[Towertalk] Re: Insulated Wire

Chuck Counselman ccc@space.mit.edu
Thu, 3 Oct 2002 21:49:23 -0400


At 7:53 PM -0400 10/3/02, K5RC wrote:
>One problem.... 468/f does not work with insulated wire. You have to
>consider the velocity factor of the jacket.

Yes and no; but mostly no.  Coaxial cable has a velocity factor 
significantly less than one, and equal to one divided by the square 
root of the dielectric constant of the insulating material that fills 
the space between the center conductor and the shield, because 100% 
of the electric stored energy of the wave(s) is stored in that space, 
in that insulating material.  In other words, the capacitance per 
unit length of the transmission line, which together with the 
inductance per unit length determines the velocity of a wave 
traveling along the line, is proportional to that dielectric constant.

With an insulated antenna wire in air or free space, typically the 
thickness of the dielectric/insulation is smaller than the diameter 
of the wire conductor and much, much smaller than the distance from 
the wire to the ground or other part of the antenna where electric 
field lines leaving the wire terminate.  Most of the electric stored 
energy is *not* stored in the insulating material.  The capacitance 
per unit length of the wire, which together with its inductance per 
unit length determines the velocity of a wave traveling along the 
wire, is only in small part determined by the dielectric constant of 
the insulation.  Per unit length, the capacitance of the wire is that 
of two capacitors connected in series: the first being the 
coaxial-cylindrical capacitor formed by the insulation; and the 
second being the capacitance between the outer surface of the 
insulation and the ground or other part of the antenna where electric 
field lines leaving the insulated wire terminate.

It should be obvious that the second capacitance is much smaller than 
the first, so that the capacitance of the series combination is 
nearly equal to the capacitance that the wire would have if it were 
solid metal, equal in diameter to the outer surface of the 
insulation.  (The exact value of capacitance is between the values 
for solid wires having diameters equal to the inner and the outer 
diameters of the insulation.)

The capacitance per unit length of a thin circular cylindrical wire 
depends only weakly, logarithmically to be exact, on the diameter of 
the wire.  Thus the resonant length of a typical wire antenna, with 
thin insulation, is not much affected by the insulation.  Nothing at 
all like the length of a standing wave inside a coaxial line.

As mentioned, the statement of the next-to-last sentence is an 
approximation.  Yes, the resonant length _is_ affected, just not 
enough to worry about in a typical HF antenna.  Other factors, such 
as proximity to ground and other conductors and dielectrics, and 
details of the feedpoint and ends of the antenna, are typically more 
important.  As you probably know if you've used insulated wire in HF 
antennas, as I have.

73 de Chuck, W1HIS