Wireless communication has taken on an important dimension courtesy of the diversity and especially the exponential increase of communicating objects. Their tools are becoming much smaller and therefore, demands of antennae with small size, light weight and high performance are highly sought after. However, broadband and multiband antennae are required to effectively meet these ever-increasing needs [1]. The different types of proposed antenna to date have their advantages and limitations in the various applications. Thus, the printed antennae have presented a very widespread interesting potential to meet these needs thanks to their easy integration on planar as well as non-planar surface [2–3]. Its narrow bandwidth [4] could have disqualified it, but, several combined approaches are exploited to reduce its size and to enhance performance. Among the most frequently used methods for optimizing the performance and miniaturization of MPA antennae are: the approach of optimization algorithms, the use of materials properties of the dielectric substrate, and the modification of the antenna geometric structure [5].
Various methods based on the optimization algorithms approaches to reduce the size of MPAs and improve their performance have been widely proposed in recent decades. Moreover, these algorithms have been more used to improve antenna properties such as directivity, gain, or bandwidth radiation pattern, but the widening of their use in the miniaturization approaches MPAs has proven their effectiveness. Among the most used optimization algorithms, we distinguish: Genetic Algorithms (GA), Particles Swarm Optimization (PSO), and Social Spider Algorithm (SSA) [5]. Whether one algorithm or the other, each has been used variously in appropriate cases.
Many researches have been conducted on GA in antenna design and they have resulted in a trade-off between enhancement property and size reduction. In [6], GA was applied during the design of a rectangular MPA of dimension 53.7 x 47.2 x 1.6 \({mm}^{3}\) resonating at 2.40 GHz having a return loss of -32 dB. According to the fitness principle of GA of each individual in a population, the converged result was achieved after the \({10}^{th}\) generation. Therefore, the proposed antenna has performed a frequency of 2.402 GHz and its size was reduced to 38.7 x 35.5 x 1.6 \({mm}^{3}\). Hence, a reduction rate of 45.8% was achieved. A similar process to the previous one was materialized in [7] on a conventional MPA of dimension 24.6 x 21 x 2 \({mm}^{3}\). Based on the fitness function, the best result was achieved after the \({40}^{th}\) generation. The size of the antenna was reduced up to 22 x 17.6 x 2 \({mm}^{3}\). Like the GA, the PSO technique has been the subject of several studies in the context of antenna miniaturization. Its principle of operation based on its two main operators which are velocity update and position update has been of paramount importance in the optimization of antenna parameters. At each iteration, each particle is accelerated towards the previous best position of the particles [8]. This method was used on a Fractal Planar Inverted-F antenna at the 3rd iteration of Minkowsi Fractal in [9]. The Inverted-F antenna resonated at 434 MHz was designed as reference. However, the application of a large number of PSOs up to 60 iterations was also necessary for the particles to converge. Thus, the results revealed that more than 68% reduction in the size of the proposed antenna compared to the conventional reference PIFA antenna was obtained.These methods are becoming increasingly popular in antenna miniaturization operations, but the determination of their fitness and the complexity of their calculations are opportunities for other methods to emerge.
Likewise, many advanced miniaturization techniques based on the use of high permittivity substrates and magneto-dielectric materials have gained ground in the race for antennae miniaturization methods. In [10], a high permittivity material was used on a rectangular star shape slotted MPA of dimension 28.5 × 37.56 \({mm}^{2}\), engraved in a FR-4 dielectric substrate of 4.3. This reference antenna considered as the basic antenna has been designed to operate at 2.4 GHz and 5 GHz resonant frequencies. However, for this same antenna, the FR-4 had been replaced by Rogers RT 6010 of permittivity 10.2. Then the same frequencies could only be reached after a series of decreasing variation of the patch dimension. Thereby, the size of the proposed antenna with \({\epsilon }_{r}=10.2\) was \(18.53 x 23.78 {mm}^{2}\), thus an overall size reduction of 75.42%. In that work, it was inconveniently noted that the level of impedance matching had remained relatively low. The magneto-dielectric material has revolutionized the technique of antenna miniaturization methods. These materials, which cannot be found naturally, have undergone rapid development thanks to the technological advanced of Nano-science. In [11], a \({Na}_{2}{WO}_{4}-{Ni}_{0.2}{Cu}_{0.2}{Zn}_{0.6}{Fe}_{204}\) sintered ceramic fabricated at a temperature of about 900°C for employed as dielectric substrate in the microstrip antenna resonating at 433MHz. That approach has greatly reduced the size by up to 60%. Cases of miniaturization of antennae using the method of magneto-dielectric materials raised and exploited in this work present some difficulties relating to the condition of obtaining the magneto-dielectric material. It is observed that the atmosphere could reach a temperature of 900°C, which does not favor the design of miniaturized antennae in areas less provided with specialized laboratories. The harsh conditions of the meta-material manufacturing environment as specified in [12] limits its accessibility to the greatest number of designers of miniaturized antennae. However, bumped into the complexity, either of the meta-materials manufacturing or of its design process, many other researchers have opted for the modification of the geometric structure of the antennae for their miniaturizations.
The miniaturization of MPA using the modification technique of their geometry structures has been widely proposed by several designers of miniaturized antennae. That approach was preferred by many to reduce the complexities of the methods mentioned above. These methods can be grouped into: Defected Ground Structure Approach (DGSA), and Defected Patch Structure Approach (DPSA). Slots and notches from the simplest to the most complex have been implemented in several research works on the miniaturization of MPAs. In [13], the DGSA was used on a conventional MPA of dimension 67 x 64 x 1.5 \({mm}^{3}\), which resonated at 2.45 GHz in the ISM band. After the referenced antenna was then modified with DGSA as represented in Fig. 2 (b) in [13], to recover the same characteristics of the original antenna, the size has undergone a decreasing variation up to 37.9%. However, a similar reasoning as before was carried out on the ground plane of an MPA by the creation of Complementary Split Ring Resonator in [14]. A significant gain improvement and size reduction were achieved. From a reference MPA resonating at 2.56 GHz of dimension 35.42 x 27.42 \({mm}^{2}\), tooth-shaped slots were created along its lengths as shown in Fig. 3 in [15]. The operation frequency has become 1.7 GHz and size has reduced up to 87.88%. Moreover, meandered types slots combined to slotted Square Spiral have been cut from the patch in [16] for effective size reduction to achieve resonance frequency bandwidth from 402 MHz to 405 MHz. The results of these miniaturization methods based on meandered slots were certainly convincing, but some difficulties were noted such as: no clear design of equations or procedure, non-planar, complex geometry as elaborated in [17]. Faced with the complexity of this miniaturization approach, some antenna designers have opted for the defective patch method using fractal shapes whose geometric properties are known.
Fractal geometry has been introduced in antenna design since the work of Nathan Cohen in 1988 [18]. Its self-similarity, self-scaling and space-filling properties have been of significant contribution in antennae design as well as their size reduction. The most common fractal shapes found in antenna design are: Sierpinski shape, Minkowski fractal shape, Koch, Hilbert, Cantor, Peano fractal, and tree-shaped fractal. A modified Sierpinski Carpet was applied in a conventional MPA of dimension 39 x 60 x 1\({ mm }^{3}\) which was designed to resonate at a frequency of 1.8 GHz in [19]. After the second iteration, the central rectangular slot was replaced by a circular slot. The proposed antenna was able to resonate at the same frequency with a size reduction of 45.15%. Similar to the previous antenna, the Sierpinski Carpet was applied to part of a much smaller antenna of dimension 6 x 3.9 x 1.6 \({mm}^{3}\). It was designed for Ku/K/Ka Band applications. After the second iteration of Sierpinski, as it was shown in Fig. 4 [20], a significant reduction was obtained. The Koch curve was applied to the four patch sides until the third iteration. At each iteration, the antenna was evaluated, and the resonant frequency decreased as the number of iterations increased. A great reduction from 81 \({mm}^{2}\) of the initiator to 37.18 \({mm}^{2}\) of the proposed antenna was realized. In [23], the Hilbert generating curve was used on the two lengths of the basic rectangular shape at the first iteration. At the second iteration, the Hilbert curve generator was modified, but at the third iteration, only the transmission line had an increase in width at the patch connection point as shown in Fig. 1 [23]. The patch was engraved on a two-layer substrate made of FR4 dielectric material and Rogers RT/Duroid 5880(tm). The proposed antenna had achieved three frequencies bands which can be used in C, X and Ku band applications with considerable size reduction. In [3], the Minkowski Island fractal approach was used. However, a slotted shape has been integrated in the center of the patch to form a Minkowski Island patch antenna. That technique has allowed reducing 58.7% of the proposed antenna size compared to the conventional antenna.
Some MPA miniaturization approaches have been extensively studied and discussed in this introductory part by noting their advantages and disadvantages, their fields of application as well as their conditions of realization as they were related in the various works. It emerges from this study how much easier it is to make a miniaturized antenna based on fractal geometry, because of its low weight, its reduced size, its ease of design, its low cost. Therefore, this article will propose a series of three MPA miniaturization methods based on Conventional Minkowski Curve and Modified Minkowski Curve, fed by an edge transmission line. The main objective of this work is to achieve MPAs much smaller than the conventional MPA antenna using the Minkowski miniaturization technique while keeping the resonance frequency at 15.53 GHz, suitable for Ku-band communications. The paper is organized as follows: After the introduction on MPA miniaturization techniques, in section 2 is presented the design of miniaturized microstrip antennae. The results of the simulation and the discussion are given in section 3. Section 4 presents a comparison of this work with antenna miniaturization works using Minkowski fractal. Finally, section 4 presents the conclusion.