logistic_guy
Full Member
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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 \(\displaystyle \frac{V_{o}}{V_{i}} = \frac{-R_2/R_1}{[1 + (\omega_1 /j\omega)][1 + (\omega /\omega_2)]}\) where \(\displaystyle \omega_1 = \frac{1}{C_1R_1}\) and \(\displaystyle \omega_2 = \frac{1}{C_2R_2}\). Assuming that the circuit is designed such that \(\displaystyle \omega_2 \gg \omega_1\), find approximate expressions for the transfer function in the following frequency regions:
(a) \(\displaystyle \omega \ll \omega_1\)
(b) \(\displaystyle \omega_1 \ll \omega \ll \omega_2\)
(c) \(\displaystyle \omega \gg \omega_2\)
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 \(\displaystyle 40\) dB in the “middle-frequency range,” a low-frequency \(\displaystyle 3\)-dB point at \(\displaystyle 200\) Hz, a high-frequency \(\displaystyle 3\)-dB point at \(\displaystyle 200\) kHz, and an input resistance (at \(\displaystyle \omega \gg \omega_1\)) of \(\displaystyle 2\) k\(\displaystyle \Omega\).
my attemb
according to this website
masteringelectronicsdesign.com
the transfer function for the inverting amplifier is \(\displaystyle V_o = -V_i\frac{R_2}{R_1}\) which can be written as \(\displaystyle \frac{V_o}{V_i} = -\frac{R_2}{R_1}\)
but the circuit in the website don't have capacitors \(\displaystyle C_1\) and \(\displaystyle C_2\)
what should i do in this case?
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 \(\displaystyle \frac{V_{o}}{V_{i}} = \frac{-R_2/R_1}{[1 + (\omega_1 /j\omega)][1 + (\omega /\omega_2)]}\) where \(\displaystyle \omega_1 = \frac{1}{C_1R_1}\) and \(\displaystyle \omega_2 = \frac{1}{C_2R_2}\). Assuming that the circuit is designed such that \(\displaystyle \omega_2 \gg \omega_1\), find approximate expressions for the transfer function in the following frequency regions:
(a) \(\displaystyle \omega \ll \omega_1\)
(b) \(\displaystyle \omega_1 \ll \omega \ll \omega_2\)
(c) \(\displaystyle \omega \gg \omega_2\)
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 \(\displaystyle 40\) dB in the “middle-frequency range,” a low-frequency \(\displaystyle 3\)-dB point at \(\displaystyle 200\) Hz, a high-frequency \(\displaystyle 3\)-dB point at \(\displaystyle 200\) kHz, and an input resistance (at \(\displaystyle \omega \gg \omega_1\)) of \(\displaystyle 2\) k\(\displaystyle \Omega\).
my attemb
according to this website
How to Derive the Inverting Amplifier Transfer Function – Mastering Electronics Design
the transfer function for the inverting amplifier is \(\displaystyle V_o = -V_i\frac{R_2}{R_1}\) which can be written as \(\displaystyle \frac{V_o}{V_i} = -\frac{R_2}{R_1}\)
but the circuit in the website don't have capacitors \(\displaystyle C_1\) and \(\displaystyle C_2\)
what should i do in this case?