# RE: New formula for secondary resonant frequency

```Original poster: "John H. Couture by way of Terry Fritz <twftesla-at-uswest-dot-net>" <couturejh-at-worldnet.att-dot-net>

Hi Kurt -

Thank you for the info on your coil/s self capacitance formula based on the
Medhurst K-value table. The formula I used for the JHCTES Ver 3.1 and Ver
3.2 programs is the following Medhurst one.

Ccoil = 5.08*3*((.0563*Hs/Rs)+(.38*sqrt(Rs/Hs)) +.08)

This formula appears to have an accuracy of better than 2% for Tesla coils
with secondaries with H/D ratios of less than about 5 when compared with
measured values. The accuracy of the measured values are not shown so it is
not possible to know exactly the accuracy of the above formula. As most
Tesla coils are designed with H/D ratios of less than 5 I do not think I
will change the JHCTES at this time. In fact I am amazed the JHCTES is
producing these accuracies.

John Couture

-------------------------------

-----Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Sunday, February 04, 2001 12:01 PM
To: tesla-at-pupman-dot-com
Subject: Re: New formula for secondary resonant frequency

Original poster: "Kurt Schraner by way of Terry Fritz <twftesla-at-uswest-dot-net>"
<k.schraner-at-datacomm.ch>

Hello John,

With x=H/D, im using my own precision-fit formula (avg.deviation
0.27%; max. 1.05%) to the Medhurst K-value table, which was used
by Bert Pool, in his Excel-design sheet, for 1 < H/D < 8. The
function, due to its relatively few parameters etc., behaves
plausibly for slight extrapolation of H/D > 8 (tried up to 10).

Eqn	K=a+b*x+c*x^(1.5)+d*ln(x)/x+e/x^2

a	3.174612104
b	-0.350587741
c	0.087994211
d	-4.628698069
e	-2.451606171

Then Co[pF] = K*D[cm]

I'm aware however, Medhurst himself proposed a formula:

K= 0.1126*x + 0.08 + 0.27/sqrt(x)

...with Co[pF] = K*D[cm]

which he claims to fit his 5% precise data, for 0.163 < H/D <
29.2, closely (to 2..3% --> I'm getting 4.8% avg. and 7.7%max.
error for H/D=1...8). But I've seen, my own fit is introducing
less error in addition to his 5% table, for the range of 1 < H/D
< 8 mostly used for TC's.

Greets
Kurt Schraner

Tesla list wrote:
>
> Original poster: "John H. Couture by way of Terry Fritz
<twftesla-at-uswest-dot-net>" <couturejh-at-worldnet.att-dot-net>
>
> Kurt -
>
> What are you using for the Medhurst equation?
>
> John Couture
>
<snip>

```