Wide Bandpass and Narrow Bandstop Microstrip Filters Based on Hilbert Fractal Geometry: Design and Simulation Results

PLOS ONE, Dec 2019

This paper presents new Wide Bandpass Filter (WBPF) and Narrow Bandstop Filter (NBSF) incorporating two microstrip resonators, each resonator is based on 2nd iteration of Hilbert fractal geometry. The type of filter as pass or reject band has been adjusted by coupling gap parameter (d) between Hilbert resonators using a substrate with a dielectric constant of 10.8 and a thickness of 1.27 mm. Numerical simulation results as well as a parametric study of d parameter on filter type and frequency responses are presented and studied. WBPF has designed at resonant frequencies of 2 and 2.2 GHz with a bandwidth of 0.52 GHz, −28 dB return loss and −0.125 dB insertion loss while NBSF has designed for electrical specifications of 2.37 GHz center frequency, 20 MHz rejection bandwidth, −0.1873 dB return loss and 13.746 dB insertion loss. The proposed technique offers a new alternative to construct low-cost high-performance filter devices, suitable for a wide range of wireless communication systems.

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Wide Bandpass and Narrow Bandstop Microstrip Filters Based on Hilbert Fractal Geometry: Design and Simulation Results

Editor: Fuli Zhang, Northwestern Polytechnical University, China Received: August Wide Bandpass and Narrow Bandstop Microstrip Filters Based on Hilbert Fractal Geometry: Design and Simulation Results Yaqeen S. Mezaal 0 1 Halil T. Eyyuboglu 0 Jawad K. Ali 1 0 Electronic and Communication Engineering Department, Cankaya University , Ankara , Turkey, 1 Microwave Research Group, Electrical Engineering Department, University of Technology , Baghdad , Iraq This paper presents new Wide Bandpass Filter (WBPF) and Narrow Bandstop Filter (NBSF) incorporating two microstrip resonators, each resonator is based on 2nd iteration of Hilbert fractal geometry. The type of filter as pass or reject band has been adjusted by coupling gap parameter (d) between Hilbert resonators using a substrate with a dielectric constant of 10.8 and a thickness of 1.27 mm. Numerical simulation results as well as a parametric study of d parameter on filter type and frequency responses are presented and studied. WBPF has designed at resonant frequencies of 2 and 2.2 GHz with a bandwidth of 0.52 GHz, 228 dB return loss and 20.125 dB insertion loss while NBSF has designed for electrical specifications of 2.37 GHz center frequency, 20 MHz rejection bandwidth, 20.1873 dB return loss and 13.746 dB insertion loss. The proposed technique offers a new alternative to construct low-cost high-performance filter devices, suitable for a wide range of wireless communication systems. - Introduction The fractal term which indicates broken or fragmented parts was invented less than thirty years ago by one of historys most innovative mathematicians, Benoit Mandelbrot, in his pioneer work, The Fractal Geometry of Nature. Mandelbrot explained that many fractals are found in the nature that they could precisely form certain irregularly shaped objects or spatially non standardized phenomena in nature that cannot be attributed to Euclidean geometry, such as mountains or blood vessels. This means that fractals are in use with non-integer dimension. By expanding the idea of a fractional dimension, he concluded the term of fractal. He also described fractal as an irregular or fragmented geometric structure that can be divided into parts: each of which is (or approximately) a smaller-size copy of the whole. Mathematically, fractals are a kind of composite geometric shapes regularly display the property of self similarity, such that a small segment of it can be reduced as a fractional scale replica of the whole [1]. Fractals may be either random or deterministic. All obtainable fractal objects in nature are random in that they have been fashioned arbitrarily from non determined steps. Fractals that have been generated as a result of an iterative procedure, produced by consecutive dilations and conversions of a primary set, are deterministic. The fundamental fractal curves can be classified into six categories; these are Cantor, Koch, Minkowski, Hilbert, Sierpinski and Peano fractal geometries. All have the benefits of smallness and excellent quality performance. These properties attribute to fractals two basic properties: selfsimilarity and space-filling. Self-similarity stands for a piece of the fractal geometry seems to be like that of the total structure for all time while the spacefilling property means a fractal outline can be packed in a limited region as the iteration increases without increasing the whole area. The conventional fractals that generated by definite mathematic techniques always have exact self-similarity which can be known as well-regulated fractals. At present, fractal theory has been applied in many scientific research domains, and certainly turns on huge interests of microwave engineering researchers for designing latest microwave circuits and enhancing their performance in addition to miniaturization. However, this relevance rather dominantly focuses on antennas design as compared with other microwave circuit design including filters. Fractal structures can vary the current distribution of filter, and make it distributes along the conductor surface as opposed to the original simple patch surfaces, so the electric length will be increased [2, 3]. In this respect, fractals are going toward the design of a new generation of compact RF and microwave passive networks for wireless devices. Any wireless system relies on what is called the RF front-end stage which includes antennas, filters and diplexers, along with other passive elements such as capacitors, inductors and resistors. There is no problem whether the system is as influential as a cellular base-station, as sensitive as a super conducting satellite receiver or as small as a system-on-chip wireless device, the compactness and integration of such a front-end becomes always a key issue in terms of performance, robustness, packaging and cost. Fractal technology has been already applied in the miniaturization of another essential part of the wireless front-end. Compact fractal antennas for h (...truncated)


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Yaqeen S. Mezaal, Halil T. Eyyuboglu, Jawad K. Ali. Wide Bandpass and Narrow Bandstop Microstrip Filters Based on Hilbert Fractal Geometry: Design and Simulation Results, PLOS ONE, 2014, Volume 9, Issue 12, DOI: 10.1371/journal.pone.0115412