Analysis of an AC LC ladder circuit with spiral vector theory

The author analyzes an AC LC ladder circuit with spiral vector theory whose state variables are time-varying complex numbers. The author obtains the analytical general solutions that consists of one fundamental frequency element and three transient oscillation frequency elements. With a numerical example, it is found that different initial phase angles of voltage source will yield completely different transient state and the author considers it is a chaos phenomenon. The author also obtains instantaneous reactive power of the circuit that has no definitions in conventional AC circuit theory. All results show that spiral vector theory is effective in AC circuit analysis