📐 Op-Amp Golden Rules and Feedback Circuits

Learning Objectives

  • State the three ideal op-amp assumptions and the two "golden rules" that follow from them.
  • Decide when the golden rules are valid, and recognize the two situations where they break down.
  • Derive and apply the gain formulas for the inverting amplifier, non-inverting amplifier, and voltage follower.
  • Solve exam-style problems, including design tasks where you pick resistor values for a target gain.

Quick Review

In the last lesson you treated transistors as controlled switches, and the habit that made those problems easy was this: assume a region, then check that the assumption is consistent. The op-amp gives you exactly the same workflow. You assume the device is operating linearly, apply the golden rules, compute the output, and then verify the answer is physically reachable.

Two tools from Module 1 do the heavy lifting here: Kirchhoff's current law at a node, and the voltage-divider idea from series networks. Everything below is just those two things wearing a triangular hat.

Theory

What "ideal" buys you

An ideal op-amp has three properties:

  • Infinite open-loop gain $A$
  • Infinite input impedance, which means no current flows into either input terminal
  • Zero output impedance, meaning the output can drive any load without drooping

Real parts (741, TL072, LM358) only approximate these, but for exam problems and most first-pass design work the ideal model is accurate to within a few percent.

The two golden rules

[!IMPORTANT] Golden Rule 1: No current flows into the inverting ($V_-$) or non-inverting ($V_+$) input. Golden Rule 2: With negative feedback, the op-amp drives its output until $V_- = V_+$. This is called a virtual short.

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