A voltage pulse travels down a 50Ω line and meets the load — matched, shorted, or open.
What TDR Sees
Time Domain Reflectometry is how EE's "look down" a transmission line without cutting it open. You send a fast voltage step into the line and watch what comes back. The amplitude and sign of the reflection tells you exactly what's at the far end — no reflection = matched, inverted = short, in-phase = open, and everything in between if the load impedance is neither 0 nor ∞.
The Reflection Coefficient
At the load, the voltage and current must obey both the line's characteristic impedance Z₀ and the load's impedance Z_L. The boundary condition forces a reflected wave with amplitude:
Γ = (Z_L − Z₀) / (Z_L + Z₀)
- Z_L = Z₀ → Γ = 0: The pulse is absorbed. No reflection.
- Z_L = 0 (short) → Γ = −1: The pulse inverts and reflects.
- Z_L = ∞ (open) → Γ = +1: The pulse reflects in phase, doubling the voltage.
- Z_L = 2Z₀ → Γ = +1/3: Part of the pulse reflects in phase.
- Z_L = Z₀/2 → Γ = −1/3: Part of the pulse inverts on reflection.
The Telegrapher's Equations
A transmission line is not a lumped wire — it's a distributed RLC network. At every point along the line, there's series inductance and shunt capacitance per unit length. A voltage wave propagates at a characteristic velocity v = 1/√(LC) with a characteristic impedance Z₀ = √(L/C). The reflection and transmission at boundaries follow directly from conservation of energy and charge at the junction.
TDR is used practically for cable fault location, PCB trace characterisation, and soil moisture measurement — wherever you need to know what's at the far end of a wire without going there.