- Amplifier Gain Definition: Amplifier gain is the measure of an amplifier’s ability to increase the magnitude of a signal, expressed as a ratio without units.
- Types of Gain: Amplifier gain can be current gain, voltage gain, or power gain, each comparing different output and input parameters.
- Decibel Gain Definition: Decibel gain is defined as 10 times the logarithm (base 10) of the power ratio between the amplifier’s output and input.
- Advantages of Decibel Scale: The decibel scale makes it easier to handle large variations in gain and simplifies calculations in cascaded amplifier systems.
- Human Hearing and Decibels: The human ear perceives sound logarithmically, making the decibel scale ideal for representing sound intensity gains.
An electronic amplifier uses energy from a power supply to produce an output signal controlled by a smaller input signal. The signal quantity may be voltage, current or power. Gain is the ratio of a specified output quantity to the corresponding input quantity. The ratio is dimensionless, but its numerical value depends on frequency, source and load impedance, bias point and signal level.
Current gain is output current divided by input current. Voltage gain is output voltage divided by input voltage. Power gain is output power divided by input power. For example, if an amplifier has an input voltage of 2.5 VRMS and an output of 50 VRMS at the same frequency, its voltage-gain magnitude is 20:
This is a large-signal ratio for the stated conditions. Incremental or small-signal gain is the change in output divided by a small change in input around an operating point. Gain can differ between DC and AC and can change with frequency. Consistent rms value measurements are suitable for periodic AC gain; the input and output must refer to the same waveform component and measurement bandwidth.
Decibel Gain or dB Gain
Amplifier gain is a dimensionless ratio. The decibel, symbol dB, is a special name for a base-10 logarithmic ratio quantity, with 10 dB equal to 1 bel. A dB value must identify the underlying quantity and any reference condition.
For power, decibel gain converts the conventional ratio Poutput / Pinput to 10 log10(Poutput / Pinput). A voltage-gain magnitude is commonly written as 20 log10|Vout/Vin|. That expression corresponds directly to a power ratio when the compared impedances are equal; otherwise the impedance ratio must also be included. The same condition applies to 20 log10 of a current ratio.
The table converts power-gain ratios to decibels.
| Power gain ratio | Power gain in decibels |
| 1000 | 30 dB |
| 100 | 20 dB |
| 10 | 10 dB |
| 1 | 0 dB |
| 0.1 | -10 dB |
| 0.01 | -20 dB |
| 0.001 | -30 dB |
| 0.0001 | -40 dB |
Why should we use Bel Scale or Decibel Scale to represent Gain?
The logarithmic dB scale represents a wide range of ratios with compact numbers. It is also used for sound levels, although perceived loudness is not set by one universal tenfold-power rule. Hearing sensitivity depends on frequency, level and the listener. Other fields also use logarithmic scales when values cover many orders of magnitude.
For cascaded stages, compatible linear gain ratios multiply and their dB values add. If two stages have power-gain ratios of 3 and 5, the total power-gain ratio is 15. Their gains are 10 log10(3) = 4.77 dB and 10 log10(5) = 6.99 dB. The total is 10 log10(15) = 11.76 dB, which also equals 4.77 dB + 6.99 dB. This addition is valid when the stage gains use consistent reference and loading conditions.
