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Short note: Amplifier design flow and stability

Short answer

Design flow starts with transistor S-parameters and stability analysis: if K>1 and |Δ|<1 (or μ>1) the device is unconditionally stable; otherwise stability circles define safe Γ_S, Γ_ L. Then calculate unilateral (Γ_S=S11*, Γ_ L=S22*) or simultaneous conjugate match gains and synthesize matching networks.

Write a short note on microwave amplifier design flow and stability analysis.

A microwave amplifier is designed from the transistor's S-parameters at the operating frequency and bias. The aim is the required gain (or noise figure) while staying stable.

Design flow

 Specs: f, gain, NF, bandwidth
              |
 Choose transistor + bias, get [S]
              |
 Stability check: K, |Δ| (or μ)
     | stable          | potentially unstable
     |            stability circles,
     |            pick ΓS, ΓL in stable region
              |
 Unilateral? (U small) -> ΓS=S11*, ΓL=S22*
 else bilateral: ΓMS, ΓML (B1, C1, B2, C2)
              |
 Matching networks (Smith chart, stubs)
              |
 Bias network, layout, simulate, tune

Stability analysis

An amplifier can oscillate if the input or output reflection coefficient has magnitude greater than 1 (negative resistance):

Γin  = S11 + S12 S21 ΓL / (1 − S22 ΓL)
Γout = S22 + S12 S21 ΓS / (1 − S11 ΓS)
Δ = S11 S22 − S12 S21
K = (1 − |S11|² − |S22|² + |Δ|²) / (2|S12 S21|)
  • Unconditionally stable: K > 1 and |Δ| < 1 (or μ > 1). Any passive source and load can be used.
  • Potentially unstable: otherwise. Stability circles in the Γ_L and Γ_S planes show which terminations to avoid, and the design must use terminations in the stable region (or add resistive loading).

✓ Answer checked by Claude Opus 5.5 (high effort)

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