Lab 3 & 4 ECE 3709L

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Electrical Engineering

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Feb 20, 2024

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Lab 3 & 4 OP Amp Integrator Analysis ECE 3709L-07 March 2 nd , 2023 Objectives

To build, simulate and analyze op amp integrator circuit which is used in PID controllers using both hardware and software, and obtain solid understanding of the op amp integrator behavior. Pre-Lab Task A1 Understanding Op Amp LM741 Finding the specifications of LM741 a. The supply voltage rating is ± 22V. b. The input voltage rating ± 15V. c. The differential input voltage is ± 30V. Task A2 Transfer function of Op Amp Integrator Circuit 1. Verifying H(w) V out ()= R 3 R 1 + R 2 jCR 2 + 1 + R 3 ∗ V ¿ () H ()= V out V ¿ = R 3 R 1 + R 2 jCR 2 + 1 + R 3 H ()= V out V ¿ = R 3 ( j R 2 C + 1 ) ( R 1 + R 3 ) ( j R 2 C + 1 ) + R 2 H ()= V out V ¿ = − R 2 R 1 + j V out V ¿ C R 1 R 2 2. Gain = 0.9818 Phase Shift = 92.03 ⁰ Lab Section B1. Op Amp Gain and Phase Shift for Different Frequencies

* Note Capacitor value = 0.33 uF, Also the Op Amp is being supplied with +/- 22V Table 1 Results of Experiment B1 Frequenc y Hz Calc H () Calc V out Meas V out Error V out Magnitud e (Gain) Phase deg Amplitud e V Phase deg Amplitud e V Phas e deg Amplitud e Phase 20 4.37 143.2 6 6.55 143.2 6 6.494 143. 4 0.009 0.001 80 1.732 108.5 1 2.60 108.5 1 2.585 108. 6 0.006 0.009 160 0.901 99.51 1.35 99.51 1.345 99.5 7 0 0.000 6 320 0.4551 94.78 0.68 94.78 0.68 94.7 7 0.004 0.000 1 640 0.229 92.39 0.342 92.39 0.3412 92.3 5 0.002 0.000 4

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Graphs for B1 0 100 200 300 400 500 600 700 0 1 2 3 4 5 6 7 Magnitude vs Frequency Frequency Magnitude 0 100 200 300 400 500 600 700 0 1 2 3 4 5 6 7 Phase Deg vs Frequency Phase Deg Magnitude

0 100 200 300 400 500 600 700 0 1 2 3 4 5 6 7 Measured Amplitude vs Frequency Amplitude Magnitude B2. Circuit maximum/minimum gain and phase shift Table 2 Results for Experiment B2 Frequency Hz Gain Phase Shift Maximum Minimum Maximum Minimum 1-19 8.119 6.612 177.9 144.8 21-79 6.384 2.614 142 108.8 81-159 2.556 1.353 108.4 99.59 321-639 0.677 0.3418 94.75 92.35

B3. Simulation in Simscape Simscape Diagram Input and Output Voltages on the Same Scope

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Parameters used in this circuit were as followed: R1 = 3.3kOhms R2 = 18kOhms R3 = 1.3kOhms C = 0.33uF Frequency = 20Hz Yellow = Output Source Blue = Input Source B4. Analysis of Op Amp Integrator behavior using Simscape Input vs Output of Pulse Voltage Source

Yellow = Output Source Blue = Input Source Simulated parameters: Vin(t) = 1.5cos(2  20 t), R1 = 3.3 k  , R2 = 18 k  , R3 = 1.3 k  , C = 0.33 μF

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