Hi,

Tesla coil is represented by these two 2º order equations if resistance is R1=R2=0

(1/C1) q1 + L1 q1'' + M q2'' = 0 ("primary" net kirchoff equation)

(1/C2) q2 + L2 q2'' + M q1'' = 0 ("secondary" net kirchoff equation)

I know from two scientific articles that characteristic equation is:

(1 - M^2/(L1 L2) ) D^4 + (w1^2 + w2^2) D^2 + (w1^2 w2^2) = 0

with wi = 1/sqrt(Li Ci)

I couldn´t find any source where it is derived and would like to check it. The problem is that I have no clue about how to get to that 4th order characteristic equation!

maybe a change of variable?

If someone could help many thanks.