Non-Ideal Op-Amp gain derivation

[gfd43tg]

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

 

[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

 

[rude man]

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.

 

[gfd43tg]

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.

 

[The Electrician]

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.

 

[gfd43tg]

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?

 

[The Electrician]

Here's the result I get:

 

[Jony130]

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.