Re: New formula for secondary resonant frequency

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

Original poster: "Kurt Schraner by way of Terry Fritz <twftesla-at-uswest-dot-net>" <k.schraner-at-datacomm.ch>

Paul -

thank you very much for the good news about usefulness of my
results. I'd like to give you the most complete experimental
doc's of my coils, ...but, if it comes to precision: it's a
bottomless pit! ;o). Even geometric data appear doubtful! 

>Paul wrote:

<snip>
...
> Agreed. In the case of the B&W coil, the lack of a well defined
> ground surface provides an ambiguous termination of the external
> E-field, so the coil is outside the domain of the formula.

In fact, all my measurements suffer from this shortcoming. The
situation for B&W may be seen at

http://home.datacomm.ch/k.schraner/bw_sec.htm

> My attempts to model coils at high elevation have all failed dismally,
> due possibly to the poor definition of the return path for the
> external field - all were measured indoors. I'm still hoping that
> someone will setup a coil outdoors and high up over a good ground
> plane, so that I can see if the problem persists. Meanwhile I can
> only model reliably for b <= 1.0 and the formula is only regressed
> against data for 0.033 < b <= 0.5.
> 

The b-values were entered just from memory; they have not been
recorded before. Recognizing the influence of fb on Fres not
being too critical, I felt doing so justified.

You are right about:

> The Sk-12cm which is a smaller coil, low down, should be quite
> accurate.
> However, for Sk-12cm, something is wrong: 22 awg = 0.6438 mm diam,
> so 921 turns spans 593 mm, this is longer than your coil. Perhaps
> you can look into this?

My wire diameter was only 0.6mm originally, but at the time, I
was only using a lookup table, from which were taken truncated
integers for the AWG size. I've checked the geometric data of the
coil as well, again. The updated data look like:


Coil     Sk-12cm
turns     921 
h        0.585 
d        0.1212
b        0.2   
awg      22.6076

Fres,cal  398.0  Paul's formula
Fres,exp  368  
Diff       8.1%  cal-exp

Fres,cal  370.4  Wheeler/Medhurst
Diff      0.7%    cal-exp


I confess, a new Fres-experiment (with harmonics recording too!)
might be opportune: by the time, measuring Fres for this coil, I
was not yet owning the higher precision equipment of now. The
RF-signal-generator was only an old Heathkit laboratory
generator, where the f was read from the dial-scale. I'll go to
check it with my HP frequency counter. The problem of a compltely
new measurement is: I might need to remove a glued corona-ring
from the top of this coil, in order to perform the new
measurements, which can destroy the coil.

Paul wrote:
> Your coil Sk-Long is particularly interesting, as it falls into
> the large h/d category in which modeling predicts a resonant
> frequency some 10% higher than Medhurst. Your measurement falls
> in between the two, and I suspect that it may suffer some of the
> problems similar to the Sk-B&W, in that it is quite a large coil
> to be measured indoors.

> If it becomes possible to measure this coil
> in a large room or outdoors, over a reasonable ground plane, the
> result would be interesting. My prediction is that the absence
> of nearby walls and ceiling will reduce the external capacitance and
> raise the frequency to nearer that of the formula.

I'll try this, when the weather gets easy for it. The
measurements for this coil have been teaching me, how sensitive
to the (-capacitive-) environment such tests behave: A 0.5m free
wiping end of the winding wire, at the top of the bare coil, was
showing large movements of the resonance peak weaveform-amplitude
on my oscilloscope, when just pushed to vibration by hand.
> 
> I just ran Sk-Long through the precision model to obtain the following
> predictions for operation in an open space at b=0.5 over a ground
> plane radius at least 2m:
> 
> Ldc=67.6 mH, Cdc=35.3pF
> f1: 155.9 kHz (Lee=45.7mH, Les=52.6mH, Cee=17.2pF, Ces=19.9pF)
> f3: 383.7 kHz
> f5: 544.9 kHz
> 
> which unsurprisingly is close to the formula prediction.

Thank you for doing this calculation. I measured the values as
follows:

L =67.6 mH, ---> Measured at 120 Hz
L =67.7 mH, ---> Measured at 1 kHz

f1: 147.7 kHz 
f3: 382.45 kHz
f5: 558.42 kHz
f7: 709.28 kHz

Instruments:
Siemens Level Oscillator W2087 (200Hz...1620kHz)
Tektronix 7623 Oscilloscope
HP 5216A Electronic Counter ( up to 12.5MHz )

> 
> I also ran Sk-Long with walls introduced at radius 2m, and a ceiling
> at height 2.3m. The result is
> f1: 147.2 kHz
> which is close to your measured value. Clearly, the presence of
> walls and ceiling may well be responsible for the discrepancy with the
> formula.

The size of my living room, where i tested the coil is:
 4.93m x 4.48m x 2.84m(=heigth)
The coils have been positioned in one corner, about >= 1.5m
distance from the walls, which appears to be in a plausible
relation to your guess of 2m. I didn't record the exact height of
the base-winding in all my tests, but it should have been in the
vicinity of about 0.5m for this coil.

Best regards
Kurt Schraner