Computation of the phase and amplitude noise in microwave oscillators and a simplified calculation method for far enough from the carrier offsets

New results regarding phase and amplitude noise analysis in microwave oscillators for moderate offset frequencies from the carrier are presented. Although the phase noise process in an oscillator is a large signal non-stationary process, it is proved that for the purpose of phase noise calculations for moderate offset frequencies, the phase noise process can be considered as a small signal stationary process and by this assumption, a valid approximation of the phase noise spectrum at these offset frequencies is obtained. By this consideration, a simplified approach for the purpose of the phase and amplitude noise spectrum calculations, at far enough from the carrier offset frequencies, by avoiding the numerical ill-conditioning of the harmonic balance equations, is presented. Owing to the presence of the common phase process in the circuit variables, for the practical resolution of the noise relations, it is necessary to introduce an extra constraint on the phase or the amplitude process. Here, it is theoretically proved that this constraint will not change the total noise spectrum of the oscillator. Another form of conversion matrix analysis is presented and the cause of error in the computation of the phase noise at offset frequencies near to the carrier is investigated. The theoretically verified characteristics of phase and amplitude noise analysis methods have been observed in a P-HEMT oscillator at 10.23 GHz.