Part 4 · Impedance Matching

Series & shunt paths

One idea: series L/C ride a constant-R circle; shunt L/C ride a constant-G circle on the Smith chart.

Move from a starting Z

Gold = const-R family · teal hint = const-G · path shows the element you choose

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

Start Z —

End Z —

Component —

Path type —

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

Z_start = —

L = —

Z_end = —

Try it: series L from pure R — arc slides on the gold circle. Switch to shunt C — the path bends along a different family (const G). Matching is sequencing these strokes.

The one idea

You never “jump” arbitrarily on the Smith chart. Each physical element forces a one-dimensional path:

\text{series:}\quad Z \leftarrow Z + jX \quad\Rightarrow\quad R=\text{const}

\text{shunt:}\quad Y \leftarrow Y + jB \quad\Rightarrow\quad G=\text{const}

Why that matters

Designing a match is choosing a short sequence of allowed strokes that ends near the chart center. Part 5 practices reading a point; Part 6 uses the full matcher to chain strokes.