Re: tesla coil model

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

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:

 > Original poster: Redmo-at-aol-dot-com

 > Hello list members, I have been lurking on this list for several years now,
 > and thought I would share some computer simulation results of my small
 > static gap tesla coil. I modeled the two coupled LCR circuits as:
 >
 > l1*q1dd + m*q2dd + r1*q1d + c1/q1 = 0.
 > l2*q2dd + m*q1dd + r2*q2d + c2/q2 = 0.
 >...
 > I used the following values as measured from my small tesla coil:
 > primary: l1 = 8.8 uH, r1 = 2.07 ohms, c1 = 6.9 nF
 > secondary: l2 = 6.2 mH, r2 = 220 ohms, c2 = 9.79 pF
 > I estimated r1 from the primary ringdown with out the secondary in place
 > (30% power) and estimated r2 as 2 times the DC resistance (110 ohms, 26 awg
 > wire)
 > I first checked the model with the no loss case: r1 = r2 = 0. and k = .105
 > , I assumed primary capacitor was charged to 10 kv when the spark gap fired
 > ( t = 0.) the results were v2 (q2/c2) max = -265.5 kv at time = 7.32 uSec.

Agrees with my simulator Teslasim.
(http://www.coe.ufrj.br/~acmq/programs)

 > this v2 value agrees with v2 max = 10kv*sqrt(c1/c2) and the plot of v2,v1
 > vs time shows the first notch at 5 cycles, which agrees with theory for k =
 > .105
 > I next ran the same case with r1 = 2.07 ohms and r2 = 220 ohms. the results
 > were: v2 max = -171.9 kv at time = 5.78 uSec.

Agrees too.

 > what I found interesting was:
 > 1) The energy of the case with losses was 42% of the no loss case.

Ok too. Note that almost all the loss is in the primary resistor, and
that if you increase k the losses are smaller.

 > 2) The first notch for the case with losses was earlier than the no loss 
case.

Because some energy was lost before being transferred.

Antonio Carlos M. de Queiroz