Iterative approach investigation on the fractal Hilbert curve low-pass filters: analysis and measurements
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Iterative approach investigation on the fractal Hilbert curve low‑pass filters: analysis and measurements Souad Berhab1,2 · Mehadji Abri2 · Hadjira Badaoui2 Received: 16 January 2020 / Accepted: 14 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper the iterative rigorous approach is applied flexibly to complex Hilbert filters using structured computational grids. The wave concept iterative process (WCIP) is reviewed, focusing on their fundamental conception and simple algorithm, with the presence of defected ground structure (DGS) appearing as Hilbert curve ring (HCR) cells. The selected studied filters have shown increasing levels of sophistication and complexity that have properly contributed in evaluating the WCIP performance. To attain this purpose, the simulated computational results are demonstrated by measurements, and the iterative results, accurate enough, are obtained to some extent for the more sophisticated designs. Keywords Low-pass filter (LPF) · Defected ground structure (DGS) · Hilbert curve ring (HCR) · WCIP · Wave concept · Measurements
1 Introduction For several centuries and before Maxwell’s theory, the electromagnetism science had been mostly regarded as an experimental discipline through the scientist’s works such as Benjamin Franklin, Charles Augustin de Coulomb, André Marie Ampère, Hans Christian Oersted and Michael Faraday [1]. After the validation of the Maxwell theory in 1888, by The German physicist Heinrich Rudolf Hertz, some applications started to appear, which were developed mostly using analytical solution methods [2]. At that time, the analyzed structures were qualified by their simplest geometries, as fields radiated from the Hertzian dipole, an infinitely long straight circular wire and two coaxial cones [1]. Despite this, the analytical methods found themselves indeed limited to few objects (such as a sphere) and inadequate to model the * Souad Berhab [email protected] Mehadji Abri [email protected] Hadjira Badaoui [email protected] 1
Electronic and Telecomminications Departement, University of Kasdi Merbah Ouargla, Ouargla, Algeria
STIC Laboratory, Faculty of Technology, University of Tlemcen, Tlemcen, Algeria
2
more complex material properties and geometries [3, 4]. Until the 1940s, most EM problems were solved using the classical methods [5]. After a few years, and with the help of the rapid progress in computer hardware. Thus, advances had emerged in computational electromagnetics (CEM), which involves an array of techniques, enabling to model the interaction of electromagnetic fields with the objects like antenna, waveguides and aircraft in their actual environments using computer approximations to Maxwell’s equations [6]. In doing so, many complex electromagnetic problems have been solved faster and at less cost. CEM, which is known as an interdisciplinary field, has allowed to undertake problems that could never have been attempted [7]. The numerical methods, which have their origin in the mid-1960s, a
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