2. The differentiator circuit shown in Fig. 2 uses an OPAMP with ideal characteristics. R2 Vi R1 C'₁ - Vo + Figure 2: Differentiator circuit. (a) Using first principles derive an expression for the gain of this circuit in the frequency domain. (b) If the differentiator's corner frequency is 100 rad s-1, the high frequency gain is 40 dB, and R2 is 220k, determine the values of C₁ and R₁. (c) Sketch the Bode magnitude response for this circuit for the frequency range of 100 to 108 rad s¹. Clearly indicate the steps you followed, including the numerical workings, and assumptions made to obtain this response.

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2. The differentiator circuit shown in Fig. 2 uses an OPAMP with ideal characteristics.
R2
Vi
R1
C'₁
- Vo
+
Figure 2: Differentiator circuit.
(a) Using first principles derive an expression for the gain of this circuit in the frequency domain.
(b) If the differentiator's corner frequency is 100 rad s-1, the high frequency gain is 40 dB, and
R2 is 220k, determine the values of C₁ and R₁.
(c) Sketch the Bode magnitude response for this circuit for the frequency range of 100 to
108 rad s¹. Clearly indicate the steps you followed, including the numerical workings, and
assumptions made to obtain this response.
Transcribed Image Text:2. The differentiator circuit shown in Fig. 2 uses an OPAMP with ideal characteristics. R2 Vi R1 C'₁ - Vo + Figure 2: Differentiator circuit. (a) Using first principles derive an expression for the gain of this circuit in the frequency domain. (b) If the differentiator's corner frequency is 100 rad s-1, the high frequency gain is 40 dB, and R2 is 220k, determine the values of C₁ and R₁. (c) Sketch the Bode magnitude response for this circuit for the frequency range of 100 to 108 rad s¹. Clearly indicate the steps you followed, including the numerical workings, and assumptions made to obtain this response.
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