# Power gain

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Power gain

The power gain of an electrical network is the ratio of an output power to an input power. Unlike other signal gains, such as voltage 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 average power gain, transducer power gain and available power gain.

Average power gain

The average power gain of a two-port network, GP, is defined as:

:$G_P = frac\left\{P_\left\{load\left\{P_\left\{input$

where
*Pinput is the average power entering the network

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

:$G_P = frac\left\{4|y_\left\{21\right\}|^2 Re\left\{\left(Y_L\right)\right\}Re\left\{\left(Y_S\right)\left\{|\left(y_\left\{11\right\}+Y_S\right)\left(y_\left\{22\right\}+Y_L\right)-y_\left\{12\right\}y_\left\{21\right\}|^2\right\}$

where

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

:$G_P = frac\left\{4|k_\left\{21\right\}|^2 Re\left\{\left(M_L\right)\right\}Re\left\{\left(M_S\right)\left\{|\left(k_\left\{11\right\}+M_S\right)\left(k_\left\{22\right\}+M_L\right)-k_\left\{12\right\}k_\left\{21\right\}|^2\right\}$

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:

$G_T = frac\left\{P_\left\{load\left\{P_\left\{source,max$

where
*Psource,max is the maximum available average power at the source

Psource,max 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 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:

$G_A = frac\left\{P_\left\{load,max\left\{P_\left\{source,max$

where
*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 of the network.

References

* [http://rfic.eecs.berkeley.edu/~niknejad/ee142/pdf/lect4.pdf Lecture notes on two-port power gain]

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