1. The differentiator circuit shown in Fig. 1 uses an op-amp with ideal characteristics. R2 Vi σ R₁ Vo Figure 1: Differentiator circuit. (a) Prove that the gain of the circuit is given by the following expression using first principles for an ideal op-amp: Vo Gain = Vi -jwC₁R₂ (1 + jwC₁R₁) (b) The differentiator has unity gain at 1 kHz and the high frequency gain is 40 dB. If R2 is 120 kn, design the rest of the component values. (c) Sketch the Bode magnitude response for this circuit for the frequency range of 10° to 108 Hz.

Delmar's Standard Textbook Of Electricity
7th Edition
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Stephen L. Herman
Chapter18: Resistive-inductive Parallel Circuits
Section: Chapter Questions
Problem 13PP: In an R-L parallel circuit, IT=1.25 amps, R=1.2k, and XL=1k. Find IR
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please answer all parts of the question and please include a neat sketch of the bode plot and how you got the bode plot values thank you

1. The differentiator circuit shown in Fig. 1 uses an op-amp with ideal characteristics.
R2
Vi σ
R₁
Vo
Figure 1: Differentiator circuit.
(a) Prove that the gain of the circuit is given by the following expression using first principles for an ideal
op-amp:
Vo
Gain =
Vi
-jwC₁R₂
(1 + jwC₁R₁)
(b) The differentiator has unity gain at 1 kHz and the high frequency gain is 40 dB. If R2 is 120 kn,
design the rest of the component values.
(c) Sketch the Bode magnitude response for this circuit for the frequency range of 10° to 108 Hz.
Transcribed Image Text:1. The differentiator circuit shown in Fig. 1 uses an op-amp with ideal characteristics. R2 Vi σ R₁ Vo Figure 1: Differentiator circuit. (a) Prove that the gain of the circuit is given by the following expression using first principles for an ideal op-amp: Vo Gain = Vi -jwC₁R₂ (1 + jwC₁R₁) (b) The differentiator has unity gain at 1 kHz and the high frequency gain is 40 dB. If R2 is 120 kn, design the rest of the component values. (c) Sketch the Bode magnitude response for this circuit for the frequency range of 10° to 108 Hz.
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