The Op-Amp and the Virtual Short
Trade an enormous unreliable gain for a modest exactly predictable one. Then change the feedback element and the same chip does a different job.
Skip to the animationAn op-amp's open-loop gain is enormous and unreliable, so negative feedback is used to force its inputs to nearly equal voltages — the virtual short — after which the closed-loop behaviour depends only on the feedback network and not on the amplifier at all.
Why the raw gain is unusable
Open-loop gain is 10⁵ or more, and it varies by an order of magnitude between devices and with temperature. Ten microvolts across the inputs saturates the output. Used open-loop, an op-amp is a comparator and nothing else.
The virtual short
Return part of the output to the inverting input and the loop becomes self-correcting: any difference between the inputs is amplified enormously and fed back in the direction that reduces it.
Rearranging V_out = A(V₊ − V₋): for a finite output with A = 10⁵, the input difference must be around 100 µV. Not zero, but negligible. Combined with the near-zero input current, the two golden rules — no voltage across the inputs, no current into them — solve almost every op-amp circuit by inspection.
It is a consequence of the feedback, not a property of the device. Break the loop and it evaporates immediately, which is why it does not apply to a comparator.
Gain from resistors alone
| Configuration | Gain | Input impedance | Notes |
|---|---|---|---|
| Inverting | −R_f / R_in | R_in | The inverting input is a virtual earth |
| Non-inverting | 1 + R_f / R_in | Enormous | Cannot give a gain below 1 |
| Voltage follower | 1 | Enormous | A buffer — impedance conversion only |
| Summing | −(R_f/R₁·V₁ + R_f/R₂·V₂ …) | Each R | Virtual earth makes the inputs independent |
A appears in none of these. A 4:1 spread in open-loop gain becomes a fractional error in the closed-loop gain. That trade — an enormous unreliable gain for a modest exactly predictable one — is the central move in analogue design.
Why 'operational'
The loop forces the output to whatever makes the feedback element satisfy the input. A resistor gives a scale factor, a capacitor gives an integral, a diode gives a logarithm. The feedback network defines the mathematical operation, which is where the name comes from.
Where the ideal model fails
| Non-ideality | Typical value | Where it bites |
|---|---|---|
| Input offset voltage | A few mV, or µV for precision parts | DC precision, high-gain stages |
| Input bias current | nA (bipolar) to pA (FET) | High source impedances |
| Finite gain-bandwidth | 1–100 MHz | Any AC application |
| Slew rate | 0.5–100 V/µs | Large fast signals — and no feedback can fix it |
| Finite output swing | 1–2 V from each rail | Low-supply designs; rail-to-rail parts exist |
Choosing a part is almost entirely a question of which of these your circuit cares about. The ideal model gets you the topology; the datasheet gets you the part number.
Gain-bandwidth and stability
Open-loop gain rolls off at 20 dB per decade, making the gain-bandwidth product roughly constant: a 1 MHz part gives a gain of ten to 100 kHz, or a hundred to 10 kHz.
That roll-off is deliberate internal compensation. Without it the phase shift around the loop would reach 180° while the gain still exceeded one, and the amplifier would oscillate — the same Bode analysis as any control loop.
Feedback to the other input
Return the feedback to the non-inverting input and the loop drives the difference away from zero instead of toward it. The output latches to a rail, and the circuit becomes a comparator with hysteresis — a Schmitt trigger.
The two thresholds are what stop a slow, noisy input from chattering. Structurally the only difference from an amplifier is which pin the feedback resistor lands on.
The numbers you will be asked for
- Open-loop relation
V_out = A · (V₊ − V₋)
- Inverting gain
A_v = −R_f / R_in
- Non-inverting gain
A_v = 1 + R_f / R_in
- Gain-bandwidth product
GBW = A_cl × f_3dB
- Integrator
V_out = −(1/RC) ∫ V_in dt
- Slew rate limit
f_max = SR / (2π · V_peak)
Watch it work
Check yourself
question 1 / 4
One question at a time. Pick an answer to see why it is right or wrong, then move on — there is no score to keep and nothing is saved.