How this instrument works
Operational amplifiers ('op-amps') are extremely high-gain differential amplifier chips that, on their own, are far too sensitive to use directly — even a tiny input difference drives the output to its supply rail. In practice, op-amps are almost always used with external feedback resistors that tame that raw gain down to a precise, predictable value, set entirely by the ratio of two resistors rather than by the op-amp's own (imprecise, temperature-dependent) internal gain.
There are two standard single-resistor-pair configurations. The inverting amplifier feeds the input signal through Rin into the op-amp's inverting terminal, with Rf feeding back from the output to that same terminal; its gain is -Rf/Rin — negative because the output is flipped in phase relative to the input, and its magnitude can be less than, equal to, or greater than 1 depending on the resistor ratio.
The non-inverting amplifier instead feeds the signal into the op-amp's non-inverting terminal directly, with Rf and Rin forming a feedback divider from the output back to the inverting terminal; its gain is 1 + Rf/Rin — always positive (no phase flip) and always at least 1, since even Rf = 0 gives a gain floor of exactly 1 (a unity-gain buffer).
Both formulas assume an 'ideal' op-amp with infinite open-loop gain and infinite input impedance — an excellent approximation for real op-amps used well within their bandwidth and voltage limits, which is why these two equations are the starting point for essentially all op-amp amplifier design, from audio preamps to sensor signal conditioning.
- Choose Amplifier configuration — Inverting or Non-inverting.
- Enter Feedback resistor Rf (Ω) — the resistor connecting the output back to the inverting input.
- Enter Input resistor Rin (Ω) — the resistor the input signal passes through.
- Read Voltage gain (V/V) for the resulting gain: negative for inverting (a phase-flipped output), positive and at least 1 for non-inverting.
- Switch between configurations with the same Rf/Rin values to see directly how the two formulas diverge — inverting can produce gain magnitudes below 1, non-inverting never can.
Worked example — non-inverting amplifier, Rf = 10kΩ, Rin = 1kΩ
Choose Amplifier configuration = Non-inverting, enter Rf = 10000 and Rin = 1000. Voltage gain (V/V) reads 11.0. Working through the formula: 1 + 10000/1000 = 1 + 10 = 11.
This is a standard non-inverting gain-of-11 stage — a common building block wherever a small sensor or signal source needs boosting without inverting its phase, and it's the textbook example for this configuration precisely because a clean 10:1 resistor ratio produces an easy-to-verify round gain figure of 11 (not 10 — the '+1' from the non-inverting formula's feedback-divider floor is the detail that trips up beginners comparing it to the inverting case).
Questions
Why does the non-inverting gain formula have a '+1' that the inverting formula doesn't?
In the non-inverting configuration, the input signal connects directly to the op-amp's non-inverting terminal, and the feedback network (Rf and Rin) only sets how much of the output is fed back for comparison — even with Rf = 0, the output still has to equal the full input signal to satisfy the op-amp's feedback condition, giving a gain floor of exactly 1. The inverting configuration has no such floor because the input current path and the feedback path share the same node (the inverting input, held at a 'virtual ground'), so the gain is a pure ratio -Rf/Rin that can go all the way down toward 0 as Rin grows relative to Rf.
Why is inverting-amplifier gain negative?
The negative sign reflects a 180-degree phase inversion between input and output — when the input signal rises, the inverting configuration's output falls, and vice versa. The magnitude of the gain, |Rf/Rin|, tells you how much the signal is amplified or attenuated, while the negative sign tells you the output waveform is flipped upside-down relative to the input waveform, not that the amplifier is somehow 'reducing' the signal.
Can the inverting configuration have a gain magnitude less than 1?
Yes — unlike the non-inverting configuration, which always has gain magnitude of at least 1, the inverting configuration's gain is a pure ratio -Rf/Rin with no floor. If Rin is larger than Rf, the gain magnitude is below 1, meaning the circuit attenuates (reduces) the signal while still inverting its phase — useful when you need phase inversion without amplification, something the non-inverting configuration simply cannot do.
What happens to non-inverting gain if Rf is set to 0?
With Rf = 0, the non-inverting formula gives gain = 1 + 0/Rin = 1 exactly — this is the classic unity-gain buffer (voltage follower) configuration, where the output simply tracks the input voltage one-to-one. It's commonly used not to amplify a signal at all, but to take advantage of the op-amp's high input impedance and low output impedance, isolating a sensitive signal source from a demanding load without changing its voltage level.
Do these formulas hold for any resistor values, no matter how large or small?
In the ideal-op-amp approximation used here, yes — the formulas depend only on the Rf/Rin ratio, not the absolute resistor values. In real circuits, though, extremely small resistors draw excessive current and can overload the op-amp's output stage, while extremely large resistors introduce more thermal noise and make the circuit more sensitive to the op-amp's non-zero input bias current — which is why practical designs usually keep resistor values in a moderate range (roughly hundreds of ohms to a few hundred kilohms) even though the pure gain formula doesn't require it.