A new methodology is presented for the efficient harmonic-balance simulation of injection-locked oscillators with complex multivalued and disconnected curves. It is illustrated through its application to high-order subharmonically injection-locked oscillators. A graphical technique is applied to analyze the oscillator-phase sensitivity with respect to the input signal, required for the injection-locked operation. The intricate synchronized-solution curves are obtained with the new method, which enables a global exploration of all the coexistent periodic solutions. These solutions can belong to different curve sections, in a multivalued response, or to disconnected synchronization curves. The method is based on the calculation of a series of phase-dependent outer-tier admittance functions, which provide the oscillator response to the injection signal. Coexistent solutions are simultaneously obtained through a contour-plot intersection, without the need for continuation techniques. The method is illustrated through application to an oscillator synchronized to low-frequency sinusoidal signal by means of a nonlinear-transmission line. The analysis and design techniques have been successfully validated through comparison with independent simulations and measurements.

This work was supported by the Spanish Ministry of Economy and Competitiveness under the research project TEC2014-60283-C3-1-R, the European Regional Development Fund (ERDF/FEDER) and Juan de la Cierva Research Program IJCI-2014-19141 and by the Parliament of Cantabria under the project Cantabria Explora 12.JP02.64069.