On Apr 10, 4:13 am, "Keith Dysart" wrote:



Why don't you analyze my example:

(Since the Grand PoohBah Power Master seems unwilling, here, for your
consideration, I give you...)


Generator with
291.4 Ohm ------------ 291.4 Ohm line ---- 50 Ohm load
Source Impedance Pfor2=100w--
--Pref2=50w

What is the power emitted by the generator into the line?
-- Assuming lossless line, 50W of course; 50V@1A at the load.

Where does Pref2=50W go?
-- Into satisfying the boundary conditions at the generator
to line interface. We have way to little info to
determine if the generator dissipates more, or less, or
the same, as if it were terminated in 291.4 ohms.

Are there ghosts?
-- Some people believe in them. I've never seen on--Oh not
THAT kind of ghost. Well, not at the load, but certainly
at the generator, if the generator is putting out a signal
that's an interesting enough function of time. TDRs really
do work.

What is the magnitude?
-- Of what? We have enough info to resolve Vf, If, Vr and Ir
on the line, and if we knew the line length and
the excitation, we could be a lot more definitive about
things, but since steady-state excitation doesn't
produce ghosts... but the reflection coefficient at the
line-load interface is -1/sqrt(2), so that's the voltage
ratio we'll see between the forward and reverse waves.

What power would the generator emit if the line was terminated
with 291.4 Ohms?
-- "100 watts, of course." For those who don't immediately see
that, it's not difficult to go through some math to show that
the power delivered to a load is independent of the load
impedance so long as magnitude((Zload-Rgen)/(Zload+Rgen)) is
constant--that is, so long as the magnitude of the reflection
coefficient is constant--as it is along a lossless line...
and from that, find the Thevenin or Norton equivalent of the
source in this example ... and from that, figure the power
that source will deliver to a matched load.

Please do not modify the example for analysis since this may change
the results.

There is much to be learned by trying examples that may challenge
your expectations.

:-) This reminds me of some thoughts I posted a long time ago about
lines whose Zo is somewhat reactive. For example, if a linear
sinusoidal source of impedance Zo is connected to a line also of
impedance Zo, what load maximizes the power in the load? If you keep
magnitude((Zload-Zo)/(Zload+Zo)) constant, is the power dissipated in
the load independent of the phase angle of (Zload-Zo)/(Zload+Zo)?

...Keith

Cheers,
Tom