Richard Clark wrote:
As for the math, you will find it by
the reams, once you've been overwhelmed with the arcana of hyperbolic
descriptions of a novel physics that have to proceed its proof.

A scattering parameter analysis, described in HP Application Note
95-1 (available on the web) is ideal for analyzing what happens
at a match point in a typical ham radio antenna system.

b1 = s11(a1) + s12(a2)

b2 = s21(a1) + s22(a2)

b1 is the net forward voltage, b2 is the net reflected voltage
a1 is the incident forward voltage, a2 is the incident reflected voltage

Quoting from HP AN 95-1: Another advantage of s-parameters springs
from the simple relationship between the variables a1, a2, b1, and
b2, and various power waves:

|a1|^2 = Power incident on the input of the network.
(forward power incident on the match point)

|a2|^2 = Power reflected from the load.

|b1|^2 = Power reflected from the input port of the network.
(power reflected from the match point back toward the source)

|b2|^2 = Power incident on the load.

The previous four equations show that s-parameters are simply
related to power gain and mismatch loss, quantities which are
often of more interest than the corresponding voltage functions.

|s11|^2 = Power reflected from the network input divided by
power incident on the network input

|s22|^2 = Power reflected from the network output divided by
power incident on the network output

|s21|^2 = Power delivered to a Z0 load divided by power available
from a Z0 source

|s12|^2 = Reverse transducer power gain with Z0 load and source

End quote.

b2 is the voltage reflected back toward the source and

b2 = s21(a1) + s22(a2)

It should be obvious that b2 cannot be zero unless there exists
total destructive interference between s21(a1) and s22(a2), i.e.
s21(a1) is equal in magnitude and opposite in phase to s22(a2).
--
73, Cecil http://www.qsl.net/w5dxp



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