Summary

This paper extends the Part 1 time-domain analysis of a 2nd-order PLL with a proportional+integral (lead-lag) loop filter into the Z-domain, deriving discrete transfer functions and examining discrete-time behavior. The reader will learn how to analyze stability, transient response, and design loop-filter coefficients for digital implementations.

Key Takeaways

• Derive the closed-loop z-domain transfer function for a 2nd-order digital PLL with a proportional+integral loop filter.
• Analyze stability and transient response using pole-zero plots, root-locus and z-plane methods.
• Design digital PI (lead-lag) loop-filter coefficients to meet bandwidth and damping specifications.
• Translate continuous-time PLL parameters to discrete equivalents using common mappings (e.g., bilinear/Tustin) and assess their effects.

Who Should Read This

Engineers experienced in DSP or control theory who design or implement digital PLLs for communications, radar, or real-time systems and who are comfortable with z-transform and stability analysis.

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