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HOW REFLECTIONS TAKE PLACE IN TRANSMISSION LINES


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For a complete and utterly mind boggling explanation of this, see "Electromagnetics" by John D. Kraus.

In the meantime though, here's a simplistic "Transmission Lines for Dummies" view of what's happening, and I guess a few radio engineers out there will be shaking their heads in dismay after reading it. But it's as simple as I can make it.

A travelling electromagnetic wave is characterised by a changing electric field and a changing magnetic field perpendicular to each other. They maintain each other, in that the changing electric field causes the changing magnetic field and vice versa, and they propogate each other through space in a direction perpendicular to both fields. Since the magnitude of both fields is oscillating sinusoidally as they move through some medium, they can each be visualised as a waveform shape (180 degrees out of phase with each other).

Using a transmission line such as two parallel conductors, one can guide that wave along and through the medium that separates them, with the electric field producing a potential difference between the two conductors, and the changing magnetic field inducing a current through the two conductors .

The ratio of the voltage V across the conductors at some point along the line and the current I through the conductors at that point is called the 'characteristic impedance' of the line, Z; Z = V / I, just like Ohm's law except that impedance is a complex value, and not necessarily purely resistive. Consider that the voltage is proportional to the E.M. wave's electric field, but the current is proportional to the rate of change of the E.M. wave's magnetic field, and so the two are out of phase, and the impedance can thus be complex. The characteristic impedance of the line is dependent upon the permittivity and permeability of the medium separating the conductors, among other things, and determines the phase and magnitude of the currents and voltages present at a point along the line as the wave passes.

When a wave travelling along the transmission line arrives at some load terminating the line, simplistically one can imagine that the changing voltage across the load will now cause a change in the current through the load; a current whose phase and magnitude are determined by the load's own impedance.

Still simplistically, this load's current must flow through the conductors to which it is connected (where else can it go? It's the end of the line), and thus will combine additively to the current already there. Maybe you prefer instead to think of the wave's current flowing through the load, causing the load to drop a voltage, and that voltage combines additively to the value already existing on the line. Same thing, different point of view.

If the load's current/voltage does not match the wave's current/voltage then it is clear that the load will impose conditions upon the line which contradict what is already happening there due to the wave. The two conditions interfere additively (in the wave sense), resulting in a new wave propogating back along the transmission line as a reflection.

However, when the voltage/current of the load and wave match perfectly, there is no perturbation of existing line conditions, and no reflected wave is generated. In other words, no energy is returning back along the line. Under these circumstances, the entire energy of the original wave is completely dissipated in the load.

For this system to exhibit such behaviour, the load must exhibit the same voltage/current relationship as the line itself. In other words, the impedance of the load must be identical to the characteristic impedance of the transmission line. In the case of 50 Ohm coaxial cable, the characteristic impedance happens to be real, and thus a purely resistive 50 Ohm load is sufficient to prevent reflections.

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