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

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

doi:10.1093/ietele/e90-c.3.628

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

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

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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.

Publication: IEICE TRANSACTIONS on Electronics Vol.E90-C No.3 pp.628-633

Publication Date: 2007/03/01

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Online ISSN: 1745-1353

DOI: 10.1093/ietele/e90-c.3.628

Type of Manuscript: PAPER

Category: Integrated Electronics

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Chia-Yu YAO, Chun-Te HSU, Chiang-Ju CHIEN, "Stability Analysis of Fourth-Order Charge-Pump PLLs Using Linearized Discrete-Time Models" in IEICE TRANSACTIONS on Electronics, vol. E90-C, no. 3, pp. 628-633, March 2007, doi: 10.1093/ietele/e90-c.3.628.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/electronics/10.1093/ietele/e90-c.3.628/_p

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@ARTICLE{e90-c_3_628,
author={Chia-Yu YAO, Chun-Te HSU, Chiang-Ju CHIEN, },
journal={IEICE TRANSACTIONS on Electronics},
title={Stability Analysis of Fourth-Order Charge-Pump PLLs Using Linearized Discrete-Time Models},
year={2007},
volume={E90-C},
number={3},
pages={628-633},
abstract={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.},
keywords={},
doi={10.1093/ietele/e90-c.3.628},
ISSN={1745-1353},
month={March},}

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TY - JOUR
TI - Stability Analysis of Fourth-Order Charge-Pump PLLs Using Linearized Discrete-Time Models
T2 - IEICE TRANSACTIONS on Electronics
SP - 628
EP - 633
AU - Chia-Yu YAO
AU - Chun-Te HSU
AU - Chiang-Ju CHIEN
PY - 2007
DO - 10.1093/ietele/e90-c.3.628
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E90-C
IS - 3
JA - IEICE TRANSACTIONS on Electronics
Y1 - March 2007
AB - 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.
ER -