Available Gain
Understanding Available Gain
Three power gain definitions exist for two-port networks, each useful for different design situations. Available gain (GA) assumes the output is conjugate-matched and varies only with the source impedance. Operating gain (GP) assumes the input is conjugate-matched and varies only with the load impedance. Transducer gain (GT) accounts for mismatch at both ports and varies with both source and load impedances. When both ports are simultaneously conjugate-matched, all three are equal and represent the maximum available gain (MAG).
Available gain is the natural choice for noise analysis because the noise figure definition (IEEE standard) assumes that the available signal-to-noise ratio is measured at the output. The available power includes all power that could be extracted by a conjugate-matched load. This convention ensures that mismatch loss at the output does not artificially inflate the noise figure, since mismatch attenuates signal and noise equally and does not degrade the SNR.
Gain Definitions
GA = (1 − |ΓS|²) × |S21|² / (|1 − S11ΓS|² × (1 − |Γout|²))
where Γout = S22 + S12S21ΓS/(1 − S11ΓS)
Transducer Gain:
GT = (1 − |ΓS|²) × |S21|² × (1 − |ΓL|²) / |Δ|²
where Δ = (1 − S11ΓS)(1 − S22ΓL) − S12S21ΓSΓL
Maximum Available Gain:
MAG = |S21/S12| × (K − √(K² − 1))
Valid only when K > 1 (unconditionally stable)
Friis Cascade (using available gain):
Ftotal = F1 + (F2 − 1)/GA1 + (F3 − 1)/(GA1 × GA2) + …
Gain Definition Comparison
| Gain Type | Depends On | Assumes | Used For |
|---|---|---|---|
| Available (GA) | ΓS only | Output conjugate-matched | Noise figure, LNA design |
| Operating (GP) | ΓL only | Input conjugate-matched | PA design, load-pull |
| Transducer (GT) | ΓS and ΓL | Nothing (actual conditions) | System gain budgets |
| MAG | S-parameters only | Both ports conjugate-matched | Device comparison, max capability |
| MSG | |S21/S12| | K = 1 boundary | Conditionally stable devices |
Frequently Asked Questions
What is the difference between available gain, transducer gain, and operating gain?
Available gain assumes output conjugate-matched, depends only on source impedance. Transducer gain depends on both source and load, representing actual conditions. Operating gain assumes input conjugate-matched, depends only on load. When both ports are conjugate-matched, all three equal the maximum available gain (MAG). Each serves a different design context: GA for LNAs, GP for PAs, GT for system budgets.
Why is available gain used in noise figure calculations?
Noise figure is defined as SNR degradation assuming available power at the output. The Friis cascade formula Ftotal = F1 + (F2−1)/GA1 + ... uses available gain because it correctly accounts for noise contribution without including output mismatch loss, which attenuates signal and noise equally and should not be counted as noise degradation.
What is maximum available gain (MAG)?
MAG is the available gain when the source is also conjugate-matched (ΓS = Γin*), representing the absolute maximum gain. It exists only when K > 1 (unconditionally stable). For K < 1 (conditionally stable), MSG = |S21/S12| is reported instead. MAG = |S21/S12| × (K − √(K²−1)).