Series & Shunt Paths — Impedance Matching

Part 4 · Impedance Matching

Series and shunt paths

Key point: you do not jump on the Smith chart. Series L or C rides constant \(R\). Shunt L or C rides constant \(G\).

Gold is constant \(R\). Teal is the constant-\(G\) family. Violet is this element. Green is \(Z_0\). Frequency is 1 GHz.

1
Series L on 50 Ω.
Start 50.0 + j0.0. Amount gives 28.50 nH. End is 50.0 + j179.1. Path type is const. R. The real part did not move.
2
Series C, same circle, other way.
Start 50.0 + j40.0. 14.50 pF. End is 50.0 + j29.0. Still const. R. The capacitor ate some of the +jX.
3
Shunt C leaves the gold circle.
Start 100.0 + j0.0. 6.90 pF. End is 5.1 − j21.9. Path type is const. G. \(R\) changed because this is an admittance move.
4
Shunt L, other susceptance.
Start 75.0 + j0.0. 16.00 nH. End is 48.2 + j35.9. Still const. G. The arc bends the other way.
5
More series L, same circle.
Back to 50.0 + j0.0. Amount at the stop, 40.50 nH. End is 50.0 + j254.5. Same gold circle as step 1, longer violet arc.

A match is one series stroke and one shunt stroke that land on the center. Part 5 is how to read the point you are aiming from.

Gold = const-\(R\) · teal = const-\(G\) hint · violet = this element

Element Start R (Ω) Start X (Ω) Amount (0 → full) f (GHz)

const R (series) const G (shunt hint) this path match (Z₀)

Mini Smith · red start · violet end

Start Z—

End Z—

Component—

Path type—

Series adds \(X\). Shunt adds \(B\).

\[ Z \leftarrow Z + jX \quad\Rightarrow\quad R=\mathrm{const} \]

Z_start = —

L = —

Z_end = —