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Roy Lewallen · December 20th 07, 11:20 PM posted to rec.radio.amateur.antenna

wrote:

But Ian,

I don't propose to upstage or speak for Ian, but I'll add my comments in
advance to his response.

Suppose the box is labeled -j567 ohms.

Then I ask, "at what frequency is this impedance -j567?".

I find that the impedance for -j567 ohms is 4 Mhz.

And in this case we have four black boxes which all measure -j567 ohms
at that same frequency.

Now I take a length of 600 ohm VF = 1 transmission line and vary the
length until I am at resonance with whatever is in the black box at 4
MHz. Resonance would imply 90 degrees total phase shift.

My measurement shows that the length of 600 ohm line to cause this
effect is 43 degrees.

Assuming my measurement is correct, doesn't that tell us a little more
about what is inside the box? It isn't just "any" -j567 ohm impedance
that can cause resonance with a 43 degree 600 ohm line. It is probably
not a discreet capacitor, it would likely be some sort of transmission
line or something that that has 10 deg length, correct?

No, that's not correct. As I've said several times before, you can't
tell anything about the contents of the boxes by doing measurements at a
single frequency, except to determine the terminal impedance at that
frequency. No matter what kind of test you do (at that one frequency at
which the impedances are the same), you cannot distinguish among them.
You can't tell which box is which, or detect anything about them which
is different. If you have a theory which predicts otherwise, you should
investigate where the flaw in the theory is. If you're not convinced,
simply describe in detail the tests you would do and the numerical
results you expect to get for the different boxes. Anyone with a
background in transmission line theory (which include several regular
group participants) will be able to tell you what results you should
expect from your tests, which will be the same for all the boxes. And
several of us are also able to make decent measurements as well as
provide equations to show why. That's how engineering is done.

With a few more measurements, we can determine the Zo of the
transmission line that "appears' to be in the black box, correct and
essentially verify that it a transmission line.

Not if you measure only at the one frequency. Not only can you not tell
the Z0, you can't even tell if it's a transmission line at all. It might
be a capacitor, a complex LC network, or some combination of
transmission lines, capacitors, and inductors.

We should be able to
both measure and calculate Zo.

If we choose our independent measurements carefully enough, we should
be able to define exactly what is in the black box with only 2
terminals.

It's a bit frustrating to continue posting the same thing over and over
and see continued claims that the boxes can be distinguished. We'd both
save a lot of bandwidth if you would, instead of just claiming that you
can do it, show that you can. Even theoretically -- describe the tests
you would make and the results you would expect which would be different
for each box. Then we'd have something which could be discussed objectively.

I agree you need more than a smith chart (which was where I made my
mistake before).

Yes, I'm afraid you'll need a lot more.

Let me reiterate that the contents of the boxes can certainly be
distinguished with tests made at multiple frequencies. But the objective
of my comments has been to counter the claim that there's some terminal
property such as "electrical degrees" which the various lines (box
contents) have which is different at the single frequency at which their
reactances are the same. I hear this claim still being made, but so far
not any evidence to support it. When such evidence (not including
typical Cecil-style hand-waving, but real numbers) is presented, I'll be
glad to point out where it's in error.

Roy Lewallen, W7EL