The telegrapher's equations
A transmission line is not a lumped wire — it is a distributed LC network. Every infinitesimal slice has series inductance and shunt capacitance per unit length, and the telegrapher's equations describe how voltage and current ripple through that ladder. The upshot is a wave that travels at velocity carrying a characteristic impedance . Reflection and transmission at a boundary then fall straight out of conserving charge and energy at the junction — there is no extra physics, just bookkeeping at the discontinuity.
Where it shows up
TDR is the everyday tool for cable fault location: the round-trip time of the echo times the propagation velocity gives the distance to a break or crimp, and the sign of Γ tells you whether the fault is an open or a short. The same trick characterises PCB traces for signal integrity, profiles connector mismatches, and even measures soil moisture — anywhere you need to know what sits at the far end of a wire without travelling there yourself.
The knobs
- Load — selects the termination: Matched (Γ = 0), Short (Γ = −1), Open (Γ = +1), Z_L = 2 Z₀ (Γ = +1/3), or Z_L = Z₀ / 2 (Γ = −1/3). Watch the returning pulse flip colour and shrink as Γ changes sign and magnitude.
- Speed — scales how fast the pulse propagates, stretching or compressing the round trip so you can follow the reflection in slow motion or watch it ring at pace.