Echo and Source Boundary Depth Scans

Echo One-Way Delay Three-Row Scan

A transmission-line echo ledger doubles the one-way delay to predict when a reflection returns to the source. The round-trip times are exact only for the declared line lengths, propagation speed, lossless line, and sharp reflection boundary; real measurements include dispersion, attenuation, finite rise time, connector mismatch, temperature-dependent velocity, calibration error, and time/voltage uncertainty.

Round-trip echoes are scanned across exact one-way delays. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Round trip is twice the one-way delay

Each row keeps the signal speed fixed and changes the line length. The return time is the doubled one-way delay.

2tone=2⋅2 s=4 sL=6 m2t_{\text{one}}=2\cdot2\ \text{s}=4\ \text{s}\qquad L=6\ \text{m}
One-way delay echo scanLonger checked lines produce later round-trip echoes.outecholaunch 0 sone way 2 sround trip 4 secho 4 s

Round trip is twice the one-way delay

Each row keeps the signal speed fixed and changes the line length. The return time is the doubled one-way delay.

2tone=2⋅4 s=8 sL=12 m2t_{\text{one}}=2\cdot4\ \text{s}=8\ \text{s}\qquad L=12\ \text{m}
One-way delay echo scanLonger checked lines produce later round-trip echoes.outecholaunch 0 sone way 4 sround trip 8 secho 8 s

Round trip is twice the one-way delay

Each row keeps the signal speed fixed and changes the line length. The return time is the doubled one-way delay.

2tone=2⋅6 s=12 sL=18 m2t_{\text{one}}=2\cdot6\ \text{s}=12\ \text{s}\qquad L=18\ \text{m}
One-way delay echo scanLonger checked lines produce later round-trip echoes.outecholaunch 0 sone way 6 sround trip 12 secho 12 s