Maximum Power Transfer Theorem
Maximum power is transferred from a source with impedance Z_s = R_s + jX_s to a load Z_L when the load is the complex conjugate of the source:
Z_L_opt = Z_s* = R_s − jX_s (conjugate match) P_max = |V_s|² / (4·R_s) [maximum available power] η = P_L / P_max = (1 − |Γ_L|²) / |1 − Γ_s*·Γ_L|² [transducer efficiency]
Three Types of Matching in RF
| Match Type | Goal | Use Case |
|---|---|---|
| Conjugate match | Max power transfer: Z_L = Z_s* | Amplifier output, TX antenna |
| Noise match | Min noise figure: Γ_s = Γ_opt | LNA input (Γ_opt ≠ Γ_in*) |
| Real match (50 Ω) | Z = 50 Ω at both ports | System integration, cascade |
Conjugate Match vs 50 Ω Match
In a 50 Ω system, conjugate matching reduces to real matching: Z_L = Z_s* = 50 Ω when Z_s is purely real. But for a transistor amplifier with Z_s = 30+j20 Ω at the gate, conjugate matching requires Z_L = 30−j20 Ω — the matching network must cancel the reactive part and transform the real part to 50 Ω.
Simultaneous Conjugate Match (SCM)
For a bilateral amplifier (S₁₂ ≠ 0): Input and output are interdependent. SCM conditions: Γ_s = Γ_in* = (S₁₁ + S₁₂·S₂₁·Γ_L / (1 − S₂₂·Γ_L))* Γ_L = Γ_out* = (S₂₂ + S₁₂·S₂₁·Γ_s / (1 − S₁₁·Γ_s))* Requires K > 1 (unconditional stability) for solution to exist.
RF View Auto Matching: RF View's Auto Matching synthesizes a network that conjugate-matches (or noise-matches) the device impedance to 50 Ω at the target frequency — one tap, from your device's S-parameter file.