Amplifier gain is the ability to assess an amplifier’s amplifying capabilities in terms of an output/input ratio is useful since amplifiers may raise the amplitude of an input signal. The output/input magnitude ratio of an amplifier is referred to as gain in technical terms. Gain is a unitless measurement since it is a ratio of equal units (power out / power in, voltage out / voltage in, or current out / current in). Gain is represented by the capital letter “A” in mathematics.
For example, if an amplifier takes in an AC voltage signal measuring 2 volts RMS and outputs an AC voltage of 30 volts RMS, it has an AC voltage gain of 30 divided by 2, or 15:
Correspondingly, if we know the gain of an amplifier and the magnitude of the input signal, we can calculate the magnitude of the output. For example, if an amplifier with an AC current gain of 3.5 is given an AC input signal of 28 mA RMS, the output will be 3.5 times 28 mA, or 98 mA:
I defined the gains and signal magnitudes in terms of “AC” in the final two cases. This was done on purpose to highlight a key point: electrical amplifiers react differently to AC and DC input signals and may magnify them to varying degrees. Amplifiers frequently magnify fluctuations or variations in input signal magnitude (AC) at a different ratio than stable input signal magnitudes (DC). The reasons behind this are far too complicated to describe at this time, but the truth remains. Before doing gain calculations, it’s important to know if you’re dealing with AC or DC signals and gains.
Electrical amplifier gains may be expressed in terms of voltage, current, and/or power, in both AC and DC. A summary of gain definitions is as follows. The triangle-shaped “delta” symbol (Δ) represents a change in mathematics, so “ΔVoutput / ΔVinput” means “change in output voltage divided by change in input voltage,” or more simply, “AC output voltage divided by AC input voltage”:
When numerous amplifiers are staged, the product (multiplication) of their individual gains yields an overall gain equal to the sum of the individual gains. (See diagram below) If a 1 V signal is applied to the input of the gain of 3 amplifiers in the Figure below, a 3 V signal from the first stage is further amplified by a gain of 5 at the second stage, resulting in a 15 V ultimate output.