Re: Resonant Frequency

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Malcolm Watts by way of Terry Fritz <twftesla-at-qwest-dot-net>" <m.j.watts-at-massey.ac.nz>

Hi Ed,

On 22 Feb 2002, at 11:36, Tesla list wrote:

> Original poster: "by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<Esondrmn-at-aol-dot-com>
> 
> I just read a comment from Paul Nicholson about the self resonant frequency 
> of a solenoid secondary being higher than the 1/4 wave frequency for the
same 
> length of wire in free space.  I would have guessed it would have been lower 
> due to the added self capacitance of the solenoid secondary.  I just did
some 
> calcs on my 6.0" secondary.  The self resonant frequency is 263 khz.  The 
> quarter wave frequency calculated for a 1604 foot long wire is 146 khz.  So 
> why does this come out backwards from what I expected?

     When I first discovered this for myself, the best explanation I 
could come up with was that the increase in mutual inductance as you 
coil the wire up does not completely compensate for the drop in C as 
the resonant structure gets shorter. If you look at the 
characteristic impedance of the two, you see that it climbs as the 
wire gets bundled up but never gets to infinity. That suggests that 
Cself in a longwire is very high to begin with.

     In connection with this, I've seen the idea mentioned that by 
connecting the resonator base to zero impedance, shunt impedance 
climbs to some tremendous value. I believe this to be a fallacy. 
Given that it is necessarily limited (albeit to some 10's if not 
100's of MOhms) to start with given limited coil Q, it cannot go 
beyond what the surroundings and copper losses dictate. Instead, the 
resonant mode starts changing as the coil is now "bound" at both ends.

Regards,
Malcolm