Series & Shunt Paths

Along the way

1
Each element is one-dimensional. A single L or C has one value. On the chart that is one allowed curve, not a free jump.
2
Series adds \(jX\) → constant \(R\) (gold). \(Z \leftarrow Z + jX\). The real part does not move. Series L climbs toward the open; series C drops toward the short.
3
Shunt adds \(jB\) → constant \(G\) (teal). Work in \(Y = 1/Z\). Shunt C increases susceptance; shunt L decreases it. Same idea, admittance wallpaper.
4
Amount is the component value. Drag it and the violet path grows from the red start. Frequency scales how much L or C you need for the same arc.
5
A match is a sequence of strokes. Typical L-section: one series + one shunt, chosen so the path ends on the green center. Part 6 chains them in the tool.

Gold circles = constant \(R\). Teal hint = the \(g=1\) family (constant \(G\)). Violet = the element you picked. Green = \(Z_0\).

Next: Part 5 — read a point (\(z\), \(Z\), \(\Gamma\)) so you can aim these strokes.

Move from a starting \(Z\)

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—

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

Z_start = —

L = —

Z_end = —

Try it: “Series L” from pure \(R\) — the violet arc slides on the gold circle. Switch to “Shunt C” — the path bends along the teal family instead. Matching is sequencing those two kinds of stroke.

Analog Intuition

Move from a starting \(Z\)