Re Secondary Coil Resonant Frequency?

To: "'Tesla List'" <tesla-at-poodle.pupman-dot-com>
Subject: Re Secondary Coil Resonant Frequency?
From: Tesla List <tesla-at-stic-dot-net>
Date: Sun, 2 Nov 1997 22:23:06 -0600
Approved: tesla-at-stic-dot-net


From: 	Malcolm Watts[SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent: 	Sunday, November 02, 1997 3:20 PM
To: 	Tesla List
Subject: 	Re Secondary Coil Resonant Frequency?

Hello Adam,
            here is your solution....

> From:   Adam[SMTP:absmith-at-tiac-dot-net]
> Sent:   Saturday, November 01, 1997 9:15 PM
> To:     tesla list
> Subject:    Secondary Coil Resonant Frequency?
> 
> 
> Someone asked the following question a while back, and there was no 
> satisfactory answer.  The question was:  How do you calculated the 
> resonant freq. of a secondary, with and without the toroid?
> 
> The TESLA-EQ.TXT has a formula, but just calculates the 1/4 wavelength 
> frequency that corresponds to the length of wire used.  Does this number 
> have any value to us at all?

Unfortunately that doesn't always work -in fact it hardly ever does. 

> It seems like finding the self inductance of the coil and the 
> self-capacitance and using these values to calculate the frequency by 
> 1/(2pi*sqrt(LC)) would give the correct results, and such calculations 
> could also be made to include the toroid.
> 
> But, how do you find these two values by calculation alone (before 
> building the thing)??? Do you have to resort to a messy Biot-Savart 
> calculation, or is there a quick approximation?
> 
> Could someone give us solved example of how it is really done??? (that's 
> a challenge!) 

Cself = HD where D is coil diameter in cm and H is a value that 
depends on coil h/d thus:

h/d = 2,  H = 0.51
h/d = 5,  H = 0.81   with fairly linear interpolation.

H bottoms at at 0.46 for h/d = 1.

Lself : use Wheler's formula for single layer solenoids.

Malcolm