What are transducer, available and operating power gain?

Three power gains describe an amplifier two-port. Transducer gain G_T = power delivered to the load / power available from the source; operating (power) gain G_P = power delivered / power input to the network; available gain G_A = power available from the network / power available from the source. With source and load both at Z₀, G_T = |S₂₁|².^[1][2]

What is the transducer gain formula?

GT = [(1 − |ΓS|²)/|1 − ΓinΓS|²] · |S21|² · [(1 − |ΓL|²)/|1 − S22ΓL|²], where Γin = S11 + S12S21ΓL/(1 − S22ΓL). In the unilateral approximation (S₁₂ = 0) the three factors become independent source, device and load gains, simplifying design with constant-gain circles.^[1]

What are MAG and MSG?

If the device is unconditionally stable (K > 1), simultaneous conjugate matching gives the maximum available gain MAG = |S21/S12|·(K − √(K² − 1)). If it is only conditionally stable, the maximum stable gain MSG = |S21/S12| (the value at K = 1) is a useful upper figure. Datasheets often plot “MSG/MAG” versus frequency.^[2][3]

What other gain metrics exist?

• Unilateral power gain U (Mason’s): invariant to lossless reciprocal embedding; f_max is where U = 1.
• Current gain h₂₁: f_T is where |h₂₁| = 1.
• Insertion gain: ratio of load power with and without the amplifier.

Frequently asked questions

See also

• S-parameters
• Amplifier stability
• LNA design
• Maximum power transfer

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

1. “Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.
2. “Microwave Transistor Amplifiers: Analysis and Design, 2nd ed.”. G. Gonzalez, Prentice Hall. 1997.
3. “Stability and Power-Gain Invariants of Linear Twoports”. J. M. Rollett, IRE Transactions on Circuit Theory, vol. 9, no. 1, pp. 29-32. March 1962.
4. “The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.”. T. H. Lee, Cambridge University Press. 2004.