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Re: Medhust and 1/4-wave resonance of coils.

Hi Gavin,

I think you may have misunderstood the postings.

Medhust C is the correction you must add to a much larger tuning capacitor
that is connected across a  coil if you want to accurately calculate the
resonance frequency.  Medhurst measured several different sized coils and
calculated an empirical relationship from them.  Now because the average
Tesla coil does not have a large C across it  should not work.

I was trying to explain that although Medhurst formula is not applicable it
does work reasonably well even though the correct formula should be  fr =
1/(4 pi sqr(L * Cintrinsic))  (if you believe its a transmission line).

Note the intrinsic C of the coil  (I now use that term as self C or true
self C tends to be confused with other C's)  is what you would measure
with an LC bridge it is not Medhust C. This is what created the confusion at
least for me.

More comments below::


>Original Poster: "Gavin Dingley" <gavin.dingley-at-astra.ukf-dot-net>
>
>Hi Malcolm, Rob and all,
>I have been following the recent posts on adjustment of the medhurst
>formula and it's use in calculating the 1/4-wave resonance of secondary
>coils in TCs. Now I am just going to summarize what has been said so as
>to be corrected on any point I may have misunderstood.
>
>Modeling the coil as a transmission line is difficult because the
>inductance per unit length is effected by mutual inductance between
>turns.

Well actually the inductance per unit length is zero.  But if you use mutual
inductance per unit length which does not go to zero it all works out fine
except that now you have dispersion.  Because the adjacent parts of the coil
are out of phase or have different amplitudes.  So that at short wave
lengths the velocity is much higher
than at long waves lengths.

>Also the capacity per unit length is effected by the inter-turn
>capacity between turns.

That is not a problem in long coils because adjacent turns are at almost the
same voltage so it will have a small effect. It will have a more significant
effect as the coil is made shorter or the number of turns are reduced which
increases the voltage between the turns. ie strictly the equation is only
valid for long coils. It should be possible to include the inter-turn C or
(internal C) as Medhurst calls it but your getting to a point of diminishing
returns where other factors are significant such as the end effects,
Maxwell's equation and c.

>This results in the secondary coil seeming to be
>more of a lumped LC circuit, rather than a transmission line.
>
>Using the formula:
>
>fr = 1/(2 pi sqr(L C))
>
>where L is the inductance and C the self capacity of the coil. The self
>capacity can be calculated with the medhurst formula. This results in a
>reasonably close frequency of resonance.
>
>However, Rob Jones states that the medhurst value for self capacity is
>based upon only the geometry of a hollow cylinder and so does not
>incorporate inter-capacity between coil turns. He stated that for short
>coils Cself = 3 * Cmed, while for long coils
>Cself = 2 * Cmed.

I dont believe that is what I have said.
>
>Using transmission line theory, a value of Cself = 2.46 * Cmed results
>as a general rule. Now because 2.46 is about ((2 * pi) / 4)^2, the
>formula:
>
>fr = 1/(2 pi sqr(L * Cmed * 2.46))
>
>becomes
>
>1 / (4 * srq(L * Cmed)) *

I assume you mean intrinsic C not Cmed.  In which case you are correct but I
started from the last equation derived from circuit theory.

Perhaps this will help

 f=1 / (4*H*SQR( M * Cintrinsic/H)

For long coils the mutaul inductance per unit length is equal to
the total inductance divided by its length hence:

f=1 / (4*H*SQR( L/H * Cintrinsic/H) =1 / (4*SQR( L * Cintrinsic)


QED
>
>Are there any limits to this formula regarding coil length, to frequency
>wave length (i.e. a point where a coil starts to act as a transmission
>line)?

The formula is accurate for  long coil for their fundamental resonance
frequency because it does not include end effects and dispersion.  Although
because end effects are apparently small it does produce reasonable answers
for normal coils.

Although that was not the purpose of the formula. Its purpose was to show
how the standard transmission line equations do work if you put intrinsic C
in them.  When I first tried the transmission line equation I used med C but
got the wrong frequency because I was using the wrong C.  I  imagine that
others did the same thing and concluded that the transmission line equations
did not apply.  But because I was convinced that mutli resonances could only
be explained if it was a transmission line and I had directly observed the
delay  I struggled on to try to find out what was going. My posts are the
results of that investigation.

>
>Is there yet a similar formula for bi-polar coils?

Yes just remove the 4.
>
>
>MEDHURST FORMULA
>I have come across the following for the Medhurst formula:-
>
>Cmed = (0.256479 * H) + (0.78646 * D) pF

I cant check that at the moment but from memory it looks correct.
>
>H is coil height in inches and D is coil diameter, also in inches.
>
>Is this correct, and if so, does it have any H/D ratio limits?


As explained above its only accurate with a large additional C so if you
have a 50ft diameter top load it will give you a very accurate answer.

>
>I know this post is more a bunch of statements rather than questions,
>but I want to clarify that I have got it right.
>
>Thanks in advance,
>
>Regards,
>
>Gavin, U.K.
>
>>>* I think Cmed should be Ctrue or Cself in this equation or the actual
>capacitance of the cylinder in free space. - Terry <<
>
>
>