Unilateral max gain with design flow chart

In a unilateral design S12 is taken as zero, so the input and output can be conjugate-matched independently: Γs = S11* and ΓL = S22*.

Assumed S-parameters (Z0 = 50 Ω)

S11 = 0.5∠−150°, S12 ≈ 0, S21 = 3.0∠60°, S22 = 0.4∠−40°.

With S12 = 0, Δ = S11S22 and K → ∞; since |S11| < 1 and |S22| < 1 the device is unconditionally stable.

Maximum unilateral gain

GTU,max = GS,max · G0 · GL,max
GS,max = 1/(1 − |S11|²) = 1/(1 − 0.25) = 1.3333 → 1.25 dB
G0     = |S21|² = 9.0                  → 9.54 dB
GL,max = 1/(1 − |S22|²) = 1/(1 − 0.16) = 1.1905 → 0.76 dB
GTU,max = 1.3333 × 9 × 1.1905 = 14.29
        = 1.25 + 9.54 + 0.76 = 11.55 dB

Matching terminations needed:

• Γs = S11* = 0.5∠150° → Zs = 50(1+Γs)/(1−Γs) = 17.72 + j11.81 Ω
• ΓL = S22* = 0.4∠40° → ZL = 76.76 + j46.99 Ω

The input matching network must transform the 50 Ω source to 17.72 + j11.81 Ω, and the output network must transform the 50 Ω load to 76.76 + j46.99 Ω. Each can be a shunt open stub plus a series line, or an L-section, designed on the Smith chart.

Answer: GTU,max = 14.29 ≈ 11.55 dB (for the assumed S-parameters).

Design flowchart

 +------------------------------+
 | Specs: f, gain, Z0, BW, NF   |
 +------------------------------+
               |
 +------------------------------+
 | Choose transistor, bias;     |
 | get [S] at design frequency  |
 +------------------------------+
               |
 +------------------------------+
 | Compute Δ, K (and μ)         |
 +------------------------------+
               |
      K>1 and |Δ|<1 ?
     yes |          | no
         v          v
 Uncond. stable   Draw stability circles;
         |        pick Γs, ΓL in stable
         |        region (or stabilise)
         +----+-----+
              |
   Unilateral? (U small, S12≈0)
   yes: Γs=S11*, ΓL=S22*
   no : Γs=ΓMS, ΓL=ΓML (bilateral)
              |
 +------------------------------+
 | Compute GS, G0, GL -> GT     |
 +------------------------------+
              |
 +------------------------------+
 | Design input/output matching |
 | (stubs or L-C) on Smith chart|
 +------------------------------+
              |
 | Bias network, layout, simulate
              |
   Specs met? -- no --> revise
              | yes
            Build & test

Key points of the flow:

1. The gain is split into three independent blocks: input match (GS), transistor (G0) and output match (GL).
2. The unilateral figure of merit U is checked. If the error bounds 1/(1±U)² are small (under about ±0.5 dB), the unilateral design is accepted; otherwise a bilateral (simultaneous conjugate match) design is used.
3. After matching, a bias network with RF chokes and DC blocks is added, and the circuit is simulated and tuned.