Kurokawa's noise spectra of microwave oscillators in terms of closed-loop gain

In this study, the authors have derived the amplitude and phase-noise spectra of microwave oscillators based on the Kurokawa's method. The derived formulations are expressed in terms of the closed-loop gain of feedback circuits, which can be easily calculated by a special oscillation test element available in commercial microwave CAD software. To verify the derived formulations, the phase noise of a Colpitts oscillator is calculated and compared with the results computed by a commercial harmonic balance simulator.