This paper aims to provide a symplectic conservation numerical analysis method for the study of nonlinear LC circuit.
The flux linkage control type nonlinear inductance model is adopted, and the LC circuit can be converted into the Hamiltonian system by introducing the electric charge as the state variable of the flux linkage. The nonlinear Hamiltonian matrix equation can be solved by perturbation method, which can be written as the sum of linear and nonlinear terms. Firstly, the linear part can be solved exactly. On this basis, the nonlinear part is analyzed by the canonical transformation. Then, the coefficient matrix of the obtained equation is still a Hamiltonian matrix, so symplectic conservation is achieved.
Numerical results reveal that the method proposed has strong stability, high precision and efficiency, and it has great advantages in long-term simulations.
This method provides a novel and effective way in studying the nonlinear LC circuit.
