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Calculate power gain from two-port S-parameters

calculates the transducer power gain of the 2-port network by:`g`

= powergain(`s_params`

,`z0`

,`zs`

,`zl`

,'Gt')

$${G}_{t}=\frac{{P}_{L}}{{P}_{\text{avs}}}=\frac{(1-{\left|{\Gamma}_{S}\right|}^{2}){\left|{S}_{21}\right|}^{2}(1-{\left|{\Gamma}_{L}\right|}^{2})}{{\left|(1-{S}_{11}{\Gamma}_{S})(1-{S}_{22}{\Gamma}_{L})-{S}_{12}{S}_{21}{\Gamma}_{S}{\Gamma}_{L}\right|}^{2}}$$

where,

*P*is the output power and_{L}*P*_{avs}is the maximum input power.*Γ*and_{L}*Γ*are the reflection coefficients defined as:_{S}$$\begin{array}{l}{\Gamma}_{S}=\frac{{Z}_{S}-{Z}_{0}}{{Z}_{S}+{Z}_{0}}\\ {\Gamma}_{L}=\frac{{Z}_{L}-{Z}_{0}}{{Z}_{L}+{Z}_{0}}\end{array}$$

calculates the available power gain of the 2-port network by:`g`

= powergain(`s_params`

,`z0`

,`zs`

,'Ga')

$${G}_{a}=\frac{{P}_{\text{avn}}}{{P}_{\text{avs}}}=\frac{(1-{\left|{\Gamma}_{S}\right|}^{2}){\left|{S}_{21}\right|}^{2}}{{\left|1-{S}_{11}{\Gamma}_{S}\right|}^{2}(1-{\left|{\Gamma}_{out}\right|}^{2})}$$

where

*P*_{avn}is the available output power from the network.*Γ*is given by:_{out}$${\Gamma}_{\text{out}}={S}_{22}+\frac{{S}_{12}{S}_{21}{\Gamma}_{S}}{1-{S}_{11}{\Gamma}_{S}}$$

calculates the operating power gain of the 2-port network by:`g`

= powergain(`s_params`

,`z0`

,`zl`

,'Gp')

$${G}_{p}=\frac{{P}_{L}}{{P}_{\text{in}}}=\frac{{\left|{S}_{21}\right|}^{2}(1-{\left|{\Gamma}_{L}\right|}^{2})}{(1-{\left|{\Gamma}_{\text{in}}\right|}^{2}){\left|1-{S}_{22}{\Gamma}_{L}\right|}^{2}}$$

where

*P*_{in}is the input power.*Γ*_{in}is given by:$${\Gamma}_{\text{in}}={S}_{11}+\frac{{S}_{12}{S}_{21}{\Gamma}_{L}}{1-{S}_{22}{\Gamma}_{L}}$$