gives us H(s) at the frequency s = j2π. Calculate the phasor V in . Calculate the phasor V out . Calculate the phasor V out V ¿ . Express it as a complex number. Compare this answer to H ( s ) = − s R 2 R 1 s + 1 R 1 C 1 when s = j2π. Also compare this answer to -s when s = j2π. Remember, our high-pass filter circuit is approximating an inverting differentiator , which has a transfer function of -s. Make sure you include your calculations and comparisons in your report. Create a signal that represents the Fourier series of a Triangle wave Now we are going to use Wavegen custom to make two sin/cos waves at the same time. Change the type of wave settings from Simple to Custom. You can find the pulldown menu for this in the toolbar that looks similar to the figure below. 3

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