Re: Quarter Wavelength Frequency

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

Original poster: biomed-at-miseri.winnipeg.mb.ca 


See my comments below.  These are mostly theoretical from my college days
and other reading related to tesla coils.

Shaun Epp



 >Original poster: Jared E Dwarshuis <jdwarshui-at-emich.edu>

 >Hello my name is Jared Dwarshuis and my friend?s name is Lawrence
 >Morris. We have been experimenting with wire length resonance (as well
 >as two part resonant transformer designs). We have found that matching
 >wire length to L.C. is critical to the operation of our integer
 >wavelength coils.

Are you talking about the standard 1/4 wave or 1/2 wave (bipolar) tesla
coils, or are you winding them more than that?  Tuning a coil past one
voltage maximum (at the end of the selenoid, or both ends for a bipolar) is
a waste and creates corona problems where you don't want them!

 >We use an inductor that is wrapped around a donut or toroidal form,
 >because this inductor has no ends. It is the closest possible fit to
 >the derivation of the classic inductor formulae L = uo Nsqrd Area/
 >length. Because we have formed our inductor from a single loop of wire
 >we have a boundary constraint, this coil can now only form integer
 >wavelengths which it does very nicely, at even multiples of the
 >fundamental wire length frequency.

 >It may be the case that cylindrical coils can deviate enough from the
 >ideal inductance formulae to cause discrepancies between wire length
 >and L.C. resonance, or perhaps current nodes are not exactly where
 >people think they are, and this has lead people to believe that wire
 >length has no significance (an understandable mistake).

Wire lengths only affects the number or turns you can put on a form for a
given diameter of the form!  Each turn of a selenoid is magnetically linked
to the adjacent turns of the selenoid, hence inductance occures within the
selenoid.  Capacitance occures between the adjacent turns of the coil
because of there physical proximity and the fact that there is a voltage
difference between them.  These two elements, mutual inductance and self
capacitance, set the resonant frequency of the secondary coil, not the
wavelength the wire used to wind the coil.  The wavelength formual is for a
straight wire, not looped like in a coil where inductance comes more into
play.  Granted there is a small amound of inductance and capacitance on a
piece of straight wire, which doesn't affect the wavelength formula, or
maybe this is where the propagation velocity comes from.  Once you loop the
wire like a coil, you have self inductance and interwinding capacitance!


 >When we match the L.C. frequency to the wire length frequency we
 >believe that it minimizes interference between the two distinct
 >resonant energy storing mechanisms. Clearly L.C. resonance occurs in
 >systems that ignore wire length (such as the primary inductor), but
 >when the wire length is also considered in design, the dynamics change.
 >Our experiments indicated that it was impossible to find a top end
 >capacitor pair that would kill the wire length resonance entirely, so
 >we are inclined to believe that when your primary is tuned to the wire
 >length, the wire length resonance will be the dominant energy storing
 >mechanism.

There is always going to be some energy that is coupled into the secondary
coil from the primary coil.  You maybe near enough to resonance that you
get  appreachable energy transfer, but this has nothing to do with
wavelength, just that you are close enough in frequency to get energy out
of the secondary.

Shaun Epp