Unilateral Transducer Gain
When a transistor's reverse transmission S12 is small enough to ignore (the unilateral approximation), the maximum transducer power gain is the intrinsic gain |S21|² boosted by conjugately matching the input and output. This tool splits the maximum gain into its source-match, device, and load-match contributions from the S-parameter magnitudes.
Equations & Parameters ▸
\(G_{TU,\max} = \dfrac{|S_{21}|^2}{\left(1-|S_{11}|^2\right)\left(1-|S_{22}|^2\right)} = G_{S,\max}\cdot|S_{21}|^2\cdot G_{L,\max}\)
\(G_{S,\max} = \dfrac{1}{1-|S_{11}|^2}, \qquad G_{L,\max} = \dfrac{1}{1-|S_{22}|^2}\)
\(G_{S,\max} = \dfrac{1}{1-|S_{11}|^2}, \qquad G_{L,\max} = \dfrac{1}{1-|S_{22}|^2}\)
| S11 | Input reflection magnitude (dB, e.g. −6). |
| S21 | Forward transmission (gain) magnitude (dB). |
| S22 | Output reflection magnitude (dB). |
| GS, GL | Extra gain from conjugately matching the source and load. |
| GTU,max | Maximum unilateral transducer gain. Valid when |S12| is negligible. |
References: D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012. · G. Gonzalez, Microwave Transistor Amplifiers, 2nd ed., Prentice Hall, 1997.
Inputs
dB
Input matchdB
Forward gaindB
Output matchResults
Maximum gain
GTU,max—
Contributions
Source match GS—
Device |S21|²—
Load match GL—
Diagram