A bode plot study of tuning Resonant Transformers.
1) Primary and Secondary Resonance Top left circuit
Starting with the base input frequency the primary resonance is the RC series resonance f= 1/{2.pi.(LpCp)^1/2} and the secondary resonance f= 1/{2.pi.(LsCs)^1/2} where Ls=Lp.n^2 secondary inductance = primary inductance x turns ratio squared. Turns Ratio n = Ns/Np in this convention.
2) Primary Resonance only below top left. f= 1/{2.pi.(LpCp)^1/2}
3) Secondary Resonance Top mid-right tuned Secondary Resonance Ls=Lp.n^2 so f= 1/{2.pi.(LsCs)^1/2}
4) Secondary Resonance Top right tuned to Mutual Inductance M = m(Lp.Ls)^1/2 where coupling coefficient m=1, this tuning didn’t result in any improved coupling. with Cs reactance matching M mutual reactance.
5) Middle of top left Secondary Resonance tuned to double base frequency 2.f = 1/{2.pi.(LsCs)^1/2} improvement
6) Lower left Secondary Resonance tuned to Fourth harmonic of base frequency 4.f= 1/{2.pi.(LsCs)^1/2} near convergence on bode plot maximum output of Resonant Transformer.
7) Primary Mutual resonant at the Mutual Inductance f= 1/{2.pi.(M.Cp)^1/2}, Secondary Resonance at f= 1/{2.pi.(LsCs)^1/2} improved performance. Middle right.
8) Mixed mode start at Primary Resonance Mutual and Secondary Resonance then switch to Ring Down mode switch to Primary Resonance Feed and Secondary Fourth Order Harmonic frequency increases 4 fold in this mode.
Toggle the switches to observe the resonant peaks switch in and out, Bottom right.
