In electrical engineering, 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 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, GP, is defined as:
G P = P L P I {\displaystyle G_{P}={\frac {P_{\mathrm {L} }}{P_{\mathrm {I} }}}}
where
PL 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. PI 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 power gain of a two-port network, GT, is defined as:
G T = P L P S m a x {\displaystyle G_{T}={\frac {P_{\mathrm {L} }}{P_{\mathrm {S\ max} }}}}
where
PL is the average power delivered to the load PS max is the maximum available average power at the source In terms of y-parameters this definition can be used to derive:
G T = 4 | y 21 | 2 ℜ ( Y L ) ℜ ( Y S ) | ( y 11 + Y S ) ( y 22 + Y L ) − y 12 y 21 | 2 {\displaystyle G_{T}={\frac {4|y_{21}|^{2}\Re {(Y_{\mathrm {L} })}\Re {(Y_{\mathrm {S} })}}{{\bigl |}(y_{11}+Y_{\mathrm {S} })(y_{22}+Y_{\mathrm {L} })-y_{12}y_{21}{\bigr |}^{2}}}}
where
YL is the load admittance YS is the source admittance This result can be generalized to z, h, g and y-parameters as:
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