Explanation
Consider the case where the far end of the cable is shorted (that is, it is terminated into zero ohms impedance). 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 down the cable towards the short. When the pulse hits the short, no energy is absorbed at the far end. Instead, an opposing pulse reflects back from the short towards the launching end. It is only when this opposing reflection finally reaches the launch point that the voltage at this launching point abruptly drops back to zero, signalling the fact that there is a short at the end of the cable. That is, the TDR had no indication that there is a short at the end of the cable until its emitted pulse can travel down the cable at roughly the speed of light and the echo can return back up the cable at the same speed. It is only after this round-trip delay that the short can be perceived by the TDR. Assuming that one knows the signal propagation speed in the particular cable-under-test, then in this way, 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.
Note that a theoretical perfect termination at the far end of the cable would entirely absorb the applied pulse without causing any reflection. In this case, it would be impossible to determine the actual length of the cable. Luckily, perfect terminations are very rare and some small reflection is nearly always caused.
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:
Where Zo is defined as the characteristic impedance of the transmission medium and Zt 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 Zt. 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.
Read more about this topic: Time-domain Reflectometer
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