Design and Optimization of Miniaturized Microstrip Patch Antennas Using a Genetic Algorithm

Abstract

The main objective of this work is to propose an approach for improving the performance of miniaturized microstrip patch antennas (MPAs) that are loaded with a thin film consisting of a high relative permittivity material. The method uses a thin film to decrease the antenna’s resonance frequency while keeping the antenna’s patch dimensions. For the enhancement of the antenna’s performance with a thin film, the dimensions of the patch of the designed antenna are optimized utilizing genetic algorithms (GAs). The resonance frequency of the microstrip patch antenna was changed from 5.8 GHz to 4.0 GHz, and the area of the proposed antenna was minimized by around 60%, especially in comparison to a conventional antenna alone without thin film. Most of the performances of the proposed antenna such as the return loss, bandwidth, and voltage standing wave ratio (VSWR) were improved.

1. Introduction

Nowadays, wireless devices are widely employed in a variety of domains, including telecommunications, aeronautics, medical, and military. The growing use of these systems has led manufacturers to focus on the improvement of wireless devices. Therefore, microwave circuit technology has shown a considerable development in recent years [1,2,3,4,5].

This evolution became possible after the significant progress in electronics and numerical information processing techniques. The connection between these terminals, mobile phones, computers, base stations, and other infrastructures is carried out by electromagnetic waves [6].

The antenna is one of the most essential elements of wireless systems. These elements transform the electrical signal into electromagnetic signals and radiate these in space and vice versa [7]. The antenna takes up the most space in the communication system chain; thus, increasing the antenna’s total size makes the implementation of a wireless device difficult in a small area [8].

In recent decades, reducing the size of antennas has been one of the main focuses in the designers of antennas. Miniature antennas are especially used in micro-fabrication technologies to manufacture wireless devices [9,10]. In fact, the length of an ordinary antenna that operates at some frequency is generally of the order of a half-wavelength of that frequency [8], e.g., the conventional length of an antenna resonating at 1 GHz in the case of a dielectric constant of 2.2 is approximately 100 mm. However, this length is practically unacceptable for several devices. Moreover, most devices such as satellite, radio frequency identification (RFID) chips, and phones need the use of multiple antennas [11,12,13,14]. Thus, the development of wireless devices will continue to challenge researchers to design smaller antennas.

In the literature, there is a large variety of antennas that are used in various domains of wireless systems. The simplest is the wire antenna that is used as a loop or dipole antenna. Another antenna type is the aperture antenna that appears as a horn shape. Planar antennas, such as microstrip antennas, have been used extensively during the past three decades [15]. Many researchers have focused on microstrip patch antennas. Despite their narrow bandwidth, the microstrip patch antennas have many advantages compared to other conventional antennas such as low manufacturing costs, low volume, weight, and thickness, simplicity of manufacturing, and the possibility of integrating discrete elements [16].

For several years, many studies have focused on the miniaturization of antennas. However, these techniques have been confronted with a difficult problem due to the gain and bandwidth fundamental limit that depends on the antenna size [17].

Generally, there are three principal ways to miniaturize an MPA: introducing slots, shorting and folding, and material loading. During the first method (introducing slots), the reduction of the size of a patch antenna can be realized by creating slots or changing the shape of the patch. For the purpose of obtaining a large electrical length in a small area [18], miniaturized patches can be optimized using a genetic algorithm (GA) [17,19,20]. However, this technique will be complicated because the geometry of the antenna and its gain will be very low. Fractal geometries are employed to reduce the size of the microstrip patch antenna. However, this antenna suffers from a considerable reduction in bandwidth [21]. The second technique (shorting and folding) is the ground plane deformation. In this method, researchers use defected ground structures (DGSs) to miniaturize the antenna. In the literature, DGSs have several shapes: simples ones, e.g., spiral, H-shape, and U-shape or complex ones, for example, split-ring resonators (SRRs) [22,23]. The realization method is simple but there is no standard design procedure and it provides a low efficiency and a narrow bandwidth. The third and simplest method to miniaturize a patch antenna (material loading) is the utilization of a substrate with a high relative permittivity (ε_r), as the antenna’s resonance frequency is scaled by $1/\sqrt{{\epsilon }_r{\mu }_r}$ (μ_r is the relative permeability of the substrate). Nevertheless, the last technique suffers from a decrease in the bandwidth when a substrate with a high relative permittivity is used [24,25,26,27,28].

The main contribution of this work is to propose a method for enhancing the performances of miniaturized microstrip patch antennas loaded with a thin-film material with high relative permittivity. First, a thin film was used to decrease the antenna’s resonance frequency while keeping the antenna’s patch dimensions. Next, to enhance the antenna’s performance with a thin film, a GA-based method was employed to determine the dimensions of the antenna’s patch. A GA is a robust searching and optimization technique that can be applied to a wide range of electromagnetic problems. [29,30,31]. GAs are inspired by Darwinian ideas of natural selection and evolution. This technique has been utilized to improve several performances of MPAs such as bandwidth [32], gain [33], and size [19,23,34,35,36] and to reduce the maximum sidelobe level [37]. GAs have been used to design an antenna for 5G applications, which requires operating at multiple bands while offering excellent gain and efficiency across all bands [38,39].

2. Methodology

For miniaturizing the MPA’s dimensions and enhancing its performance, a thin-film material with very high dielectric permittivity (ε_r2 = 250) and low loss (tan δ = 0.02), i.e., ferroelectric material (B_0.8S_0.2TiO₃) [40,41] is loaded into the patch. The flowchart in Figure 1 shows the processing steps to integrate the thin-film material in the antenna.

First, an ordinary antenna operating at 5.8 GHz is designed. The dimensions of the first design are determined on the basis of a published study [42]. Next, a thin-film material with different thicknesses is integrated to obtain a miniaturized antenna (that operates at 4 GHz). Finally, the new MPA’s dimensions are optimized. The return loss is used as a reference parameter in the GA-based optimization process to enhance the final designed antenna’s performances (return loss, bandwidth, and VSWR).

2.1. Initial Geometry of the Antenna

Figure 2 depicts the structure of the patch antenna’s initial geometry. This initial structure has been studied in detail in [42]. For a microstrip patch antenna with D₁ << L₁, D₁ << W₁, and L₁ > W₁ > D₁ (the length and width of the patch are L₁ and W₁, respectively, while the height of the substrate is D₁), the dominant mode is the TM₀₁₀ mode. The resonance frequency (f_r) and bandwidth (Δf) are given [25,42,43] as follows:

$$f_r=\frac{1}{2L_1\sqrt{{\epsilon }_r}\sqrt{{\epsilon }_0{\mu }_0}}$$

(1)

$$\frac{\Delta f}{f_r}\approx 3.77\frac{{\epsilon }_r-1}{{\epsilon }_r^2}\frac{L_1{D}_1}{\lambda W_1}$$

(2)

where μ₀ and ε₀ are the permeability and permittivity in free space, respectively, while λ is the wavelength.

From Equation (1), the antenna’s size can be reduced by the use of a substrate with high relative permittivity due to its refractive index (n = $\sqrt{{\epsilon }_r}\sqrt{{\epsilon }_0{\mu }_0}$). For this reason, a thin-film material with high dielectric permittivity has been used. In this study, a ferroelectric material that has a relative permittivity ε_r2 = 250 has been used [38,41]. However, the use of a high relative permittivity substrate results in a narrow bandwidth. Indeed, from Equation (2), one observes that as ε_r increases, the bandwidth decreases, as the stored electrical energy increases [28]. To solve this problem, the values of the patch corresponding to the new antenna (antenna with the thin-film material) have been optimized. Then, the return loss and VSWR are considered parameters in the GA-optimization process to enhance its performance.

2.2. Antenna with the Thin-Film Material

Figure 3 depicts the structure of the studied antenna (with a thin-film material). This was designed as a rectangular patch on two substrates. The first substrate (lower substrate) is FR-4 with thickness D₁ equal to 1.58 mm and permittivity ε_r1 equal to 4.4. The second substrate (upper substrate) consists of a thin film of a ferroelectric material B_0.8S_0.2TiO₃ (BST) of thickness D₂ and is characterized by a very high dielectric permittivity (ε_r2 = 250) [39,41].

The goal of the work is the miniaturization of the antenna. The antenna’s dimensions operating at 5.8 GHz have been used for an antenna that operates at 4 GHz. Since the resonance frequency (f_r) of a patch antenna is determined by the patch’s dimensions and the substrate’s relative permittivity [25,42], a thin film of BST was integrated, and its thickness was varied until the desired resonance frequency. Note that the desired resonance frequency in this work is 4 GHz.

2.3. GA-Based Optimization of the Patch Parameters of the Antenna with the Thin-Film Material

A genetic algorithm is a stochastic search technique based on Darwin’s theory of evolution [44]. This technique plays an important role in solving problems involving possible solutions in a large search space where classical methods cannot be used. The most important advantage of GA over other methods such as Particle Swarm Optimization (PSO) is the accuracy [45]. Except for the drawback of being computationally expensive due to the GA (time-consuming), this technique has the following advantages [46]:

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Optimization is possible for continuous or discrete variables,

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Ability to work with a large number of variables,

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It is well suited to parallel computers.

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It works with numerically generated data, experimental data, or analytical functions.

GA uses the concepts of biological evolution to resolve optimization problems. Principles based on gene combinations in biological reproduction are employed to repeatedly modify a population of individual points. Thanks to its random nature, GA enhances the chances of identifying a global solution. Therefore, this proves to be extremely effective and stable while searching for global optimum solutions [47].

The purpose of a GA is to compute the extrema of a function identified in a space of data. An evolutionary process is utilized to resolve a problem using GA, in which possible solutions (chromosomes) will be utilized to develop new solutions. Such a group of possible solutions will be named a population. For the objective of creating the next generation of the population, only one population (particular) will succeed and will be employed. Solutions utilized for creating novel solutions (offspring) are selected based on their fitness function. The chromosome with the greatest chance of reproducing is the most suited. Figure 4 shows the GA-based method flowchart to optimize the model parameters. The GA-base optimization method consists of the following steps [44]:

• Generation of the initial population: A binary string is used to represent all chromosomes, to exemplify chromosome X: 11110000 and chromosome Y: 11001100.
• The initial population is produced via a mechanism capable of creating a non-homogeneous population of individuals that will serve as a basis for future generations. Population size and the total number of individuals directly influence the convergence of the GA. Because the goal is the identification of the optimal values of L₁ and W₁, the population size is set to 30 and the number of individuals is set to 2.
• Selection: The fitness function is used to evaluate and classify populations. For the next generation, populations offering the best fitness rates will be selected.
• Crossover: from parents, genes are recombined to form a novel chromosome; chromosome X: 11110000 and Chromosome Y: 11001100 might be crossed over after the fourth locus to form two new offspring chromosomes, 11111100 and 11000000. With a constant probability (CP), the crossover is applied to the population. Usually, this constant relies on the application and it is very large [48]. In this work, CP has been set to 0.9.
• Mutation: for producing novel offspring, a few chromosome bits are changed. In binary encoding, some randomly selected bits may be modified from 1 to 0 or vice versa, for example, chromosome 11110110 can possibility be changed in the third location to produce chromosome 11110010. In general, in this operator, it is suitable to choose a low probability of mutation (MP). Typically, MP ranges from 0.01 to 0.3. [48,49]. In this work, MP is equal to 0.05.
• Evaluation Function: for any optimization method, the evaluation function is the most important stage in the optimization procedure’s success. Moreover, it presents the relation between the physical problem to be optimized and the GA. The best solution is one, which diminishes the fitness function (σ). The aim of the study is the minimization of the maximum return loss magnitude (S₁₁) at three frequencies, f₁ = 3.8 GHz, f_r = 4.0 GHz, and f₂ = 4.2 GHz (to widen the bandwidth while keeping the resonance frequency at 4 GHz). In this case, σ is defined as [50]:

$$\sigma =\underset{\forall n}{min(S_{11n})}$$

(3)

where n is the index that refers to sample points in the S₁₁ versus frequency function.

In order to improve the antenna’s performance (with the thin film), GA was utilized to optimize the microstrip antenna’s patch dimensions (L₁ and W₁). The purpose of the optimization is to obtain the lowest S₁₁ (dB) value at the resonance frequency of 4 GHz, as well as a value less than −10 (dB) for f₁ and f₂. The stop condition is that the number of generating iterations, which is set to 1000, is reached. The GA-based optimization process of the microstrip patch antenna with the thin film is illustrated in Figure 5.

The optimization process runs in two phases. Firstly, the design of the miniaturized antenna begins via an antenna operating at 4 GHz by integrating a thin-film material with high effective permittivity whose bandwidth is 127.4 MHz, return loss is 19.42 dB, and VWSR is 1.86 as the initial state. In order to enhance these last performances (bandwidth, return loss, and VWSR), the GA method has been integrated for the optimization of the patch dimensions to decrease the fitness function.

3. Results and Discussion

3.1. Miniaturization of the Microstrip Patch Antenna

The numerical analysis was done with two electromagnetic simulators: High-Frequency Structure Simulator (HFSS), which employs the finite element method in the frequency domain, and Computer Simulation Technology (CST), which utilizes the finite integration approach in the time domain. The antenna’s initial structure (conventional MPA) is depicted in Figure 1 with its dimensions listed in

Table 1. Dimensions of the initial structure antenna.

W1 × L1 (mm2)	W2 × L2 (mm2)	W3 × L3 (mm2)	D1 (mm)	W2 (mm)
15.9 × 11.26	0.71 × 13.31	3.02 × 11.81	1.58	0.01–0.1

.

Figure 6 presents the results of the proposed antenna without integration of the thin-film material obtained by HFSS and CST. The simulation results produced from the two simulators indicate excellent agreement.

For comparison, Figure 7 displays the return loss of the patch antenna without and with a thin-film material (10 μm thick of the ferroelectric material B_0.8S_0.2TiO₃). The antenna operating frequency shifted from 5.81 GHz to 5.31 GHz for the HFSS and CST simulators. This variation is a consequence of the variation in the effective permittivity of the ferroelectric–dielectric substrate due to the integration of a thin-film material, which has a relative permittivity of 250.

For the purpose of studying the effect of the thickness of the thin-film material on the antenna’s performance, a parametric analysis was carried out by varying the thickness (D₂). Figure 8 depicts the results. It can be seen that the resonance frequency changes with the change in the thin-film thickness. The thicker the film, the more the resonance frequency decreases. For example, the resonance frequency for D₂ = 0.01 mm is 5.31 GHz and it shifts to 4.00 GHz when D₂ = 0.1 mm. These results present an excellent agreement with previous results [24,25,26,27,28,29,30].

For the aim of measuring the reduction rate related to the antenna size, a novel antenna (conventional antenna) was designed to operate at 4 GHz, i.e., at the operating frequency of the designed antenna. After studying this antenna’s performance, it appears that the patch must have the following dimensions: W₁ = 22.82 mm and L₁ = 17.40 mm. For comparing the two antenna sizes operating at 4 GHz, two rectangular are drawn in Figure 9. The dark rectangle depicts the microstrip patch antenna with a thin-film material, whereas the light rectangular represents a conventional antenna (without the thin film). This figure shows that the miniaturization approach proposed in this study delivers a 55% reduction in the size of the radiating element.

Figure 10 presents the radiation pattern (for the two principal plans E and H). The figure shows the principal plans at 4 GHz. Phi = 0° and theta = all values for plan E, compared with phi = 90° and theta = all values for the H plan. The radiation pattern reveals that those antennas (proposed and conventional) have nearly the same radiation behavior, and the proposed antenna has an approximately omnidirectional characteristic for the E plan and H plan, especially at the resonance frequency (4 GHz).

3.2. GA-Optimization of the Antenna with a Thin-Film Material with High Permittivity

The GA method was then used to enhance the performance of the miniaturized antenna by minimizing the fitness function in the second phase. For comparison, the results are given in Figure 11 and

Table 2. Comparison of the proposed microstrip patch antenna operating at 4 GHz with the conventional antenna, antenna with a thin film, and antenna with a thin film optimized by GA.

Antenna	Patch Dimensions (W1 × L1) (mm2)	Return Loss (dB)	Bandwith (MHz)	VSWR	Gain (dB)
Conventional	22.1 × 16.84 (372.16)	−33.7	118.4	1.04	3.88
With thin film	15.90 × 11.26 (179.04)	−19.42	127.4	1.86	3.89
With thin film and GA	13.76 × 11.32 (155.04)	−29.81	147.8	1.06	3.63

. The proposed antenna conserved about 40% of the global area of the conventional antenna at a resonance frequency of 4 GHz, and its performance in terms of the return loss and VSWR improved by about −10.39 dB and 0.8, respectively, thus increasing the bandwidth of the antenna by 29.4 MHz.

Table 3. Comparison of the proposed antenna with reference miniaturized patch antennas.

Antenna	${\mathit{f}}_{\mathit{r}}^{\mathit{a}}$ (GHz)	${\mathit{f}}_{\mathit{r}}^{\mathit{b}}$ (GHz)	Return Loss (dB)	Bandwith (MHz)	Miniaturization Rate (%)	Gain (dB)
N. Herscovici et al. [19]	3.000	1.738	−24	10	42	1
P. Soontornpipit et al. [51]	0.405	0.4035	−15	20	/	/
H. Elftouh et al. [35]	5.700	3.000	≈−38	/	50	2.14
M. Lamsalli et al. [34]	4.900	2.160	−20	≈10	82	5.82
M. S. Sharawi et al. [22]	5.040	2.450	≈−25	≈50	76	−0.8
M K. Dhakshinamoorthi et al. [36]	3.000	2.3958	−12.5	30	24.4	/
	4.000	2.4022	−13.5	22	45.8	/
Proposed	5.800	4.000	−29.81	147.8	≈60	3.63

illustrates a quantitative comparison between the proposed antenna and miniaturized antennas reported in previously published works in terms of different parameters (gain, rate of miniaturization, return loss, and bandwidth). It is worth noting that in terms of bandwidth, the proposed miniaturized patch antenna outperformed the reference antennas. The performances of the proposed antenna were comparable to those of the reference antennas in terms of the return loss, rate of miniaturization, and gain. The initial and final resonance frequencies of the suggested antenna and reference antennas are also given in Table 3. In comparison to the reference antennas provided in Table 3, the proposed antenna reflects a compromise between the size, gain, and bandwidth.

4. Conclusions

A new method for designing and optimizing miniaturized microstrip patch antennas for application in telecommunications is presented. A thin-film material with high permittivity is used for reducing the antenna’s resonance frequency while keeping the patch dimensions of the antenna constant. For the purpose of enhancing the performances of miniaturized antennas, a genetic algorithm is utilized for the estimation of the optimal parameters of the patch of the antenna with a thin film. The results indicate that the designed antenna’s resonance frequency changed from 5.8 GHz to 4.0 GHz and the area of the proposed antenna was reduced by around 60%, especially in comparison to a conventional antenna alone without thin film. Therefore, most of the performances of the proposed antenna such as the bandwidth, return loss, gain, and VSWR improved.

Finally, the performances of the proposed antenna were compared to those of reference antennas reported in the literature. It is worth noting that the proposed method can be easily exploited for designing filters or antennas with diverse frequencies or geometries. The use of an alternative optimization method, such as particle swarm optimization (PSO), and other thin-film materials such as KTN (KTa_1-xNb_xO₃) can be investigated in future work to improve the performance of the miniaturized microstrip patch antenna.