Harmonic-balance techniques for the design of coupled-oscillator systems in both unforced and injection-locked operation

This paper presents harmonic-balance techniques for the analysis and synthesis of coupled-oscillator systems. Compared to previous works, a realistic calculation of the system solution is carried out, using accurate models of the linear and nonlinear elements and taking into account the influence of harmonic terms. Good harmonic-balance convergence is enabled by the system symmetry. The techniques allow an accurate determination of the oscillator elements and tuning voltages in order to achieve a particular phase distribution. Different operation modes are studied and compared. Unforced operation is initially considered. Then, single and double injection from an external synchronization source is analyzed. The instability phenomena delimiting the maximum achievable phase shift are studied through pole-zero identification and bifurcation-detection techniques. Phase noise is calculated through the carrier modulation and conversion-matrix approaches. For validation, an array of four oscillators, operating at 5 GHz has been designed and implemented with very good experimental results.