Re: THOR resonance freq. simulation vs.measurement results

["Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

Tesla list wrote:
> 
> Original poster: "Marco Denicolai" <Marco.Denicolai-at-tellabs.fi>

> >To compute Z0 and T for a coil, use:
> >
> >T=(pi/2)*sqrt(Cm*L)
> >Z0=(2/pi)*sqrt(L/Cm))

> I made a quick and dirty model with MicroSim at
> http://www.saunalahti.fi/dncmrc/th_frq.htm. The 2nd and 3th res. freq. still
> don't match exactly: 240 kHz and 447 kHz instead of 222 kHz and 346 kHz. It
> seems like the model frequency shifting effect is less severe that what I
> actually measured.
> 
> Any suggestion?

Try:

T=sqrt(2*Cm*L)
Z0=sqrt(L/(2*Cm))

This models better the behavior of the coil (transmission line) at low
frequency. 
Comes from the comparison between the output admittances of a lumped
model and a transmission line model, up to second-order terms in 
frequency.

You may also try to vary the term Cm in the formulas above,
searching for a best fit, since it's empirical anyway.
The remaining error I guess that is consequence of the fact that a 
simple transmission line model doesn't describe a long coil, specially
a vertical coil above ground, perfectly. Maybe a lumped model with a
series of coupled LC sections behaves better. 

Some time ago I made measurements of the resonances of a vertical 
coil, and found that all the resonances were shifted to low frequency,
not following the expected 1:3:5:7:... ratios of an ideal transmission
line. Can you verify this by measuring the resonances without the 
top terminal?

Antonio Carlos M. de Queiroz