Nonlinear analysis tools for the optimized design of harmonic-injection dividers

New nonlinear analysis tools for harmonic-injection dividers are presented based on bifurcation concepts. The advantage of these tools is their application simplicity and efficiency, which has enabled their use for actual circuit design and optimization. The tools allow control over the divided frequency and output power and predict the variation of the synchronization bands versus the circuit element values, which facilitates design correction. They have been extended to the analysis and optimization of phase-locked harmonic-injection dividers, which contain a low-frequency feedback loop. The use of this loop, together with the accuracy of the analysis, has enabled the implementation of novel frequency-division functions, such as the division of variable order, versus a circuit parameter, or the division by fractional order. The output noise of the frequency dividers is analyzed through the conversion-matrix approach, studying the noise variation along the division bands. The new techniques have been applied to the design of a frequency divider by order 4 and 5, with 18-GHz input frequency, and excellent agreement with experimental results has been obtained.