Complete and Systematic Simulation Tools for Frequency Divider Design

In this study, a two-stage simulation method is presented for the efficient design of frequency dividers using harmonic balance. The first stage uses a modified conversion matrix approach to select the subharmonic loads of the active element enabling the frequency division by a given order $N$. The second stage makes use of an auxiliary generator to obtain and modify the sub-harmonic-power curve versus the input power or input frequency. Systematic simulation tools are used to eliminate common hysteresis phenomena, which require additional constraints to minimize the disturbance of the original frequency-division bands and output power. A harmonic-balance technique to distinguish between subcritical flip bifurcations, associated with hystereses, and supercritical ones is presented, to our knowledge, for the first time. A technique is also derived to transform subcritical bifurcations into supercritical ones. The techniques have been successfully applied to a frequency divider by 2 at 630 MHz.