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The power gain of an electrical network
Electrical network

An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources, and switches....
 is the ratio of an output power
Power (physics)

In physics, power is the rate at which mechanical work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time....
 to an input power. Unlike other signal
Signal

Signal, signals, signaling, or signalling may refer to:...
 gain
Gain

In electronics, gain is a measure of the ability of a electrical network to increase the Power or amplitude of a Signal . It is usually defined as the mean ratio of the Signalling of a system to the Signalling of the same system....
s, such as voltage
Voltage

Electrical tension is the potential difference between two points of an electrical or electronic circuit, expressed in volts. It is the measurement of the potential for an electric field to cause an electric current in an electrical conductor....
 and current
Electric current

Electric current is the flow of electric charge. The electric charge may be either electrons or ions.The International System of Units unit of electric current intensity is the ampere....
 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 average power gain, transducer power gain and available power gain.

e

In terms of y-parameters this definition can be used to derive:

where

This result can be generalized to z, h, g and y-parameters as:

where

e

Psource,max may only be obtained from the source when the load impedance
Impedance

Impedance may refer to:*the ratio of the voltage phasor to the electric current phasor, as in**Electrical impedance, a measure of opposition to time-varying electric current in an electric circuit....
 connected to it (i.e.






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The power gain of an electrical network
Electrical network

An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources, and switches....
 is the ratio of an output power
Power (physics)

In physics, power is the rate at which mechanical work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time....
 to an input power. Unlike other signal
Signal

Signal, signals, signaling, or signalling may refer to:...
 gain
Gain

In electronics, gain is a measure of the ability of a electrical network to increase the Power or amplitude of a Signal . It is usually defined as the mean ratio of the Signalling of a system to the Signalling of the same system....
s, such as voltage
Voltage

Electrical tension is the potential difference between two points of an electrical or electronic circuit, expressed in volts. It is the measurement of the potential for an electric field to cause an electric current in an electrical conductor....
 and current
Electric current

Electric current is the flow of electric charge. The electric charge may be either electrons or ions.The International System of Units unit of electric current intensity is the ampere....
 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 average power gain, transducer power gain and available power gain.

Average power gain


The average power gain of a two-port network
Two-port network

A two-port network is an electrical circuit or device with two pairs of terminals . Two terminals constitute a port if they satisfy the essential requirement known as the port condition: the same current must enter and leave a port....
, GP, is defined as:

where
  • Pload is the average power delivered to the load
  • Pinput is the average power entering the network


In terms of y-parameters this definition can be used to derive:

where
  • YL is the load admittance
  • YS is the source admittance


This result can be generalized to z, h, g and y-parameters as:

where
  • kxx is a z, h, g or y-parameter
  • ML is the load value in the corresponding parameter set
  • MS is the source value in the corresponding parameter set


Transducer power gain


The transducer power gain of a two-port network, GT, is defined as:

where
  • Pload is the average power delivered to the load
  • Psource,max is the maximum available average power at the source


Psource,max may only be obtained from the source when the load impedance
Impedance

Impedance may refer to:*the ratio of the voltage phasor to the electric current phasor, as in**Electrical impedance, a measure of opposition to time-varying electric current in an electric circuit....
 connected to it (i.e. the equivalent input impedance
Input impedance

The input Electrical_impedance, Electrical load impedance, or external impedance of a electrical network or electronic device is the Th?venin's theorem electrical impedance looking into its input....
 of the two-port network) is the complex conjugate
Complex conjugate

In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. Thus, the conjugate of the complex number...
 of the source impedance, a consequence of the maximum power theorem]

Available power gain


The available power gain of a two-port network, GA, is defined as:

where
  • Pload,max is the maximum available average power at the load
  • Psource,max is the maximum available average power at the source


Similarly Pload,max may only obtained when the load impedance is the complex conjugate of the output impedance
Output impedance

Any linear electric or electronic circuit or device which generates a voltage may be represented as an ideal voltage source in series with an Electrical impedance....
 of the network.