Impedance Matching — TDR-Style Playground

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Pick a mismatched load and a matching network. The Smith chart shows the load rotating toward the center as you slide the stub position. The TDR trace V(t) shows the source-end voltage: a step appears at the round-trip time when the load reflects; when the match is perfect, the trace stays flat. Single-stub and quarter-wave-transformer modes are auto-computed; you can also drag d and â„“ to see what happens when the match is off.

📡 EMFT Hub 🌊 Plane Waves ⌬ Smith Chart ⏱ TDR ▦ S-params ⚡ Matching ← Home

Line + load

λ = vp·c / f. Round-trip time 2L/vp sets where the TDR step appears.

Matching network

For a short-circuited stub: Bstub = −Y0 cot(βℓ). For open: Bstub = +Y0 tan(βℓ).

Presets

① Transmission line (source → distance d → stub → load)
The stub sits at distance d from the source; the load is at the end. The stub is a short (red) or open (blue) transmission-line section of length â„“.
② Smith chart — watch the rotated load reach the center
The blue point is the load. Rotating it CW by d (toward the generator) is the matching-network input point; the stub adds a susceptance that lands the combined point on the center.
ZL (load) Z(d) (rotated, before stub) Zin (matched)
③ TDR trace V(t) — the source-end voltage vs time
At t=0 the source launches Vincident. At t = 2L/vp, the reflection from the load comes back; if matched, this step vanishes and the trace stays flat. The marker shows the current round-trip time.
Load & line
ZL = R + jX
—
YL = G + jB
—
ΓL = (ZL−Z0)/(ZL+Z0)
—
|ΓL|
—
VSWR (load only)
—
Matching network
d (distance from load)
—
â„“ (stub length)
—
Stub B (susceptance)
—
Zin (at source)
—
Result after matching
|Γin| residual reflection
—
VSWR (matched)
—
Return loss
—
Status
—
The residual reflection = Γ at the source. |Γin| < 0.01 is excellent; < 0.1 is good; > 0.1 means the match is off.