Cecil Moore wrote:
Ian White GM3SEK wrote:
Roy has posed a test problem that is very easy to understand, and can
be solved unambiguously by simple arithmetic. Solving it using
S-parameters will take time and some depth of understanding, but we
can be confident that they WILL give exactly the same result in the end.
It's not Roy's results that are flawed. It's his premises. If
one has a 100v source with a 50 ohm series impedance feeding
a 200 ohm resistor, Roy's results are perfect. But when we add
that 1/2WL of 200 ohm line, it changes things from a circuit
analysis to a distributed network analysis. Much more energy
is stored in the system, using the transmission line, than has
reached the load during steady-state. Roy tries to completely
ignore the stored energy and alleges that there is no energy in
the reflected waves. But there is *exactly* the same amount of
energy stored in the feedline as is required for the forward
waves and reflected waves to posssess the energy predicted by
the classical wave reflection model or an S-parameter analysis
or an analysis by Walter Maxwell of "Reflections" fame.
. . .
Ah, the drift and misattribution has begun. I'll butt in just long
enough to steer it back.
I made no premises, and have not made any statement about energy in
reflected waves. I only reported currents and powers which I believe are
correct. Nothing you or anyone has said has indicated otherwise. I do
question the notion of bouncing waves of average power, and have
specifically shown that H's statement about the source resistor
absorbing all the reflected power, when its value is equal to the line
impedance, is clearly false. (The "reflected power" is 18 watts; the
resistor dissipates 8.) I haven't seen any coherent explanation of the
observable currents and power dissipations that's consistent with the
notion of bouncing current waves. Perhaps your dodging and hand-waving
has convinced someone (the QEX editor?), but certainly not me.
It's not a 200 ohm line, it's a 50 ohm line. (I see that I neglected to
state this when giving my example, and I apologize. But it can be
inferred from the load resistance and SWR I stated.)
It baffles me how you think you can calculate the line's stored energy
without knowing its time delay. The calculation of stored energy is
simple enough, but it requires knowledge of the line's time delay. A
half wavelength line at 3.5 MHz will store twice as much energy as a
half wavelength line at 7 MHz, all else being equal. Even if you knew
the frequency (which I didn't specify), you'd also need to know the
velocity factor to determine the time delay and therefore the stored
energy. I'm afraid your methods of calculating stored energy are in error.
But if you think the stored energy is important and you find (by
whatever calculation method you're using) that it's precisely the right
value to support your interesting theory, modify the example by doubling
the line length to one wavelength. The forward and reverse powers stay
the same, power dissipation in source and load resistors stay the same,
impedances stay the same -- there's no change at all to my analysis or
any of the values I gave. But the energy stored in the line doubles.
(Egad, I hope your stored energy calculation method isn't so bizarre
that it allows doubling the line length without doubling the stored
energy. But I guess I wouldn't be surprised.) So if the stored energy
was precisely the right amount before, now it's too much by a factor of
two. And if you find you like that amount of stored energy, double the
line length again.
I can see why you avoid the professional publications.
Roy Lewallen, W7EL
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