On Dec 14, 11:53 pm, "AI4QJ" wrote:
"Keith Dysart" wrote in message

...





On Dec 14, 10:00 pm, "AI4QJ" wrote:
"Keith Dysart" wrote in message

...

On Dec 14, 9:10 pm, "AI4QJ" wrote:
Where did the extra black box come from and who made the restriction
on
frequency? I should be able to use any voltage or frequency I want,
don't
you think?

The original problem statement discused -j567 as
an impedance. This is implicitly frequency dependant.

Not if I change the capacitance.

Each of the different ways mentioned for obtaining -j567
will produce a different impedance if the frequency is
changed. They were all frequency dependant.

The Smith chart is normalized for impedance
and frequency.

The smith chart is normalized *only* by Zo.

Tell me, how is Zo related to frequency :-)

Or better, tell me how the smith
chart is normalized by frequency?

Everything is done in terms of degrees along a wave.
This implicitly normalizes for frequency.

There is a specific recognized usage of the term "normalize" when referring
to a smith chart. It does not involve frequency.

Agreed. But I needed a word to capture the similar concept
for frequency so I chose "normalize". Feel free to propose
another, and possibly less confusing, word.

When allowed to excite the black boxes with different
signals there are many ways to determine an internal
equivalent circuit. The question here was did the various
ways of making -j567 affect the results for sinusoidal
single frequency excitation.

In the example, -j567 was merely due to a phase change due to the abrupt
impedance discontinuity. You are the one who suggested putting things in
black boxes. I suppose you could devise ways to phase shifts due to -j567
in
black boxes but I will have to leave that to you since you are the one
who
brought up the idea.

Several ways were mentioned for obtaining the -j567:
a capacitor, some length of 100 ohm line, a different
length of 600 ohm line. Regardless of how the -j567
impedance is obtained, the same input impedance
to the 600 ohm line results. And yet each appears
to have a different phase shift occurring at the terminals.

Putting things in black boxes is a thought experiment
which helps isolate which aspects are important.
Any box containing a circuit which produces -j567
at the terminals will result in exactly the same
impedance at the input to the 600 ohm line, so
clearly -j567 is important.

Is the "phase shift" at the discontinuity important
when the results can be determined without knowing
the value. In fact, the "phase shift", in all the
examples, was computed last, after all the results
were known. How important can it be?

Do you suggest that there is no phase shift?

I suggest that there is no value in thinking about
the "phase shift" at the discontinuity (which depending
on the black box chosen might not be present), and
merely think about the results of connecting the
-j567 impedance to the 600 ohm line.

The value is more obvious when applying the concept to a loaded whip
antenna.

I am not convinced. The value is still being determined
by accounting for all the other phase shifts and then
subtracting from 90. I would be more convinced of the
utility if the value could be computed from first principles
and then used, for example, to compute the length of
the whip.

Then how do you explain the smith chart results?

Starting with the 100 ohm line, the normalized
input impedance was computed using the Smith
chart. This impedance was denormalized and then
renormalized to the 600 ohm. The new value was
plotted on a new Smith chart (the chart normalized
to 600 ohms) and the length of the 600 ohm line
was determined. The two lines have lengths, call
them Z1len and Z2len. 90 - (Z1len + Z2len) will
give a number which Cecil/you have called the
"phase shift" at the discontinuity. Alternatively,
it is just what happens when -j567 is attached
to the appropriate length of 600 ohm line.

But you have 10 degrees of 100 ohm line and you have 43 degrees of 600 ohm
line.

You also have resonance at 1/4W.

For 1/4W resonance you must have 90 degrees.

What happened to the missing 37 degrees?

Perhaps, like the missing dollar, it is simply a number
with no meaning.

If some do not care, then I agree that it is not important. It comes out of
a black box for all they care.

Others find it fascinating what nature does in order to keep following its
rules. I would never go through all the trouble to calculate this using math
but with the smith chart calculating for you, information like this jumps
out at you. When it does, many people yawn, others relate it to how antennas
with loading coils work and reveals one reason why Dr. Corum had to make
corrections for the true behavior of coils

Well I am not sure about the "true" nature of coils. When I look
at one of those coils, I think it is one big complicated mess of
distributed capacitance and inductance. There is intra and inter
turn capacitance and capacitance to ground. A mess.

Some say such a coil can be adequately modelled using a lumped
inductor. Corum thinks he can do better, but I doubt that even he
would claim that he has the "true" nature of such coils.

As an aside, allowing the possibility of this "phase shift" at
the joint, how would you compute the phase shift when a
parallel stub is used, or when multiple parallel stubs are
used to obtain the desired result? And which stub will be
used to define the 90 degrees from which the others are
subtracted?

....Keith