CR · Operational amplifier

The Ideal Op-Amp and the Virtual Short

An op-amp has enormous gain, so under negative feedback it drives its two inputs equal on its own. Learn to read the amplifier’s gain straight from the resistor ratio using that single rule.

Design the gain with one resistor ratio

Slide the feedback resistor ratio Rf/Rg. Thanks to the virtual short, the output becomes (1 + Rf/Rg) times the input. Set the ratio so the output is exactly three times the input.

Feedback ratio Rf/RgRf/Rg = 0.50

Voltage gain G

G = 1 + 0.50 = 1.50

Far from ×3

Two rules: virtual short and zero input current

An ideal op-amp amplifies the tiny voltage difference between its two inputs by nearly infinity. When the output is fed back to the inverting input, the op-amp adjusts its output so as to drive that difference to zero. The result is that the two input voltages become equal — this is the virtual short. At the same time the ideal input resistance is infinite, so no current at all flows into the input terminals.

The two rules turn gain into a resistor ratio

In a non-inverting amplifier the signal enters the plus input, while the output is divided by Rf and Rg and sent to the minus input. The virtual short makes the minus input equal to the input voltage, and zero input current means the current through Rg passes straight on through Rf. Solve the two conditions and the output becomes 1 + Rf/Rg times the input. The op-amp’s huge gain drops out, leaving only the external resistor ratio.

That is why the circuit is stable and predictable

The raw gain of any individual op-amp is wild and drifts with temperature, but the gain of the amplifier built around it is fixed by the ratio of two resistors. Pick precise resistors and you get a precise gain. The virtual short is the first handle for solving a host of circuits — inverting amplifiers, summers, integrators — you only change where the input goes and how the feedback is wired.

ObserveV− = V+

Feedback makes the two inputs equal.

Choosei_in = ? (R_in = ∞)

The ideal input resistance is infinite.

Fill inG = 1 + ?

Non-inverting gain is one plus the ratio.

On your ownG = 3 → RfRg = ?

G = 3 means Rf/Rg = 2.

Back to the first screen

As you slid the feedback ratio, the output grew to (1 + Rf/Rg) times the input, and at Rf/Rg = 2 it was exactly three times. The op-amp’s own enormous gain appears nowhere in the formula. Because negative feedback ties the two inputs together and holds the input current at zero, the gain was held by nothing but the ratio of two resistors.

An ideal op-amp has infinite gain, infinite input resistance and zero output resistance. Under negative feedback the two input voltages become equal (virtual short V+ = V−) and the input current is zero. From these two rules the non-inverting gain is G = 1 + Rf/Rg, set by the external resistor ratio alone, independent of the op-amp’s own gain.