Question

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 -R2/R where a).-idGK, and as = 1/GR2. Assuming that the circuit is designed such that ind approximate expressions

Derive the transfer function of the circuit in Fig.P2.93(foranidealopamp)andshowthatitcanbewritten in the form
Vo Vi = −R2/R1 [1+(ω1/jω)][1+j(ω/ω2)] whereω1=1/C1R1 andω2=1/C2R2.Assumingthatthecircuit is designed such that ω2 ω1, find approximate expressions
for the transfer function in the following frequency regions: (a) ωω1 (b) ω1 ωω2 (c) ωω2
Vo
FigureP2.93
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-frequencyrange,”alow-frequency3-dBpointat 200Hz,ahigh-frequency3-dBpointat200kHz,andaninput resistance (at ωω1) of 2 k.