Topband: electrical wavelength

[Pete Smith N4ZR]

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
> _______________________________________________
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>