Echo and Source Boundary Depth Scans

Line Impedance Reflection Three-Row Scan

A line-impedance reflection scan holds the load and incident step fixed while changing the line impedance seen by the boundary. The reflection coefficients and returned voltages are exact only for the declared impedances and ideal lossless-line assumptions; real cables have tolerance, attenuation, dispersion, connector mismatch, finite rise time, source/load parasitics, temperature effects, and voltage/impedance measurement uncertainty.

The same load boundary is scanned across line impedance values. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Line impedance changes the same load boundary

The load and incident step are fixed here. Changing the line impedance changes the mismatch seen by the return.

Γ=8 Ω16 Ω=12Vback=3 V\Gamma={8\ \Omega\over16\ \Omega}=\frac{1}{2}\qquad V_{\text{back}}=3\ \text{V}
Line-impedance reflection scanThe same load reflects differently for each line impedance.incidentline 4 ohmload 12 ohmGamma 1/2in 6 Vback 3 V

Line impedance changes the same load boundary

The load and incident step are fixed here. Changing the line impedance changes the mismatch seen by the return.

Γ=6 Ω18 Ω=13Vback=2 V\Gamma={6\ \Omega\over18\ \Omega}=\frac{1}{3}\qquad V_{\text{back}}=2\ \text{V}
Line-impedance reflection scanThe same load reflects differently for each line impedance.incidentline 6 ohmload 12 ohmGamma 1/3in 6 Vback 2 V

Line impedance changes the same load boundary

The load and incident step are fixed here. Changing the line impedance changes the mismatch seen by the return.

Γ=0 Ω24 Ω=0Vback=0 V\Gamma={0\ \Omega\over24\ \Omega}=0\qquad V_{\text{back}}=0\ \text{V}
Line-impedance reflection scanThe same load reflects differently for each line impedance.incidentline 12 ohmload 12 ohmGamma 0in 6 Vback 0 V