Size reduction and bandwidth enhancement of snowﬂake fractal antenna B. Mirzapour and H.R. Hassani Abstract: A new small-size and wideband fractal antenna in the shape of a snowﬂake is proposed. Various iterations of this fractal antenna with probe feed and capacitively coupled feed are com- pared and an optimised design is presented. It is shown that, with an air-ﬁlled substrate and capaci- tive feed, an impedance bandwidth .49% and, with a slot-loading technique, a reduction of about 70% in patch surface size compared with an ordinary wideband Koch fractal antenna are achiev- able. The simulation via a ﬁnite-element programme, and measured results on the return loss and the E and H-plane radiation patterns of the proposed antennas are presented and shown to be in good agreement. 1 Introduction Owing to the progress in wireless communication systems and increase in their applications, small-size and wideband antennas are in great demand. These have recently received a great deal of attention from researchers creating new antenna structures. One such structure is the fractal-shaped antenna. Fractal antennas, due to the concept of self-similarity and inﬁnite complexities and detail in their geometrical proper- ties, allow for smaller, multiband and broadband antenna design [1]. Miniaturisation of fractal antennas has been shown for the Koch wire monopole [2–4], Sierpinski monopole [5] and microstrip rectangular patch antennas [6–8] where fractal boundaries are incorporated along the patch edge to reduce the size of the patch. On bandwidth enhancement, Borja and Romeu [9] have given results on the microstrip Koch antenna resulting in 17% bandwidth (3.2 – 3.8 GHz), whereas Nahshon et al. [10] have used the same structure along with a cavity and a sleeve-type of feed to obtain a maximum 72% bandwidth (10 – 21 GHz). In [11], signiﬁcant size reduction along with ultra-wide band behaviour with frequency notches in the range is offered via a Koch fractal slot fed by a fork-like microstrip line. Since the original work of Mandelbrot [12], a wide variety of new shapes and applications for fractals continue to be found [13]. Snowﬂake, naturally occurring fractal geo- metry, is one such shape that can be employed for antenna design [14]. In this paper, we report the study of a new design of snowﬂake fractal for a small-size and broadband antenna based on the natural shape of snowﬂake crystals [14]. Unlike the original Koch antenna construction reported in the literature in which smaller elements are added to the basic structure, in the new design, for higher iterations, the smaller elements are subtracted, leading to antenna structures similar to snowﬂakes found in nature [14]. Through proper selection of the feed and slot-loading tech- nique, signiﬁcant bandwidth enhancement and size reduction compared with the original Koch antenna can be achieved. A 49% increase in bandwidth and 70% reduction in radiating surface area through both simulation and experiments are obtained. Return loss and radiation pattern results are provided. Details are described and results are presented and discussed. 2 Antenna geometry The structure of the proposed antenna is based on the modi- ﬁcations made to the original Koch fractal antenna. The original Koch antenna starts out with two united solid equilateral triangles in the same plane, as illustrated in stage 1 of Fig. 1. This is the simplest Koch antenna. Higher iterations of the Koch antenna are constructed by adding smaller and smaller triangles to the structure, as shown in stages 2–4 of the same ﬁgure. The design pro- cedure of the original Koch antenna is provided in [15]. To obtain the new proposed antenna, a simple method is to subtract, and not add, the small triangular patches from the original Koch antenna. The resulting antenna is illustrated as the black area of Fig. 1 for four sequences of iterations. It is obvious that this procedure is inverse to that of constructing the original Koch antenna; as such, one might be able to call this proposed antenna ‘inverse Koch’ or ‘snowﬂake antenna’. The original Koch antenna is usually deﬁned in terms of an equivalent radius of circle, R 2 , and a number, which deﬁnes the order of iteration (Fig. 1). Similarly, the same deﬁnition can be used to characterise the new snowﬂake geometry, shown with radius R 1 . As can be seen in the next section, the radiating surface of the new optimised snowﬂake antenna can be almost as small as one-third of that of the original Koch antenna. To obtain a large impedance bandwidth behaviour from such an antenna, usually a thick substrate along with an air/foam is employed. Direct probe-fed microstrip antennas with a thick substrate have the problem of large probe reac- tance but capacitive feeding the patch antenna overcomes such problems. It has been shown that good impedance # The Institution of Engineering and Technology 2008 doi:10.1049/iet-map:20070133 Paper ﬁrst received 10th February and in revised form 1st October 2007 The authors are with the Shahed University, Electrical & Computer Engineering Department, No. 7, Unit 7, Shahrokh Alley, Africa Blvd, Tehran 1915713495 , Iran E-mail: hassani@shahed.ac.ir IET Microw. Antennas Propag., 2008, 2, (2), pp. 180–187 180