Amplifier gain quantifies the amplification capacity of an amplifier by assessing the ratio of its output to input, which is particularly valuable when amplifiers increase the amplitude of an input signal. In technical terminology, the magnitude ratio of output to input in an amplifier is termed “gain.” Gain is a dimensionless measurement because it involves a ratio of identical units (such as power out/power in, voltage out/voltage in, or current out/current in). In mathematical notation, gain is typically represented by the uppercase letter “A.”
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:
Likewise, when we have knowledge of an amplifier’s gain and the amplitude of the input signal, we can determine the amplitude of the output signal. For instance, if an amplifier possesses an AC current gain of 3.5 and is supplied with an AC input signal of 28 mA RMS, the resulting output will be 3.5 times 28 mA, equaling 98 mA.
In the last two cases, I intentionally defined gains and signal magnitudes using the term “AC” to emphasize a crucial point: electrical amplifiers react differently to AC and DC input signals, resulting in varying levels of amplification. Amplifiers often amplify fluctuations or variations in input signal magnitude (AC) at a different rate than stable input signal magnitudes (DC). While the detailed reasons for this phenomenon are complex and beyond the scope of this explanation, the fundamental fact remains. Before embarking on gain calculations, it is essential to determine whether you are dealing with AC or DC signals and their respective 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 multiple amplifiers are cascaded in a series, their individual gains are multiplied together to produce a total gain equivalent to the sum of the individual gains. (Refer to the diagram below.) In the scenario depicted in the figure below, if a 1 V signal is introduced at the input of a series of three amplifiers with a gain of 3 each, the initial stage yields a 3 V output. This 3 V signal is subsequently amplified by a factor of 5 in the second stage, resulting in a final output of 15 V.
