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Re: H/D Ratios



Subject:       Re: H/D Ratios
       Date:   Wed, 28 May 1997 11:34:12 +1200
       From:   "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
Organization:  Wellington Polytechnic, NZ
         To:   tesla-at-pupman-dot-com


Hello John, all,
                 Some interesting points in your reply....

>   From:   "John H. Couture" <couturejh-at-worldnet.att-dot-net>
>     To:   Tesla List <tesla-at-pupman-dot-com>
> 
> >       From:   "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
> >Organization:  Wellington Polytechnic, NZ
> >         To:   tesla-at-pupman-dot-com
> >
> >> I have seen several references to a physical 1/4 wavelength of wire
> >> being used to wind a secondary. What is the 1/4 wave length based on?
> >> Is it free space or based on some velocity factor? Is there some magic
> >> to be had by striving for this.
> >> 
> >> Based on no facts at all my next secondary will have a H/D ratio of PI.
> >> It just seems right.
> >
> >Love it :)
> >     The quarter wavelength thing: In the distributed resonator, no 
> >matter what the length of wire, the profile is 1/4 wavelength at 
> >resonance. Well, that is _strictly_ true for no top load (or nearly 
> >so because like a standard antenna, there is an end capacitance 
> >effect that requires the physical length of the straight wire to be 
> >somewhat shorter than the free-space length). As soon as one adds a 
> >topload, the antenna/coil will resonate at a lower frequency because 
> >of the additional capacitance. That makes the structure shorter than
> >90 degrees electrically at its resonant frequency. The lower the L/C 
> >ratio, the more the electrical length trends towards zero degrees.
>      I'd better stop there. I think I may have started writing a book.
> 
> ----------------------------  Big snip
> >
> >Other comments welcome,
> >Malcolm
> 
> ------------------------------------------------------------------
> 
>   Malcolm -
> 
> I agree with you that the 1/4 wavelengths and antenna concepts for
> Tesla coils does not stand up to what is found with real world
> coils. In the TC data I have collected the secondaries of almost all
> of the coils do not conform to the 1/4 wavelength theory either for
> the actual or electrical wavelength.
> 
> This makes sense because the TC is a resonant air core transformer
> with a copacitance load and 1/4 wavelengths are not important. The
> TC is a dual RCL circuit where both primary and secondary circuits 
> must have the same resonant frequencies  for optimum output. TCs
> operate the same as standard resonant transformers and helical
> antenna concepts are not involved.
> 
> The fact that the maximum voltage is next to the top capacitance
> is typical for a transformer when the voltage is measured across
> the secondary coil with one end grounded. This is why any size
> capacitive topload can be used as long as the dual RCL circuits are
> in tune.

Agree. But I do have to point out that the coil of wire itself can be 
viewed as a Tx line because of the way L and C is distributed in it.
It is definitely not lumped but does progressively get there as more 
top C is added. With little or no topload, it is really the current 
distribution that defines the behaviour. Since there is little loading 
for the top turns the current is nearly zero in the top turns before 
discharging starts. The top turns do not contribute much to the 
inductance at all if capacitive loading is not lump-connected across 
the coil.

> Tesla always said his TC invention was not for Hertzian waves but
> for currents. Helical antennas, etc. that are Hertzian wave devices
> are not involved. I now think that the VSWR is also not involved
> because there is no transmission line to couple the coil and
> capacitor load. Note that an antenna is a resistive load at the end
> of an RF transmission line. This is not the TC type of circuit.

Agree except for the fact that one can model the coil itself as a 
line (transmitting energy to Ctop). 

> The H/D ratio concept has only to do with maximum inductance and
> little to do with transformer operation. However, higher inductance
> does mean more output with resonant tranformers.

Well that depends really on what is put in (which is why I constantly 
appeal to conservation of energy for capacitive discharge driven 
devices where there is a well defined capacitance associated with 
the secondary). I should also note that being only a fraction of a 
wavelength long, energy never ends up being lumped in a coil with 
little topload and hence is distributed according to the line 
capacitance distribution. Another point about Lsec is that the closer 
k gets to one, the closer output voltage matches the pri-sec turns 
ratio (which of course gets higher as Lsec gets higher if Lp remains 
constant).
    I also note that h/d ratio has a very pronounced effect on the Q 
of the coil. Several sources relate Q and VSWR by: VSWR = 4*Q/PI or 
thereabouts.
    Although a whip antenna looks resistive at the base, that says 
nothing about the V/I distribution along its length which is very 
similar to the coil.
    I also must reiterate my opinion that the high-L thing is 
important with regard to getting Zsurge high in the primary (given 
that one tends to use larger and larger primary caps as power level 
is upped).

Thanks for the comments,
Malcolm

P.S. - bearing the above picture in mind, It is my intention to try 
physically modelling the coil using a string of lumped L's and C's.
This is neither unique nor original. Greg Leyh produced a nice SPICE 
model which did exactly that and came up with results I think look
good. My idea is to do the same, but grade the structure using 
progressively smaller L's (and the same C's) as one gets to the "top".
I don't know if there is any great merit in doing this but I would 
sure like to see the differences.