Gain question (Op-amp/capacitors)

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Discussion Overview

The discussion revolves around the analysis of an op-amp circuit involving capacitors and resistors, focusing on deriving the gain expression Vo/Vs. Participants are exploring the application of phasor analysis and Kirchhoff's Voltage Law (KVL) in this context.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • Some participants propose using phasor form and KVL to analyze the circuit, but express uncertainty about how to derive the gain Vo/Vs.
  • One participant requests clearer presentation of the work, noting that images provided are too fuzzy to follow effectively.
  • A participant mentions the final equation derived, indicating that Z1 represents resistor impedance, Z2 another resistor, and Z3 capacitor impedance, but does not clarify how this relates to Vo/Vs.
  • Another participant suggests writing a pair of equations with current i on the left-hand side and equating them to eliminate the i term, aiming to relate output voltage to Vs.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the approach to derive Vo/Vs, with multiple methods and uncertainties expressed throughout the discussion.

Contextual Notes

There are limitations in the clarity of the provided images and the assumptions regarding the circuit configuration, which may affect the analysis. The discussion also relies on the ideal op-amp assumption, specifically that the differential input is zero.

CoolDude420
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Homework Statement


3df2cc6f92.png


Homework Equations

The Attempt at a Solution


507c6fd57e.png

[/B]
My approach was to put them into phasor form and do a KVL loop. However I don't see how I'm going to get Vo/Vs in here?

Vs = i(Z1) + i(Z2 parallel Z3) + Vo
 
Last edited:
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CoolDude420 said:

Homework Statement


View attachment 211602

Homework Equations

The Attempt at a Solution


View attachment 211603
[/B]
My approach was to put them into phasor form and do a KVL loop. However I don't see how I'm going to get Vo/Vs in here?
Could you type your work into the forum window please? Your images are a bit too fuzzy for me to follow. Also, there is a LaTeX tutorial under INFO at the top of the page under Help/How-To.

It sounds like you are trying to user the correct approach, and I'll download your images to see if I can clean thenm up enought for me to be of some help on your questions...
 
berkeman said:
Could you type your work into the forum window please? Your images are a bit too fuzzy for me to follow. Also, there is a LaTeX tutorial under INFO at the top of the page under Help/How-To.

It sounds like you are trying to user the correct approach, and I'll download your images to see if I can clean thenm up enought for me to be of some help on your questions...

My apologies. The final equation I got was this. Where Z1 = resistor impedance, Z2 = other resistor, Z3 = capacitor impedance
Vs = i(Z1) + i(Z2 parallel Z3) + Vo
 
An additional equality for an ideal OP-AMP, differential input is zero, i.e., v+ = v–

Write a pair of equations having i on their left-hand side, then equate them so the i term disappears, leaving you with an equation relating output voltage to Vs.
 

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