Stability Conditions
An amplifier is stable when it does not oscillate for any passive source and load termination. This is assessed from the device S-parameters:
Rollett's K-factor: K = (1 − |S₁₁|² − |S₂₂|² + |Δ|²) / (2·|S₁₂|·|S₂₁|) Δ = S₁₁·S₂₂ − S₁₂·S₂₁ Unconditionally stable: K > 1 AND |Δ| < 1 (Both conditions must be met simultaneously) Alternative: μ-factor (single-parameter test): μ = (1 − |S₁₁|²) / (|S₂₂ − Δ·S₁₁*| + |S₁₂·S₂₁|) > 1 → stable
Interpreting K at Different Frequencies
| K Value | Stability Status | Risk |
|---|---|---|
| K > 1 (and |Δ|<1) | Unconditionally stable | No oscillation risk |
| K < 1 | Potentially unstable | Oscillation for some Γ_s, Γ_L |
| K < 0 | Always unstable | Avoid this design point |
Stabilization Methods
- Series resistor at input: Reduces |S₂₁|, improves K but degrades NF
- Shunt resistor at output: Loads output, improves K at low frequencies
- Feedback resistor: Reduces |S₁₂|, improves stability and bandwidth flatness
- Lossy stabilization: Add 20–33 Ω at gate (LNA) — trades NF for stability
Stability Circles
Input stability circle: locus of Γ_s values giving |Γ_out| = 1 Output stability circle: locus of Γ_L values giving |Γ_in| = 1 If K > 1: all terminations in/out of Smith chart are stable If K < 1: only certain regions of Γ_s, Γ_L planes give stability
RF View: Load amplifier .s2p file to view S12 isolation and all four S-parameters. Check S21/S12 ratio and S11/S22 levels to get an intuitive feel for stability before computing K analytically.