Lets say I have a lossless coaxial cable with a characteristic impedance of 50 ohms. The length of the cable is very long compared to the the wavelength of the relevant signals on the coaxial cable. This is an obvious transmission line.
Now, lets say I attach an ordinary 50 ohm through-hole resistor to the end of the transmission line by attaching one lead of the resistor to the inner conductor of the coaxial line and the other lead of the resistor to the outer conductor. From what I have learned, this should result in no reflections in the transmission line when a source generates a signal at the other end of the coaxial cable because the transmission line is matched to the load.
In this situation, what is happening at the junction between the coaxial line and the leads of the resistor? Would the leads of the resistor (although very short) not make up a sort of transmission line with its own characteristic impedance? I know that characteristic impedance is not dependent on length of the transmission line, but if characteristic impedances do not match, there will be reflections. Why would there be no reflections?
Best Answer
The leads of the resistor will (mainly) introduce parasitic inductance. This will make the resistor not behave exactly like a resistor, but like an LR series combination.
Of course this means that when the inductive term becomes significant, the termination will no longer be matched to the characteristic impedance of the transmission line, and you will get reflections.
If you increase the frequency further (to try to make these leads look like transmission lines) you'll probably get into a regime where you must do a full electromagnetic analysis (to find how much they radiate, like little antennas) before they ever act like transmission lines.
There's no reflection when you terminate a transmission line with a matched load because the ratio of I to V in the load is equal to the ratio of I to V in the forward travelling wave on the transmission line. Therefore, there's no impedance mismatch at the connection of the line to the load.
Looked at more mathematically, you can say the solution to the boundary value problem for the transmission line with a matched load is to have no reflection.