[Antennas] Re: 600 Ohm Ladder Line

[Barry L. Ornitz]

Durwydd MacTara asked:

> I need the necessary formula(e) to make some 600 ohm ladder 
> line. This stuff is almost impossible to find in today's 
> market!  Also need to make some from resistance wire for a 
> 500W termination for a non resonant Rhombic.

For two wires of equal diameter, d, and center to center 
spacing of D, the equation for the impedance of the parallel 
wires in air is:

    Z = 120 *arccosh(D/d)                         [Eqn. 1]

where: arcosh(x) = inverse hyperbolic cosine(x) 
                 = ln(x + sqrt(x^2-1)).

Note that this formula is slightly more accurate than the one 
published by the ARRL in their various handbooks.  If you make 
the assumption that the ratio of the diameters is very large, 
you can approximate the arccosh by using the logarithm of 2*x 
instead.  Then if you use base 10 logs instead of natural 
logs, you get the more commonly found equation:

    Z ~ 276*log10(2*D/d)                           [Eqn. 2]

If the wire is #12 AWG (diameter 0.0808 inches), and the 
spacing is 6 inches the impedances are:

    Z = 120 * arccosh(6/0.0808) = 600.076 ohms from Eqn. 1, 
and
    Z = 276 * log10(12/0.0808)  = 599.408 ohms from Eqn. 2.

So the approximation is quite good for large ratios of sizes, 
but for 0.125 inch spacing, the differences are more 
significant: 120.402 ohms versus 135 ohms for the 
simplification.

For the resistive termination, high loss transmission line is 
generally used if you cannot find the necessary high power 
non-inductive resistor.  Laport's book, "Radio Antenna 
Engineering", suggests the use of galvanized steel or 
stainless in making these transmission lines.  The idea is to 
use a high resistivity material, and if it is magnetic 
(permeability greater than unity) the losses will be all that 
much higher.  Nichrome alloys are also in common use.  Small 
gauge stainless welding wire is more commonly available.

For those interested in rhombic antennas and their various 
cousins (half-rhombics, Vee's, and terminated longwires), 
Laport's book is the "Bible".  It has been out of print for 
many years, but the demand is still high as evidenced by the 
scarcity of used books and the high prices they bring when 
they do appear.

        73,  Dr. Barry L. Ornitz     WA4VZQ     ornitz@tricon.net