On Jun 23, 4:41*pm, dave wrote:
but what is your second source? *you can always represent the second
source in that case in terms of the transmitter output so the second
input can be eliminated giving you a single port model.

a1 is the normalized forward voltage on the 50 ohm feedline from the
source. a2 is the normalized reflected voltage on the 291.4 ohm
feedline from the load. Those are the two sources associated with the
impedance discontinuity inside the black box. a2 could just as easily
be from a second generator instead of a reflection.

When the single-port model is used, if the impedance is not an
impedor, i.e. if the impedance is virtual, the reflection coefficients
are virtual reflection coefficients that do not reflect anything and
do not absorb power. I will repeat an earlier assertion:

Since a virtual impedance is result of the superposition of a forward
wave and a reflected wave, a virtual impedance cannot re-reflect the
reflected wave, i.e. one cannot re-reflect the reflected wave while at
the same time the reflected wave is being used to generate an
impedance. It has to be one or the other. Otherwise, there is a
violation of the conservation of energy principle. RF EM ExH energy
cannot be used simultaneously to generate a virtual impedance while at
the same time being re-reflected.

If the reflected wave is re-reflected, it must be by an impedance
other than the virtual impedance generated by the reflected wave
itself. If the reflected wave is being used to generate a virtual
impedance, it cannot at the same time be being re-reflected.

On Jun 24, 6:27 am, dave wrote:
p.s. if the separation between the two ports is just the discontinuity
connection 'point' then the voltages must be the same and the currents
are exact opposites only because of the direction convention defined,
there can be no difference measuring on one side of a point to the
other.

The total voltage and total current on both sides of the impedance
discontinuity must be equal. But the superposition components do not
have to be equal and, in fact, cannot be equal. In the case of the Z0-
matched example, the forward voltage on the 50 ohm side is 70.7 volts
while the forward voltage on the 291.4 ohm side is 241.4 volts. In
order for the total voltage to be the same, the reflected voltage on
the 291.4 ohm side, which is 170.7 volts, must be subtracted from the
241.4 volts of forward voltage to yield a total of 70.7 volts. For the
Z0-matched example:

Vfwd1 = Vfwd2 - Vref2

70.7v = 241.4v - 170.7v

Please note that the Z0-match point is at a voltage minimum on the
291.4 ohm feedline. 1/4WL toward the load, the total voltage is
241.4+170.7=412.1 volts (in a lossless system).
--
73, Cecil, w5dxp.com