Re: How to Tune a Flat Spiral Coil

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

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

Dave Thomson wrote:
> The 6.23mH coil is a trifilar coil in a wye formation.

Ok, lets stick with that one for now, so things don't get too
confusing.

> It's not physically possible that the turns count for each of the
> three strands would be 224 with the dimensions of this coil. I have
> not physically counted the wires.  Next time I have to coil apart,
> I'll count the turns.

Yes, do that if you get the chance, because your L and R measurements
both point to having rather more turns than you believe.
Are your single-strand and trifilar coils of roughly the same
construction - maybe you can weigh them to see if they have the same
amount of copper in them?

For now, I'll assume 224x21awg because that is the model that fits the
measurements, in fact, 222 turns fits better, so I'll use that!

     74.6 turns      222 turns       Measured
L       0.7mH          6.2mH         6.20mH to 6.25mH
R       1.8 ohm        5.3 ohm       5.2 ohm to 5.3 ohm

> On the wye coil mentioned above, the primary is 1/4" above the
> secondary.  The last turn of the secondary is 1/2" radius away from
> the inside turn of the primary.  The primary is composed of 3.5
> turns of 1/4" OD copper tubing with about 1/4" space between turns.

Right, I'll put that into the model...here we go:

units inches
secondary {
   radius1 1/4/2     ;  Core is a 1/4" brass bolt
   radius2 13.75/2   ;  Outer diameter of 13.75"
   height 0 conductor 21 awg
   turns 222         ; Assumed value to match L and R measurements
}
primary {
   radius1 13.75/2 + 1/2  ; Inner of primary is 1/2" beyond sec outer
   radius2 13.75/2 + 1/2 + 1/2*3.5  ; 3.5 turns at 1/2" pitch
   height 1/4
   conductor 1/4/2     ; 1/4" OD copper tubing
   turns 3.5
}

    SCNY.L| SCNY.R|    PRMY.L| PRMY.R| SCNY-PRMY.M|SCNY-PRMY.K
6201.85 uH|   5.29|  10.05 uH|   0.00|    96.76 uH|     0.3875

So your primary should measure 10.0 uH, and the system has a k factor
of around 0.39,  that's a pretty high k factor compared with normal
TCs, but you are still below the critical k value at which the primary
and secondary resonances merge into one, so that's good.

> I measured 345KHz as the resonant frequency on the single wound
> coil...voltage reading was above 20V.  When tuned to 345KHz the
> voltage was down to 1.7V...I used a 470 Ohm resistor.

Good work.  Your ideas may be wacky, but I'm getting the impression
that your're OK at taking measurements!

> ... wye coil using the same technique, I got a resonant
> frequency of 325KHz. 

OK, then to tune your 10.0uH primary to this 325kHz would require a
primary cap of around 24nF, or 0.024uF. 

> the wye coil required a .02uF capacitor

Looks like you are tuning more or less correctly then.  Great stuff. 

The voltage step-up ratio from primary to secondary should be around
sqrt( 6230/10.0) or around 25, ie a 10kV bang would give a secondary
peak of 250kV providing nothing breaks down first.

Can you go on to measure the next two higher resonances above 325kHz? 

> I find that grounding the outer end does not change the operation
> of the coil much.  Only when the system is out of tune does a ground
> seem to make any difference.

Yes, a mere 3/4" gap from secondary outer to primary inner will
effectively clamp the outer end(s) of the secondary to earth by virtue
of the (probably quite large) capacitance between the two. So adding
a ground to the outer might not make much difference.

Great job with the measurements.  Everything fits together, except for
your conviction about the turns.

Harvey wrote (in a parallel thread):
> I think that we can also categorize flat wound
> spirals as a sort of reverse effect where the coil
> appears more as a single plate capacity, in which case
> the resonant frequency instead goes far below what
> the quarter wavelength consideration gives

Hi Harvey, we can test that with Dave's measured Fres.  325khz has
a free-space quarter wave of around 230 metres, and the wire length
of each strand, I'm assuming, is 124 metres (based on 222 turns!),
which would be a free-space straight-line 1/4 wave resonance at around
600kHz.  Thus, I think you're right Harvey, the Fres (of this spiral
at least) is far below the original wire resonance, which is opposite
to what happens in a solenoid secondary. 

Two things could cause this: Either or both:
a) The effective inductance is very high, due to the action of 
internal (in this case radial) capacitance.  We see this effect is
short H/D solenoids, and I rather think it may be much more pronounced
with the spiral, especially a narrow one!!!
b) The total external capacitance of the secondary is much greater, 
either because this is a characteristic of the spiral itself, or 
because Dave's setup is adding extra C, eg by the coil being sat on a
table, proximity of primary, or something like that.

I'm really hoping for (a) because that will make spiral TCs very
efficient (cf John Freau efficiency theory).  We really don't want
(b) because that will decimate efficiency (much more bang energy is
needed to reach a given voltage).

> observation made with a single 50 ft spiral is that
> scoping shows a 1 us cycle time for its resonant
> frequency, thus this is actually almost a 5 fold
> reduction of the quarterwave length value.

Please report the dimensions and turns of this spiral, and we'll work
it out.  

> its increased voltage between winds compared
> to the traditional high H/d tesla secondary would
> seemingly make it only a candidate for reduced
> performance.

A very good point. Take Dave's 250kV over 220 turns, thats rather
higher than in a conventional TC. 

Once the tssp simulator is modified to do these coils, all, I hope,
will be revealed.

And finally, Dave, please don't try to say Ohm's law doesn't work in
a spiral - instead, try to bottom this turns issue!
--
Paul Nicholson
--