# Non-Ideal Op-Amp gain derivation

1. Mar 5, 2014

### Maylis

1. The problem statement, all variables and given/known data
Problem statement is in the attachment HW 5, it is problem #1.

2. Relevant equations

3. The attempt at a solution
I am just stuck with a whole bunch of variables and this just looks like a complete mess

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2. Mar 5, 2014

### Jony130

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

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3. Mar 5, 2014

### rude man

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.

4. Mar 5, 2014

### Maylis

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: Mar 5, 2014
5. Mar 5, 2014

### The Electrician

You must have made an error in your arithmetic. I get -99.9889 for the gain.

6. Mar 5, 2014

### Maylis

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?

7. Mar 6, 2014

### The Electrician

Here's the result I get:

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8. Mar 6, 2014

### Jony130

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.