Novel dissipative Lagrange-Hamilton formalism for LC/van der pol oscillator with new implication on phase noise dependency on quality factor

A novel method of doing co-ordinate transformation for LC/van der pol(vdp) oscillator is proposed. It allows vdp to be solved as a conservative system by applying Hamiltonian formulation using calculus of variation. The procedure is developed to calculate the constant of integration, a generalized concept of energy. Such constant of integration, which is different from energy, has implication on the dependency of phase noise on quality factor Q. This is examined, which shows that the traditional dependency on Q is not totally correct.