Editing Time-domain reflectometer (section)

== Explanation ==
If the far end of the cable is shorted, that is, terminated with an impedance of zero ohms, and when the rising edge of the pulse is launched down the cable, the voltage at the launching point "steps up" to a given value instantly and the pulse begins propagating in the cable towards the short. When the pulse encounters the short, no energy is absorbed at the far end. Instead, an inverted pulse reflects back from the short towards the launching end. It is only when this reflection finally reaches the launch point that the voltage at this point abruptly drops back to zero, signaling the presence of a short at the end of the cable. That is, the TDR has no indication that there is a short at the end of the cable until its emitted pulse can travel in the cable and the echo can return. It is only after this round-trip delay that the short can be detected by the TDR. With knowledge of the [[velocity of propagation|signal propagation speed]] in the particular cable-under-test, the distance to the short can be measured.

A similar effect occurs if the far end of the cable is an open circuit (terminated into an infinite impedance). In this case, though, the reflection from the far end is polarized identically with the original pulse and adds to it rather than cancelling it out. So after a round-trip delay, the voltage at the TDR abruptly jumps to twice the originally-applied voltage.

Perfect termination at the far end of the cable would entirely absorb the applied pulse without causing any reflection, rendering the determination of the actual length of the cable impossible. In practice, some small reflection is nearly always observed.

The magnitude of the reflection is referred to as the reflection coefficient or ''ρ''. The coefficient ranges from 1 (open circuit) to −1 (short circuit). The value of zero means that there is no reflection. The reflection coefficient is calculated as follows:
<math display="block">\rho = \frac{Z_\text{t} - Z_\text{o}}{Z_\text{t} + Z_\text{o}}</math>
where ''Z''<sub>o</sub> is defined as the characteristic impedance of the transmission medium and ''Z''<sub>t</sub> is the impedance of the termination at the far end of the [[transmission line]].

Any discontinuity can be viewed as a termination impedance and substituted as ''Z''<sub>t</sub>. This includes abrupt changes in the characteristic impedance. As an example, a trace width on a printed circuit board doubled at its midsection would constitute a discontinuity. Some of the energy will be reflected back to the driving source; the remaining energy will be transmitted. This is also known as a scattering junction.