Run the numbers and for RG-6 we see that sq root of L/C is good above a
couple hundred kHz.
Dave WX7G
On Sep 10, 2012 2:37 PM, "Jim Brown" <jim@audiosystemsgroup.com> wrote:
> On 9/10/2012 10:44 AM, Tom W8JI wrote:
>
>> I firmly do not believe that is true.
>>
>> Velocity factor in cable is the square root of the inverse of dielectric
>> constant.
>>
>
> Tom,
>
> Respectfully, I suggest that you go back to your college textbook on the
> fundamentals of Transmission Lines. The equations for Zo, velociity of
> propagation, and attenuation are COMPLEX -- that is, they contain real and
> imaginary components. The "formula" you cite is the result of
> simplification to remove those complex elements. It's good at VHF and is
> "close" for HF, but becomes increasing erroneous as you go down in
> frequency.
>
> 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.
>
> 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.
>
> 73, Jim K9YC
> ______________________________**_________________
> UR RST IS ... ... ..9 QSB QSB - hw? BK
>
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UR RST IS ... ... ..9 QSB QSB - hw? BK
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