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# Half-power point

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

In the characterization of antennas the half-power point relates to measurement position as an angle and describes directionality.

## Amplifiers and filters

This occurs when the output voltage has dropped to 1/2 (~0.707) of the maximum output voltage[a] and the power has dropped by half.[b] 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]

## Notes

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

## References

1. ^ "Power bandwidth - MATLAB powerbw". uk.mathworks.com. Retrieved 5 August 2017.
2. ^ Schlessinger, Monroe (1995). Infrared technology fundamentals (2nd ed., rev. and expanded. ed.). New York: M. Dekker. ISBN 0824792599.
3. ^ Antenna Introduction / Basics (PDF), retrieved 2017-08-08