How do you analyze PLL loop dynamics and design the loop filter for optimal performance?

PLL loop dynamics are analyzed using linearized s-domain model: Phase detector gain Kpd (V/rad), VCO gain Kvco (rad/s/V), divider ratio N, and loop filter transfer function F(s). Open-loop gain = Kpd*Kvco*F(s)/N. Design goals: Phase margin > 60 degrees for stability, Loop bandwidth (typically 1/10 to 1/20 of reference frequency) trades off lock time vs phase noise, Damping factor around 0.707 for critical damping. For charge-pump PLL, second-order filter with series R-C creates a zero for phase margin; third-order adds pole to reduce reference spurs. Phase noise analysis requires considering VCO noise, reference noise, and loop bandwidth effects.