A Nonlinear Transient Analysis of Regenerative Frequency Dividers

This paper introduces a nonlinear analysis of tuned regenerative dividers that explores into the transient behavior of the system. Broadly, two such divider implementations have been dealt with, tuned regenerative dividers and injection locked dividers. A detailed nonlinear analysis based on the application of Stroboscopic concept and the first-order perturbation method is used to derive closed-form expressions for start-up condition, output amplitude, maximum operating bandwidth, and frequency spectrum when regenerative dividers go out of ldquolockingrdquo range. Based on the developed theory, design guidelines for high frequency regenerative dividers have been charted out. The results are verified through extensive numerical and SpectreRF simulations of several gigahertz dividers in 0.18- CMOS technology.