Improved Structured Filter Design And Analysis Of Perturbed Pll Systems With Convex Optimizations
Phase-locked loops (PLLs) are essential circuits that are widely used in many applications such as communication and electronic systems. The importance of this circuit has prompted a great interest among researchers in studying and analyzing the stability and performance of PLL systems. Although...
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Main Author: | |
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Format: | Thesis |
Language: | English |
Published: |
2020
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Subjects: | |
Online Access: | http://eprints.usm.my/48037/1/Improved%20Structured%20Filter%20Design%20And%20Analysis%20Of%20Perturbed%20Pll%20%20Systems%20With%20Convex%20Optimizations.pdf |
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Summary: | Phase-locked loops (PLLs) are essential circuits that are widely used in many applications
such as communication and electronic systems. The importance of this circuit
has prompted a great interest among researchers in studying and analyzing the stability
and performance of PLL systems. Although many analyses are based on linearized
models of the PLL system, the stability of the PLL is not guaranteed as the system may
be interrupted by internal and external perturbations which include nonlinear behavior
from the PLL components as well as time delay. As these perturbations lead to higher
probability of performance degradation and instability, recent works have shown an increasing
amount of research into a more accurate modeling of PLL system and analysis
on the impacts of such uncertainties to the overall system’s behavior. In this study, a
new approach to systematically model the nonlinear behavior of the PLL and to design
the filter which is responsible to determine the system’s stability and performance is
proposed. This approach is based on the H¥ control synthesis which is also integrated
with a suitable nonlinear stability criterion. The resulting methods are then formulated
into convex optimization problems which can guarantee optimality of the designed parameters.
The results are then extended to applications of frequency synthesis which is
also subject to the unwanted perturbations. A further extension of the proposed method
is on the analyses of the PLL system that is also subject to time delay, which may be
inherent from the system itself or artificially introduced to meet a certain PLL design
requirement. The current findings reveal that the tracking capability of the PLL system
can be theoretically enforced via the proposed methods which consequently lead to a
wider lock range by 59% and a faster acquisition time by 22% as compared to the linear
approximation method. Additionally, the results also show that the PLL system with
the filter designed via the proposed method outperforms the existing methods. For example,
when the proposed method is compared with the (Ahmad, 2017), the proposed
method is able to produce a larger lock-in range by 87% with faster acquisition time by
5733% than that method. The results are also validated via a series of simulations and
experiments which demonstrate the efficiency of the proposed methods in enhancing
the frequency synthesis PLL performance. Apart from that, the analyses on the PLL
subject to both nonlinearity and time delay have additionally been found to be beneficial
in PLL design due to the systematic modeling method introduced along with
the convex optimization techniques. It can also be concluded that this study has led
to a new approach to further improve the real PLL structure with low computational
complexity in the design and analysis methods. |
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