Reflections at Boundaries

Lower Load Reflects a Negative Step

A lower-load-reflects-a-negative-step ledger shows that a load below the line impedance sends back an inverted voltage echo. The 2 ohm load against a 4 ohm line gives Gamma = -1/3, so the stated 12 V incident step reflects as -4 V only inside the ideal lossless-line model. Real lines add loss, dispersion, connector discontinuities, source impedance, finite rise time, calibration limits, finite precision, and measurement uncertainty.

A load below the line impedance returns an inverted step. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A lower load gives a negative coefficient

The load is 2 ohms and the line is 4 ohms, so the coefficient is -1 over 3.

Γ=2 − 42+4=−13\Gamma={2\,-\,4\over 2+4}={-1\over 3}
Lower load reflectionThe negative coefficient is computed from the load mismatch.incidentreflectedline 4 ohmload 2 ohmGamma -1/3in 12 Vback -4 V

The reflected step changes sign

A coefficient of -1 over 3 sends a 12 volt step back as -4 volts.

V−=−13⋅12 V=−4 VV_{-}={-1\over 3}\cdot 12\ \text{V}=-4\ \text{V}
Negative reflected stepThe reflected label carries the sign of the mismatch.incidentreflectedline 4 ohmload 2 ohmGamma -1/3in 12 Vback -4 V