Walter Maxwell wrote:
Cecil, how about doing me a favor and humor me a little.

How about solving my example, the one that Steve took from Reflections and then
trashed. To repeat, 100 w, 70.71 v source, 50-ohm lossline terminated in a 3:1
mismatch and perfectly matched at the input with a rho = 1.0.

Here's the configuration.

100W XMTR--50 ohm line--x-tuner-y--1wl 50 ohm line---150 ohm load

The tuner function is replaced by a 1/4WL series section which
performs *exactly* the same function so we can see what is really
happening inside the tuner. The match point is at 'x', not at 'y'.
The system is NOT matched at 'y'. Therefore, Dr. Best's system is
not matched at the output of the tuner. His choice to use a tuner
for that illustration, instead of a 1/4WL transformer, was a very
bad one and has obviously led to a lot of confusion and misunderstanding.

rho=0.268 rho=-0.268 rho=0.5
100W XMTR---50 ohm line---x---1/4WL 86.6 ohm line--y--1wl 50 ohm line---150 ohm load
VF1=70.7V-- VF2=96.58V-- VF3=81.65V--
--VR1=0V --VR2=25.9V --VR3=40.82V
PF1=100W-- PF2=107.76W-- PF3=133.33W--
--PR1=0W --PR2=7.76W --PR3=33.33W

The mismatched impedance discontinuity at 'y' is interesting because
we have forward power and reflected power flowing to/from both directions.
That's what happens at a tuner output. The actual match point is at the
tuner input at 'x'.

At point 'y' on the 50 ohm line we have a V1y of 70.7V corresponding to
the 100W forward power that made it through the impedance discontinuity.
This can also be calculated by using the transmission coefficient. Since
the impedance is a step-down impedance, tau = 1-rho

V1y = VF2(1-rho) = 96.58(0.732) = 70.7V

V2y will be VR3(rho) = 40.82(0.268) = 10.94V

VF3 = 70.7V + 10.94V = 81.65V. (133.33W)

The modified S-parameter analysis works once again and this time it
is at an unmatched impedance discontinuity at point 'y'.

We could also do the modified S-parameter analysis at point 'x'.

V1x = VF1(1+rho) = 70.7V(1.268) = 89.6V

V2x = VR2(rho) = 25.9V(0.268) = 6.94V

VF2 = V1 + V2 = 89.64V + 6.94V = 96.58V (107.7W)
--
73, Cecil http://www.qsl.net/w5dxp



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