Abstract: A new formulation is presented for the analysis of phase-locked loops (PLL). It is based on the use of a realistic reduced-order model for the voltage-controlled oscillator, extracted from harmonic-balance (HB) simulations. An HB formulation of the reduced-order PLL equations enables an efficient analysis of the PLL in unlocked conditions, and therefore, prediction of common hysteresis phenomena. The injection-pulling effects in the presence of interference signals are analyzed taking into account the nonlinearity of the phase detector. The interfered PLL in locked conditions is analyzed with a single-tone HB formulation of the reduced-order system, whereas a two-tone HB analysis is used for the analysis in unlocked conditions. The frequency-domain formulation enables an accurate and efficient prediction of the effect of the interferer on the hold-in and lock-in ranges, here investigated, to our knowledge, for the first time. The analysis has been successfully applied to a PLL operating at 5.3 GHz.

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