Re: LC III

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Hi All,

Ed Phillips wrote:
> How much improvement in accuracy do you get using the
> distributed model?

Not very much on Fres.  I think I made a mistake in an earlier
post.  It's the larger h/d coils which show the most error when
using Medhurst, not the smaller - I may have said that the wrong
way round earlier.

I seem to recall you have software to calculate Fres via Cmed and
Ldc.  It would be interesting to compute a few hypothetical coils
and plot their velocity factors against h/d ratio.  They will come
out scattered around the curve

 http://www.abelian.demon.co.uk/tmp/ph1.gif

We know this because I think you used that same procedure to arrive
at that curve in the first place. The question is, how much spread
do you get?  And how does the spread vary with h/d?

The red dots mark the output of a distributed model and the green
dots come from measured frequencies.  Plotting those alongside
another set of dots from a Medhurst calculation would allow us to
see a clear comparison of the typical spread and trend of all
three.  BTW, the curve ph1(h/d) is the function
 ln(h/d) * 0.39 + 1.19,
chosen to fit the plotted points.

> I always got within 5% of predicting the unloaded SRF, and
> often within a couple or better.  Seems to me that's plenty
> good enough for the average coiler's use.

Indeed yes, and there's plenty of Medhurst based coil design
software out there which nobody is complaining about. In most
coils, there's so many un-modelled factors affecting the frequency
that there's no point demanding 1% accuracy before you begin
building.

Cmed was obtained by loading the test coils heavily with various
shunt capacitors, measuring Fres of each and plotting the effective
capacitance, then extrapolating in a straight line down to zero
shunt capacitance to reveal the residual 'self-capacitance' of
the coil.   The test conditions enforced a largely uniform current
through the coil, so Ldc applies.  The self capacitances thus
produced were intended for use as corrective offsets when designing
tuned circuits for radios.  These applications tend also to operate
with uniform current (meaning - the external circuit capacitance is
rather larger than the coil self-C), so that Cmed works very well
in the intended application.

When we use Cmed to model an unloaded Tesla coil, we now have zero
extra shunt capacitance, and the only resonant C is the 'residual'
that Medhurst extrapolated to.  Two sources of error now emerge.
First, the current is no longer uniform so the effective inductance
is no longer Ldc.  Second, the new current distribution induces a
different voltage distribution, so the effective self capacitance
will not be quite the same as Cmed.

The non-uniform current profile is a base-heavy cosinusoid in
coils which have h/d greater than about one or two.  This gives
a lower effective inductance than Ldc [1].   With this base-heavy
non-uniformity, more of the voltage rise occurs in the lower half
of the coil, and the effect of this is to make the self capacitance
a little higher than it was when the current was uniform during the
Medhurst test.

Thus, the effective inductance is less than Ldc, and the effective
C is greater than Cmed.   The two errors cancel to some extent in
the LC product, so the error in the frequency determination ends
up not too bad.

A greater error is noticed when impedances are compared, especially
on large h/d coils.    The coiler expects the top voltage to equal
2 * pi * Fres * L times the base current, where L is the effective
inductance.  If Ldc is used for this, the result may be over 20%
higher than actually found.  When comparing impedances, there is
no favourable cancellation of the error as there is with the
frequency estimate.

Often, Medhurst predictions seem to do better than suggested in
these comments.  The predictions are on the low side of actual
frequency in most cases, and all the unmodelled effects such as
pri-sec capacitance and capacitance to walls and floors act to
lower the actual frequency, hence reducing the apparent error.

Distributed models allow us to do extra stuff, for example,
we can...
*) deal with other coil shapes than solenoids.
*) model overtones as well as the fundamental.
*) take account of the coil's surroundings and fittings such
   as strike rings, etc.
*) account correctly for the shielding effect on self-C when a
   toroid is fitted.
*) calculate what the currents and voltages are doing inside the
   coil, whereas the lumped model only tells us what is at the
   terminals (providing correct equivalent reactances are used).

So, it's not just about accuracy, but detail as well.

> I always thought the Corum's made a fetish over their
> "transmission-line" approach, to the point where what could have
> been a simple paper because a lengthy and somewhat tangled one.

I've only ever come across two papers by them, they were both
pretty poor, containing errors and unsupported claims, irrelevant
concepts and misleading statements, and they seemed complicated and
confusing.  They seemed keen to make a mountain out of a mole
hill, when really all that was needed to solve the coil was
Coulomb's law, Faraday's law, conservation of charge, and a bit of
elementary calculus.

> Point is that one can be happy without going into any theory at
> all and no one should be discouraged by not understanding the
> stuff that's been written.

Absolutely agree.  None of this is important for coil building
and Cmed with Ldc remains a very useful lumped model for the coil.
Nor is there any reason to believe that distributed models will
ever lead to any significant improvement in coils.

> If one wants to take a "mathematical approach" all of the
> necessary design equations to come up with a successful first
> coil can be written on a single 3" x 4" file card.

Indeed.  But there's no doubt a lot of coilers who like to
understand a bit more about what is going on.  Not content with
simply following a recipe and making sparks, they want to get a
feel for the physics.  The long debates in the list archives over
the years make that clear.

I see Jared has now hung his hat firmly on the peg of pseudo-
science.   Obviously no amount of evidence or explanation will
budge him from stubborn adherence to his unfounded belief system.
There's a certain morbid fascination in witnessing it, but sadly,
we're obliged to refute him again every time he tries to mislead
a newbie.

[1]  The variation of effective inductance resulting from the
     non-uniform coil current is tabulated by coil shape in
     http://www.abelian.demon.co.uk/tssp/pn100502.html
--
Paul Nicholson
Manchester, UK.
--