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Re: [TenTec] NEC, ground, grounds, and radials

To: tentec@contesting.com
Subject: Re: [TenTec] NEC, ground, grounds, and radials
From: Jack Mandelman <modelman@ieee.org>
Reply-to: k1vt@arrl.net, Discussion of Ten-Tec Equipment <tentec@contesting.com>
Date: Sat, 08 Jan 2011 10:09:33 -0500
List-post: <tentec@contesting.com">mailto:tentec@contesting.com>
Forget about the formulas!  None of the discussed formulas is sufficiently 
accurate of the wide ranges of S/d discussed.  All are approximations that are 
reasonably valid only over their limited domains.

A much more practical engineering approach would be to apply a finite-element 
analysis of LaPlace's equation using the boundary conditions appropriate to the 
geometry of interest.  For these types of problems a 2-D quasi-static analysis 
provides much better accuracy than any formulas presented.

Jack K1VT


>I believe it was Jerry who pointed me to the accurate formula a couple
>of years ago on this very List. I was considering how to build low
>impedance balanced line with a Zo in the range 50 Ohms to 70 Ohms for a
>Hexbeam application. One look at the published curves told me it
>couldn't be done; but Jerry put me right!

>Steve G3TXQ

>On 08/01/2011 02:05, Dr. Gerald N. Johnson wrote:
>>/  Like my curves its center to center. The upper trace is using the 276/
>>/  log formula and the lower one is the 120 inv hyperbolic cosine function./
>>/  Mine has the spacings on a log scale his is a liner scale. The upper/
>>/  trace formula is increasingly inaccurate below 300 ohms impedance with/
>>/  87,000 percent error at a spacing just a hair wider than the conductors/
>>/  touching. The wrong formula says you can't get a Z0 less than 87 ohms/
>>/  (as published in QST last summer again), but the correct formula gets/
>>/  down to practically zero Z0 just before the conductors make contact./
>>/  http://www.geraldj.networkiowa.com/papers/CSVHF2010/lztl1.JPG//
>>/  http://www.geraldj.networkiowa.com/papers/CSVHF2010/lztl2.JPG//
>>/  73, Jerry, K0CQ/
>>/  On 1/7/2011 7:46 PM, Jack Mandelman wrote:/
>>/>  Steve,/
>>/>  In your plot how are you defining S, the spacing between conductors?  Is 
>>/>  center to center?  Is it consistent for both the approximated and actual/
>>/>  curves?  It appears that only the actual curve uses the center to center/
>>/>  definition; in the limit as S-->d  the inner edge to inner edge spacing 
>>/>  to zero, and Zo also goes to zero./
>>/>  Jack K1VT/

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