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.
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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)