Topband: electrical wavelength

[Tom W8JI]

> Likewise, Zo is only sqrt (L/C) at VHF.  The more complete equation is 
> sqrt [ (R+J omega L) /( G + J omega C) ]  At VHF, the equation SIMPLIFIES 
> to sqrt (L/C)  At low audio frequencies, and up to VHF, G is insignificant 
> (leakage) so the complete practical equation is sqrt  [(R+ j omega L) / j 
> omega C]  Note that this results in Zo being complex, and a proper 
> measurement will confirm that this is true. There are MANY references to 
> complex Zo in the ham literature. Frank Witt published some work about 
> this, now available in one of the ARRL Anthologies. N6BV's TLW software, 
> published in the ARRL Handbook, uses complex impedance data for its 
> transmission line calculations, although it ignores the variability of Vf.

I don't know why you are dragging complex impedance into velocity of 
propagation through the cable. It is late summer, and too warm for that.

Everyone knows and agrees, or should know and agree, Zo is complex. That 
isn't the issue, it certainly is not news, and you failed to provide any 
example at all why Vf varies.

All you said is Zo is complex, which anyone knows, and the Handbook "ignores 
Vf variability".

> At low audio frequencies, Zo is much, much larger than the VHF value, and 
> Vf is much, much slower than the VHF value. Both properties begin a rapid 
> transition to their VHF values and go though at least half of it within 
> the audio spectrum, approaching the VHF values asymptotically. By 2 MHz, 
> both are within a few percent of the VHF value.
>
> All of this was WELL KNOWN more than a century ago, and Oliver Heavyside 
> did a lot of work on applications to equalize lines. While it is often 
> assumed in modern times that equalization of telephone circuits was done 
> only for the amplitude response, equalization is equally important for the 
> TIME response.  To get your head around that, consider speech where the 
> "highs" arrive much sooner than the "lows."
>
> Here's a simple test you can do with any 50 ohm signal source you can read 
> to an accuracy of at least 0.1 percent and a decent voltmeter across the 
> source  Cut a quarter wave open stub for the lowest frequency you can 
> observe and measure the first resonance to as many digits as you can, then 
> repeat for the third, fifth, seventh, and ninth resonances.  If you can 
> hit the precise null and read enough digits, you can plot the variation in 
> Vf.  Or do the same with any vector analyzer, carefully reading the 
> frequencies of each null.


I already did that. Didn't change.

A hunk of F6 cable about 200 feet long shows about 0.3% variation from 5.199 
MHz to 25.977 MHz.
That same  hunk of cable shows 0.24% variation from 5.199 MHz to 52.119 MHz

A 100 ft piece of LMR400 type cable shows 0.07 % variation in Vf from 4.023 
MHz to 40.261 MHz, and 0.18% from 4.023 to 56.423 MHz.

Where can I find cable like you have, or a meter like you have?

I would expect a large variation at audio, where the skin depth of 
conductors is woefully inadequate, or where we are measuring things that are 
mismatched, or measuring things too short. Plus, we all know audio things 
like silk insulation and oxygen free conductors changing sound. :-)

Rather than telling me what I need to go read, which doesn't seem to apply 
unless we start getting into some severe dielectric or inductance change 
issues, please give me a reference that shows Vf changes so dramatically 
with frequency. I already know Zo is complex.

None of my books, nor the Internet, confirms what you say about a large 
variation. Neither does a real network analyzer.

Perhaps I have bad cables of two very different types, and all the dozens of 
cables a cable manufacturer sent me over the years were all bad in the same 
way.

73 Tom