Dejan V. Tošić

On the analytical solution of some families of transcendental equations

The problem of finding the exact analytical closed-form solution of some families of transcendental equations is studied, in some detail, by the Special Trans Function Theory (STFT). The mathematical genesis of the analytical closed-form solution is presented, and the structure of the theoretical derivation, proofs and numerical results confirm the validity and base principle of the STFT. Undoubtedly, the proposed analytical approach implies the qualitative improvement of the conventional analytical and numerical methods.

Symbolic analysis and design of control systems using Mathematica

Contemporary computer tools can generate a tremendous amount of numerical data so the user might easily lose insight into the phenomenon being investigated. Those who use powerful computer algebra systems must thoroughly understand the assumptions that underlie the software. In this paper, the role and importance of symbolic computation in control engineering and signal processing is exemplified. Real-life application examples are presented in which systems are symbolically solved and simulated with Mathematica. We introduce an original approach to algorithm development, system design and symbolic processing that successfully overcomes some problems encountered in the traditional approach. Benefits of symbolic methods and the role of computer algebra systems are highlighted from the viewpoint of both academia and industry.

Advanced filter design

Classical filter design techniques return only one design from an infinite collection of alternative designs, or fail to design filters when solutions exist. These classical techniques hide a wealth of alternative filter designs that are more robust when implemented in analog circuits, digital hardware, and embedded software. We present (1) case studies of optimal analog and digital IIR filters that cannot be designed with classical techniques, and (2) the formal, mathematical framework that underlies their solutions. We have automated the advanced filter design techniques in software.

A new symbolic analysis approach to the DC load flow method

Abstract A new symbolic analysis approach is proposed to the DC load flow method. The power system network parameters are given by symbols and the system active line power flows are derived analytically as closed-form symbolic expressions. An original program SALF is presented as a universal tool to find the line powers by an automated computer-aided algorithm. The theory of the DC load flow method is reviewed. The approach is illustrated by standard network examples. The approach exposed is targeted at researchers and experts dealing with analysis, planning and operation of transmission power system networks.

On the Exact Analytical Solutions of Certain Lambert Transcendental Equations

The subject matter of this paper is the Special Trans Functions Theory (STFT) in finding the exact analytical closed form solutions (the new special tran functions) of certain Lambert transcendental equations. Note that these Lambert transcendental equations frequently appear in applied physics and engineering domain. The structure of the theoretical derivations, proofs, and numerical results confirms validity and basic principles of the STFT. Undoubtedly, the proposed exact analytical approach implies the qualitative improvements of the conventional methods and techniques.

MORE ABOUT SINGULAR LINE GRAPHS OF TREES

We study those trees whose line graphs are singular. Besides new proofs of some old results, we offer many new results including the computer search which covers the trees with at most twenty vertices.

A note on the modeling of transmission-line losses

We consider uniform lossy transmission lines characterized by their primary parameters. Exact and approximate formulas for the characteristic impedance and propagation coefficient are reviewed and discussed for low-loss lines. Approximating the characteristic impedance by its real part can lead to erroneous results for the input impedance of short- and open-circuited stubs. This problem is analytically demonstrated on electrically short stubs. Results obtained using the exact and approximate expressions are compared with numerical solutions that are generated by various circuit simulation software.

Compact Dual-Band Bandpass Waveguide Filter with H-Plane Inserts

A novel compact dual-band bandpass waveguide filter is presented in this paper. H-plane metal inserts with complementary split-ring resonators are implemented as resonating elements in the standard (WR-90) rectangular waveguide. Design starts from the models of the waveguide resonators with two resonant frequencies (9GHz and 11GHz) using a single flat or folded metal insert. Further, folded inserts are used for the second-order dual-band filter design. The equivalent circuits are proposed for the considered waveguide resonators and filter. A good agreement of the amplitude responses obtained for three-dimensional electromagnetic models and microwave circuits is achieved. Finally, compact dual-band bandpass waveguide filter is proposed as a novel solution using miniaturized inverters for both central frequencies. Compact filter model is further modified in order to obtain solution customized for easier fabrication. For the compact filter model, amplitude response is experimentally verified. The required filter response is preserved, as verified by a good agreement of the results obtained for the original dual-band filter and for the compact filter solutions.

Design and analysis of bandpass waveguide filters using novel complementary split ring resonators

This paper presents models of the bandpass waveguide filters using novel complementary split ring resonators. These resonators are employed as single-mode and dual-mode. Dual-mode resonators are developed from the single-mode ones. The filter response is analyzed in terms of various parameters of the resonators. The possibility to independently tune single-mode resonators, contained in the dual-mode resonator, is also investigated, in order to evaluate this solution for modeling of the resonators with multiple resonant frequencies.

Symbolic approach to 2D biorthogonal diamond-shaped filter design

Currently, a popular method for the design of nonseparable multidimensional FIR filters is the application of the well known McClellan transform, for the selected sampling lattice. Derivation of these transforms is straightforward, yielding closed-form expressions for the impulse response matrices. Hence, this problem is ideally suited for computer-aided, fully automated symbolic analysis. This paper presents a new general symbolic implementation of the McClellan transformation for the construction of diamond shaped filters, in Mathematica. The source code and design examples are given.