The power gain of an
electrical network
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources ...
is the ratio of an output
power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
to an input power. Unlike other
signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...
gain
Gain or GAIN may refer to:
Science and technology
* Gain (electronics), an electronics and signal processing term
* Antenna gain
* Gain (laser), the amplification involved in laser emission
* Gain (projection screens)
* Information gain in de ...
s, such as
voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
and
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
gain, "power gain" may be ambiguous as the meaning of terms "input power" and "output power" is not always clear. Three important power gains are operating power gain, transducer power gain and available power gain. Note that all these definitions of power gains employ the use of average (as opposed to instantaneous) power quantities and therefore the term "average" is often suppressed, which can be confusing at occasions.
Operating power gain
The operating power gain of a
two-port network
A two-port network (a kind of four-terminal network or quadripole) is an electrical network ( circuit) or device with two ''pairs'' of terminals to connect to external circuits. Two terminals constitute a port if the currents applied to them sat ...
, G
P, is defined as:
:
where
*P
load is the maximum time averaged power delivered to the load, where the maximization is over the load impedance, i.e., we desire the load impedance which maximizes the time averaged power delivered to the load.
*P
input is the time averaged power entering the network.
If the time averaged input power depends on the load impedance, one must take the maximum of the ratio--not just the maximum of the numerator.
Transducer power gain
The transducer power gain of a two-port network, G
T, is defined as:
where
*P
load is the average power delivered to the load
*P
source,max is the maximum available average power at the source
In terms of
y-parameters
Admittance parameters or Y-parameters (the elements of an admittance matrix or Y-matrix) are properties used in many areas of electrical engineering, such as power, electronics, and telecommunications. These parameters are used to describe the e ...
this definition can be used to derive:
:
where
*Y
L is the load admittance
*Y
S is the source admittance
This result can be generalized to z, h, g and y-parameters as:
:
where
*k
xx is a z, h, g or y-parameter
*M
L is the load value in the corresponding parameter set
*M
S is the source value in the corresponding parameter set
P
source,max may only be obtained from the source when the load
impedance connected to it (i.e. the equivalent
input impedance The input impedance of an electrical network is the measure of the opposition to current ( impedance), both static ( resistance) and dynamic ( reactance), into the load network that is ''external'' to the electrical source. The input admittance (the ...
of the two-port network) is the
complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if a and b are real, then) the complex conjugate of a + bi is equal to a - ...
of the source impedance, a consequence of the
maximum power theorem In electrical engineering, the maximum power transfer theorem states that, to obtain ''maximum'' external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its ou ...
.
Available power gain
The available power gain of a two-port network, G
A, is defined as:
where
*P
load,max is the maximum available average power at the load
*P
source,max is the maximum power available from the source
Similarly P
load,max may only be obtained when the load impedance is the complex conjugate of the
output impedance of the network.
References
Lecture notes on two-port power gain
{{DEFAULTSORT:Power Gain
Electrical parameters
Two-port networks
Audio amplifier specifications
Transfer functions