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

Hi Gavin,

Sorry I should have said replace the 4 with a two to convert to a bipolar
coil.

Regards Bob (Robert A Jones)

-----Original Message-----
From: Tesla List <tesla-at-pupman-dot-com>
To: tesla-at-pupman-dot-com <tesla-at-pupman-dot-com>
Date: Sunday, May 21, 2000 7:01 PM
Subject: Re: Medhust and 1/4-wave resonance of coils.


>Original Poster: "Robert Jones" <alwynj48-at-earthlink-dot-net>
>
>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 <<
>>
>>
>>
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