[Antennas] Complex Transmission Line Impedance

[Barry L. Ornitz]

I agree fully with George's comments:

> Jim, you seem to prefer keeping this discussion on the ]
> reflector when your objections properly belong in a private 
> forum. However, that is your choice. . .
>
> Let me be as brief as I can.

> You have chosen to view a very complex subject through the 
> convenient knothole of "typical amateur radio HF" practices. 
> Consequently, you have reached conclusions which while they 
> work well enough in that area, are NOT generally true, and 
> neither Wes nor I are in error for pointing this out to
> you.

Earlier George had written:

>> 2. depending upon the frequency range involved, the 
>> reactive component Xo of Zo may or may not be of 
>> importance.

And Jim replied:

> *****DEFINITELY********  Especially when the frequency range 
> is within the normal range for the particular transmission 
> lines application (where line losses are tolerable)

This clearly shows he still does not understand and is trying 
to pick bits and pieces of information out of context from 
accepted texts.

Actually transmission lines show the most complex 
characteristic impedance effects at low frequencies - where 
their losses are the lowest.  At such frequencies, the 
dielectrics are nearly perfect (polyethylene and 
polytetrafluoroethylene have negligible losses at such 
frequencies).  Likewise below the frequency where the inner 
conductor diameter is the same as the skin depth, the series 
resistance is the least.

I discovered the reality of a complex characteristic impedance 
several years ago in a particular instrumentation problem I 
was working on.  I was trying to measure extreme high 
frequency mechanical vibration on a piece of equipment located 
in a hazardous area (explosive vapors).  I was using a 100 ohm 
half-bridge strain gage to measure the mechanical deflection 
of the equipment.  Thus my output signal (millivolts) came 
from an essentially 50 ohm resistive source.

In the lab, I was easily able to measure signals on a FFT 
spectrum analyzer up to several hundred kilohertz with a mock-
up of the mechanical system.  Because of the explosive 
environment, my strain gage was connected by several hundred 
feet of 50 ohm, double shielded coaxial cable to the analyzer 
in a safe location.  Power to the bridge came from an 
intrinsically safe supply.  Double shielding was used to 
minimize noise pickup on the low level signals.  In 
retrospect, shielded twisted pair with a full bridge gage 
might have been a better choice.

Cable losses at these frequencies should have been a small 
fraction of a decibel, yet I saw great differences in the 
spectrum between the lab hookup and the process hookup.

It turned out that I had not considered the fact that the 
cable no longer had a resistive 50 ohm characteristic 
impedance.  Even though the cable length of a few hundred feet 
was a small fraction of a wavelength, it was enough to cause 
considerable dispersion in the waveforms and very significant 
apparent attenuation versus frequency effects.

Once I realized what was happening, I calculated the real 
cable characteristic impedance as a function of frequency and 
used this to mathematically "deconvolve" the data to get the 
correct spectra.  It matched the lab data perfectly after 
this.

This example shows the importance of a complex characteristic 
impedance.  In fact, any shielded wire at low frequencies 
shows considerable capacitive effects.  Knowing when and where
to use the resistive approximation to characteristic impedance
is important and well worth discussing here.

        73,  Barry L. Ornitz     WA4VZQ     ornitz@tricon.net