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" <[email protected]> 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
