In
electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
, 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 sou ...
is the ratio of an output
power to an input power. Unlike other signal
gains, such as
voltage
Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
and
current 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, , is defined as:
:
where
* 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.
* is the time-averaged input power to 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
A transducer is a device that Energy transformation, converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, M ...
power gain of a two-port network, , is defined as:
where
* is the average power delivered to the load
* is the maximum available average power at the source
In terms of
y-parameters this definition can be used to derive:
:
where
* is the load
admittance
In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the multiplicative inverse, reciprocal of Electrical impedance, impedance, analogous to how Electrical resistanc ...
* is the source admittance
This result can be generalized to z, h, g and y-parameters as:
:
where
* is a z, h, g or y-parameter
* is the load value in the corresponding parameter set
* is the source value in the corresponding parameter set
may only be obtained from the source when the load impedance connected to it (i.e. the equivalent
input impedance 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 numbers, then the complex conjugate of a + bi is a - ...
of the source impedance, a consequence of the
maximum power theorem.
Available power gain
The available power gain of a two-port network, , is defined as:
where
* is the maximum available average power at the load
* is the maximum power available from the source
Similarly 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