Lab VIII Op Amps 2 Integrator and Differentiator

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306

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Electrical Engineering

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Dec 6, 2023

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CMPE 306 Lab VIII: Op Amps 2: Integrator and Differentiator Circuits (revision 1 4/9/2014) (revised for Keysight Equipment 10/13/2023) Created by: EFC LaBerge based on 2008 lab by Dr. L. Yan and Ryan Helinski April 2014 October 2023

1 1. Purpose and Introduction The purpose of this lab is to study the use of an operational amplifier to implement circuits that provide integration and differentiation of analog input signals. By the end of this lab session, students will be able to perform the following tasks: 1. Verify the integrator/differentiator operation by means of an LTSPICE simulation. 2. Construct an integrator and a differentiator circuit on the breadboard. 3. Measure and illustrate characteristics of integrator and differentiator circuits. 4. Perform analyses on measured data to demonstrate the limitations of the differentiator and integrator circuits as a function of the frequency of the input signal. 2. Pre-Lab This lab portion should be done using the circuit file Lab8_RC1 provided on Blackboard. Figure 1 shows the first circuit for today’s lab. For a sinusoidal voltage source, instead of the DC voltage value enter the SINE command with the following parameters: SINE( DCoffset, Amplitude, Freq, Tdelay, Theta, Phi, Ncycles) For the capacitor C1 in Figure 1 , I have sinusoidal voltage source with a DCoffset of 0 Volts, an amplitude ( not peak-to-peak) of 1V, Freq = 500 Hz (cycles/second), Tdelay = 0 seconds, Theta = 0 radians and Phi = 0 degrees. LTSPICE generates 1000 cycles, or two seconds worth of data. The form of the sinusoidal voltage is where is the amplitude, is the frequency in Hz, and is the unit step function. v 3 ( t ) = A sin 2 π f ( t − t delay ) + θ + 2 π 360 φ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ u ( t − t delay ), 0 ≤ t < N cyles f A f u ( t )

2 Figure 1 LTSPICE Circuit #1 Showing Sinusoidal Voltage Source and Transient Response Command 1. Load the circuit file LabVIII_RC1.cir containing the circuit of Figure 1 . Run the simulation. 2. From plotting window (which should come up immediately), select the Add Traces option. Add the trace for V(vin) and V(vout). You should see a plot that looks like Figure 2 . Collaborate with your lab partner to answer the following questions. Why does the blue (vout) curve have the shape it does? Identify the transient and steady state regions. Figure 2: Square Wave input V(vin) and RC output V(vout) U1 LT1190 V1 12V 2 V V 2 1 V3 SINE(0 1 500 0 0 0 1000) R1 10kohm R2 1megaohm C1 100nF +12V V 2 1 - +12V -12V Vout Vin LT1190 is equivalent to your TL074 Quad Op Amp I used it for LTSPICE reasons, just use the TL074 in this lab. .tran 1e-5 500e-3 0ms 50ms 100ms 150ms 200ms 250ms 300ms 350ms 400ms 450ms 500ms V 0 . 1 - V 8 . 0 - V 6 . 0 - V 4 . 0 - V 2 . 0 - V 0 . 0 V 2 . 0 V 4 . 0 V 6 . 0 V 8 . 0 V 0 . 1 V(vin) V(vout)

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3 Figure 3 LTSPICE CIrcuit #2 Showing Sinusoidal Voltage Source and Transient Response Command 3. Perform the following computation to estimate the amplitude of the output sine wave ࠵? !"# , where is the frequency of the input sine wave, and is the amplitude of the input sine wave 4. Change the time scale of the plot and look at the region between 440 ms and 460 ms. The input voltage is a sine wave. Verify that the output voltage is a cosine wave, with the amplitude computed in Step 3. With your partner, discuss how this circuit approximates an integrator circuit, where , 1 where is the gain factor computed in step 3. 5. Load the circuit LabVIII_RC2.cir from Blackboard. This circuit is shown in Figure 3 . Following the guidance given above, set the voltage source to be the same pulsed source as in Figure 1 , and set the capacitor to a value of 100nF with 0V initial condition. Add the transient command. 6. Simulate the circuit, and plot the input and output voltages, as in Step 2. 7. Repeat step 3, this time using the expression . Compare the computation to your simulated output. 8. Change the time scale of the plot and look at the region between 440 ms and 460 ms. The input voltage is a sine wave. Verify that the output voltage is a cosine wave, with the amplitude 1 The math symbol means “is proportional to”, that is, the result is the desired result multiplied by some constant. U1 LT1190 V1 12V 2 V V 2 1 V3 SINE(0 1 500 0 0 0 1000) R1 10kohm C1 100nF +12V V 2 1 - +12V -12V Vout Vin LT1190 is equivalent to your TL074 Quad Op A I used it for LTSPICE reasons, just use the TL074 .tran 1e-5 500e-3 V out = G ( f ) × V in = − R 2 R 1 × V in 1 + (2 π fR 2 C ) 2 f = 500 Hz V in = 1V V out ( t ) ∝ V in ( t ) dt 0 t ∫ G ( f ) V out = G ( f ) × V in = 2 π fR 1 CV in ∝

4 computed in Step 3. With your partner, discuss how this circuit approximates a differentiator circuit, where , where is the gain factor computed in step 3. 9. Provide the plots you generated in LTSPICE in your lab report. You might find it helpful to print them as PDF files and then insert the PDF files. 3. Equipment This lab exercise uses the following equipment: 1) Keysight Arbitrary Function Generator 2) Keysight Digital Storage Oscilloscope 3) BNC-to-BNC cable 4) Two BNC-to-alligator cables. 5) 1 MΩ, 10kΩ, 20kΩ, quad op amp package as in Lab VI. 6) 100nF and 10nF capacitors. 7) Your personal USB drive. 4. . Procedure 4.1. Op-Amp based integrator circuit 1. Consider the circuit shown in Figure 1 (use Figure 1, not Figure 3!) . Use the expression given in Step 3 of the pre-lab to estimate the amplitude of the output response at 500 Hz. 2. Use input of 2 V (peak-to-peak) 500 Hz square wave with zero DC offset to the circuit in 1). Save your oscilloscope display to your USB drive showing both V i (t) (yellow) and V o (t) (PR1) (green). This is Plot 1. Verify the input and output relation prediction in 1). 3. Repeat 2) for 1kHz. Remember that you will need to recomputed the frequency- dependent gain term. ). Save your oscilloscope display to your USB drive showing both V i (t) (yellow) and V o (t) (green). This is plot 2 4. Change to 20k and repeat 2). ). Save your oscilloscope display to your USB drive showing both V i (t) (yellow) and V o (t) (green). This is Plot 3. 5. Change V i (t) to a triangle wave and repeat 2), 3), and 4). ). Save your oscilloscope display to your USB drive showing both V i (t) (yellow) and V o (t) (green). This is Plot 4 6. Change V i (t) to a sine wave and repeat 2), 3), and 4). ). Save your oscilloscope display to your USB drive showing both V i (t) (yellow) and V o (t) (green). This is Plot 5. 7. Use the lab computer or your laptop to show Plot 1 – Plot 5 to your lab instructor. V out ( t ) ∝ dV in dt G ( f ) R 1

5 4.2. Op-Amp based differentiator circuit 1. Construct the circuit shown in Figure 3 , (Figure 3, not Figure 1 or Figure 2!). Compute the expected amplitude of the output using the expression given in Step 7 of the prelab. 2. Configure the AFG to provide a 1V (peak-to-peak) 1 kHz sine wave input. 3. Apply the input to the circuit and print out both . Compare the amplitudes with the computed amplitude. From Step 1 of this section. ). Save your oscilloscope display to your USB drive showing both V i (t) (yellow) and V o (t) (PR1) (green). This is Plot 6. 4. Change Vi (t) to a triangle wave and repeat 2). Save your oscilloscope display to your USB drive showing both V i (t) (yellow) and V o (t) (PR1) (green). This is Plot 7. 5. Display Plot 6 and Plot 7 on the lab computer or your laptop. Show your lab instructor Plot 6 and Plot 7 4.3. Preparation for Next Lab For the lab report for this week, please include all of the plots that you were asked to save, and all of the values you were asked to record, and the computations you were asked to make. Partners should participate in the derivations. Please indicate in your report if your partner participated or not. 5. Tear Down and Clean Up 1. Turn off the power supply, AFG, and oscilloscope and set the multimeter to the OFF position. Return the multimeter to your TA for storage. 2. Save your images or data to your memory stick. Then close the program and sign off of the computer. 3. Put your resistors and capacitors chip back in your lab kit. Return your lab kit to the TA for storage. 4. Return the BNC cables and BNC-to-alligator cables and hang them neatly in their proper rack. 5. Police your lab area: leave it neat and clean. 6. If you’re using your own laptop, there’s nothing else to clean up. 7. If you’re using the lab computer, save whatever work you want to your USB drive. Close LTSPICE if necessary. Eject your drive. V in ( t ), and V out ( t )

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