inverting amplifier

logistic_guy

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Apr 17, 2024
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here is the question

Derive the transfer function for the operational amplifier (an ideal op amp) in the figure and show that it can be written in the form VoVi=R2/R1[1+(ω1/jω)][1+(ω/ω2)]\displaystyle \frac{V_{o}}{V_{i}} = \frac{-R_2/R_1}{[1 + (\omega_1 /j\omega)][1 + (\omega /\omega_2)]} where ω1=1C1R1\displaystyle \omega_1 = \frac{1}{C_1R_1} and ω2=1C2R2\displaystyle \omega_2 = \frac{1}{C_2R_2}. Assuming that the circuit is designed such that ω2ω1\displaystyle \omega_2 \gg \omega_1, find approximate expressions for the transfer function in the following frequency regions:

(a) ωω1\displaystyle \omega \ll \omega_1
(b) ω1ωω2\displaystyle \omega_1 \ll \omega \ll \omega_2
(c) ωω2\displaystyle \omega \gg \omega_2

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\displaystyle 40 dB in the “middle-frequency range,” a low-frequency 3\displaystyle 3-dB point at 200\displaystyle 200 Hz, a high-frequency 3\displaystyle 3-dB point at 200\displaystyle 200 kHz, and an input resistance (at ωω1\displaystyle \omega \gg \omega_1) of 2\displaystyle 2 kΩ\displaystyle \Omega.

op_amp.png


my attemb
according to this website


the transfer function for the inverting amplifier is Vo=ViR2R1\displaystyle V_o = -V_i\frac{R_2}{R_1} which can be written as VoVi=R2R1\displaystyle \frac{V_o}{V_i} = -\frac{R_2}{R_1}
but the circuit in the website don't have capacitors C1\displaystyle C_1 and C2\displaystyle C_2
what should i do in this case?☹️
 
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