Bounce Ledgers and Termination Audit

Successive Bounces Shrink by Boundary Coefficients

A successive-bounces-shrink-by-boundary-coefficients ledger treats each traveling wave as multiplied by the boundary coefficient it reaches. The 8 V wave reflecting to 4 V and then returning as -2 V is exact only for the stated ideal load and source coefficients. Real lines add loss, dispersion, connector discontinuities, source/load tolerance, finite rise time, calibration limits, finite precision, and measurement uncertainty.

Each traveling wave is multiplied by the boundary it reaches. 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 load boundary multiplies by its coefficient

The first incoming wave is 8 volts and the load coefficient is 1 over 2, so the outgoing wave is 4 volts.

8⋅12=48\cdot {1\over 2}=4
Load reflection rowThe load row uses the checked load coefficient.linew0w1w2w3load Gamma 1/2source Gamma -1/2load total 9 V

The source boundary multiplies the returning wave

The returning 4 volt wave sees source coefficient -1 over 2, giving -2 volts forward.

4⋅−12=−24\cdot {-1\over 2}=-2
Source reflection rowThe next forward wave is checked by the source coefficient.linew0w1w2w3load Gamma 1/2source Gamma -1/2load total 9 V