I thought we were talking about RF.
73, Pete N4ZR
The World Contest Station Database, at www.conteststations.com
The Reverse Beacon Network at http://reversebeacon.net, blog at
reversebeacon.blogspot.com,
spots at telnet.reversebeacon.net, port 7000 and
arcluster.reversebeacon.net, port 7000
On 9/10/2012 4:36 PM, Jim Brown 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
_______________________________________________
UR RST IS ... ... ..9 QSB QSB - hw? BK
|