Line Open Short

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The two extreme line terminations — open and short — showing voltage doubling and cancellation.

The same $Z_C=100\mathrm{\Omega }$, $\tau =250\mu \mathrm{s}$ line as the Bergeron demo, but terminated at the extremes. The selector picks a near-short (1 Ω), a matched 100 Ω, or a near-open (10 kΩ), giving reflection coefficients of roughly $-1$, $0$ and $+1$.

A 100 V ideal step is applied to a lossless line with Zc = 100 Ω and τ = 250 µs, and the far end is terminated at the two extremes that bracket everything else a line can meet. The reflection coefficient is Γ = (R_L − Zc) / (R_L + Zc), so the 10 kΩ position stands in for an open end (Γ ≈ +1), the 1 Ω position for a short (Γ ≈ −1), and 100 Ω sits exactly in between at Γ = 0.

The sample opens on the open end, which is the striking one: the arriving wave has nowhere to send its current, so it launches a reflection that cancels the current and — because voltage and current in a wave are locked together with a direction-dependent sign — adds the voltage. Vr jumps to nearly 200 V, twice the applied 100 V. That doubling is not a numerical artifact; it is why energizing an unloaded line is treated as a real overvoltage hazard.

Step the selector to the 1 Ω position and the picture inverts. Vr barely moves off zero — about 2 V per round trip — while the sending-end current climbs in stages toward the 100 A a 1 Ω load will draw, because a short reflects with the opposite sign. Because an ideal source also reflects with Γ = −1, the round-trip product is close to +1 here and close to −1 for the open case: the short produces a slow monotonic climb toward the steady state, while the open swings between roughly 198 V and near zero with a 1 ms period and barely decays across the whole 2 ms window. Used in the EMT course, Chapter 8 (travelling waves and the Bergeron line).