tesla coil model

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

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.

where: l1,r1,c1 are the primary circuit inductance,resistance and capacitance
            l2,r2,c2 are the secondary circuit inductance,resistance and 
capacitance
            m = mutual inductance = k*sqr(l1*l2) were k = coupling coef.
q1,q1d and q1dd are the primary charge, charge dot ( current ) and charge 
double dot ( current dot ).
q2,q2d and q2dd are the secondary charge, charge dot ( current ) and charge 
double dot ( current dot ). dot is the time derivative.

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. 
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.
what I found interesting was:
1) The energy of the case with losses was 42% of the no loss case.
2) The first notch for the case with losses was earlier than the no loss case.

Russ Edmonds