Re: NEC-LIST: Linear Phased Antenna Array

Minimum conductor loss for equal-resistivity inner and outer
conductors (i.e. both copper or both aluminum), for a given coaxial
cable outer conductor diameter, results when the D/d ratio is about
(!) 3.59112:1. Generally at HF and on into VHF, the loss in the
dielectric is negligible, for good dielectrics such as Teflon and
polyethylene (and air). That D/d ratio is independent of the
dielectric, so when you fill the space with solid polyethylene, the
"min atten" impedance is around 50 ohms; that's LOWER than the ~77 ohm
value for air dielectric with that D/d, not higher.

With respect to "max power handling," one should qualify that. If
temperature rise is the limiting factor in power handling, then
clearly you want minimum attenuation to maximize power handling. That
tends to be the case for CW signals. For example, RG-213 is rated at
5000 working volts RMS, which corresponds to 0.5 megawatts at 50 ohms,
which would cause way too much power dissipation for polyethylene, or
even Teflon, dielectric cable at HF...or even at DC! On the other
hand, if you are transmitting pulses at very low duty cycle, the line
may be voltage limited, and then the max power handling would occur
for a line with a lower D/d...again, it's D/d, not Z0, that's found
from the fundamental voltage gradient calc. Finally, if you want line
with a given outside diameter that will handle the greatest _voltage_,
that will occur at an intermediate D/d...a bit over 50 ohms in
air-dielectric line as I recall. (Neither the voltage-limited power
nor the max voltage handling cases are things I generally care much
about! But the attenuation is.)

There's a simple formula for estimating the matched-line attenuation
of coax in the "Transmission Lines" chapter of "Reference Data for
Engineers." It has terms for both conductor and dielectric loss.
You can use it and the impedance formula given D, d and dielectric
constant (and dielectric power factor, if you want to include the
dielectric loss term) of the dielectric to find the D/d value for
min atten...though I believe you'll be forced to use a numerical
technique to find the min. An interesting exercise is to do the
same calc for line with an aluminum outer and copper inner and foam
insulation with v.f. around 0.8.

Cheers,
Tom
K7ITM

Dan Bathker wrote:
>
> I recall 77 ohms gives minimum loss and something like 30 ohms gives
> max power handling. 50 ohms was a rough compromise. Hope this helps.
>
> dan bathker
>
> At 11:55 AM 2/27/2001 +0900, Hideho YAMAMURA wrote:
> >Dear All,
> >
> >Could anybody tell me why the characteristic impedance of 50 ohms in
> >coax. cables became a standard value ?
> >
> >I have believed that this is the minimum loss condition, but I found
> >in an old Mushiake's book that it is around 77 ohms for air dielectric
> >solid metal coax, and even higher when dielectric material filled.
> >
> >I highly appreciate any information.
> >
> >I apologize if this is not an suitable subject for the list, but I
> >believe someone else may want to know too.
> >
> >==================================================
> >Hideho YAMAMURA,
> >Senior-Engineer,
> >Hardware Technology Engineering Department,
> >Advanced Product and Technology Development Operation,
> >Enterprise Server Division,
> >Hitachi, Ltd.
> >==================================================
Received on Thu Mar 15 2001 - 05:15:21 EST