In low power, battery-operated, portable applications, like cell phones, PDAs, digital cameras, etc., miniaturization at a low cost is a prominent driving factor behind product development and marketing efforts. As such, power supplies in portable applications must not only conform and adapt to their highly integrated on-chip and in-package environments but also, more intrinsically, respond quickly to fast load dumps to achieve and maintain high accuracy. The frequency-compensation network, however, limits speed and regulation performance because, in catering to all combinations of the output capacitor, its equivalent series resistance Resr, and the power inductor resulting from tolerance and modal design targets, it must compensate the worst-case condition and therefore restrain the performance of all other possible scenarios. Sigma-delta control, which addresses this issue in buck converters by easing its compensation requirements and offering one-cycle transient response, has not been able to simultaneously achieve high bandwidth, high accuracy, and wide LC-Resr compliance in boost (step-up) converters. This thesis investigates and presents techniques to achieve sigma-delta control in boost converters by essentially using explicit current and voltage control loops. The proposed techniques are developed conceptually and analytical expressions for stability range and transient response are derived. The proposed concepts are validated and quantified through PCB and IC prototypes to yield 1.41 to 6 times faster transient response than the state of the art in current-mode boost supplies, and this without any compromise in LC-Resr compliance range.

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The design of nearly linear-phase recursive digital filters using constrained optimization is investigated. The design technique proposed is expected to be useful in applications where both magnitude and phase response specifications need to be satisfied. The overall constrained optimization method is formulated as a quadratic programming problem based on Newton’s method. The objective function, its gradient vector and Hessian matrix as well as a set of linear constraints are derived. In this analysis, the independent variables are assumed to be the transfer function coefficients. The filter stability issue and convergence efficiency, as well as a ‘real axis attraction’ problem are solved by integrating the corresponding bounds into the linear constraints of the optimization method. Also, two initialization techniques for providing efficient starting points for the optimization are investigated and the relation between the zero and pole positions and the group delay are examined. Based on these ideas, a new objective function is formulated in terms of the zeros and poles of the transfer function expressed in polar form and integrated into the optimization process. The coefficient-based and polar-based objective functions are tested and compared and it is shown that designs using the polar-based objective function produce improved results. Finally, several other modern methods for the design of nearly linear-phase recursive filters are compared with the proposed method. These include an elliptic design combined with an optimal equalization technique that uses a prescribed group delay, an optimal design method with robust stability using conic-quadratic-programming updates, and an unconstrained optimization technique that uses parameterization to guarantee filter stability. It was found that the proposed method generates similar or improved results in all comparative examples suggesting that the new method is an attractive alternative for linear-phase recursive filters of orders up to about 30.

The design of nearly linear-phase recursive digital filters using constrained optimization is investigated. The design technique proposed is expected to be useful in applications where both magnitude and phase response specifications need to be satisfied. The overall constrained optimization method is formulated as a quadratic programming problem based on Newton’s method. The objective function, its gradient vector and Hessian matrix as well as a set of linear constraints are derived. In this analysis, the independent variables are assumed to be the transfer function coefficients. The filter stability issue and convergence efficiency, as well as a ‘real axis attraction’ problem are solved by integrating the corresponding bounds into the linear constraints of the optimization method. Also, two initialization techniques for providing efficient starting points for the optimization are investigated and the relation between the zero and pole positions and the group delay are examined. Based on these ideas, a new objective function is formulated in terms of the zeros and poles of the transfer function expressed in polar form and integrated into the optimization process. The coefficient-based and polar-based objective functions are tested and compared and it is shown that designs using the polar-based objective function produce improved results. Finally, several other modern methods for the design of nearly linear-phase recursive filters are compared with the proposed method. These include an elliptic design combined with an optimal equalization technique that uses a prescribed group delay, an optimal design method with robust stability using conic-quadratic-programming updates, and an unconstrained optimization technique that uses parameterization to guarantee filter stability. It was found that the proposed method generates similar or improved results in all comparative examples suggesting that the new method is an attractive alternative for linear-phase recursive filters of orders up to about 30.

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Diploma thesis deals with circuits contain fractional-order elements. The first part of this paper deals with this problem, there were also described methods of design fractionalorder elements and types of circuits containing the fractiona-order elements which can be applied in practice. Used active elements for practical part can be found in the second chapter. Design of GIC circuits and implementation of fractional-order element inside the circuit are shown in the last chapture. Parasitic analysis and stability of frequency filter containing fractional-order element had been also described.