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The "Medhurst" method for the self-capacitance of an air-core coil


  Malcolm Watts sent me a copy of his BASIC program that calculates the self-
capacitance of an air-core coil using the "Medhurst" method.  I examined the
BASIC program and found that it have a bad data point in the "H" array.  Note
that the H values go down to 0.46 and then increase.  Line #260 ends in 0.46,
0.46,0.46 and line #270 starts with 0.7,0.48,0.5,0.52. The 0.7 at the start of
line #270 should be 0.47.  To verify this I plotted the data and got a smooth
curve by assuming 0.47 while 0.7 results in a very noticeable spike.

  I have developed an analytic formula using the Medhurst data that predicts
the same capacitance values within 1/3 of a picofarad at the given values of
the M-array in the program.  The formula is a continuous expression - unlike
the BASIC program, which uses a piece-wise linear technique - so it should be
more accurate at values that are not exactly on the original data points (this
would include extrapolating beyond the end of the original data points).

  I the process of generating the analytic formula I noticed that a plot of the
original Medhurst data actually shows 2 linear curves having slightly different
slopes and intersecting at about R=30. I seriously doubt that anything physical
that could exhibit this effect so I assume that measurement errors are the real
cause (Medhurst may have switched coil forms or wire size at R=30 to handle the
larger coil aspect ratios).

  I tried tracking down the original Medhurst paper by searching for a copy of
the Radiotron Designer's Handbook (edited by Langford-Smith) only to discover
that it is out of print.  A local library has informed me that they can get it
but it will take at least 6 weeks. I found two copies of the Radiotron book in
a bookstore - a 3rd edition and a 4th edition. The used 3rd edition was priced
at $30 but it did not have the Medhurst paper in it.  The used 4th edition had
the Medhurst paper in it but it was priced at *only* $110 (I passed on buying
it and examined the article while in the store).

  The Medhurst paper references the following 2 issues of "Wireless Engineer":

    1. Volume 24, #281 (Feb. 1947) page 35
    2. Volume 24, #282 (Mar. 1947) page 80

  So far I'm having even less success with these publications as I did with the
Radiotron book.  If anyone has access to these articles I will pay for copying
and mailing costs to get copies.  I would like to determine how the original
data were taken to find out why the breakpoint occurs in the linear portion of
the plotted curve.  Although my analytic formula *very accurately* matches the
original data points I'd prefer that it matched reality rather than noisy data.
Medhurst claims his data are good to about 5% and my match to his data is much
better than that.  Any help with these articles (and a pointer to a reasonably
priced copy of the Radiotron book) would be appreciated.

  Thank you.

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    Micheal Cranford      Resident Skeptic      Intel P6 Architecture Labs