[HBR] 160 Meter Coil Data

[Walt Hutchens]

Dan said:
> When I ran the program (its from Australia by the way), and posted
> the table of errors, you could see the 3 points that the error
> crossed zero.  But one point was very near the band edge.  Probably
> since the error was so small, the program didn't try to improve it.

I've never tried to work on one of these programs (and no longer even
have the time to learn the languages to do it) but I'd bet that
everything depends on how you approach the problem.  The center crossing 
point (of a three point fit) probably can be placed over a considerable
range, at least in many cases.

> I would have thought that the center tracking point would either be
> in the center of the band (average of the band limits) or the
> geometric mean (square root of the product of the band limits).

The two basic approaches that come to my mind are a closed-form solution
-- you just solve some rather messy simultaneous equations and you get
all the values -- and iteration of approximate solutions toward an optimum.

In the case of a closed solution you'd have to pick a crossing point
(arithmetic or geometric mean, perhaps something else), I think.   The
advantage would be that it is closed form -- you could do it with a
pencil and paper and pretty quickly with even a primative
(non-programmable) calculator.  The disadvantage (fairly slight) is that
you probably wouldn't get very close to the smallest error in every
case, although with three points that might not be very important.

Doing it iteratively you'd pick any set of values you wanted to start
with, compute the 'goodness' of the solution, then alter the values,
recalculate goodness and accept the new values if the solution is
better.  There are often clever algorithms for altering solutions as in
the (now long forgotten!) pencil and paper method for calculating a
square root.  However with such a simple set of equations and modern
computers you could perfectly well simply alter a variable at random,
recalculate the others that are dependent, and go from there.  In this
case, do exactly what you'd do with a screwdriver: perturb the
inductance, recompute the trimmer and padder values for the correct end
points, and compute the goodness as a function of the error at some
number of intermediate points -- 10, 100, whatever.

This has the advantage that whatever you think is 'good,' the program
will give you those numbers.  'Minimize the maximum absolute error,'
'minimize the sum of absolute errors,' 'minimize the RMS value of the
errors' ... whatever.

However, each different measure of goodness will give a somewhat
different crossing point.  And there's a lot of calculation involved --
this is a computer method.  Of course eveyone has a computer these days.

It may be that this program simply looks for ANY three point solution -- 
they're all going to be pretty good.

> I downloaded the source code and will look at it when I get time to
> see if I can figure out how it works.

If you make any improvements, I'd sure like to have a copy!

Walt
KJ4KV