= Gain
{disambiguate=electronics}
{title2=$A_v,\ G_P$}
{wiki}
= Electronic gain
{synonym}
\b[Electronic gain] expresses how an electronic circuit scales a specified input signal quantity into an output quantity. For a linearized voltage amplifier around its <operating point>, the <voltage gain> is $A_v=\delta v_{\rm out}/\delta v_{\rm in}$. At a sinusoidal frequency it can be a complex <phasor> ratio, specifying both amplitude ratio and <phase shift>. <Power gain> instead compares the average power delivered to the load with the average signal power entering the amplifier:
$$
G_P=\frac{P_{\rm load}}{P_{\rm in}}.
$$
State the input/output quantities, frequency, load and operating conditions when specifying gain. A <transimpedance amplifier> relates output <electric potential difference> to input current and has a dimensional transfer ratio in ohms.
For an original circuit example, use an inverting <operational amplifier> with input <resistor> $R_1=10\,\mathrm{k\Omega}$, feedback <resistor> $R_2=100\,\mathrm{k\Omega}$ and load $R_L=1\,\mathrm{k\Omega}$. In its ideal negative-feedback linear regime,
$$
A_v=-\frac{R_2}{R_1}=-10.
$$
An input of $50\,\mathrm{mV}$ <root mean square> therefore gives $0.50\,\mathrm V$ <root mean square> at the output, with a phase inversion. The manufacturer's primary explanation derives this resistance-ratio gain using the input and feedback currents.<Op-Amps, Comparator Circuit by Renesas>[Op-Amp Basics (1), Figure 2 and the derivation of the inverting gain]{ref} Suitable supplies, output-current capability and <amplifier output range> are assumptions of this worked model, not specifications of a particular device.
Here the input resistance is $R_1$ in the ideal model. For resistive ports and root-mean-square signal amplitudes,
$$
G_P=|A_v|^2\frac{R_{\rm in}}{R_L}.
$$
The example input power is $0.25\,\mathrm{\mu W}$ and load power $0.25\,\mathrm{mW}$, giving $G_P=1000$. The additional output energy comes from the amplifier's supply, controlled by the input signal. The <impedance condition for converting voltage gain to power gain> is essential: voltage magnitude alone does not specify load power.
<Voltage gain> is conventionally expressed as $20\log_{10}|A_v|$ <decibels>, while <power gain> uses $10\log_{10}G_P$. This example has <voltage gain> $20\,\mathrm{dB}$ and <power gain> $30\,\mathrm{dB}$; the two expressions agree when the resistive input and load impedances are equal. A negative <voltage gain> indicates phase inversion; its magnitude enters the logarithm.
A direct test drives a small sine wave into the input and measures the actual terminal signals with an <oscilloscope>. Sweeping frequency reveals the <frequency response>; increasing amplitude reveals <amplifier clipping> or other departure from the assumed linear gain. Keep the load and measurement impedances specified. Gain can amplify input noise along with signal, so the <signal-to-noise ratio> requires its own measurement.
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