Derive the transfer function of the circuit shown in figure below (for an ideal op amp)...

 

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Derive the transfer function of the circuit shown in figure below (for an ideal op amp) and show that it can be written in the form - V. -R2/R1 V," [1+ ( +j) Where w1 = 1/C,R1 and w2 = 1/ C2R2. Assuming that the circuit is designed such that w2 >> w1, find approximate expressions for the transfer function in the following frequency regions: (a) w << W1 (b) wi << w < W1 (c) w >> w2 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 60dB in the "middle frequency range", a low-frequency 3-dB point at 10 Hz, a high-frequency 3-dB point at 10 kHz, and an input resistance (at w >> w1) of 1 kQ. C2 R2 RI Vi Derive the transfer function of the circuit shown in figure below (for an ideal op amp) and show that it can be written in the form - V. -R2/R1 V," [1+ ( +j) Where w1 = 1/C,R1 and w2 = 1/ C2R2. Assuming that the circuit is designed such that w2 >> w1, find approximate expressions for the transfer function in the following frequency regions: (a) w << W1 (b) wi << w < W1 (c) w >> w2 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 60dB in the "middle frequency range", a low-frequency 3-dB point at 10 Hz, a high-frequency 3-dB point at 10 kHz, and an input resistance (at w >> w1) of 1 kQ. C2 R2 RI Vi