Reading the Smith Chart

Along the way

1
The chart is the \(\Gamma\) plane with a \(Z\) grid. Click anywhere: that is \(\Gamma\). The inverse map \(z = (1+\Gamma)/(1-\Gamma)\) is the impedance.
2
Gold = constant \(R\). The highlighted gold circle through the point is this \(r\). The bold circle through the center is \(r = 1\) — real part already equal to \(Z_0\).
3
Teal = constant \(X\). The highlighted teal arc is this \(x\). Upper half is \(+X\) (inductive); lower half is \(-X\) (capacitive).
4
Landmarks. Center = match. Left rim = short. Right rim = open. The horizontal diameter is purely real \(z\).
5
Shunt thinking uses a \(Y\) grid. Same red point, const-\(G\) / const-\(B\) wallpaper. The full matcher toggles it — you’ll want both when placing series vs shunt elements.

\(Z_0 = 50\,\Omega\) on this page. Highlighted gold / teal are this point’s \(R\) and \(X\), not just the printed grid.

Next: Part 6 — guided tasks in the Smith matcher. Part 7 — a real ESP32 2.4 GHz pin.

Click the chart or use a preset

\(Z_0 = 50\,\Omega\) · gold / teal highlight follow the red point

this R (const-R) this X (const-X) match (Z₀)

Smith · click anywhere inside the disk

Normalized z—

Z (Ω)—

Γ—

|Γ| / RL—

1 − |Γ|²—

\[ \Gamma \]

= —

\[ z = \dfrac{1+\Gamma}{1-\Gamma} \]

= —

\[ Z = z\,Z_0 \]

= —

\[ |\Gamma| \]

= —

\[ \mathrm{RL} = -20\log_{10}|\Gamma| \]

= —

Highlighted gold circle = this \(R\). Highlighted teal arc = this \(X\). Center = \(Z_0\).

Try it: click the right rim (open), left rim (short), and the center (match). Then land on the bold \(r=1\) circle through the center — real part is already \(Z_0\); only \(X\) is left to cancel.

Analog Intuition

Click the chart or use a preset