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

HI Gavin,

On 19 May 00, at 17:57, Tesla List wrote:

> 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. Also the capacity per unit length is effected by the inter-turn
> capacity between turns. This results in the secondary coil seeming to be
> more of a lumped LC circuit, rather than a transmission line.

My measurements indicate that the C/length is little affected by inter-
turn capacitance. Consider this: Suppose I have a coil which is 1 
foot in diameter and three feet long. According to Medhurst it has a 
fixed Cself since Cself depends only on diameter and height. I have 
wound coils starting with a closewound right out to 6 tuns total on 
this very form and found that Medhurst's assumption about 
capacitance being invariant is absolutely right. But let's suppose he 
has boo-booed and fiddled his values etc. etc.

       Consider the lumped resonance formula. Fr is proportional to 
the inverse of SQRT(LC). But the same is true for the propagation 
velocity formula put forward by R. Jones.  So the "true" or intrinsic 
C of the coil must be invariant in his case also. So Cself for a coil 
used as a grounded resonator really is invariant and does not 
depend on wire spacing. QED.

> 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 cannot agree about the conditional factor (but am open to being 
proved wrong). I think C self depends on coil area alone (ignoring 
proximity to other objects). My measurements seem to indicate that 
anyway. What differences there are seem to be very much less 
than a 2/3 factor.
 
> 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)) *

Not if I understand correctly.  The two are fundamentally different 
approaches. The classical lumped formula incoporates 2PI.  The 
transmission line equation is based on the propagation velocity of a 
line which is defined as being 1/SQRT(LC). This can be related to 
the fundamental resonant frequency by considering that for 1/4 
wave resonance, the signal only has to propagate 1/4 of the 
distance or altenatively in 1/4 of the time of a whole cycle. Hence 
the "4" factor. I think raw approximations play no part in this. Am I 
right RJ?

> 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)?
> 
> Is there yet a similar formula for bi-polar coils?
> 
> 
> MEDHURST FORMULA
> I have come across the following for the Medhurst formula:-
> 
> Cmed = (0.256479 * H) + (0.78646 * D) pF
> 
> 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?
> 
> 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 <<

Regards,
Malcolm