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
>Correct!
>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
>>it/
>>/> 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
>>goes/
>>/> to zero, and Zo also goes to zero./
>>/>/
>>/> Jack K1VT/
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