Gain (electronics)

Lore & Background

In electronics, gain quantifies a two-port circuit’s ability to increase a signal’s power or amplitude by drawing energy from a power supply. It is defined as the mean ratio of output signal amplitude or power to the input signal amplitude or power. Gain is frequently expressed in logarithmic decibel (dB) units. A gain greater than one (above 0 dB) indicates amplification, a defining trait of active devices; passive circuits exhibit a gain of less than one. The term is ambiguous without context, as it may refer to voltage gain, current gain, or power gain. In audio and general-purpose amplifiers, especially operational amplifiers, gain typically means voltage gain, whereas in radio frequency amplifiers it usually denotes power gain. For sensors with dissimilar input and output units, gain must be specified with units, such as “5 microvolts per photon” for a photosensor’s responsivity. For a bipolar transistor, gain normally refers to forward current transfer ratio: either the static ratio hFE (beta, Ic divided by Ib at an operating point) or the small-signal current gain hfe (the slope of Ic versus Ib). Gain generally varies with signal frequency; unless stated otherwise, it refers to gain within the passband, the equipment’s intended operating frequency range. In antenna design, gain has a distinct meaning: the ratio of radiation intensity from a directional antenna to the mean radiation intensity from a lossless antenna. Gain can be dimensionless when comparing like units (e.g., volts per volt, amperes per ampere), but in devices like an operational transconductance amplifier, open-loop gain is expressed in siemens (mhos), as it is the ratio of output current to input voltage. Power gain in decibels is calculated as 10 log₁₀(P_out/P_in). Voltage gain in decibels uses 20 log₁₀(V_out/V_in), equivalent to power gain only when input and output impedances are equal. Similarly, current gain in decibels uses 20 log₁₀(I_out/I_in) under equal impedance conditions. A gain of factor 1 (0 dB), where input and output voltage levels and impedance match, is termed unity gain.

Reader's Guide

Gain is a fundamental concept in electronics, defining the amplification capability of circuits. Its significance lies in enabling signal processing, communication, and sensing technologies. The use of logarithmic decibel units allows convenient expression of large ratios and facilitates calculations involving cascaded stages. The distinction between voltage, current, and power gain is crucial for proper circuit design and analysis, as is the recognition that gain varies with frequency. The simplified 20 log rule for voltage gain in decibels applies only when input and output impedances are equal. Understanding gain is essential for designing amplifiers, filters, and other signal-processing systems, and its definition extends to antennas and sensors, where input and output units may differ.

Did You Know?

• Gain greater than one (greater than zero dB) is the defining property of an active device or circuit.
• The gain of a bipolar transistor normally refers to forward current transfer ratio, either hFE (beta) or hfe (small-signal current gain).
• Power gain in decibels is defined as 10 log10(Pout/Pin).
• When input and output impedances are equal, voltage gain in dB simplifies to 20 log10(Vout/Vin).