What Is Gain?

Gain describes how much an amplifier increases a signal. It is the ratio between the output signal and the input signal.

For voltage gain:

Av = Vout / Vin

For current gain:

Ai = Iout / Iin

For power gain:

Ap = Pout / Pin

Gain can be expressed as a simple ratio or in decibels (dB).

Voltage Gain in dB

For voltage measurements with the same impedance:

Gain(dB) = 20 × log10(Vout / Vin)

For example, if an amplifier receives 100 mV and produces 1 V:

Gain = 20 × log10(1 / 0.1)

Gain ≈ 20 dB

The amplifier has a voltage gain of 10 times, equivalent to approximately 20 dB.

Voltage Gain Calculator

Power Gain in dB

Power gain is calculated using:

Gain(dB) = 10 × log10(Pout / Pin)

For example, if an amplifier receives 1 W and delivers 100 W:

Gain = 10 × log10(100 / 1)

Gain = 20 dB

Therefore, a 100:1 power ratio corresponds to 20 dB of gain.

Power Gain Calculator

Gain Ratio to dB

If the gain ratio is already known, it can be converted directly to decibels.

dB to Voltage Gain

Voltage gain can be calculated from a dB value using:

Av = 10^(dB / 20)

dB to Power Gain

Power gain can be calculated from dB using:

Ap = 10^(dB / 10)

Amplifier Input and Output

An amplifier with voltage gain multiplies the input voltage:

Vout = Vin × Av

For example, a voltage gain of 10 and an input of 200 mV produces:

Vout = 0.2 × 10

Vout = 2 V

Gain in Audio Amplifiers

Audio amplifiers are commonly described by their voltage gain or power gain.

A preamplifier may provide a relatively high voltage gain while delivering only a small amount of power. A power amplifier generally has a lower voltage gain but is capable of delivering substantial power to a loudspeaker.

For example, a power amplifier with a voltage gain of 26 dB has a linear voltage gain of approximately:

Av = 10^(26/20)

Av ≈ 19.95

Therefore, an input of 100 mV would theoretically produce:

Vout ≈ 0.1 × 19.95

Vout ≈ 1.995 V

The actual output is ultimately limited by the amplifier's power supply, output stage, load and clipping level.

Negative Gain

Gain can also be negative when the output signal is smaller than the input signal.

For example:

Vout = 0.5 × Vin

The voltage gain is:

20 × log10(0.5)

≈ -6.02 dB

A negative dB value therefore represents attenuation rather than amplification.

Voltage Gain and Speaker Impedance

Voltage gain and power gain are not always interchangeable.

For a load resistance R:

P = V² / R

If the load impedance changes, the relationship between output voltage and output power also changes.

This is particularly important in audio power amplifiers driving 4 Ω and 8 Ω loudspeakers.

Gain vs Volume

Gain and volume are related but are not exactly the same thing.

Gain determines how much a circuit amplifies the signal. A volume control normally adjusts the signal level entering a subsequent stage.

For example, a power amplifier might have a fixed voltage gain while a potentiometer controls the amount of signal supplied to its input.

Common dB Values

Common Power Gain Values

20 dB Gain Does Not Mean 20 Times Power

This is an important distinction.

For voltage:

20 dB = 10× voltage ratio

For power:

20 dB = 100× power ratio

The difference occurs because voltage and power use different decibel formulas.

Voltage Gain With Different Impedances

When input and output impedances are different, voltage gain and power gain should not be converted using only the voltage ratio.

Power depends on both voltage and impedance:

P = V² / R

For a voltage ratio:

Gv(dB) = 20 log10(Vout / Vin)

For power ratio:

Gp(dB) = 10 log10(Pout / Pin)

The impedance of both the input and output circuits must therefore be considered when relating voltage gain to power gain.

Audio Amplifier Gain Example

Suppose a power amplifier requires 1 V RMS at its input and produces 20 V RMS at its output.

Av = 20 / 1

Av = 20

The voltage gain is:

Gain = 20 log10(20)

Gain ≈ 26.02 dB

If the amplifier drives an 8 Ω speaker:

Pout = 20² / 8

Pout = 50 W

This demonstrates the relationship between amplifier gain, output voltage and speaker power.

Gain and Amplifier Clipping

Increasing gain does not indefinitely increase amplifier output power. Once the amplifier reaches the limits of its power supply and output stage, further increases in input level cause clipping.

For this reason, the gain setting, input sensitivity and available supply voltage all affect the maximum clean output level.

Common Mistakes

• Using 10 × log10 for voltage gain instead of 20 × log10.
• Using 20 × log10 for power gain instead of 10 × log10.
• Confusing gain ratio with gain in dB.
• Assuming 20 dB means 20× voltage gain.
• Ignoring input and output impedance when comparing voltage and power gain.
• Assuming increasing gain always increases maximum amplifier power.
• Ignoring amplifier clipping.

Key Points

• Voltage gain: Av = Vout / Vin.
• Voltage gain in dB: 20 log10(Vout / Vin).
• Power gain in dB: 10 log10(Pout / Pin).
• 10× voltage gain is approximately 20 dB.
• 100× power gain is 20 dB.
• Negative dB represents attenuation.
• Gain and volume are different concepts.
• Actual amplifier output is limited by supply voltage, load and circuit design.