Ideal Op-Amp Model & Golden Rules
Two simple rules that unlock all of op-amp circuit analysis.
With a gain of 100,000 or more, an op-amp seems impossible to analyze — until two golden rules make it trivial.
The Operational Amplifier
An operational amplifier (op-amp) is a five-terminal device: two input terminals (V+ and V−, also called the non-inverting and inverting inputs), one output terminal, and two power-supply rails (often labeled Vcc and Vee). In practice, the power rails are almost always omitted from circuit diagrams to reduce clutter — the op-amp is drawn as a triangle with two inputs on the left and one output on the right.
Why the Open-Loop Equation Alone Is Useless for Linear Analysis
The open-loop gain A_ol is enormous — 100,000 or more. This means even a tiny difference between V+ and V− (say, 1 mV) would produce an output of 100 V, which is impossible because the output is bounded by the power rails. In open-loop operation, the op-amp simply slams to one rail or the other — it acts as a comparator, not a linear amplifier. To use an op-amp for linear amplification, we add negative feedback: a connection from the output back to the V− input that lets the op-amp self-adjust.
The ideal op-amp has infinite input impedance. This means no current flows into either the V+ or V− terminal. Any current arriving at an input node must go somewhere else in the circuit — it cannot enter the op-amp. This rule greatly simplifies nodal analysis because you can ignore the op-amp terminals as current paths.
With negative feedback, the op-amp adjusts its output to drive the voltage difference between V+ and V− to (approximately) zero. In the ideal model, we take this as exact: V+ = V−. This is called a virtual short — the two input terminals are at the same voltage, but unlike a real wire, no current actually flows between them (that's Rule 1). Together, these two rules turn a seemingly intractable high-gain device into something you can analyze with basic nodal analysis.
The golden rules only apply when there is a negative feedback path from the output to the V− input. Without feedback (or with positive feedback to V+), the op-amp saturates against a power rail and the virtual short does not hold. If you ever find yourself applying the golden rules to a circuit without negative feedback, stop — you're using the wrong tool. Those circuits are analyzed as comparators, not linear amplifiers.
- By Golden Rule 2 (virtual short), V− = V+. Since Vin is connected directly to V+, we have V+ = Vin, so V− = Vin as well.
- By Golden Rule 1 (no current into inputs), no current flows into the V− terminal of the op-amp.
- Therefore, any current flowing through Rf from the output must continue through Rg to ground — none of it enters the op-amp. This constraint is what eventually lets us derive the gain formula, but for now the key result is: V− = Vin, and the V− node is a junction of Rf and Rg only.
- By Golden Rule 2 (virtual short), negative feedback drives V+ = V−.
- Since Vin = 3 V is applied directly to V+, the voltage at V− is also 3 V.
Check your understanding
- An op-amp is a five-terminal device (V+, V−, output, two power rails) with extremely high open-loop gain — too high for useful linear analysis without feedback.
- Golden Rule 1: no current flows into either input (infinite input impedance). Golden Rule 2: with negative feedback, V+ = V− (virtual short).
- These rules only hold under negative feedback — without it, the op-amp saturates to a power rail and acts as a comparator.