Op-Amp Basics

Almost every op-amp circuit you will ever analyse by hand comes from two assumptions. Learn these and you can skip the algebra most of the time.

1. No current flows into the inputs. Input impedance is infinite.
2. The op-amp drives its output until the two inputs are at the same voltage. This is the virtual short, and it only holds when there is negative feedback.

Assumption 2 has a precondition

The virtual short is a consequence of feedback, not a property of the part. Wire the feedback to the non-inverting input and the op-amp slams to a rail instead — which is exactly how you build a comparator or a Schmitt trigger.

Inverting amplifier

With the non-inverting input grounded, assumption 2 pins the inverting node at 0 V. All of $V_{in}/R_1$ therefore has to flow through $R_f$, giving

$\frac{V_{out}}{V_{in}}=-\frac{R_f}{R_1}$

The minus sign is the whole trick: the input sees a resistor to a virtual ground, so input impedance is just $R_1$, not the op-amp’s.

Non-inverting amplifier

Feed the signal straight into the + input and divide the output back into -:

$\frac{V_{out}}{V_{in}}=1+\frac{R_f}{R_1}$

Input impedance is now the op-amp’s own, which is enormous. That is why the unity-gain buffer ($R_f=0$, $R_1=\infty$) is the default way to stop a high-impedance source from being loaded.

The assumption that breaks first

Gain is not infinite at frequency. Real parts have a roughly constant gain–bandwidth product:

$\text{GBW}=A_{CL}\cdot f_{-3\mathrm{dB}}$

A 1 MHz GBW part configured for a gain of 100 is flat to 10 kHz and no further. This is the number that quietly ruins audio designs, and it is why the Sallen-Key note insists on checking GBW against the filter’s corner frequency before you trust the response.

See also

• Sallen-Key Low-Pass Filter — two of these plus four passives
• Back to the vault