What an op-amp gain stage does
An operational amplifier (op-amp) has a huge open-loop gain, often 100,000 or more. Negative feedback through two resistors trades that excess gain for a precise, stable gain set only by the resistor ratio. The two classic stages are the non-inverting and the inverting amplifier.
The formulas
- Non-inverting amplifier: the signal goes to the + input; Rf runs from the output to the − input and Rin from the − input to ground. Gain G = 1 + Rf ÷ Rin. The output is in phase with the input, and the input impedance is very high.
- Inverting amplifier: the signal goes through Rin to the − input, the + input is grounded and Rf feeds back from the output. Gain G = −Rf ÷ Rin. The output is inverted and the input impedance equals Rin.
Gain in decibels is 20 × log10(|G|).
Example
Rf = 100 kΩ, Rin = 10 kΩ, input 0.1 V, ±12 V supply, op-amp with a 1 MHz gain-bandwidth product:
- non-inverting gain: 1 + 100 ÷ 10 = 11, or 20.8 dB;
- output: 11 × 0.1 = 1.1 V, well within the rails;
- bandwidth: 1 MHz ÷ 11 ≈ 91 kHz.
Wired as an inverting stage, the same resistors give a gain of −10 and an output of −1.1 V.
Bandwidth and noise gain
The gain-bandwidth product (GBW) is roughly constant for a voltage-feedback op-amp. The closed-loop bandwidth is GBW divided by the noise gain, which is 1 + Rf ÷ Rin for both stages. That is why an inverting stage with a gain of −1 has the same bandwidth as a non-inverting stage with a gain of 2.
Practical tips
- The output cannot swing past the supply rails. Most classic op-amps lose 1 to 2 V at each rail; rail-to-rail parts get within a few tens of millivolts.
- Keep resistors between about 1 kΩ and 1 MΩ. Low values load the output; high values add noise and offset from bias currents.
- For high gains, split the gain across two stages to keep enough bandwidth.
- Slew rate also limits large, fast signals: check that 2π × f × Vpeak stays below the datasheet slew rate.
- Add a small capacitor across Rf if the stage oscillates or to roll off high frequencies.