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.

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.

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.

Cecil did not answer the question, so I will
pose it again. If knowing the phase shift at
the terminals of the black box is important,
and you can not know it without knowing the
internals of the box, given a black box of
unknown internals but told that its terminals
present -j567 at the frequency of interest,
would you refuse to calculate the length
of 600 ohm line needed to produce 0 ohms?

I suggest that there is no need to refuse
since the only information that is required
is -j567. Whether the box achieves this with
600 ohm line ("no phase shift"), 100 ohm
line ("some phase shift"), a capacitor or
some other technique is irrelevant.

....Keith