Lessons · Engineering · The two rules that solve most op-amp circuits
Two rules that solve most op-amp circuits
With negative feedback, an ideal op-amp behaves as if no current flows into its inputs, and as if it does whatever it must to keep the two inputs at the same voltage. Those two rules solve nearly every standard circuit without touching the device's internals.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a licensed engineer. Practice material, not professional advice. What that means.
What it is for
It turns a component with enormous gain and awkward behaviour into something you can reason about in two lines. Gain becomes a ratio of two resistors, which is why op-amp circuits are designed rather than tuned.
How to think about it
Check there is negative feedback first -- the rules only hold with it. Then set the two input voltages equal, assume no input current, and the resistor network gives the answer directly.
Worked example
Rule one: no current into the inputs.Ideal, and close enough in practice.
Rule two: the inputs sit at the same voltage.Only with negative feedback.
Non-inverting gain = 1 + Rf/Rin.Straight from the two rules.
Inverting gain = -Rf/Rin.Same method, different node.
Your turn
A non-inverting amplifier has Rf = 90k and Rin = 10k. Write the gain.
1 + 90/10 =
Solve one, graded on the server
The trap
Applying the two rules without negative feedback. With positive feedback or none, the output slams to a rail and neither rule holds.