Half power point
Encyclopedia
The half power point of an electronic amplifier stage is that frequency at which the output power
has dropped to half of its mid-band level. Other names include the cutoff frequency
.
This occurs when the output voltage
has dropped by 1/√2 or 0.707 (approximately 1.5 dB
) and the power has dropped by half (approximately 3 dB
). A bandpass amplifier will have 2 half power points, whilst a low pass
amplifier will have only one. A high pass
amplifier stage will have only the lower half power point.
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.
so 
the decibel measure of a ratio r is defined as 
This mathematical coincidence also means that
(precisely, 
taking the logarithm of this equation yields 
). This approximation is notably used in loose usage of the prefix kilo- (and associated mega-, giga-, tera-, etc.) in computing to refer either to 
or 
– see kilobyte
.
Using 3 dB rather than the correct value of 3.010... yields a power factor of
which differs from a factor of 2 by about 0.24%. As logarithmic errors add, using 6 dB to approximate a factor of 4 difference yields an error of about 0.48%, and so forth.
Electric power
Electric power is the rate at which electric energy is transferred by an electric circuit. The SI unit of power is the watt.-Circuits:Electric power, like mechanical power, is represented by the letter P in electrical equations...
has dropped to half of its mid-band level. Other names include the cutoff frequency
Cutoff frequency
In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced rather than passing through.Typically in electronic systems such as filters and...
.
This occurs when the output voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
has dropped by 1/√2 or 0.707 (approximately 1.5 dB
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
) and the power has dropped by half (approximately 3 dB
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
). A bandpass amplifier will have 2 half power points, whilst a low pass
Low-pass filter
A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...
amplifier will have only one. A high pass
High-pass filter
A high-pass filter is a device that passes high frequencies and attenuates frequencies lower than its cutoff frequency. A high-pass filter is usually modeled as a linear time-invariant system...
amplifier stage will have only the lower half power point.
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.
3 dB
The half power point is approximately 3 dB because so the decibel measure of a ratio r is defined as This mathematical coincidence also means that
(precisely, taking the logarithm of this equation yields ). This approximation is notably used in loose usage of the prefix kilo- (and associated mega-, giga-, tera-, etc.) in computing to refer either to or – see kilobyteKilobyte
The kilobyte is a multiple of the unit byte for digital information. Although the prefix kilo- means 1000, the term kilobyte and symbol KB have historically been used to refer to either 1024 bytes or 1000 bytes, dependent upon context, in the fields of computer science and information...
.
Using 3 dB rather than the correct value of 3.010... yields a power factor of
which differs from a factor of 2 by about 0.24%. As logarithmic errors add, using 6 dB to approximate a factor of 4 difference yields an error of about 0.48%, and so forth.