Reflection Boundary Cross-Scan - Electromagnetic Transmission Lines: Signal Propagation and Reflections Step by Step

Reflection sign and size are scanned across load and incident 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

The boundary coefficient comes from load mismatch

A higher load sends back a same-sign step. The coefficient and reflected voltage are checked from the same boundary source.

\Gamma={Z_{\text{load}}-Z_{\text{line}}\over Z_{\text{load}}+Z_{\text{line}}}=\frac{1}{3}\qquad V_{\text{back}}=2\ \text{V}

Load impedance controls reflection sign

Line impedance and incident step are fixed. Lower, matched, and higher loads give negative, zero, and positive reflection rows.

\begin{array}{c|c|c|c|c}Z_{\text{line}}&Z_{\text{load}}&\Gamma&V_{\text{in}}&V_{\text{back}}\\4\ \Omega&2\ \Omega&\frac{-1}{3}&6\ \text{V}&-2\ \text{V}\\4\ \Omega&4\ \Omega&0&6\ \text{V}&0\ \text{V}\\4\ \Omega&8\ \Omega&\frac{1}{3}&6\ \text{V}&2\ \text{V}\\\end{array}

Incident step scales the reflected step

The coefficient is fixed here. The reflected voltage follows the incident voltage one for one.

\begin{array}{c|c|c|c|c}Z_{\text{line}}&Z_{\text{load}}&\Gamma&V_{\text{in}}&V_{\text{back}}\\4\ \Omega&8\ \Omega&\frac{1}{3}&3\ \text{V}&1\ \text{V}\\4\ \Omega&8\ \Omega&\frac{1}{3}&6\ \text{V}&2\ \text{V}\\4\ \Omega&8\ \Omega&\frac{1}{3}&12\ \text{V}&4\ \text{V}\\\end{array}