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Numerical Jitter Minimization for PLL-Based FMCW Radar Systems

This paper presents a time-domain simulation methodology for FMCW radar systems using a noisy phase-locked loop (PLL) for frequency generation. A stochastic differential equation (SDE) is employed to describe both the high-pass filtered noise in the voltage-controlled oscillator (VCO) and the low-pass filtered input noise. The exact solution of this SDE is used to directly generate the PLL phase on a discrete time grid from VCO phase noise, input noise level, and loop bandwidth. For both heterodyne and homodyne radar systems using an overdamped PLL, the simulated steady-state phase noise spectra and rms phase jitter are in excellent agreement with an analytical model. The phase jitter and rms error in a target distance measurement are minimized by optimizing the PLL loop bandwidth as a function of the target distance. The non-stationary phase noise during a linear FMCW sweep is calculated in the time domain from circuit parameters. The PLL settling time is minimized by optimizing the loop filter capacitance for a given ramp slope.