Echo and Source Boundary Depth Scans

Source Reflection Load Total Three-Row Scan

A source-boundary reflection ledger tracks how the source coefficient changes the next load voltage after a returning wave bounces again. The load totals are exact only for the declared incident voltage, source coefficient, load boundary, ideal lossless line, and sharp transitions; real lines add finite source impedance, connector mismatch, parasitics, attenuation, finite rise time, calibration drift, and voltage/time measurement uncertainty.

Source-boundary reflection is scanned through the next load total. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Source reflection changes the next load total

The first load arrival is fixed. The source boundary controls the next returned arrival, so the visible load total changes.

Vload=12 V+0 V=12 VΓS=0V_{\text{load}}=12\ \text{V}+0\ \text{V}=12\ \text{V}\qquad \Gamma_S=0
Source-boundary load totalThe bounce ledger total follows the source coefficient.linew0w1w2load Gamma 1/2source Gamma 0load total 12 V

Source reflection changes the next load total

The first load arrival is fixed. The source boundary controls the next returned arrival, so the visible load total changes.

Vload=12 V+(−3 V)=9 VΓS=−12V_{\text{load}}=12\ \text{V}+(-3\ \text{V})=9\ \text{V}\qquad \Gamma_S=\frac{-1}{2}
Source-boundary load totalThe bounce ledger total follows the source coefficient.linew0w1w2load Gamma 1/2source Gamma -1/2load total 9 V

Source reflection changes the next load total

The first load arrival is fixed. The source boundary controls the next returned arrival, so the visible load total changes.

Vload=12 V+2 V=14 VΓS=13V_{\text{load}}=12\ \text{V}+2\ \text{V}=14\ \text{V}\qquad \Gamma_S=\frac{1}{3}
Source-boundary load totalThe bounce ledger total follows the source coefficient.linew0w1w2load Gamma 1/2source Gamma 1/3load total 14 V