D **2.93 Derive the transfer function of the circuit in Fig. P2.93 (for an ideal op amp) and show that it can be written in the form Vo Vi = −R 2/R1 [1+(ω1/jω)][1+j(ω/ω2)] whereω 1 =1/C1R1 andω2 =1/C2R2. Assuming that the circuit is designed such that ω2  ω1, find approximate expressions for the transfer function in the following frequency regions: (a) ω  ω1 (b) ω1  ω  ω2 (c) ω  ω2 V o Figure P2.93 Use these approximations to sketch a Bode plot for the magnitude response. Observe that the circuit performs as an amplifier whose gain rolls off at the low-frequency end in the manner of a high-pass STC network, and at the high-frequency end in the manner of a low-pass STC network. Design the circuit to provide a gain of 40 dB in the “middle-frequency range,” a low-frequency 3-dB point at 200 Hz, a high-frequency 3-dB point at 200 kHz, and an input resistance (at ω  ω1) of 2 k.

93 - D **2.93 Derive the transfer function of the circuit in Fig. P2.93 (for an ideal op amp) and show that it can be written in the form Vo Vi = −R 2/R1 [1+(ω1/jω)][1+j(ω/ω2)] whereω 1 =1/C1R1 andω2 =1/C2R2. Assuming that the circuit is designed such that ω2  ω1, find approximate expressions for the transfer function in the following frequency regions: (a) ω  ω1 (b) ω1  ω  ω2 (c) ω  ω2 V o Figure P2.93 Use these approximations to sketch a Bode plot for the magnitude response. Observe that the circuit performs as an amplifier whose gain rolls off at the low-frequency end in the manner of a high-pass STC network, and at the high-frequency end in the manner of a low-pass STC network. Design the circuit to provide a gain of 40 dB in the “middle-frequency range,” a low-frequency 3-dB point at 200 Hz, a high-frequency 3-dB point at 200 kHz, and an input resistance (at ω  ω1) of 2 k.

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images - D **2.93 Derive the transfer function of the circuit in Fig. P2.93 (for an ideal op amp) and show that it can be written in the form Vo Vi = −R 2/R1 [1+(ω1/jω)][1+j(ω/ω2)] whereω 1 =1/C1R1 andω2 =1/C2R2. Assuming that the circuit is designed such that ω2  ω1, find approximate expressions for the transfer function in the following frequency regions: (a) ω  ω1 (b) ω1  ω  ω2 (c) ω  ω2 V o Figure P2.93 Use these approximations to sketch a Bode plot for the magnitude response. Observe that the circuit performs as an amplifier whose gain rolls off at the low-frequency end in the manner of a high-pass STC network, and at the high-frequency end in the manner of a low-pass STC network. Design the circuit to provide a gain of 40 dB in the “middle-frequency range,” a low-frequency 3-dB point at 200 Hz, a high-frequency 3-dB point at 200 kHz, and an input resistance (at ω  ω1) of 2 k.

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