Electronic – High-Speed electronics – Reflections in T-intersection

coaxhigh speedpower electronicsreflectiontdr

I'm currently attending a course on "experimental problem solving" and we just started talking about TDR (time domain reflectometry). I do understand that reflections occur whenever there is a change of impedance, and that you can terminate them by making sure the load resistance is equal to the impedance of the cable. However, we now got a question to explain why we get reflections in a "T-intersection" (not sure about the real name but basically a dongle to connect three cables together) even though we match the load resistance with each of the cables impedances. Can someone explain why this happens, or some source where you can read about these things?

Best Answer

As you know, when you apply a (matched) voltage source step function to a transmission line you will instantaneously see the characteristic impedance \$R_C\$ of the transmission line. So the current that voltage source needs to drive will be \$\frac{V_{in}}{2R_C}\$ (\$2R_C\$ for the matched series resistor + the characteristic impedance of the transmission line) and the voltage at the input of the transmission line will be \$\frac{V_{in}}{2}\$.

The waveform of the step function will propagate through the transmission line, not really "seeing" what's in front of it. At a certain moment, the signal will encounter the T-section. At this point, the wave will "see" a characteristic impedance for two transmission lines in parallel (\$\frac{R_C}{2}\$).

This change in impedance will create a backward wave to "ask" more current to drive the lower parallel resistance. This causes a backward wave (pulling the voltage in the transmission line lower). After traveling all the way back to the voltage source, that source will suddenly have to drive the larger current (\$\frac{2V_{in}}{3R_C}\$). The voltage at the input of the transmission line will also suddenly have dropped (\$\frac{V_{in}}{3}\$).

As the source is matched, no new forward wave is created. The backward wave didn't see a change in impedance after all.