\[A_{v,dB}=20\log_{10}\left(\frac{V_{out}}{V_{in}}\right)\]
Variables
AvdBvoltage gain in decibels (dB)
Voutoutput voltage (V)
Vininput voltage (V)
Description
What is this formula?
The Decibel Voltage Gain formula expresses the voltage gain of an amplifier on a logarithmic decibel scale. It is useful because amplifier gains can vary over very large ranges.
When to use it
Use this formula when comparing amplifier performance, analyzing audio circuits, signal chains, filters, instrumentation circuits, or communication systems.
Example
An amplifier receives an input voltage of 0.1 V and produces an output voltage of 2 V.
Given:
Vin = 0.1 V
Vout = 2 V
Formula:
AvdB = 20 log(Vout / Vin)
Substitution:
AvdB = 20 log(2 / 0.1)
Result:
AvdB = 26.02 dB
The amplifier has a voltage gain of approximately 26.02 dB.
Applications
Audio amplifiers, operational amplifier circuits, RF systems, signal processing, instrumentation electronics, and communication systems.