Thehalf-power point is the point at which the outputpower has dropped to half of its peak value; that is, at a level of approximately−3 dB.^[1][a]

Infilters,optical filters, andelectronic amplifiers,^[2] the half-power point is also known ashalf-power bandwidth and is a commonly used definition for thecutoff frequency.

In the characterization ofantennas the half-power point is also known ashalf-power beamwidth and relates to measurement position as an angle and describesdirectionality.

This occurs when the outputvoltage has dropped to${\displaystyle \frac{1}{\sqrt{2}}\approx \text{0.707}}$ of the filter's nominal passband voltage^[b] and the power has dropped by half.^[a] Abandpass amplifier will have two half-power points, while alow-pass amplifier or ahigh-pass amplifier will have only one.

Thebandwidth of a filter or amplifier is usually defined as the difference between the lower and upper half-power points. This is, therefore, also known as the3 dB bandwidth. There is no lower half-power point for a low-pass amplifier, so the bandwidth is measured relative toDC, i.e.,0 Hz. There is no upper half-power point for an ideal high-pass amplifier, its bandwidth is theoretically infinite.^[3] In practice thestopband andtransition band are used to characterize a high-pass.

In antennas, the expressionhalf-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 offboresight at which the antenna gain first falls to half power (approximately−3 dB)^[a] from the peak. The angle between the−3 dB points is known as thehalf-power beam width (or simplybeam width).^[4]

Beamwidth is usually but not always expressed in degrees and for the horizontal plane.It refers to themain lobe, when referenced to the peakeffective radiated power of the main lobe.Note that other definitions ofbeam width exist, such as the distance between nulls and distance between firstside lobes.

The beamwidth can be computed for arbitrary antenna arrays. Defining the array manifold as the complex response of the${\displaystyle \mathrm{m}}$ element antenna array as${\displaystyle \mathrm{A}(\theta )}$, where${\displaystyle \mathrm{A}(\theta )}$ is a matrix with${\displaystyle \mathrm{m}}$ rows, the beam pattern is first computed as:^[5][6]

$${\displaystyle \mathrm{B}(\theta )=\frac{1}{\mathrm{m}}\mathrm{A}({\theta }_0{)}^{\ast }\mathrm{A}(\theta )}$$

where${\displaystyle \mathrm{A}({\theta }_0{)}^{\ast }}$ is the conjugate transpose of${\displaystyle \mathrm{A}}$ at the reference angle${\displaystyle {\theta }_0}$.

From the beam pattern${\displaystyle \mathrm{B}(\theta )}$, the antenna power is computed as:

$${\displaystyle \mathrm{P}=|\mathrm{B}{|}^2.}$$

Thehalf-power beamwidth (HPBW) is then found as the range of${\displaystyle \theta }$ where${\displaystyle \mathrm{P}=0.5{\mathrm{P}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}$.

• Antenna aperture
• Angular resolution
• Full width at half maximum

 This article incorporatespublic domain material fromFederal Standard 1037C.General Services Administration. Archived fromthe original on 2022-01-22. (in support ofMIL-STD-188).

• Electronic amplifiers
• Antennas (radio)

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