Stability Analysis of Fourth-Order Charge-Pump PLLs Using Linearized Discrete-Time Models

Chia-Yu YAO  Chun-Te HSU  Chiang-Ju CHIEN  

IEICE TRANSACTIONS on Electronics   Vol.E90-C   No.3   pp.628-633
Publication Date: 2007/03/01
Online ISSN: 1745-1353
DOI: 10.1093/ietele/e90-c.3.628
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Integrated Electronics
charge-pump,  phase-locked loops,  state equation,  stability,  

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In this paper, we derive state equations for linearized discrete-time models of forth-order charge-pump phase-locked loops. We solve the differential equations of the loop filter by using the initial conditions and the boundary conditions in a period. The solved equations are linearized and rearranged as discrete-time state equations for checking stability conditions. Some behavioral simulations are performed to verify the proposed method. By examining the stability of loops with different conditions, we also propose an expression between the lower bound of the reference frequency, the open loop unit gain bandwidth, and the phase margin.