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Wanted to learn basic Op-Amp theory? Here you go!

## Intro

"Digital Design is stupid.. any idiot can count to one!" - Bob Widlar

I have a deep passion and respect for analog electronics. In my opinion, you can make 100 different digital circuits that perform the exact same, but you can make 100 different analog circuits that perform the same task, but they each have their own unique qualities. In my mind, analog electronics is an art, not just a science. This is what I think helps fuel my desire to learn analog design. If you are also trying to learn analog design, you will quickly find out that one of the most common and useful building blocks is an op-amp (operational amplifier). There are a thousand different articles on the same topics, but I hope to put my personal twist into this, and also include some things I had to learn from trial and error.

## The Op-Amp The symbol for an op-amp is simply a triangle, with two inputs, and one output. There is a non-inverting input (+ Pin), and an inverting input (- Pin). There are a few rules when it comes to the op-amp, these help define how you can use them in your circuits.
1. The open loop gain of an op-amp is infinite
2. No current shall flow through the inputs (infinite input impedence)
3. In a negative feedback operation, the op amp will try to make the inputs match.

However, these rules are based on an ideal op-amp. The world is far from perfect (for example, Taylor Swift exists...), so your op-amp inputs WILL have a small current flow, the input impedances are not infinite (usually they are pretty high), and the inputs will never be exactly the same.

## Inverting Operation Amplifier

One of the most common circuits you will see is the inverting op-amp. This circuit uses negative-feedback to create a voltage gain. The gain of this amplifier can be found with this simple formula; $$A_v=\frac{R_f}{R_i}$$

This is good and all... and if you test it in a simulator, you will see that it works great! Let's do some math to find out how it will act with DC voltages.
For this test, $$R_i=1k$$ and $$R_f=2k$$, our input voltage will be $$V_{in}=2.76v$$. The voltage formula for an op-amp is; $$V_o=A_v(V_+-V_-)$$.

First, let's find the voltage gain ($$A_v$$);
$$A_v=\frac{R_f}{R_i}=\frac{2000}{1000}=2$$
Then, simply plug in the variables (we can assume that at startup, the op-amp's output will be 0v);
$$V_o=A_v(V_+-V_-)=(2)(()-())$$ -- will continue writing this later... 9/21/23 - jkb --