Re-Normalizing the Smith Chart (Changing the SWR intothesame...
 

Keith wrote:
"Why the resistance to explaining this case?"

Because it should be obvious to anyone who knows enough to ask the
question.

Nevertheless, I assume the questioner is sincere so here is a simple
answer. It`s in Terman if you want more details.

Zo = sq rt Z/Y

Z = R + j omega L = line series impedance per unit length, ohms.

Y = G + j omega C = line shunt admittance per unit length, ohms.

For r-f in good lines, this reduces to:

Zo = sq rt L/C

For d-c, this reduces to:

Zo = sq rt R/G

Obviously line immpedance at d-c is likely quite different from line
impedance at r-f.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:

Keith wrote:
"Why the resistance to explaining this case?"

Because it should be obvious to anyone who knows enough to ask the
question.

Nevertheless, I assume the questioner is sincere so here is a simple
answer. It`s in Terman if you want more details.

The question was, indeed, sincere.

Zo = sq rt Z/Y

Z = R + j omega L = line series impedance per unit length, ohms.

Y = G + j omega C = line shunt admittance per unit length, ohms.

For r-f in good lines, this reduces to:

Zo = sq rt L/C

For d-c, this reduces to:

Zo = sq rt R/G

But we were discussing ideal lines, for which, if I recall correctly,
R and G are both 0.

This leaves us with Z0 = jwL/jwC (w being my font challenged excuse
for Omega)
which should, in the limit as w approaches 0, leave us with the same
answer as for RF. Or have I forgotten how to do math (which is quite
possible).

In any case, a slight modification to the experiment can get around
this difficulty. We'll just perform the experiment at a frequency
sufficiently low as to be indistinguishable from 0 given the duration
of the experiment.

Obviously line immpedance at d-c is likely quite different from line
impedance at r-f.

This would certainly be true for real world lines where the luxury of
R=G=0 does not exist.

....Keith

wrote:
But we were discussing ideal lines, for which, if I recall correctly,
R and G are both 0.

Heck, let's discuss ideal Gods whose whims control everything in an
ideal way.

This would certainly be true for real world lines where the luxury of
R=G=0 does not exist.

The luxury of R=G=0 does not exist anywhere in the known
universe. Your math model is predicated upon things that don't
(can't?) exist. Does that give you some sort of hint?

Seems to me this is just one more case of seduction by the
idealized steady-state model. "I think it, therefore it exists".
--
73, Cecil http://www.qsl.net/w5dxp



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Actually, you've made the argument backwards.

If you explanations work only the complexities of the real world
but collapse in the simplicities of the ideal world, then you
should cast grave suspicions on your explanations.

....Keith

W5DXP wrote:

wrote:
But we were discussing ideal lines, for which, if I recall correctly,
R and G are both 0.

Heck, let's discuss ideal Gods whose whims control everything in an
ideal way.

This would certainly be true for real world lines where the luxury of
R=G=0 does not exist.

The luxury of R=G=0 does not exist anywhere in the known
universe. Your math model is predicated upon things that don't
(can't?) exist. Does that give you some sort of hint?

Seems to me this is just one more case of seduction by the
idealized steady-state model. "I think it, therefore it exists".
--
73, Cecil http://www.qsl.net/w5dxp

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wrote:
If you explanations work only the complexities of the real world
but collapse in the simplicities of the ideal world, then you
should cast grave suspicions on your explanations.

That's exactly what my Baptist Preacher tells me every Sunday.
You and my preacher both must assume a supernatural realm for your
ideas to work. So first you (and my preacher) must prove that a
supernatural realm exists. I've been waiting for proof for 65
years. Please feel free to proceed.
--
73, Cecil http://www.qsl.net/w5dxp



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Jim Kelley wrote:
"It may not be a terribly useful thing to know, but it isn`t a
ficticious quantity."

Agreed. Instantaneous power is real. My point is: Work is power x time.
If time is zero, no work is done.

Best regards, Richard Harrison, KB5WZI

Jim Kelley wrote:
"It may not be a terribly useful thing to know, but it isn`t a
ficticious quantity."

Agreed. Instantaneous power is real. My point is: Work is power x time.
If time is zero, no work is done.

Best regards, Richard Harrison, KB5WZI


Is the rate of doing work zero at all instances of time? Nope.
Power is the time rate of change for doing work. It's supposed to be
important to know the formula for finding the instantaneous
rate of doing work so you can ultimately find the average
rate. Maybe you think this is unimportant. I wonder why
textbook authors think it is?
73,
Tom Donaly, KA6RUH

Tdonaly wrote:
Is the rate of doing work zero at all instances of time? Nope.
Power is the time rate of change for doing work. It's supposed to be
important to know the formula for finding the instantaneous
rate of doing work so you can ultimately find the average
rate. Maybe you think this is unimportant. I wonder why
textbook authors think it is?

Point is, one cannot have a time rate of change without a changing
time. Zero time is not changing. An electron cannot even wiggle in
zero time.
--
73, Cecil http://www.qsl.net/w5dxp



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