Interacting TEM waves.
Generally the interaction of two TEM waves is thought to be covered by Maxwell's Equations. However, I have shown (Ref.9) that this is not so. Maxwell's Equations contain only;
(1) the velocity of propagation of the TEM wave and
(2) the impedance of the medium .
They contain no additional information about electromagnetism in general, let alone information on the way two colliding TEM waves interact. Even more curiously, the empirical laws governing reflection at a resistively terminated transmission line seem to be a body of knowledge divorced from Maxwell's Equations.
Partial reflection in a transmission line.
It is found experimentally that if a TEM wave travels down a uniform transmission line (Fig.11) joined to a different transmission line , some of the energy current reflects at the discontinuity and some continues (Ref.10). The voltage reflection coefficient is found to be
In particular, if a pulse V travelling down a transmission line at the speed of light collides into a termination made up of three resistors in series, then a pulse reflects and dissipates across the termination; ( in each resistor).
The front end of a long transmission line looks exactly like a resistor. The situation remains the same in Figure 12;
three downstream coaxial cables connected in series, mimicking the three resistors, and also (Fig.13) a parallel plate transmission line delivering the pulse into three such lines in series.
Our next step is to widen the parallel plates to infinity, and this gives us our simplest situation for analysis (Fig.14). Having reached this stage, we can set out to gain the broader insights which our experimental knowledge of reflection in transmission lines gives us.
(Consideration of conservation of energy and also that the voltage across the discontinuity must be continuous lead us to the same formula for the reflection coefficient.)