Topband: electrical wavelength

[Tom W8JI]

> On 9/10/2012 9:23 AM, Jim Hoge wrote:
>> Let's do some quick math.... 234/1.82=128.57 gives us the length in feet 
>> of a quarter wave at 1.820 mHz. Multiply that by a velocity factor ( say 
>> 85% for LMR-400) and you get a length of 109.29 feet.


I think the big error, using 234 instead of ~246, is pretty important to 
everyone.

> That math is a bit too simple, because Vf VARIES as function of frequency. 
> The PUBLISHED Vf is for VHF, but the Vf is a few percent lower at 2 MHz. 
> This happens with ALL transmission lines, and is predicted by Maxwell's 
> Equations. For more on this, including measured data for coax similar to 
> LMR400, see http://audiosystemsgroup.com/Coax-Stubs.pdf

I firmly do not believe that is true.

Velocity factor in cable is the square root of the inverse of dielectric 
constant. There is no frequency sensitivity in the equation. The dielectric 
constant of polyethylene varies from 2.26 at 60Hz to 2.26 at 1 GHz.

sqrt of 2.26 is .66519

I just checked a CommScope F6 cable, the error from 5 MHz  to 35 MHz  is 
only 0.1%
That is well within instrument and foam/air consistency errors.

As a matter of fact it appears the variation I see has clear indications of 
analyzer or foam density tolerances, since it wobbles around  0.25% delta.

I tested cables for some manufacturers, and one of the ways I would look for 
bad runs was a large delta in the harmonic null positions. I can't recall 
any good cables changing 3% over HF to lower VHF.

One thing that causes a change in Vf is the same thing that causes an 
antenna's harmonics to not fall evenly with frequency. This is end-effect. 
An evenly cut cable end has electric field fringing, and that makes the last 
1/4 wave section look longer than internal sections.


> Bottom line -- you MUST measure the coax AT THE OPERATING FREQUENCY to hit 
> an exact half wave.  An easy way to do this is with an analyzer like the 
> MFJ259, which drives the line with a small manually tuned signal 
> generator, short the far end, and tune the generator until you see the 
> sharp null of the short.

The problem with doing things like this are even harmonic levels, which even 
when very low can skew results slightly. Plus we have connector lengths and 
such.

In Ham use, people do not need to get all over the top. It is far more 
important to use the right formula than to worry about a few percent wobble. 
I can't think of any systems we have that are so critical.

73 Tom