# Half-power point

The half-power point or half-power bandwidth is the frequency at which the output power has dropped to half of its peak value; that is, at a level of approximately -3 dB.[1] The half-power point is a commonly-used definition for the cutoff frequency and can be used in a variety of contexts, including the characterization of filters, optical filters, electronic amplifiers[2] and antennas.

## Amplifiers and filters

This occurs when the output voltage has dropped to 1/2 (~0.707) of the maximum output voltage[lower-alpha 1] and the power has dropped by half.[lower-alpha 2] A bandpass amplifier will have two half-power points, whilst a low pass amplifier or a high pass amplifier will have only one.

The bandwidth of an amplifier is usually defined as the difference between the lower and upper half-power points. This is therefore also known as the 3 dB bandwidth. In the case of a low pass amplifier, there is no lower half-power point so the bandwidth is measured relative to direct current, i.e. 0 rad/s.

## Antennas

In antennas, the expression half-power point does not relate to frequency: instead, it describes the extent in space of an antenna beam. The half-power point is the angle off boresight at which the antenna gain first falls to half power (approx. -3 dB) from the peak. The angle between the -3 dB points is known as the beamwidth.[3]

1. Exact: ${\displaystyle 20\log _{10}\left({\tfrac {1}{\sqrt {2}}}\right)\approx -3.0103\,\mathrm {dB} }$
2. Exact: ${\displaystyle 10\log _{10}\left({\tfrac {1}{2}}\right)\approx -3.0103\,\mathrm {dB} }$