The NF-Gain Tradeoff
For an LNA, minimum noise figure (NF_min) occurs at source reflection coefficient Γ_opt, while maximum gain occurs at conjugate match (Γ_s = Γ_in*). These are generally different points on the Smith chart — the designer must choose where to operate between these two objectives.
Noise Circles
Contours of constant noise figure F on the Γ_s plane: NF_circle(F) = center + radius, centered near Γ_opt NF_min at Γ_opt (center of innermost circle) NF = NF_min + 4Rn·|Γ_s − Γ_opt|² / (Z₀·(1−|Γ_s|²)·|1+Γ_opt|²) where Rn = equivalent noise resistance, Γ_opt = optimum noise source refl
Available Gain Circles
Contours of constant available gain G_a on Γ_s plane: G_a = G_a_max × (1−|Γ_s|²) / |1−S₁₁·Γ_s|² × 1/|S₂₁|² × ... Concentric circles centered at conjugate match Γ_s = Γ_in* Maximum gain at center (conjugate match)
Design Space
The region between noise-optimal match and gain-optimal match on the Smith chart represents the LNA design tradeoff space:
- Closer to Γ_opt: lower NF, lower gain (noise matching)
- Closer to Γ_in*: higher gain, higher NF (gain matching)
- Simultaneous noise-power match exists only for specific device topologies
Practical LNA Design with RF View
Since RF View's Auto Match performs gain matching (conjugate match), for noise-matched design, enter the known Γ_opt from the manufacturer's noise parameter data as the target impedance in the Advanced matching options.
RF View: Load LNA .s2p to view S11 (determines Γ_in* for conjugate match location). For noise matching, use manufacturer Γ_opt from noise parameter datasheet. Auto Match handles the matching network synthesis. Free on Android.