On 1/8/2011 4:31 PM, Jack Mandelman wrote:
> Jerry,
> The point that I'm making is that the formulas discussed are applicable
> only for very specific geometries. The validity of formulas breaks down
> at the extremes of the underlying physical assumptions. Formulas are
> not predictive beyond their ranges of applicability. A case in point is
> conductor cross-sectional geometry that departs from circular.
But the formula specifically says round conductors. Wheeler did much
work for other useful conductor shapes like flat.
General
> inhomogeneous dielectric distributions in the vicinity of the conductors
> is another difficult case. How would you handle these cases?
If I want precision and broad bandwidth I try to prevent those from
happening. Or I accept the variations because I'm going to have to
accept that different production runs of dielectric are going to have
different characteristics including anisotropic conditions whose
orientation I may not be able to control. Like caused by the woven
fiberglass to make the dielectric constant different perpendicular to
the fabric or along the warp and weave or at an angle to the fibers. Or
I build in a tuner at the transmitter so I can adjust for the variations
I can't control.
These are
> only a couple of examples where the classic formulas may result in
> inaccuracies. By not limiting ourselves to the strict geometries on
> which the formulas are based, we open a world of opportunities for
> innovation improving upon the state of the art. The point that I'm
> making is that finite-element analysis is state of the art, which frees
> us of the constraints imposed by formulas.
And opens us up to the foibles of handling large matrices and gives us
varying results depending on how we made the mesh modeling the none
simple shape. The math of finite elements has its own set of assumptions
and approximations that aren't always apparent.
>
> Certainly, Harold Wheeler's work is widely recognized. However, he
> relied on geometry mapping techniques for deriving his formulas. As
> such his formulas have limited applicability if one wishes to depart
> from his geometric assumptions. Because of computational limitations,
> finite-element analyses were not a practical option in his day. But it
> is a valuable tool available today, even for hams, and we should take
> full advantage of it for going beyond what formulas predict.
>
> No need to get defensive about Wheeler's work. I have the highest
> respect for his achievements. So please lighten up a bit.
>
> Jack K1VT
>
73, Jerry, K0CQ
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