Amplifier Gain Calculator

Amplifier gain is a measure of how much a circuit amplifies an input signal. It is expressed either as a dimensionless ratio (output divided by input) or in decibels (dB), which is a logarithmic scale that makes it easier to work with the very large and very small numbers that appear in electronics.

Gain formulas:

Voltage gain (Av):

• Linear: Av = Vout / Vin
• In dB: Av(dB) = 20 × log₁₀(Vout / Vin)

Current gain (Ai):

• Linear: Ai = Iout / Iin
• In dB: Ai(dB) = 20 × log₁₀(Iout / Iin)

Power gain (Ap):

• Linear: Ap = Pout / Pin
• In dB: Ap(dB) = 10 × log₁₀(Pout / Pin)

Why 20 for voltage and 10 for power

It is not an arbitrary convention. Power goes as the square of voltage, so doubling the voltage quadruples the power, and log(V²) = 2·log(V). The factor of 20 is just the 10 with that square folded in. Current follows voltage for the same reason.

There is a catch worth knowing: voltage gain in dB equals power gain in dB only when the input and output impedances are the same. An amplifier with 20 dB of voltage gain driving 8 Ω from a 10 kΩ input is not delivering 20 dB of power gain. Most of the time this does not bite, because you are comparing signals at the same impedance, but it is why RF and audio engineers are careful to say which they mean.

Why decibels at all? The scale turns multiplication into addition, which is what makes cascaded systems tractable. Rather than multiplying gains through a chain, you add the dB figures.

Common dB reference values:

The -3dB point: In amplifier and filter design, the -3dB point marks where gain has fallen to 70.7% of its maximum voltage value (or 50% of power). This is the standard definition of an amplifier’s bandwidth. A filter or amplifier “cuts off” at its -3dB frequency.

Cascaded stages: If Amplifier A has a gain of 20dB and Amplifier B has a gain of 15dB, the combined gain is simply 35dB. That is much easier than multiplying the linear ratios, which are 10× and 5.62× and come to 56.2×.

Losses go in the same sum as negative numbers. A 20 dB amplifier feeding 6 dB of cable loss into a 15 dB amplifier is 20 − 6 + 15 = 29 dB overall, and you can read the running total anywhere along the chain by adding up everything to its left. That is the entire reason RF and audio work in dB rather than ratios: a signal path becomes arithmetic you can do in your head.

Noise is the reason order matters

The dB sum is the same whichever order you cascade the stages in, but the noise figure of the chain is not. The first stage dominates, because everything after it amplifies whatever noise the first one added along with the signal. Put the low-noise amplifier first and the lossy cable second and you get a usable signal; swap them and the same total gain gives you an amplified hiss. Friis’s formula puts numbers on it, and the short version is that the front end is the only stage whose noise performance you should pay much for.