dansawyeror wrote:
The program zl_zin calculates a Zload from a known Zin. It would seem
that given a symmetrical feedline that Zin and Zload should be mirrors.
Why is that not so?

I'm not sure what you mean by "mirrors". But the relationship between
Zin and Zload is dictated by the way transmission lines transform
impedances. A better question is, why should it be anything else?

A series inductor is symmetrical, is it not? Suppose you have a series
inductor with impedance +j10 ohms in a box. Connect it to a load of 50 +
j0 ohms. Looking into the input of the series inductor, you see 50 + j10
ohms. Now put a load of 50 + j10 ohms at the output instead of 50 + j0.
Are you saying you expect to see 50 + j0 at the input? Why?

Is there a program that will calculate Zin from a known Zload?

Hopefully someone else will be able to answer that.

Roy Lewallen, W7EL

Roy,

Well the intuition was correct, however the problem is one level more complex.
The Smith chart shows the following approximate 'mirror' relationships for j=0:

Load Input Measurement
20 125
25 100
35 71
10 250
50 50

It is a "log" mirror centered on 50 Ohms. The mirror relationship holds for j /=
0, however the calculation is more complex. - Dan

Roy Lewallen wrote:
dansawyeror wrote:

The program zl_zin calculates a Zload from a known Zin. It would seem
that given a symmetrical feedline that Zin and Zload should be
mirrors. Why is that not so?


I'm not sure what you mean by "mirrors". But the relationship between
Zin and Zload is dictated by the way transmission lines transform
impedances. A better question is, why should it be anything else?

A series inductor is symmetrical, is it not? Suppose you have a series
inductor with impedance +j10 ohms in a box. Connect it to a load of 50 +
j0 ohms. Looking into the input of the series inductor, you see 50 + j10
ohms. Now put a load of 50 + j10 ohms at the output instead of 50 + j0.
Are you saying you expect to see 50 + j0 at the input? Why?

Is there a program that will calculate Zin from a known Zload?


Hopefully someone else will be able to answer that.

Roy Lewallen, W7EL

dansawyeror wrote:
Roy,

Well the intuition was correct, however the problem is one level more
complex. The Smith chart shows the following approximate 'mirror'
relationships for j=0:

Load Input Measurement
20 125
25 100
35 71
10 250
50 50

It is a "log" mirror centered on 50 Ohms. The mirror relationship holds
for j /= 0, however the calculation is more complex. - Dan

Well, yes, you can find specific relationships for various special cases
of load impedance and line length, particularly if you assume zero loss.
But only the appropriate equations, derived from basic principles, will
give you the correct relationship in the general case. Be wary of
oversimplification.

Roy Lewallen, W7EL

On Fri, 23 Dec 2005 16:10:01 -0800, Roy Lewallen
wrote:

dansawyeror wrote:
The program zl_zin calculates a Zload from a known Zin. It would seem
that given a symmetrical feedline that Zin and Zload should be mirrors.
Why is that not so?

I'm not sure what you mean by "mirrors". But the relationship between
Zin and Zload is dictated by the way transmission lines transform
impedances. A better question is, why should it be anything else?

Roy, I also wasn't quite sure of the concept of *symmetry* and
*mirror* as used by Dan.

I made the assumption (perhaps incorrectly) that the transformation is
symmetrical for an integral number of half waves of lossless
transmission line. Impedances might be seen to "mirror" (if mirror
means an exact copy) for an integral number of half waves of lossless
line.

Having made that assumption, loss introduces errors to the
"mirroring", and line lengths other than an integral number of quarter
waves aren't symmetrical in that sense.

Having read Dan's further comments, it seems he thought any length of
real line was symmetric as an impedance transformer. It might be that
you can swap A and B ends in a circuit and obtain the same behaviour,
but you can't swap Zload and Zin in the general case.

Dan, the terms you have used don't have common usage in this context,
and confuse the issue.

Owen
--

On Sat, 24 Dec 2005 01:35:01 GMT, Owen Duffy wrote:


I made the assumption (perhaps incorrectly) that the transformation is
symmetrical for an integral number of half waves of lossless
transmission line. Impedances might be seen to "mirror" (if mirror
means an exact copy) for an integral number of half waves of lossless
line.


That should have read:

I made the assumption (perhaps incorrectly) that the transformation is
symmetrical for an integral number of *quarter* waves of lossless
transmission line. Impedances might be seen to "mirror" (if mirror
means an exact copy) for an integral number of half waves of lossless
line.

Owen
--