EME108S24_Lab3_Handout

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University of California, Davis *

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108

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Electrical Engineering

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Apr 25, 2024

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1 University of California Davis EME 108 Spring 2024 Lab 3: OPERATIONAL AMPLIFIERS Learning Objectives Equipment and software 1. Learn about different types of op-amp circuits and their uses. 2. Gain practical experience in assembling circuits and calculating output voltage in electric circuits. 3. Build an inverting circuit, a summing circuit, and an integrating circuit. 4. Learn how op-amps work and determine why filtering is important. 5. Construct and analyze an operational amplifier first order system. 1. Three 𝜇𝐴741 op-amps 2. Five 100𝑘𝛺 resistors 3. One 0.01𝜇𝐹 capacitor 4. One potentiometer ( 100𝑘𝛺 max) 5. One breadboard and wires for connections 6. MyDAQ function generator and oscilloscope 7. MyDAQ Bode tool A) Lab Assignments: 1. Before your lab section starts, read through the lab handout and complete the pre-lab work in your notebook, with the following entries all in your own words (refer to EME108 Lab Notebook Template.pdf on Canvas for more information on how to write the notebook reports). Every student needs to complete their own pre-lab entry in their own notebook and let the TAs check at the start of the lab. - Title block - Objective - Equipment and setup - Responses to pre-lab questions - Concise procedure in bullet points Every student needs to complete their own pre-lab entry in their own notebook and let the TAs check at the start of the lab ( first 15 minutes). 2. Lab memo report, to be submitted to Canvas before the start of your next lab session. Each group only needs to submit one report. - Review EME108_memo_report_guidelines.pdf and EME108S24_Lab3_Memo_Instructions.pdf and use them as a checklist. - Refer to documentations provided on Canvas in the “ Engineering Writing Resources ” folder to help creating your report. B) Scenario: Your boss suddenly becomes extremely interested in 1 st order systems and asks you to construct an electrical circuit, which operates as a 1 st order system, and then analyze it for a range of input frequencies and use different methods to determine its time constant and cut-off frequency.

2 C) Prelab Questions: Before your lab section, review how to calculate output voltage in electric circuits, as explained in class. Answer the following questions in your lab notebook: 1. Consider the composite circuit shown in Figure 5. This composite circuit is the union of the three individual circuits shown in Figures 2 to 4. Use the equations in Figures 2 to 4 to write a differential equation that relates the input voltage ( 𝑒 ௜ ) and output voltage ( 𝑒 ௢ ) of the circuit in Figure 5. For your calculations, assume 𝑅 ଵ = 𝑅 ଶ = 𝑅 ଷ = 𝑅 ସ = 𝑅 ହ . (Hint: the result will be a first-order differential equation. 𝑅 ௜ is the potentiometer resistance and is variable.) 2. Assume the input to the system in Figure 5 is a sinusoidal signal 𝑒 ௜ (𝑡) = 𝐴 ∗ 𝑠𝑖𝑛 (𝜔𝑡) , the steady-state output 𝑒 ௢ of this system will also be a sinusoid 𝑒 ௢ (𝑡) = 𝐵 ∗ 𝑠𝑖𝑛 (𝜔𝑡 + 𝜙) with a different amplitude 𝐵 and a different phase angle 𝜙 . Use the result from Question 1 and your knowledge of the first-order system, write the expressions for 𝐵 and 𝜙 . 3. Based on your results from Question 2, write the expression for the magnitude ratio (output amplitude divided by input amplitude) of the system in Figure 5 and provide a sketch of its plot versus frequency. 4. Based on your results from Question 2, write the expression for the phase shift of the system in Figure 5 and provide a sketch of its plot versus frequency. 5. Use your knowledge of the first-order system and your answers from Questions 1-4, write the expression for the time constant of the composite circuit in Figure 5. 6. If we have a fast-moving input signal that we want the system in Figure 5 to follow, would we want to have a time constant of the system that is small or large? Explain why. 7. If we have a slow-moving input signal that we want the system in Figure 5 to follow, but a fast-moving noise on the input that we want to filter out, would we want to have a time constant of the system that is small or large? Explain why. 8. What’s the difference between angular frequency 𝜔 and circular frequency 𝑓 ? What are their units respectively? How are they related? 9. What does it mean if the dynamic system you are studying has a steady state gain greater than 1? D) Reference: Take a look at the following reference to improve your understanding of op-amp based circuits: 1. http://www.electronics-tutorials.ws/category/opamp/

3 E) Lab Procedures: Part 1: Testing Individual Circuits 1. Look at the pinout diagram of the op-amp shown in Figure 1, sketch in your lab notebook the wiring diagrams for the inverter, the summer, and the integrator circuit shown in Figures 2 to 4, respectively. These sketches should show which pins of the op-amp are being used for each circuit. You should understand your wiring diagrams before you attempt to build the circuits. Check your diagrams with your TA and obtain his/her signature . 2. Before building your circuit, measure the value of each resistor and each capacitor you are using to make sure you have selected the right components. Note: The potentiometer (“pot”) has three pins: call them top, middle, and bottom. The top and bottom pins are collinear, and the resistance between these two collinear pins is a constant value around 100𝑘𝛺 . Turning the adjustment screw will simultaneously change the resistance between the top and middle pins and the resistance between the middle and bottom pins. That is, if the top-middle resistance increases by 100 Ω, the middle-bottom resistance will decrease by 100 Ω. 3. Disconnect power to your myDAQ (USB cable) at this step. Using your sketches as the guide, strategically build these three individual circuits in Figures 2 to 4 with three op-amps in different places on your breadboard. Make sure to employ good circuit building practices! The three pins of the potentiometer need to be placed in three different rows on the breadboard, but wire only the top and middle pins of the potentiometer to correct op-amp pin locations, leaving the bottom pin plugged in but unused. Do not cut or bend the pins of your potentiometer. Keep your circuit clean and wires short, use railings for shared power and ground, and use color- coded wires. 4. Do not power to your myDAQ yet. You are going to use the myDAQ function generator to generate the input signal and the myDAQ oscilloscope to view both the input and the output signals. Your oscilloscope should display both the input and output waveforms. Hint: use the AO 0 channel of myDAQ to generate the input signal to your circuit, use AI 0+ to read the input signal and AI 1+ to read the output signal of your circuit. Don’t forget to connect AI0- and AI1- to ground. 5. Now test the expected functionality of each circuit . Ask your TA to check the circuit you are going to test and obtain his/her signature, before plugging the myDAQ to the computer. Disconnect the op-amps not in use from the +/-15V power during tests and remember to unplug the USB cable of the myDAQ between tests. 1) Summing circuit: Generate a sine wave with 1 kHz frequency, 2 Vpp amplitude and 0 V offset as an input , wire both 𝑒 ௜ and 𝑒 ଶ to the input signal from the myDAQ function generator. Does the output combine the signals as indicated by the given formula? Show your TA your results and obtain his/her signature.

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