A closed-form phase noise solution for an ideal LC oscillator

A closed-form impulse response is derived for a parallel RLC circuit. Modeling thermal noise as current impulse injections to the circuit, the phase and amplitude noise of an ideal LC oscillator are obtained using the closed-form RLC impulse response. Furthermore, the Taylor series expansion method is used to obtain a linearized phase noise model. For this linearized model, the phase change function obtained from our solution verifies the impulse sensitivity function (ISF) from previously published results. Meanwhile, since this close-form solution is non-linear in its original form, the proposed solution can potentially facilitate a non-linear power spectrum analysis of the phase noise in an ideal LC oscillator.