[BC] Wave lengths

[Phil Alexander]

I hope Barry won't mind too much. This is an interesting
discussion and has turned into a primer on velocity in
transmission lines so I've left the original questioner's
comments and questions, and Cowboy's replies intact. I've
added a few points to flesh out the discussion and make it
clear, because outside of transmission theory texts I don't
know where someone who is not already familiar with the
topic can go to get a good explanation of this subject.

Sorry, Barry, but sometimes trimming can be a BAD thing
for understanding and for saving; and this is something
anyone working with broadcast RF should really, really 
know.


On 20 Feb 2006 at 7:22, Cowboy wrote:

> On Sunday 19 February 2006 18:01, JYRussell at academicplanet.com wrote:
> 
> >   And what's slowing the 'RF Wave' down on it's trip 
> > along the center and outside shield of the coax is some 
> > kinda weirdness at the point where the insulation and the 
> > copper meet.   A ratio of 'where it is' versus 'where it 
> > oughta be' gives a funny version of efficiency called 
> > "velocity factor'.
> 
>  It's not efficiency.

And, it is not weirdness. All it is, is the charging time of 
a capacitor. The bigger the capacitor, the longer it takes to 
charge is one way of looking at it, as Cowboy says below.

>  The explanation of a whole bunch of small inductors in 
>  series, with a whole bunch of caps across the line between 
>  each set of inductors is a good one.

As it should be, because this is the way delay lines are 
constructed when nothing else will do (as once was generally 
the case more so than now).
 
>  ( abreviated ) How long it takes to charge the capacitance 
>  of the section affects the time it takes before the energy 
>  appears to begin charging the next section. That time 
>  constant is affected by the qualities of the dielectric.

The key is something called the "dielectric constant."  All 
insulators have a dielectric constant to some degree. The 
amount of capacity between pairs of plates of equal size 
depends on the dielectric constant of the material between 
them. Air has a low dielectric constant so it is quickly 
charged. Poly has a relatively high dielectric constant so 
if the capacitor plates are the same size the capacity will 
be much greater than for air or vacuum, hence the charging 
time will be longer. 

Consider that any conductor has an inductance. Try putting a 
bridge on a pair of wire clothes lines and shorting the 
opposite end sometime. OK, you have to put in insulator to 
perform this little experiment so the line is floating, but 
you will find a straight piece of wire (like an inner conductor 
surface, or an outer conductor inner surface which can be seen 
as a bunch of wires in parallel) has a VERY significant 
inductance. This is the inductance that is seen at the drive 
point of a slant wire feeding an old shunt antenna where you 
may see numbers like 500 or 700 ohms inductive reactance.

In coax you have an infinite number of inductors strung in 
series and at each tie point between inductors there is a 
capacity across the conductors. Really, this is basic 
transmission line theory and is good to understand for many 
purposes. If two pieces of coax are physically the same size, 
and the dielectric material of one is air while the material 
of the other is poly, you can see that each of the capacitors
will have a higher capacity in the poly line. Since everything 
else is equal, it takes more time for the wave to get through 
the poly line, and that is the result of the higher dielectric 
constant.

>  The various qualities and geometry are chosen such that they 
>  cancel, but the line "looks like" a 50 ohm ( or whatever 
>  characteristic Z ) resistor if the line were to continue into 
>  infinity, such that there is no reflected wave.

The name for this is the "surge impedance" of the line and it can
be calculated from the outer diameter of the inner conductor and
the inner diameter of the outer conductor because those are the
surfaces that form the capacitor "plates."
> 
> > so, you should be able to use the numbers for the 'velocity 
> > factor' to know pretty closely where the wave multiples are 
> > in any coax you've got the velocity factor for (if you know 
> > the f(mhz)...
> > 
> >    Have I got it so far?
> 
>  Pretty much.

Yes, he's got that part of it. You can use the free space formula;
(approximately) 300,000,000 / Hz  or  300 / MHz which is more useful,
to find the wavelength in free space in meters. Then, divide this
distance by the velocity factor of the coax (which every manufacturer
provides) to get the length of one wavelength of coax. If you want
a half wavelength or a quarter wavelength, divide that number by 2
or 4 respectively. Or, you can multiply it by 0.5 or 0.25 obviously,
to get the same answers. That is important, because in AM work it
is frequently necessary to determine the length of coax for any
number of degrees. In this case, divide the number of degrees by
360 and multiply that fraction times a wavelength of coax just as
you would multiply by 0.25 to get a quarter wave. With this info,
it is also possible to break down the design of a VHF antenna to
determine phasing and hence beam tilt, if any.

For those who need the FCC's version of the free space wavelength
up to IIRC 30 MHz, go to the Bickel Engineering pages of the
Audio Division section of the FCC site and use the AMwave program.
This varies slightly from meters = 300 / MHz, and should be used
for directional arrays and their phase sampling systems to get
full agreement with FCC calculations.

> >     So, does the negative part (the ground shield) of the coax 
> > have other weirdness where it meets the (usually) black outer 
> > cover??  Seems like that conductor has two junctions, one inner 
> > (foam) and one outer (black stuff). ??  How come half the wave 
> > isn't slowed down more than the other??
> 
>  In short, in an unbalanced sheilded line, the inside of the outer 
>  conductor  can be considered to be a seperate and distinct conductor 
>  than is the outside of the outer conductor.
> 
>  The wave is travelling on the inner surface of the conductor, and 
>  not in the conductor material itself. ( not quite correct, but 
>  close enough for this discussion at present ) Thus, the conditions 
>  on the outside surface of the outer conductor have no bearing at 
>  all on what's happening on the inner surface.

When the first Heliax was introduced, you could buy it jacketed or
unjacketed, because the 100% outer conductor was assumed to be
enough protection for many applications. That is all the outer 
plastic jacket does. It protects the cable from the environment.
As Cowboy says above, it has absolutely NO electrical effect. NONE!
Understanding the conductors as plates of a capacitor on either
side of a dielectric material (the insulator) helps understand this.

Look at a piece of rigid line. There is no outer jacket. It is just
copper pipe. (And much heavier than the outer conductor of Heliax
so it doesn't need protection, except maybe from falling ice.)

> >    I could see how ladder line (balanced, parallel lines held 
> > apart by insulators...) would have the same 'velocity effecting' 
> > factors, since they're both out in the air... but in normal 
> > 'unbalanced' coax, it would seem the outer conductor has a 
> > junction with insulation the inner conductor doesn't have... so 
> > is there a difference you can see by comparing those signals, 
> > if you know what to look for...?
> 
>  No. See above paragraph.
> 
>  Likewise, the inside of the inner conductor has no "power" there
>  at all, and can be at the same potential as the outside surface of
>  the outer conductor !

This is why the inner can be (and is, once you get to a size where it
matters) hollow. In rigid line, even 7/8" line generally has a hollow
inner conductor to allow insertion of connecting "bullets."

>  The energy is confined to the space between the surfaces, outside
>  surface of the inner, and inside surface of the outer.
> 
> > Or is the 'velocity factor' sort of a combination of all the 
> > above... ?
> 
>  Primarily dependent on the dielectric between the conductors, 
>  even in parallel conductor ladder line as well.
>  ( which is usually "mostly" air )

Velocity factor is almost entirely a function of the dielectric
constant of the insulating medium between the inner and outer
conductors, although the formation of those conductors can have
a marginal effect on their inductance, thus on V.F.

This is true except for the most common kind - anybody remember 
TV twin lead? <g> Also, its interesting variation, UHF twin lead 
with a foam filler to make the capacity and signal loss smaller?

> -- 
> Cowboy
>


Phil Alexander, CSRE, AMD
Broadcast Engineering Services and Technology 
(a Div. of Advanced Parts Corporation) 
Ph. (317) 335-2065   FAX (317) 335-9037





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