Another Theory of Everything

Basic Energy Transfer

We'll try the same set of experiments with the impedance change near the center of the transmission line. This way you can see the through-transmitted waveform continue on the right side of the demonstration.

Experiment #1: A burst of six waves are sent down a one dimensional model. With Z_r (the termination impedance) matching Z_mean the standard impedance the signal appears to continue off the right side of the demonstration.

Experiment #2: Change Z_r to 33 and press Start. Half of the energy will be reflected back to the left. Notice that the phase of the reflected wave is inverted from the source wave. Change Z_r to 200 and restart the demonstration. Again half of the energy is reflected back to the left, but this time the reflected energy is in phase with the source wave.

Experiment #3: Change Z_r to 0 (it will actually register 1^-6, impedance must always be greater than 0) and click Start. Almost all of energy will be reflected back to the left and it will be out of phase. Change Z_r to 999999 and restart the demonstration. Again almost all of the energy will be reflected and it will be in phase.

Conclusion: The transfer of energy is dependent on the ratio of the source and load impedance. Maximum energy transfer occurs when the source and load impedance are equal. A proportionate amount of energy is reflected back to the source if they are not equal.

In electronics this is called the standing wave ratio and the behavior is well understood. First compute the normalized load impedance, Z_n:

Z_n = Z_r / Z_mean

Then compute the reflection coefficient, r:

r = (Z_n - 1) / (Z_n + 1)

Finally compute the VSWR:

VSWR = (1 + abs(r)) / (1 - abs(r))

For experiment #2 with a Z_r of 33

Z_n = 33 / 100 = .33

r = (.33 - 1) / (.33 + 1) = -.66 / 1.33 = -.5

VSWR = (1 + .5) / (1 - .5) = 1.5 / .5 = 3.0

That this simulation obeys the well established rules of electronics helps to validate this approach.