Non-Ideal Op-Amp gain derivation

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Discussion Overview

The discussion revolves around the derivation of gain for a non-ideal operational amplifier (op-amp) circuit, focusing on a specific homework problem. Participants explore various methods for solving the equations involved, including the use of matrices and software tools, while addressing potential errors in calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses confusion over the complexity of the variables involved in the problem.
  • Another suggests using a matrix and math software to simplify the solution process.
  • A participant recommends substituting resistances with their conductance values to avoid fractions in the equations.
  • Multiple participants report discrepancies in their calculated gain values, with one stating a gain of -10^6 while another claims -99.9889.
  • One participant acknowledges a mistake in their calculations and proposes a correction to the numerator of the gain equation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct gain value, as discrepancies in calculations persist. There are competing views on the methods used to solve the problem and the accuracy of the results.

Contextual Notes

There are unresolved mathematical steps and potential errors in calculations that participants are attempting to clarify. The discussion reflects varying approaches to the problem without definitive conclusions.

gfd43tg
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Homework Statement


Problem statement is in the attachment HW 5, it is problem #1.


Homework Equations





The Attempt at a Solution


I am just stuck with a whole bunch of variables and this just looks like a complete mess
 

Attachments

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The best and the easiest way to solve this circuit is to use a matrix. And then use the math software and allow the computer to solve the matrix for us.
See the example
 

Attachments

Your equations look right.

I have 2 suggestions:
1. Instead of R, use G=1/R for all resistances. Makes the math look cleaner by eliminating fractions in your two basic equations.
2. Put your basic equations into math software. Don't try to solve them yourself; you are liable to make a mistake.
 
I'm plugging in the numbers in your equation Jony, and my gain is many orders of magnitude greater than Rf/Rs.

I get -10^24 for the top part of the franction, then 10^16 on the bottom part, giving 10^6 as the gain. The gain for the ideal is 100.
 
Last edited:
Maylis said:
I'm plugging in the numbers in your equation Jony, and my gain is many orders of magnitude greater than Rf/Rs.

I get -10^24 for the top part of the franction, then 10^16 on the bottom part, giving 10^6 as the gain. The gain for the ideal is 100.

You must have made an error in your arithmetic. I get -99.9889 for the gain.
 
I do it over and over and get the same result, are you getting -9.99999E+24 on the top of the fraction, and 1.000E+17 on the bottom?
 
Here's the result I get:

attachment.php?attachmentid=67305&stc=1&d=1394099970.png
 

Attachments

  • Values.png
    Values.png
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Maylis said:
I'm plugging in the numbers in your equation Jony, and my gain is many orders of magnitude greater than Rf/Rs.

I get -10^24 for the top part of the franction, then 10^16 on the bottom part, giving 10^6 as the gain. The gain for the ideal is 100.

Because I made a stupid mistake not in the matrix but in input 5. The gain is A times larger than is should. To correct this simply remove the first A in numerator

correct numerator = Ri RL (-A Rf+Ro) = Ri RL (Ro - Rf A)

Sorry for confusion.
 

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