Analog Intuition

Part 5 · Impedance Matching

Reading the Smith chart

One idea: every point is a Z (and a Γ) — gold circles are constant R; teal arcs are constant X.

Click the chart or use a preset

Z0 = 50 Ω · readout follows the red point

Normalized z —
Z (Ω) —
Γ —
|Γ| / RL —
\[ \Gamma \]
= —
\[ z = \dfrac{1+\Gamma}{1-\Gamma} \]
= —
\[ Z = z\,Z_0 \]
= —
\[ |\Gamma| \]
= —
\[ \mathrm{RL} = -20\log_{10}|\Gamma| \]
= —

Gold circles through a point share the same R. Teal arcs share the same X. Center = Z0.

Try it: click near the right rim (open), left rim (short), and the center (match). Then land on the r=1 circle (through the center) — pure reactance with R = Z0.

The one idea

The Smith chart is a map of the \(\Gamma\) plane with impedance (or admittance) gridlines overlaid. If you can read \(R\) and \(X\) from a point, you can plan strokes (Part 4) toward the center.

\[z = \frac{1+\Gamma}{1-\Gamma},\qquad Z = z\,Z_0,\qquad \Gamma = \frac{z-1}{z+1}\]

Z view vs Y view

The full matcher toggles an admittance grid (const G, B) for shunt-first thinking. Same red point — different wallpaper. You’ll use both when placing series vs shunt elements.