There has been a tremendous development in the field of patch antenna during the last two decade [3, 4]. It is the result of the overwhelming research and this technology has been quickly absorbed for consumption. A few previous research works done in this field are discussed in this section. The length of an antenna is inversely proportional to the resonant frequency of patch, that is, an antenna operating at higher frequency is smaller in size than compared to the antenna operating at lower frequency. So, to decrease the antenna dimensions required for operating the antenna at lower frequency, the electrical length of the patch should be enlarged at lower frequency. This technique has been successfully used for minimizing the antenna dimensions. A technique of improving the electrical length is by meandering the surface current path of the patch. One such research work was done by Dey and Mittra [5]. In the mentioned article, 70% size reduction of the proposed microstrip patch design is reported. In Ref. [6], authors used three meandering slots and a shorting pin on a rectangular patch to obtain the results. In Ref. [7], an innovative technique is proposed for calculating the resonant frequency of circular microstrip patch antennas using artificial neural for computer-aided design (CAD) applications. In Ref. [8], the back-propagation multilayered-perceptron network is used for calculating the resonant frequency of electrically thin and thick rectangular microstrip antennas. This technique is applicable for a wide range of substrate thicknesses and permittivity for the computer-aided design (CAD) applications of microstrip antennas. One such research work was conducted by Kuo et al. [9]. In this work, the researchers have chosen the ground plane for modification in designed antenna. A total number of three slots were loaded in the ground plane. The authors have shown that the variation seen by changing the length of the slots. For the best case, the size reduction of 56% was obtained by the authors. Some researchers also reported size reduction using inductive loading. One such research work was reported by Reed et al. [10]. In the design, the researchers have loaded a printed inductor to minimize the frequency of resonant antenna. Using this, a size reduction of 50% was achieved. A bow-tie patch antenna loaded with Sierpinski fractal was also proposed by Anguera et al. [11] which has good directivity along with compactness of 42%. One of the methods of increasing the electrical path length is by meandering the surface current path of the patch. In [13], a new method for developing computer-aided design (CAD) models for microstrip antenna is proposed using spectral domain (SD) formulation and artificial neural network (ANN) technique. In Ref. [14], design of rectangular microstrip antennas is proposed using the artificial neural network technique for the most efficient dielectric materials. In Ref. [15], the authors have suggested the combination of inductive loading and shorting pin. The authors have suggested that using the novel design, a size reduction of 75% may be achieved. A bow-tie patch antenna loaded with Sierpinski fractal was also presented by Garima et al. [16] along with compactness of 42% and good directivity. In Ref. [17], single-fed broadband square patch antenna was constructed for ultra high frequency (UHF) radio frequency identification (RFID) applications using meandered probe feeding techniques for good impedance matching. The purpose of the antenna was to optimize and modify antenna. In Ref. [18], two L-shaped patch antenna was constructed using a probe or coaxial feeding techniques. Two parallel L-shaped antennas were used to obtain better bandwidth. The bandwidth of the antenna was 6.41 GHz ranging from 3.51

to 9.65 GHz. Return-Loss of the proposed antenna is 28 dB at 3.51 GHz and 25 dB at 9.65 GHz. In [19], E-shaped antenna was constructed for wireless communications, and its applications using U-slot patch was introduced under patch antenna to increase and optimize bandwidth of the proposed antenna. The systematic study of antenna was enhanced gain, return loss, bandwidth, and radiation pattern. In Ref. [20], four mini fractal antennas were constructed to improve bandwidth and size of the antenna using coaxial feeding techniques. The proposed design was used for broadband applications. Four spring resonators form an ultra-wideband frequency. Low percentage error and high precision in less time are obtained by using a knowledge-based hybrid neural network (KBHNN) model for designing of microstrip antennas (proximity coupled), which is used for various WiMAX, WiFi, and WLAN applications. Figure 1 illustrates a simple rectangular microstrip patch antenna of substrate height h, dielectric constants εr, εy, width W, and length L.

In this chapter, synthesis is defined as to obtain dimensions (W, L) of microstrip antenna while providing the resonant frequency (fr), height of the dielectric substrate (h), and dielectric constants at the input of the ANN model (Figure 2). Dimensions of patch are computed using the designed equations of the microstrip patch antennas. For the analysis problem of patch antenna, resonant frequency (fr) or both upper and lower cutoff frequencies are obtained at the output of ANN model while providing the dimensions of patch and other parameters as the inputs of ANN model, as shown in Figure 3. This model is very significant for antenna researchers to determine the dimensions and other parameters of microstrip antenna.

The range of dielectric constants should be taken between 2.2 and 12 but the dielectric substrate should be thicker and the dielectric constant should be less for obtaining high efficiency and

Figure 1. Basic layout of rectangular patch antenna.

shape of this patch may be square, hexagonal, rectangular, trapezoidal, or any other pattern. In this chapter, rectangular microstrip patch antennas are designed for synthesis and analysis by an

There has been a tremendous development in the field of patch antenna during the last two decade [3, 4]. It is the result of the overwhelming research and this technology has been quickly absorbed for consumption. A few previous research works done in this field are discussed in this section. The length of an antenna is inversely proportional to the resonant frequency of patch, that is, an antenna operating at higher frequency is smaller in size than compared to the antenna operating at lower frequency. So, to decrease the antenna dimensions required for operating the antenna at lower frequency, the electrical length of the patch should be enlarged at lower frequency. This technique has been successfully used for minimizing the antenna dimensions. A technique of improving the electrical length is by meandering the surface current path of the patch. One such research work was done by Dey and Mittra [5]. In the mentioned article, 70% size reduction of the proposed microstrip patch design is reported. In Ref. [6], authors used three meandering slots and a shorting pin on a rectangular patch to obtain the results. In Ref. [7], an innovative technique is proposed for calculating the resonant frequency of circular microstrip patch antennas using artificial neural for computer-aided design (CAD) applications. In Ref. [8], the back-propagation multilayered-perceptron network is used for calculating the resonant frequency of electrically thin and thick rectangular microstrip antennas. This technique is applicable for a wide range of substrate thicknesses and permittivity for the computer-aided design (CAD) applications of microstrip antennas. One such research work was conducted by Kuo et al. [9]. In this work, the researchers have chosen the ground plane for modification in designed antenna. A total number of three slots were loaded in the ground plane. The authors have shown that the variation seen by changing the length of the slots. For the best case, the size reduction of 56% was obtained by the authors. Some researchers also reported size reduction using inductive loading. One such research work was reported by Reed et al. [10]. In the design, the researchers have loaded a printed inductor to minimize the frequency of resonant antenna. Using this, a size reduction of 50% was achieved. A bow-tie patch antenna loaded with Sierpinski fractal was also proposed by Anguera et al. [11] which has good directivity along with compactness of 42%. One of the methods of increasing the electrical path length is by meandering the surface current path of the patch. In [13], a new method for developing computer-aided design (CAD) models for microstrip antenna is proposed using spectral domain (SD) formulation and artificial neural network (ANN) technique. In Ref. [14], design of rectangular microstrip antennas is proposed using the artificial neural network technique for the most efficient dielectric materials. In Ref. [15], the authors have suggested the combination of inductive loading and shorting pin. The authors have suggested that using the novel design, a size reduction of 75% may be achieved. A bow-tie patch antenna loaded with Sierpinski fractal was also presented by Garima et al. [16] along with compactness of 42% and good directivity. In Ref. [17], single-fed broadband square patch antenna was constructed for ultra high frequency (UHF) radio frequency identification (RFID) applications using meandered probe feeding techniques for good impedance matching. The purpose of the antenna was to optimize and modify antenna. In Ref. [18], two L-shaped patch antenna was constructed using a probe or coaxial feeding techniques. Two parallel L-shaped antennas were used to obtain better bandwidth. The bandwidth of the antenna was 6.41 GHz ranging from 3.51

artificial neural network (ANN) modeling procedure.

56 Trends in Research on Microstrip Antennas

Figure 2. The synthesis of microstrip patch using ANN model.

Figure 3. The analysis of microstrip patch using ANN technique.

wide bandwidth. The effective thickness (he) and effective dielectric constant (εreff) are calculated using Eqs. (1) and (2), where h is thickness and εg is the geometric mean of dielectric constant.

$$h\_e = \sqrt{\frac{\varepsilon\_r}{\varepsilon\_\mathcal{S}}} h \tag{1}$$

$$
\varepsilon\_{eff} = \frac{\varepsilon\_{\mathcal{S}} + 1}{2} + \frac{\varepsilon\_{\mathcal{S}} - 1}{2} \left[ 1 + 12 \frac{h\_{\epsilon}}{W} \right]^{-\frac{1}{2}} \tag{2}
$$

If the velocity of light is denoted by C, the width of antenna is calculated using Eq. (3).

$$\mathcal{W} = \frac{\mathbb{C}}{2f\_o} \sqrt{\frac{2}{\varepsilon\_{\mathcal{S}} + 1}} \tag{3}$$

Eqs. (4) and (5) represents the real length of the patch (L).

$$L = L\_{\rm eff} - 2\Delta L \tag{4}$$

$$L = \frac{1}{2f\_r\sqrt{\varepsilon\_{eff}}\sqrt{\mu\_o\varepsilon\_r}} - 2\Delta L \tag{5}$$

The fringing property of patch gives rise to the extended electric length, which is illustrated by Eq. (6)

Design and Analysis of Microstrip Patch Antennas Using Artificial Neural Network http://dx.doi.org/10.5772/intechopen.69522 59

$$
\Delta L = 0.412h \frac{(\varepsilon\_{r\%} + 0.3) \left(\frac{w}{h} + 0.264\right)}{(\varepsilon\_{r\%} - 0.258) \left(\frac{w}{h} + 0.813\right)}\tag{6}
$$

## 2. Synthesis and analysis problem for microstrip patch antenna

Synthesis is defined as to obtain the dimensions of microstrip patch while providing the resonant frequency, thickness, and dielectric constants of the dielectric material as the input parameters of ANN model (Figure 2). Dimensions of patch are computed using the designed equations of the microstrip patch antennas. For the analysis problem of patch antenna, resonant frequency (fr) or both upper and lower cutoff frequencies are obtained at the output side of ANN model while providing the dimensions of patch (W, L) and other parameters (εr, εy , h) at the input side of ANN model (Figure 3). These ANN models are easily applicable and very useful for researchers to judge the accurate upper and lower cutoff frequency, bandwidth, resonant frequency, and accurate dimensions of patch antenna. Here εr and εy represent the electrical properties of the dielectric material.

#### 2.1. ANN architecture for microstrip antenna

There are many algorithms of ANN which is used to train the neural network [12]. In this work, back-propagation training algorithm was applied to train the neural network and to build the ANN models for patch antenna. This algorithm is explained in Section 2.1.1.

#### 2.1.1. Back-propagation algorithm

wide bandwidth. The effective thickness (he) and effective dielectric constant (εreff) are calculated using Eqs. (1) and (2), where h is thickness and εg is the geometric mean of dielectric constant.

εg � 1

s

ffiffiffiffiffiffiffiffi εr εg h r

2 1 þ 12 he

ffiffiffiffiffiffiffiffiffiffiffiffiffi 2 εg þ 1

W � ��1

2

L ¼ Lef f � 2ΔL ð4Þ

p � 2ΔL ð5Þ

ð1Þ

ð2Þ

ð3Þ

he ¼

2 þ

If the velocity of light is denoted by C, the width of antenna is calculated using Eq. (3).

W ¼ C 2f o

L ¼ 1 2f r

ffiffiffiffiffiffiffi εef f p ffiffiffiffiffiffiffiffiffi μoεr

The fringing property of patch gives rise to the extended electric length, which is illustrated by

εef f ¼ εg þ 1

Eqs. (4) and (5) represents the real length of the patch (L).

Figure 2. The synthesis of microstrip patch using ANN model.

58 Trends in Research on Microstrip Antennas

Figure 3. The analysis of microstrip patch using ANN technique.

Eq. (6)

In this algorithm, connections are done from input layer to hidden layer and to output layer. The network is trained using the gradient descent method and the error calculated is sent back to the hidden layer as well as the output layer for weight adjustments [13]. In multilayer perceptron network there are two sets of weights, namely from input layer to hidden layer and from hidden to output layer. The error due to the second set of weights is calculated using the delta rule and the error is required to propagate from output layer to input layer so that the error can be assigned proportionately to the weights which caused it. This problem is known as credit-assignment problem and helps in deciding which weights should be altered and by how much. This problem can be solved by using the error back-propagation algorithm, which works in two passes:

This algorithm uses the supervised learning mechanism.

In multilayer feed-forward networks, normally, there is an input layer, one or two hidden layers and one output layer. The raw values are given to the input layer, computations are done at the hidden layer and their activations are given to the output layer where each pattern is given a specific classification category. In this algorithm, we are giving a solution to credit assignment problem using partial derivatives to find out how weight wij effects the error which is represented by Eq. (7).

$$\frac{\partial E(t)}{\partial W\_{\vec{\eta}}(t)}\tag{7}$$

Here, partial derivatives are used because the direction of the errors can be determined, which may be positive or negative. If this derivative to be negative, this will add in weight and finally decreases the error and thus local minima can be reached (see step 6 of algorithm). This shows that if derivative of error is positive, the weight increases by adding a negative value to the weight and conversely, if negative. Procedure of taking derivative in this algorithm starts from weights of output layer to input layer, that is why, it is known as "back-propagation algorithm." Figure 4 represents the three layers fully connected feed-forward network using the back propagation algorithm [14]. It consists of three layers: one input layer, one hidden layer, and one output layer. Here, x1, x2, …, xn are the input neurons. xb is the bias input, with associated weight w1b. w1b can increase or decrease in the net output of activation function depending on its positive or negative value.

The value of w1b is kept constant throughout the process. It can be 0 or � 1. y1, y2, …, yj are the hidden neurons and O1, O2, …, Om are the output neurons. vjn represents the input hidden layer weights, that is, these are the weights associated with input layer neurons connected to hidden layer neurons. wmj represents the output-hidden layer weights, that is, these are the weights associated with hidden layer neurons connected to output layer. Input, hidden, and output layers can be represented with the help of vectors as illustrated in Eqs. (8-10).

$$\mathbf{x} = [\mathbf{x}\_1, \mathbf{x}\_2, \dots, \mathbf{x}\_n]^t \leftarrow \text{input training vector} \tag{8}$$

$$y = \left[y\_1, y\_2, \dots, y\_j\right]^t \leftarrow \text{hidden layer vector} \tag{9}$$

$$O = [O\_1, O\_2, \dots, O\_m]^t \leftarrow \text{output vector} \tag{10}$$

Figure 4. Three-layer fully connected feed-forward network.

where 't' indicates transposition of matrix.

Given are P training pairs

specific classification category. In this algorithm, we are giving a solution to credit assignment problem using partial derivatives to find out how weight wij effects the error which is represented

∂E tð Þ

Here, partial derivatives are used because the direction of the errors can be determined, which may be positive or negative. If this derivative to be negative, this will add in weight and finally decreases the error and thus local minima can be reached (see step 6 of algorithm). This shows that if derivative of error is positive, the weight increases by adding a negative value to the weight and conversely, if negative. Procedure of taking derivative in this algorithm starts from weights of output layer to input layer, that is why, it is known as "back-propagation algorithm." Figure 4 represents the three layers fully connected feed-forward network using the back propagation algorithm [14]. It consists of three layers: one input layer, one hidden layer, and one output layer. Here, x1, x2, …, xn are the input neurons. xb is the bias input, with associated weight w1b. w1b can increase or decrease in the net output of activation function

The value of w1b is kept constant throughout the process. It can be 0 or � 1. y1, y2, …, yj are the hidden neurons and O1, O2, …, Om are the output neurons. vjn represents the input hidden layer weights, that is, these are the weights associated with input layer neurons connected to hidden layer neurons. wmj represents the output-hidden layer weights, that is, these are the weights associated with hidden layer neurons connected to output layer. Input, hidden, and

x ¼ ½ � x1,x2,…,xn t input training vector ð8Þ

O ¼ ½ � O1,O2,…,Om t output vector ð10Þ

hidden layer vector ð9Þ

output layers can be represented with the help of vectors as illustrated in Eqs. (8-10).

y ¼ y1, y2,…, yj h it

∂Wijð Þt ð7Þ

by Eq. (7).

60 Trends in Research on Microstrip Antennas

depending on its positive or negative value.

Figure 4. Three-layer fully connected feed-forward network.

{x1, a1, x2, a2,…, xP, aP} and there is a bias ¼ �1, η is the learning constant. Here a1, a2, and aP are the desired output vector response.

Step 1: η > 0, Maximum error Emax is chosen.

Step 2: Weights are initialized at small random values, E 0;p 1;k 1

where E ¼ present error; p ¼ counter with in the training cycle; k ¼ training step counter.

Step 3: Now begin the training process. Input is provided to input layer and output is Calculated as given in Eqs. (11) and (12).

$$\mathbf{x} \leftarrow \mathbf{x}p, \mathbf{a} \leftarrow \mathbf{a}p$$

$$y\_j = f\left(v\_j^t \mathbf{x}\right) \text{ where } j = 1, 2, 3, 4, \dots \text{J} \tag{11}$$

$$\mathbf{M}\_k = f\left(w\_j^t y\right) \text{ where } k = 1, 2, 3, 4, \dots, K \tag{12}$$

Here f (.) is the activation function.

Step 4: Calculate the new value of error by using previous value of error, desired output ak and actual output Ok using Eq. (13).

$$E' = \frac{1}{2}(a\_k - O\_k)^2 + E \text{ where } k = 1, \text{ 2, 3, 4, ..., K} \tag{13}$$

Step 5: Now value of error for both the layer is computed.

Error signal for output layer is calculated using Eq. (14).

$$\delta\_{ik} = \frac{1}{2}(a\_k - \mathcal{O}\_k)(1 - \mathcal{O}\_k^{-2}) \text{ for } k = \text{ 1, 2, 3, 4, ..., K} \tag{14}$$

Eq. (15) represents the Value of error for middle (hidden) layer

$$\delta\_{\vec{y}\vec{j}} = \frac{1}{2} \left( 1 - y\_{\vec{j}} \right)^{2} \sum\_{k=1}^{k} \delta\_{ok} \, w\_{k\vec{j}} \, \text{for} \, \vec{j} = \ 1, \ 2, \ 3, \ 4, \ldots, \!\! \tag{15}$$

Step 6: Now weights of output layer are adjusted using Eq. (16):

$$\text{if } w\_{k\dot{j}}' = w\_{k\dot{j}} + \eta \delta\_{\dot{\alpha}} y\_{\dot{j}} \text{ where } k = 1, 2, 3, 4, \dots, K, \text{ where } \dot{j} = 1, 2, 3, 4, \dots, \text{J} \tag{16}$$

Step 7: Now weights of Hidden layer are modified using Eq. (17).

$$\boldsymbol{\sigma}\_{ji}^{'} = \boldsymbol{\sigma}\_{ji} + \eta \boldsymbol{\delta}\_{\mathcal{Y}} \boldsymbol{x}\_i \text{ for } i = \ 1, \ 2, \ 3, \ldots, I \tag{17}$$

Step 8: If p is less than P then p ¼ p þ 1 and k ¼ k þ 1 and go to step 3, otherwise return back to step 9.

Step 9: At last, the sequence of full training process is finished.

If the value of present error (E) < maximum error (Emax), then stop the training process and now check out weights of output layer w and weights of hidden layer v.

If the present value of error (E) > maximum error (Emax), then E ¼ 0, p ¼ 1 and start a new training sequence by return back to step 3.

In first step of training, η and Emax are chosen. Step 2 is the initialization step where values of p, k, E, and weights are initialized. Step 3 is feed-forward step where both hidden layer and output layer outputs are calculated. In step 4, errors are computed. In step 5, back-propagation training takes place and error signal is computed for both hidden layer and output layer. In step 7, output layer and hidden layer weights are adjusted, respectively. In step 8, it is checked if p < P, then increment p and k and go to step 3, otherwise go to step 9. In step 9, if E < Emax, the training is complete and if E > Emax, a new training cycle is started.

## 2.1.2. Learning factors of back-propagation network

The training of back-propagation networks is dependent on various parameters such as initial weights, number of layers, number of neurons per layer, and updation rule.

1. Initial weight: the choice of initial weights determines how fast the networks will converge. Typical value for choosing initial weights is between �1.00 and 1.00 or �0.5 and 0.5. The final solution may be affected by the initial weights of multilayer feed-forward networks. One method of choosing the weight wij choosing is in the range �3 ffiffiffiffiffi Oi p , 3 ffiffiffiffiffi Oi p � �,

where Oi is the number of processing elements.

If all the weights are given equal values, the network may not be trained properly. If large values are given to weights at the initial stage, then the system may be stuck at local minima very near to starting point itself. So, it is necessary to initialize with small weights uniformly distributed in a small range

$$
\Delta w(t) = -\eta \nabla E(t) + \alpha \Delta w(t-1) \tag{18}
$$

where α is the selected momentum constant having values between 0.1 and 0.8. αΔw ð Þ t � 1 is called the momentum term. t and (t�1) indicates the current and most recent training step, respectively.

	- i. The mean squared error is sufficiently small.
	- ii. The rate of change of the mean squared error is sufficiently small.
	- iii. Combination of above two criteria.

#### 2.1.3. Realization of patch antenna with numerical results

IE3D electromagnetic simulation software is used for designing of the rectangular patch antenna using the following design parameters.

Resonant frequency ¼ 4.99 GHz, dielectric constant ¼ 4.4, height of dielectric material ¼ 1.6 mm

Now, the dimensions of patch can be calculated using Eqs. (1)–(6) for 4.99 GHz resonant frequency and given by

L ¼ 13.34 mm, W ¼ 17.7 mm

Step 8: If p is less than P then p ¼ p þ 1 and k ¼ k þ 1 and go to step 3, otherwise return back to

If the value of present error (E) < maximum error (Emax), then stop the training process and

If the present value of error (E) > maximum error (Emax), then E ¼ 0, p ¼ 1 and start a new

In first step of training, η and Emax are chosen. Step 2 is the initialization step where values of p, k, E, and weights are initialized. Step 3 is feed-forward step where both hidden layer and output layer outputs are calculated. In step 4, errors are computed. In step 5, back-propagation training takes place and error signal is computed for both hidden layer and output layer. In step 7, output layer and hidden layer weights are adjusted, respectively. In step 8, it is checked if p < P, then increment p and k and go to step 3, otherwise go to step 9. In step 9, if E < Emax, the

The training of back-propagation networks is dependent on various parameters such as initial

1. Initial weight: the choice of initial weights determines how fast the networks will converge. Typical value for choosing initial weights is between �1.00 and 1.00 or �0.5 and 0.5. The final solution may be affected by the initial weights of multilayer feed-forward

networks. One method of choosing the weight wij choosing is in the range �3

If all the weights are given equal values, the network may not be trained properly. If large values are given to weights at the initial stage, then the system may be stuck at local minima very near to starting point itself. So, it is necessary to initialize with small weights

2. Learning rate (η): the learning rate affects the convergence of back-propagation. A large value of η simply increases the speed of convergence but this large value introduces instability into the learning rule causing oscillations in the learned weights and on the other hand, if η has small value, the speed of training will be less. For successful operation,

3. Number of training data: the numbers of input nodes are determined by the dimension, or size or the input vector to be classified or generalized with a certain output quality. The

4. Momentum: the gradient decent is very slow using small η and oscillates using large η. The problem of the oscillations can be sorted out by adding a momentum factor to the

ffiffiffiffiffi Oi p , 3

ffiffiffiffiffi Oi p � �

,

Step 9: At last, the sequence of full training process is finished.

training sequence by return back to step 3.

62 Trends in Research on Microstrip Antennas

2.1.2. Learning factors of back-propagation network

where Oi is the number of processing elements.

uniformly distributed in a small range

the range of η lies between10�3 and 10.

weight adjustments as illustrated in Eq. (18)

training data should be sufficient and proper for training.

now check out weights of output layer w and weights of hidden layer v.

training is complete and if E > Emax, a new training cycle is started.

weights, number of layers, number of neurons per layer, and updation rule.

step 9.

The basic design of microstrip patch antenna is shown in Figure 5. Here, 50 ohm port (Zo) is connected to the patch by using the microstrip feed line technique. Feed is the point where patch radiates maximum. Eq. (19) is used to calculate the width Wo of microstrip line, where εreff is the effective dielectric constant.

$$\mathcal{Z}\_0 = 120\Pi/[\because(\varepsilon\_{r\not\leq f})\{\mathcal{W}\_0/h + 1.393 + .667\ln(\mathcal{W}\_0/h + 1.444)\}]\tag{19}$$

which gives W0 ¼ 2.94 mm.

When IE3D electromagnetic simulation is performed, then we obtain the different resultant graph between return loss and frequency. While changing the dimension of patch, the different resultant graphs are obtained between return loss and frequency using simulation software, as shown in Figures 6–8. Here all the dimensions are taken in mm.

(1) When W ¼ 17.7, L ¼ 13.34, εr ¼ 4.4, h ¼ 1.6

Figure 5. Design of microstrip patch antenna using simulation software.

Figure 6. Simulated response of patch at 4.99 GHz resonant frequency.

Here, 4.94 GHz is the lower cutoff frequency (f1) and 5.04 GHz is the upper cutoff frequency (f2). Furthermore, only one dimension of the patch will be varied while maintaining all other parameters constant and vice versa. Frequency response between return loss and frequency are obtained, as shown in Figure 7, which gives the upper and lower cutoff frequencies (f2, f1) when the width and length of patch is 17.7 and 13.55 mm, respectively.

(2) When W ¼ 17.7 mm, εr ¼ 4.4, L ¼ 13.55 mm, h ¼ 1.6 mm

(3) When W ¼ 17.7 mm, L ¼ 14.15 mm, h ¼ 1.6, εr ¼ 4.4 mm

Design and Analysis of Microstrip Patch Antennas Using Artificial Neural Network http://dx.doi.org/10.5772/intechopen.69522 65

Figure 7. Simulated response of patch at 4.89 GHz resonant frequency.

Figure 8. Simulated response of patch at 4.77 GHz resonant frequency.

Here, 4.94 GHz is the lower cutoff frequency (f1) and 5.04 GHz is the upper cutoff frequency (f2). Furthermore, only one dimension of the patch will be varied while maintaining all other parameters constant and vice versa. Frequency response between return loss and frequency are obtained, as shown in Figure 7, which gives the upper and lower cutoff frequencies (f2, f1)

when the width and length of patch is 17.7 and 13.55 mm, respectively.

(2) When W ¼ 17.7 mm, εr ¼ 4.4, L ¼ 13.55 mm, h ¼ 1.6 mm (3) When W ¼ 17.7 mm, L ¼ 14.15 mm, h ¼ 1.6, εr ¼ 4.4 mm

Figure 6. Simulated response of patch at 4.99 GHz resonant frequency.

Figure 5. Design of microstrip patch antenna using simulation software.

64 Trends in Research on Microstrip Antennas

Figures 6–8 represent the variation of frequency range of microstrip patch antenna with respect to variation in dimensions. Around 25–30 samples are collected using the EM simulation tool for ANN training for different dimensions, which are illustrated in Table 1. It is used for the analysis of patch antenna.

Now, the neural network is constructed for rectangular microstrip patch antenna. For the analysis problem of neural network, the dimensions (W, L) are considered as the input parameters of the ANN model whereas output parameters are upper and lower cutoff frequencies,

Table 1. Simulated results for ANN analysis of patch.

which act as targets. The artificial neural network is trained by using the ANN feed-forward back-propagation training algorithm and transfer function so that error can be minimized with less computation time. Matlab neural network graphical user interface (GUI) toolbox is used as a plateform for ANN training. The "nntool" command is used for ANN training in the GUI, which will display the network or data manager window, as given in Figure 9.

After displaying this window, input and outputs are provided in the matrix form by clicking on "new data.". Now, a neural network is created by clicking on "New network." Here, the feedforward back-propagation algorithm and trainlm (Levenberg-Marquardt back-propagation Design and Analysis of Microstrip Patch Antennas Using Artificial Neural Network http://dx.doi.org/10.5772/intechopen.69522 67

Figure 9. GUI of ANN.

which act as targets. The artificial neural network is trained by using the ANN feed-forward back-propagation training algorithm and transfer function so that error can be minimized with less computation time. Matlab neural network graphical user interface (GUI) toolbox is used as a plateform for ANN training. The "nntool" command is used for ANN training in the GUI,

Inputs (dimensions of patch in mm) Targets (lower and upper cutoff frequency in GHz)

WL f1 f2 17.7 13.34 4.94 5.04 17.7 13.55 4.86 4.95 17.7 13.65 4.82 4.91 17.7 13.85 4.8 4.89 17.7 14.05 4.77 4.85 17.7 14.15 4.73 4.81 17.7 14.25 4.71 4.79 17.7 14.35 4.69 4.76 17.7 14.45 4.66 4.73 18.3 13.85 4.78 4.87 18.3 14.35 4.65 4.73 18.8 14.35 4.61 4.7 18.8 14.85 4.49 4.55 19.3 14.85 4.47 4.55 19.3 15.35 4.37 4.41 19.8 15.35 4.35 4.41 20.3 15.85 4.31 4.37 20.3 16.35 4.29 4.35 20.8 16.35 4.27 4.33 20.8 16.85 4.26 4.33 21.3 16.85 4.21 4.27 21.3 17.35 4.16 4.21 21.8 17.35 4.14 4.19 21.8 17.85 4.02 4.04 22.3 17.85 3.99 4.01 22.3 18.35 3.92 3.93

66 Trends in Research on Microstrip Antennas

After displaying this window, input and outputs are provided in the matrix form by clicking on "new data.". Now, a neural network is created by clicking on "New network." Here, the feedforward back-propagation algorithm and trainlm (Levenberg-Marquardt back-propagation

which will display the network or data manager window, as given in Figure 9.

Table 1. Simulated results for ANN analysis of patch.

training function) are applying where supported transfer functions are purelin (linear transfer function) and tansig (hyperbolic tangent sigmoid transfer function).

#### 2.1.4. Analysis of microstrip patch antenna using artificial neural network

The network architecture is one of the basic building blocks for ANN to be deployed. It determines how the number of layers and number of neurons are decided in the different layers and how these layers are interconnected with each other through corresponding weights. The numbers of inputs and output layers are always constant, that is, a single layer is required at the input and output sides but it is very tough task to determine the number of hidden layers and the number of neurons in it. The rule-of-thumb method is used for deciding the number of neurons in the hidden nodes. According to this rule, the total numbers of hidden layer neurons are summation of the size of output layer plus 2/3 of the input layer size. The number of hidden layer neurons should be less than twice of the number of neurons in input layer. The size of the hidden layer neurons is between the input layer size and the output layer size. But the above three methods for determining the number of hidden nodes are not always true because not only the input layer and the output layer determines the size of the hidden layer neurons but also the dataset of training samples, types of architecture, the training algorithm, and complexity of the activation function applied on the neurons decides it. Multiple hidden layers are used in the applications where accuracy is the criteria and training time is not important. Usually, one or two hidden layers are adequate for resolving any nonlinear complex task. The third hidden layer can be added for improving accuracy, but this will increase overall complexity of the neural network and the total training time will be increased. Four hidden layers are not used in the neural network architecture because it cannot follow the rule of thumb. If there are three hidden layers then total neurons in hidden layers ¼ 2 (3 � 2/3) (twice of input). Minimum hidden layer must be used in ANN to reduce the complexity and training time. As shown in Figure 10, neural network architecture consists of

Figure 10. Neural network architecture for microstrip patch antenna.

three layers. It has one input, one hidden, and one output layer. Input, hidden, and output layer consists of two neurons. Inputs W and L are applied at the input neurons while outputs f1 and f2 are obtained from the output neurons. The ANN training graph results for the analysis of microstrip patch antenna are shown in Figure 11, which shows that 21 epochs are required for ANN training. The full sets of input samples are passed through the artificial neural network for minimization of the error in the back-propagation algorithms, which is known as an epoch. Training graph reveals that error reduced from 101 to nearly 104 , as shown in Figure 11.

Trained results (f1 and f2) for ANN analysis of patch are given in Table 2.

## 2.1.5. Synthesis of microstrip patch antenna using artificial neural network

Synthesis is defined as to obtain the dimensions of microstrip patch (W, L) as targets while providing the cutoff frequencies (f1, f2), thickness and dielectric constants of the dielectric material as the input parameters of ANN model. Around 25–30 samples are collected for ANN training which is obtained by varying the dimensions of microstrip patch antenna using electromagnetic simulation software as illustrated in Table 3. It is used for the synthesis of patch antenna. Trained Results (W, L) for ANN Synthesis of patch is illustrated in Table 4. The neural network is trained by using back-propagation algorithm. The ANN training graph

Figure 11. ANN training results for analysis of microstrip patch antenna.

Table 2. Trained results for ANN analysis of patch.

three layers. It has one input, one hidden, and one output layer. Input, hidden, and output layer consists of two neurons. Inputs W and L are applied at the input neurons while outputs f1 and f2 are obtained from the output neurons. The ANN training graph results for the analysis of microstrip patch antenna are shown in Figure 11, which shows that 21 epochs are required for ANN training. The full sets of input samples are passed through the artificial neural network for minimization of the error in the back-propagation algorithms, which is known as an epoch.

Synthesis is defined as to obtain the dimensions of microstrip patch (W, L) as targets while providing the cutoff frequencies (f1, f2), thickness and dielectric constants of the dielectric material as the input parameters of ANN model. Around 25–30 samples are collected for ANN training which is obtained by varying the dimensions of microstrip patch antenna using electromagnetic simulation software as illustrated in Table 3. It is used for the synthesis of patch antenna. Trained Results (W, L) for ANN Synthesis of patch is illustrated in Table 4. The neural network is trained by using back-propagation algorithm. The ANN training graph

, as shown in Figure 11.

Training graph reveals that error reduced from 101 to nearly 104

Figure 10. Neural network architecture for microstrip patch antenna.

68 Trends in Research on Microstrip Antennas

Trained results (f1 and f2) for ANN analysis of patch are given in Table 2.

2.1.5. Synthesis of microstrip patch antenna using artificial neural network

Figure 11. ANN training results for analysis of microstrip patch antenna.

Table 3. Simulated results for ANN synthesis of patch.

Table 4. Trained results for ANN synthesis of patch.

Inputs (lower and upper cutoff frequency in GHz) Targets (dimensions of patch in mm)

Inputs (lower and upper cutoff frequency in GHz) Targets (dimensions of patch in mm)

f1 f2 W L 4.94 5.04 17.6823 13.2641 4.86 4.95 17.6905 13.751 4.82 4.91 17.7813 13.8311 4.8 4.89 17.8317 13.8756 4.77 4.85 17.8594 13.9008 4.73 4.81 17.9753 14.0034 4.71 4.79 18.0396 14.0602 4.69 4.76 18.0393 14.0613 4.66 4.73 18.1438 14.154

f1 f2 W L 4.73 4.81 17.7 14.15 4.71 4.79 17.7 14.25 4.69 4.76 17.7 14.35 4.66 4.73 17.7 14.45 4.78 4.87 18.3 13.85 4.65 4.73 18.3 14.35 4.61 4.7 18.8 14.35 4.49 4.55 18.8 14.85 4.47 4.55 19.3 14.85 4.37 4.41 19.3 15.35 4.35 4.41 19.8 15.35 4.31 4.37 20.3 15.85 4.29 4.35 20.3 16.35 4.27 4.33 20.8 16.35 4.26 4.33 20.8 16.85 4.21 4.27 21.3 16.85 4.16 4.21 21.3 17.35 4.14 4.19 21.8 17.35 4.02 4.04 21.8 17.85 3.99 4.01 22.3 17.85 3.92 3.93 22.3 18.35

Table 3. Simulated results for ANN synthesis of patch.

70 Trends in Research on Microstrip Antennas

results for the synthesis of microstrip patch antenna is shown in Figure 12 which shows that 100 epochs are required for ANN training and error get reduced from 102 to nearly 102 .

Figure 12. ANN training results for synthesis of microstrip patch antenna.

Network errors and weights are obtained in matrix form during ANN training as given below.

#### Network errors:

[0.20766 0.10947 0.018694 �0.031744 �0.05942 �0.17535 �0.23957 �0.2393 �0.34378 0.41415 0.039568 0.26975 �0.041452 0.055095 �0.015806 �0.038441 0.1054 �0.084949 0.21663 �0.14213 0.074867 �0.18731 0.084323 �0.085043 0.12542 �0.025298;

�0.31411 �0.20102 �0.1811 �0.025609 0.14918 0.14663 0.1898 0.28873 0.296 �0.073367 0.094171 �0.14313 0.071068 �0.28069 0.12893 �0.32561 �0.14788 0.17943 �0.00094985 0.18709 �0.087086 0.14741 �0.065711 0.11766 �0.17911 0.038876]

## Weights

[1.0349 3.4722;

3.0377 2.2758]

## 3. Conclusion

In this work, the rectangular microstrip patch antenna is designed using the artificial neural network modeling procedure. Here synthesis refers to forward side and analysis refers to reverse side of the problem. Therefore in synthesis problem, the geometric dimensions such as length and the width of antenna are obtained with more accuracy in less time as compared to simulation software while providing resonant frequency, thickness, and dielectric constant at the input side of the ANN model. In the analysis problem of patch antenna, resonant frequency or both upper and lower cutoff frequencies of patch antenna are obtained at the output side of the ANN model while providing the dimensions of patch (W, L) and other parameters at the input side of the ANN model with much accuracy in less time.

Now the future work in this work includes trying more topologies to obtain more compact patch antennas, filters, and many other microwave/RF modeling design using artificial neural network for different band of applications such as ultra-wideband (UWB), Global System for Mobile communications (GSM), and WiMAX applications.

## Appendix

#### MATLAB program for finding out the dimensions of microstrip patch antenna using the ANN

NNTWARN OFF disp\_freq ¼ 100; max\_epochs ¼ 8000; %1r ¼ 0.013; err\_goal ¼ 0.009;

p ¼ [4.94 4.86 4.82 4.8 4.77 4.73 4.71 4.69 4.66 4.78 4.65 4.61 4.49 4.47 4.37 4.35 4.31 4.29 4.27 4.26 4.21 4.16 4.14 4.02 3.99 3.92;

5.04 4.95 4.91 4.89 4.85 4.81 4.79 4.76 4.73 4.87 4.73 4.7 4.55 4.55 4.41 4.41 4.37 4.35 4.33 4.33 4.27 4.21 4.19 4.04 4.01 3.93];

tx ¼ [17.7 17.7 17.7 17.7 17.7 17.7 17.7 17.7 17.7 18.3 18.3 18.8 18.8 19.3 19.3 19.8 20.3 20.3 20.8 20.8 21.3 21.3 21.8 21.8 22.3 22.3;

13.35 13.55 13.65 13.85 14.05 14.15 14.25 14.35 14.45 13.85 14.35 14.35 14.85 14.85 15.35 15.35 15.85 16.35 16.35 16.85 16.85 17.35 17.35 17.85 17.85 18.35];

%bus6

Network errors and weights are obtained in matrix form during ANN training as given below.

[0.20766 0.10947 0.018694 �0.031744 �0.05942 �0.17535 �0.23957 �0.2393 �0.34378 0.41415 0.039568 0.26975 �0.041452 0.055095 �0.015806 �0.038441 0.1054 �0.084949 0.21663 �0.14213

�0.31411 �0.20102 �0.1811 �0.025609 0.14918 0.14663 0.1898 0.28873 0.296 �0.073367 0.094171 �0.14313 0.071068 �0.28069 0.12893 �0.32561 �0.14788 0.17943 �0.00094985

In this work, the rectangular microstrip patch antenna is designed using the artificial neural network modeling procedure. Here synthesis refers to forward side and analysis refers to reverse side of the problem. Therefore in synthesis problem, the geometric dimensions such as length and the width of antenna are obtained with more accuracy in less time as compared to simulation software while providing resonant frequency, thickness, and dielectric constant at the input side of the ANN model. In the analysis problem of patch antenna, resonant frequency or both upper and lower cutoff frequencies of patch antenna are obtained at the output side of the ANN model while providing the dimensions of patch (W, L) and other

Now the future work in this work includes trying more topologies to obtain more compact patch antennas, filters, and many other microwave/RF modeling design using artificial neural network for different band of applications such as ultra-wideband (UWB), Global System for

MATLAB program for finding out the dimensions of microstrip patch antenna using the ANN

parameters at the input side of the ANN model with much accuracy in less time.

Mobile communications (GSM), and WiMAX applications.

0.074867 �0.18731 0.084323 �0.085043 0.12542 �0.025298;

0.18709 �0.087086 0.14741 �0.065711 0.11766 �0.17911 0.038876]

Network errors:

72 Trends in Research on Microstrip Antennas

Weights

[1.0349 3.4722; 3.0377 2.2758]

3. Conclusion

Appendix

NNTWARN OFF

disp\_freq ¼ 100;

err\_goal ¼ 0.009;

%1r ¼ 0.013;

max\_epochs ¼ 8000;

[w1,b1,w2,b2] ¼ initff(p,2,'tansig',tx,'purelin');

Tp ¼ [disp\_freq,max\_epochs,err\_goal];

[w1,b1,w2,b2,epochs,tr] ¼ trainbpx(w1,b1,'tansig',w2,b2,'purelin',p,tx,tp);

```
gil ¼ simuff(p,w1,b1,'tansig',w2,b2,'purelin')
```
save patch1.mat;

Find the output:

P ¼ [4.94 ; 5.04];

Result ¼ simuff(p,w1,b1,'tansig',w2,b2,'purelin')

outputs:

[17.683 ; 13.265]

## Author details

Vivek Singh Kushwah1 \* and Geetam Singh Tomar2

\*Address all correspondence to<EMAIL_ADDRESS>
1 Amity University, Madhya Pradesh, India

2 Govt. THDC Engg. College, Tihri, Uttarakhand, India

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[6] Wong KL, Tang CL, Chen HT. A compact meandered circular microstrip antenna with a

[7] Sağıroğlu S, Güney K, Erler M. Resonant frequency calculation for circular microstrip antennas using artificial neural networks. International Journal of RF and Microwave

[8] Karaboğa D, Güney K, Sağıroğlu S, Erler M. Neural computation of resonant frequency of electrically thin and thick rectangular microstrip antennas. Microwaves, Antennas and

[9] Kuo YL, Chiou TW, Wong LK A novel dual-band printed inverted-F antenna. Microwave

[10] Reed S, Desclos L, Terret C, Toutain S. Patch antenna size reduction by means of induc-

[11] Anguera J, Puente C, Borja C, Montero R, Soler J. Small and high-directivity bow-tie patch antenna based on the Sierpinski fractal. Microwave and Optical Technology Let-

[12] Güney K, Sağıroğlu S, Erler M. Generalized neural method to determine resonant frequencies of various microstrip antennas. International Journal of RF and Microwave

[13] Mishra RK, Patnaik A. Designing rectangular patch antenna using the neurospectral method. Antennas and Propagation, IEEE Transactions. 2003;51(8):1914–1921

[14] Tqürker N, Günes F, Yildirim T. Artificial neural design of microstrip antennas. Turkish

[15] Ansari JA, Yadav NP, Mishra A, Kamakshi, Singh A. Broadband rectangular microstrip antenna loaded with a pair of u-shaped slot. International Journal of Microwave and

[16] Garima, Bhatnagar D, Saini JS, Saxena VK, Joshi LM. Design of broadband circular patch microstrip antenna with diamond shapeslot. Indian Journal of Radio & Space Physics.

[17] Wang Z, Fang S, Fu S, Jia S. Single-fed broadband circularly polarized stacked patch antenna with horizontally meandered strip for universal UHF RFID applications. IEEE

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74 Trends in Research on Microstrip Antennas

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**Recent Trends to Microstrip Antennas Research**

**Provisional chapter**

## **Circularly Polarized T-Stub Coupled Microstrip Antenna Structure for WLAN Structure for WLAN**

**Circularly Polarized T-Stub Coupled Microstrip Antenna**

DOI: 10.5772/67931

Milind Thomas Themalil Milind Thomas Themalil Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67931

#### **Abstract**

In this chapter, a novel feeding mechanism for single layer microstrip patch antenna to generate circular polarization using electromagnetically coupled microstrip T junction is presented. The antenna structure eliminates the need for capacitors in the RF path for active antenna applications in wireless local area network (WLAN). The simulated results were verified by measurement using the vector network analyzer.

**Keywords:** active antenna, DC isolation, T-stub coupled, circularly polarized

## **1. Introduction**

Wireless local area networks (WLAN) use antennas with different standards having characteristics such as miniaturization, conformability, wideband operation, multiple resonances and good gain. New microstrip antenna designs hence provide an ideal solution due to these features [1, 2]. Active antennas integrate the circuit with radiation properties into a monolithic microwave integrated circuit; a significant research area in recent years. Broadband wireless communications have increased rapidly in recent years demanding quality of service, security, handover and increased throughput for the wireless local area networks. The aim of next generation wireless communication is high-speed networking service enabling multimedia communication. An important high data rate wireless broadband communication standard is ETSI high performance local area network type 2 (HIPERLAN 2) which uses 5.15–5.725 GHz band with omni-directionality. Dual circularly polarized antennas, as far as active integrated antennas are concerned, are compact and single layered.

A drawback of single layered patch antenna structures, whether probe fed or microstrip line fed, for active antennas with dual polarization, is their DC contact between ports via the patch.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Active antennas require DC isolated ports. A solution is to embed additional capacitors in the RF path or use multilayered structures like aperture coupling. High Q lumped RF capacitors are monetarily expensive and complicated to model in the design process of active antennas, with an increase in the physical size and cross polarization levels. Circular polarization provides flexibility in antenna orientation between transmitter and receiver, better mobility, weather penetration features and reduction in multipath fading effects. However, some inherent limitations include the attainable impedance and axial ratio bandwidths [3, 4]. Plenty of investigations have been carried out on this subject, which include design of circularly polarized microstrip antennas with single feed and narrow axial ratio bandwidth and also with double feed with relatively wide axial ratio bandwidth. The structure presented in this chapter is capable of providing DC as well as RF isolation, direct 50 Ω matching and increased bandwidth compared to other single layer feeding mechanisms. The antenna is circularly polarized in broadside direction which is an attractive feature for WLAN applications. Good gain and axial ratio bandwidth are attained.

#### **2. Design of the antenna structure**

The antenna structure presented in this chapter consists of two-coupled microstrip T junctions on adjacent sides of a square patch as shown in **Figure 1**. The T junctions transform the high radiation resistance of the patch to lower impedance [5]. The microstrip Ts have DC isolation between them; there is no need for capacitors in the RF path in dual polarized active antenna applications [6, 7]. The small width of the microstrip T causes the currents in the two

**Figure 1.** Top view of the microstrip T-stub coupled patch antenna.

arms of the microstrip Ts to be in opposite directions to the excited TM modes. Therefore, the radiation pattern of the structure is not affected significantly by the microstrip T. By controlling the length of the T arm and the distance between the patch and the T arm, we can achieve 50 Ω impedance match. Dimension of the patch is 16.8 mm × 16.8 mm. The T-arms provided on both radiating and non-radiating edge are fed by a co-axial probe. Two rectangular slots loaded on the patch on opposite sides provide circular polarization as in **Figure 1**. Slot loading on opposite edges significantly improves bandwidth besides providing circular polarization [8]. The co-axial probe feed point is 10 mm to the left of centre and 3 mm below the centre of the patch. In this simulation, a 6 dBi gain bandwidth of 350 MHz is obtained.

The antenna was fabricated on a 1.6 mm thick PTFE substrate with dielectric constant εr = 2.32 and loss tangent tanδ = 0.001. The fabricated antenna prototype is shown in **Figure 2**.

**Figure 2.** Photograph of fabricated microstrip T-stub coupled patch antenna.

Active antennas require DC isolated ports. A solution is to embed additional capacitors in the RF path or use multilayered structures like aperture coupling. High Q lumped RF capacitors are monetarily expensive and complicated to model in the design process of active antennas, with an increase in the physical size and cross polarization levels. Circular polarization provides flexibility in antenna orientation between transmitter and receiver, better mobility, weather penetration features and reduction in multipath fading effects. However, some inherent limitations include the attainable impedance and axial ratio bandwidths [3, 4]. Plenty of investigations have been carried out on this subject, which include design of circularly polarized microstrip antennas with single feed and narrow axial ratio bandwidth and also with double feed with relatively wide axial ratio bandwidth. The structure presented in this chapter is capable of providing DC as well as RF isolation, direct 50 Ω matching and increased bandwidth compared to other single layer feeding mechanisms. The antenna is circularly polarized in broadside direction which is an attractive feature for WLAN applications. Good gain and axial ratio bandwidth are attained.

The antenna structure presented in this chapter consists of two-coupled microstrip T junctions on adjacent sides of a square patch as shown in **Figure 1**. The T junctions transform the high radiation resistance of the patch to lower impedance [5]. The microstrip Ts have DC isolation between them; there is no need for capacitors in the RF path in dual polarized active antenna applications [6, 7]. The small width of the microstrip T causes the currents in the two

**2. Design of the antenna structure**

80 Trends in Research on Microstrip Antennas

**Figure 1.** Top view of the microstrip T-stub coupled patch antenna.

## **3. Simulated and measured results for the structure**

The simulated and measured resonance frequencies are 5.22 and 5.205 GHz as shown in **Figures 3** and **4**, respectively. The simulated and measured return losses are −27 and −25 dB as shown in **Figures 3** and **4**, respectively. Simulated axial ratio is shown in **Figure 5**. Minimum axial ratio is 0.2 dB. The simulated and measured −10 dB impedance bandwidths are 380 MHz as shown in **Figure 6** and 350 MHz as shown in **Figure 4**.

The simulated results of radiation pattern and gain of the structure are presented in **Figures 7** and **8**, respectively. Radiation is in the broadside direction and the highest gain obtained is 6.5 dBi. The 6 dBi gain bandwidth product is 350 MHz which is well within the range of the WLAN application in the 5.2 GHz band. A good gain is obtained throughout the entire range of application and the antenna has 77% antenna efficiency as shown in **Figure 9**.

**Figure 3.** Simulated return loss.

**Figure 4.** Measured return loss.

**Figure 5.** Simulated axial ratio.

**Figure 6.** Simulated VSWR.

**Figure 7.** Simulated radiation pattern.

**Figure 5.** Simulated axial ratio.

**Figure 3.** Simulated return loss.

82 Trends in Research on Microstrip Antennas

**Figure 4.** Measured return loss.

**Figure 8.** Simulated gain.

**Figure 9.** Simulated efficiency.

**Tables 1** and **2** show the simulated and measured results.

**Table 1.** Simulated results.

**Table 2.** Measured results.

## **4. Conclusion**

A compact and broadband circularly polarized microstrip patch antenna structure with T-shaped electromagnetically coupled ports was designed, simulated, fabricated and tested. The antenna structure is intended for active antenna WLAN applications. The simulated results are verified by the measurement using the vector network analyzer. For active antenna applications, the structure does not need any capacitor in the RF path of the circuit.

## **Acknowledgements**

The author would like to acknowledge the work of Dr. Anders Rydberg and Dr. Dhanesh Kurup of the Signals & Systems Division, Uppsala University, Sweden for inspiring the present chapter. Deepest gratitude to Dr. J S Roy of KIIT University, Bhubaneswar, India and Dr. Bhaskar Gupta of Jadavpur University, Kolkata, India for supervising the author's Ph.D Thesis. The author would like to thank the Electronics & Communication Engineering Department of Birla Institute of Technology, Ranchi, India and the Electronics & Telecommunication Engineering Department of Jadavpur University, Kolkata, India for their research facilities. The author would also like to acknowledge the Microwave Laboratory Division, Department of Electronics and Communication Engineering, Indian Institute of Science (IISc.), Bangalore, India for their research and measurement facilities. The author is extremely grateful to Believers Church Caarmel Engineering College, Kerala, India for their inspiration, encouragement and support.

## **Author details**

Milind Thomas Themalil

Address all correspondence to<EMAIL_ADDRESS>
Research & Development, Believers Church Caarmel Engineering College, Kerala, India

## **References**

**Tables 1** and **2** show the simulated and measured results.

**Return loss bandwidth**

**Max. gain (dBi) 6 dBi gain**

5.22 GHz −27 dB 380 MHz 6.5 dBi 350 MHz 0.2 dB 180 MHz 77%

**bandwidth**

**Min. axial ratio**

**3 dB axial ratio bandwidth** **Efficiency**

**Figure 8.** Simulated gain.

84 Trends in Research on Microstrip Antennas

**Figure 9.** Simulated efficiency.

**Table 1.** Simulated results.

**Return loss S11 10 dB**

**Resonance frequency**

**Chapter 5**

**Provisional chapter**

## **Bio-Inspired Microstrip Antenna**

**Bio-Inspired Microstrip Antenna**

Alexandre Jean René Serres, Georgina Karla de Freitas Serres, Paulo Fernandes da Silva Júnior, Raimundo Carlos Silvério Freire, Josiel do Nascimento Cruz, Tulio Chaves de Albuquerque, Maciel Alves Oliveira and Paulo Henrique da Fonseca Silva Alexandre Jean René Serres, Georgina Karla de Freitas Serres, Paulo Fernandes da Silva Júnior, Raimundo Carlos Silvério Freire, Josiel do Nascimento Cruz, Tulio Chaves de Albuquerque, Maciel Alves Oliveira and Paulo Henrique da Fonseca Silva Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.69766

#### **Abstract**

[3] Chung KL. A wideband circularly polarized H-shaped patch antenna, IEEE Transactions

[4] Chang FS, Wong KL, Chiou TW. Low-cost broadband circularly polarized patch antenna.

[5] Kurup DG, Rydberg A, Himdi M. Compact microstrip T – coupled patch antenna for dual polarization and active antenna applications. Electronics Letters. 2002;**38**(21):1240-1241

[6] Choi DH, Park SO. Active integrated antenna using a T shaped microstrip coupled patch

[7] Chang K, Hummer KA, Gopalakrishnan GK. Active radiating element using FET source integrated with microstrip patch antenna. Electronics Letters. 1988;**24**:1347-1348

[8] Roy JS, Thomas M. Design of a circularly polarized microstrip antenna for WLAN.

IEEE Transactions of Antennas and Propagation. 2003;**51**:3006-3009

antenna. Microwave & Optical Technology Letters. 2005;**44**(5):434-436

Progress In Electromagnetic Research, PIER M. 2008;**3**:79-90

of Antennas and Propagation. 2010;**58**:3379-3383

86 Trends in Research on Microstrip Antennas

In the last few years, bio‐inspired solutions have attracted the attention of the scientific community. Several world‐renowned institutions have sponsored and created laborato‐ ries in order to understand the forms, functions and behavior of living organisms. Some methods can be highlighted in the search for geometric representation of the shapes found in the nature, the fractal geometry, the polar geometry, and the superformula of Gielis. This chapter is focusing on bio‐inspired microstrip antennas, especially on leaf‐ shaped antennas from the Gielis superformula that open a vast research field for more compact antennas with low visual impact.

DOI: 10.5772/intechopen.69766

**Keywords:** bio‐inspired, Gielis superformula, compact antenna, leaf‐shaped antennas, visual impact

## **1. Introduction**

From the 1990s, with the advent of the Internet, the popularization of portable terminals (lap‐ tops, mobile phones, etc.) favored the telecommunications industry and the infrastructure of networks experienced a remarkable growth [1, 2]. When the information age emerges from an increasingly networked world, the digital information, and communication technology

and reproduction in any medium, provided the original work is properly cited.

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, permeate the society and are increasingly important to their development [3, 4]. Modern wire‐ less applications demand esthetic, multifunctional, and portable terminals that operating in multiple frequency bands and can integrate different wireless services: 4G, Wi‐Fi, Bluetooth, NFC, GPS and so on. Future trends toward 5G systems also require enhanced mobile broad‐ band for emergent applications [5].

With the rapid advance of wireless communication systems, the use of antennas in base sta‐ tions and portable terminals must meet increasingly stringent criteria, such as miniaturiza‐ tion, integration with other systems, and multiband or broadband operation [1–4]. Due its attractive features, low‐profile microstrip antennas (MSA) and arrays are well suitable to meet the demands of fixed or mobile wireless applications [6–9].

Antenna parameter specifications change according to application. Indeed, fixed antennas must have high gain, stable radiation pattern, and bandwidth tolerance; embedded anten‐ nas should be efficient in radiation and possess larger beam width [3]. In short‐range UWB wireless systems, the antenna bandwidth exceeds the lesser of 500 MHz or 20% of the center frequency [9]. Thus, impedance bandwidth, gain, radiation pattern, and polarization are fun‐ damental parameters for antenna designers to take into account.

A trend in the application of antennas for modern wireless systems is the use of compact antennas with stable radiation coverage over a wideband [2–4]. An antenna must be compact in many situations: embedded antennas, wearable antennas, camouflaged antennas, and so on. However, most often an antenna electrically small narrows the impedance bandwidth, reduces gain, and limits control of the resulting radiation pattern [4, 6, 9].

Various institutions around the world have invested resources and established research cen‐ ters with focus on biologically inspired engineering as the Massachusetts Institute Technology, the London College, and the Harvard University, for example. This research branch looks in nature similar solution to the problems encountered in engineering. With appropriate adjustments, it is possible to adapt the solutions used by the nature of the engineering prob‐ lems [10]. According to [11], the development of a bioinspired methodology requires three steps: identification of analogies, with structures and methods that are similar; understand‐ ing, detailed modeling of actual biological behavior; and engineering, which is the process of model simplification and adjustments to technical applications.

The researches that use the bio‐inspired geometry for the development of antennas are recent and can be divided into two groups: antennas with bio‐inspired geometries in animals and antennas with bio‐inspired geometries in plants. Bio‐inspired antennas in animals try to use internal organs or external parts of the animals which work analogously to the operation of the antennas used in the communication systems. A biomimetic antenna in the shape of a bat's ear [12] can be cited, a biologically inspired electrically small antenna arrays that mimic the hearing mechanism of such insects [13], an antenna system based on the wasp's curved antennas [14] and a biologically inspired vascular antenna reconfiguration mechanism [15]. Research on antennas with bio‐inspired plant geometries uses the plants or part of them (stem, leaves, and flowers) to develop antennas for various frequencies and technologies. The study of microstrip antennas with models bio‐inspired on leaves (leaf‐shaped antennas) has aroused the interest of researchers due to the good results. The leaves present similar characteristics to fractals as, for example, the reduction of the total dimensions with the increase of perim‐ eter. Furthermore, the leaves have a light‐harvesting reaction center complex, i.e., an array of antennas capable of operating in the visible light range (400–700 nm) with characteristics which analog to satellite dishes. The main purpose of the leaf shape is to capture the sunlight to transform it in chemical energy by a photosynthesis process. The bioinspired on leaves open a vast research field for more compact antennas with low visual impact. Among the published works, the following can be highlighted. A leaf‐shaped monopole antenna with an extremely wide bandwidth is introduced in Ref. [16] and a leaf‐shaped bowtie slot antenna for UWB applications in Ref. [17]. A band‐notched tulip antenna for UWB applications is pre‐ sented in Ref. [18] and a wide‐band tulip‐loop antenna in Ref. [19]. More recently, a MIMO antenna using castor leaf‐shaped quasi‐self‐complementary elements for broadband applica‐ tions and a bio‐inspired design of directional leaf‐shaped printed monopole antennas for 4G 700 MHz band are presented in Refs. [20] and [21], respectively.

This chapter discusses the design of innovative bio‐inspired microstrip antennas with frac‐ tal, polar, and Gielis shapes, which are optimized for wireless applications. Section 2 pres‐ ents the different methods to generate bio‐inspired shapes. In section 3 are presented some applications including esthetic wearable antennas and antenna arrays. In this last section, the results obtained from the Gielis superformula are highlighted due to the simplicity and flexibility of the formulation. Simulations are performed using ANSYS Electronics Desktop. Measurements of prototypes are compared to simulations and classical designs as circular printed monopole antenna in some cases.

## **2. Bio‐inspired shapes**

permeate the society and are increasingly important to their development [3, 4]. Modern wire‐ less applications demand esthetic, multifunctional, and portable terminals that operating in multiple frequency bands and can integrate different wireless services: 4G, Wi‐Fi, Bluetooth, NFC, GPS and so on. Future trends toward 5G systems also require enhanced mobile broad‐

With the rapid advance of wireless communication systems, the use of antennas in base sta‐ tions and portable terminals must meet increasingly stringent criteria, such as miniaturiza‐ tion, integration with other systems, and multiband or broadband operation [1–4]. Due its attractive features, low‐profile microstrip antennas (MSA) and arrays are well suitable to meet

Antenna parameter specifications change according to application. Indeed, fixed antennas must have high gain, stable radiation pattern, and bandwidth tolerance; embedded anten‐ nas should be efficient in radiation and possess larger beam width [3]. In short‐range UWB wireless systems, the antenna bandwidth exceeds the lesser of 500 MHz or 20% of the center frequency [9]. Thus, impedance bandwidth, gain, radiation pattern, and polarization are fun‐

A trend in the application of antennas for modern wireless systems is the use of compact antennas with stable radiation coverage over a wideband [2–4]. An antenna must be compact in many situations: embedded antennas, wearable antennas, camouflaged antennas, and so on. However, most often an antenna electrically small narrows the impedance bandwidth,

Various institutions around the world have invested resources and established research cen‐ ters with focus on biologically inspired engineering as the Massachusetts Institute Technology, the London College, and the Harvard University, for example. This research branch looks in nature similar solution to the problems encountered in engineering. With appropriate adjustments, it is possible to adapt the solutions used by the nature of the engineering prob‐ lems [10]. According to [11], the development of a bioinspired methodology requires three steps: identification of analogies, with structures and methods that are similar; understand‐ ing, detailed modeling of actual biological behavior; and engineering, which is the process of

The researches that use the bio‐inspired geometry for the development of antennas are recent and can be divided into two groups: antennas with bio‐inspired geometries in animals and antennas with bio‐inspired geometries in plants. Bio‐inspired antennas in animals try to use internal organs or external parts of the animals which work analogously to the operation of the antennas used in the communication systems. A biomimetic antenna in the shape of a bat's ear [12] can be cited, a biologically inspired electrically small antenna arrays that mimic the hearing mechanism of such insects [13], an antenna system based on the wasp's curved antennas [14] and a biologically inspired vascular antenna reconfiguration mechanism [15]. Research on antennas with bio‐inspired plant geometries uses the plants or part of them (stem, leaves, and flowers) to develop antennas for various frequencies and technologies. The study of microstrip antennas with models bio‐inspired on leaves (leaf‐shaped antennas) has aroused

band for emergent applications [5].

88 Trends in Research on Microstrip Antennas

the demands of fixed or mobile wireless applications [6–9].

damental parameters for antenna designers to take into account.

model simplification and adjustments to technical applications.

reduces gain, and limits control of the resulting radiation pattern [4, 6, 9].

## **2.1. Fractal and polar transformations**

From a mathematical point of view, a fractal refers to a set in Euclidean space with specific properties, such as self‐similarity or self‐affinity, simple and recursive definition, fractal dimension, irregular shape, and natural appearance [22]. Fractal geometry is the study of sets with these properties, which are too irregular to be described by calculus or traditional Euclidian geometry language [22, 23].

Fractals are resort to conventional classes, such as geometrical fractals, algebraic fractals, and stochastic fractals [24]. Two common methods used to generate mathematical fractals are iter‐ ated function systems (IFS) and Lindenmayer systems [22–25].

Lindenmayer system (or L‐system) was initially conceived to model growth phenomena in biological organisms [26]. An L‐system grammar performs an initial string of symbols (axiom) and includes a set of production rules that may be applied to the symbols (letters of the L‐sys‐ tem alphabet) to generate new strings.

In **Figure 1** are shown four examples of fractal iterations using IFS and L‐system.

Like fractals, polar transformations give rise to a wide class of shapes. A polar transformation is defined in this chapter through a vector function *v* →(*t*) = (*x*(*t*), *y*(*t*)), *t* ≥ 0, that is, for each real value, *t* is associated with a vector in ℜ2 , Eq. (1). An example of an esthetic polar transforma‐ tion is defined by Eq. (2) and presented in **Figure 2** for *k* varying up to *k* = 24 petals.

**Figure 1.** IFS and L‐system prefractals: (a) Koch curve; (b) modified Barnsley fern; (c) Koch island; (d) Minkowiski island.

**Figure 2.** Esthetic space‐filling polar transformation for *k* varying up to *k* = 24.

#### Bio-Inspired Microstrip Antenna http://dx.doi.org/10.5772/intechopen.69766 91

$$\begin{aligned} \vec{v}(t) & \colon I \to \Re^u\\ t & \to \vec{v}(t) \end{aligned} \tag{1}$$

$$\vec{v}(t) = \left( 1 + \frac{\cos(t)}{2} \right) \cdot \left( \cos\left(\frac{2t - \text{sen}(2t)}{k}\right) , \sin\left(\frac{2t - \text{sen}(2t)}{k}\right) \right) , \quad 0 \le t \le k\pi \tag{2}$$

$$\begin{aligned} \vec{v}(t) & \colon I \to \Re^u\\ t & \to \vec{v}(t) \end{aligned} \tag{1}$$

$$\vec{v}(t) = \left( 1 + \frac{\cos(t)}{2} \right) \cdot \left( \cos\left(\frac{2t - \sin(2t)}{k}\right) \cdot \sin\left(\frac{2t - \sin(2t)}{k}\right) \right), \quad 0 \le t \le k\pi \tag{2}$$

#### **2.2. Gielis superformula**

Like fractals, polar transformations give rise to a wide class of shapes. A polar transformation

tion is defined by Eq. (2) and presented in **Figure 2** for *k* varying up to *k* = 24 petals.

→(*t*) = (*x*(*t*), *y*(*t*)), *t* ≥ 0, that is, for each real

, Eq. (1). An example of an esthetic polar transforma‐

T : (1, 0, 0, 1, 0, 0, -)

T :4 (1, 0, 0, 1, 2, 0, -)

T :2 (0.5, -0.866, 0.866, 0.5, 1, 0, -) T :3 (0.5, 0.866, -0.866, 0.5, 1.5, 0.866, -)

{ 1

*a*) *b*)

*c*) *d*)

**Figure 1.** IFS and L‐system prefractals: (a) Koch curve; (b) modified Barnsley fern; (c) Koch island; (d) Minkowiski island.

k = 2 k = 6 k = 8 k = 16 k = 24

: F+F+F+F { → F-F+F+FF-FF+F

is defined in this chapter through a vector function *v*

value, *t* is associated with a vector in ℜ2

90 Trends in Research on Microstrip Antennas

T : (0, 0, 0, 0.16, 0, 0, 0.1)

T :2 (0.5, 0.04, -0.04, 0.85, 0, 1.6, 0.86) T :3 (0.2, -0.16, 0.23, 0.22, 0, 1.6, 0.96) T :4 (-0.15, 0.18, 0.26, 0.24, 0, 0.44, 1)

: F+F+F+F { :F→ F+F-F-F+F

**Figure 2.** Esthetic space‐filling polar transformation for *k* varying up to *k* = 24.

{ 1

The superformula is a generalization of the superellipse and was first proposed by Johan Gielis in 2003 [27]. With this model, it is possible to describe mathematically a wide variety of natural and abstract forms, such as leaf and flower shapes, for example. Gielis started from the concept of superellipses (3) and obtained the superformula (4), which is based on the idea that many natural forms can be interpreted as modified circles. To obtain this result, it was used polar coordinates, replacing *x* = *r* . cos(*ϕ*) and *y* = *r* . sinϕ in addition to introducing the argument *m*/4, which confers rotational symmetry in some structures, and the possibility of using different values of exponent *n* for each term (through *n*1 *, n*2 *, n*3 ).

$$\left|\frac{x}{a}\right|^n + \left|\frac{y}{b}\right|^n = 1\tag{3}$$

$$\left|\frac{\mathbf{x}}{\overline{a}}\right|^{n} + \left|\frac{\mathbf{y}}{\overline{b}}\right|^{n} = \mathbf{1} \tag{3}$$

$$r(\boldsymbol{\varphi}) = \frac{1}{\left\{ \left( \left| \frac{1}{\overline{a}} \cos \left( \boldsymbol{\varphi} \frac{\mathbf{m}}{4} \right) \right| \right)^{n} + \left( \left| \frac{1}{b} \sin \left( \boldsymbol{\varphi} \frac{\mathbf{m}}{4} \right) \right| \right)^{m} \right\}^{\frac{1}{n}}} \tag{4}$$

From the manipulation of the six parameters (*a*, *b*, *m*, *n*1 , *n*2 , *n*3 ) of (4), called the Gielis super‐ formula, it is possible to generate and modify several shapes. The superformula can also be multiplied by other mathematical functions, generating other forms. In order to illustrate the possibilities of the superformula, some examples of star shaped, leaf shaped, butterfly shaped, and flower shaped were generated. These shapes can be seen, with all the parameters used, in **Tables 1**–**4**, respectively.

**Table 1.** Star‐shaped geometries.

**Table 2.** Leaf‐shaped geometries.

**Table 3.** Butterfly‐shaped geometries.

**Table 4.** Flower‐shaped geometries.

## **3. Applications in microstrip antennas**

The bio‐inspired shapes are generated using the software MATLAB© in format DXF.

The simulations were performed with the commercial software ANSYS Electronics Desktop™, and the measurements in the Radiometry Laboratory of the Federal University of Campina Grande, with the VNA Agilent Technologies, model E5071C‐280 (9 kHz–8.5 GHz) and the Measurements Laboratory of the Federal Institute of Paraíba (IFPB), Campus João Pessoa, using the VNA of Agilent Technologies model N5230A (300 kHz–13.5 GHz). The characterization of denim substrate was performed by the probe method using a VNA of Agilent model E5071C (300 kHz–20 GHz).

The rigid antennas were designed using a low‐cost fiberglass laminate (FR4) as dielectric sub‐ strate with a thickness of *h* = 1.5 mm, dielectric constant of εr = 4.4, and loss tangent of 0.02.

The wearable bio‐inspired antennas were designed using a denim as dielectric substrate with a thickness of h = 1 mm, dielectric constant of εr = 2.14 and loss tangent of 0.08, and flexible copper.

## **3.1. Wearable bio‐inspired prefractal antennas**

**3. Applications in microstrip antennas**

**Table 4.** Flower‐shaped geometries.

**Superformula parameters**

**Table 3.** Butterfly‐shaped geometries.

**Table 2.** Leaf‐shaped geometries.

**Superformula parameters**

**Superformula parameters**

92 Trends in Research on Microstrip Antennas

The bio‐inspired shapes are generated using the software MATLAB© in format DXF.

**Shape** *a b m n***1** *n***2** *n***3 Function** *φ*

**Shape** *a b m n***1** *n***2** *n***3 Function** *φ*

**Shape** *a b m n***1** *n***2** *n***3 Function** *φ*

1 1 2 500 1000 1000 1 0:2*π*

2 2 3 1 1 1 1 0:2*π*

2 2 2 1 1 2 1 0:2*π*

1 1 4 0.2 0.5 15 |cos(*mϕ*)| 0:2*π*

1 1 4 0.2 0.5 15 1 0:2*π*

1 1 4 0.2 0.5 15 |cos(2*mϕ*)| 0:2*π*

1 1 10 0.1 10 0.01 1 0:2*π*

10 1 100 1 0 4 1 0:2*π*

1 1 2.5 100 2.7 2.7 |cos(*mϕ*)| 0:2*π*

The simulations were performed with the commercial software ANSYS Electronics Desktop™, and the measurements in the Radiometry Laboratory of the Federal University of Campina Grande, with the VNA Agilent Technologies, model E5071C‐280 (9 kHz–8.5 GHz) and the Measurements Laboratory of the Federal Institute of Paraíba (IFPB), Campus João Pessoa, using The use of wearable antennas are necessary some characteristics as easy interaction with the body, low visual impact, preferably low cost, and flexible structure [28], and for this reason, the materials used in the manufacture of the wearable antennas must follow some require‐ ments: easy interaction with the body, flexible structure, reduced visual impact, and prefer‐ ably low cost [28].

**Figure 3** shows the development of wearable textile patch antenna generated by L‐systems with *k* = 4 interactions. **Figure 3(a)** illustrates the original bio‐inspired shape, and **Figure 3(b)**

**Figure 3.** Development of wearable textile patch antenna generated by L‐systems: (a) original shape, (b) image generated by MATLAB, (c) top layer prototype, (d) bottom layer prototype and (e) comparison between simulated and measured return loss.

presents the image generated by MATLAB® using turtle algorithm. **Figure 3(c)** and **(d)** show the top and bottom layers of the prototype built, respectively.

As observed in **Figure 3(e)**, the antenna presents an UWB behavior operating between the C‐ Band (4–8 GHz) and X‐Band (8–12 GHz), with measured bandwidth of 5.95 GHz (5.9–1.85 GHz), and good relationship between simulated and measured results, with difference in bandwidth of 17%.

## **3.2. Bio‐inspired polar microstrip antennas**

**Figure 4** shows frequency resonance of bio‐inspired polar microstrip antenna for *k*‐interac‐ tions (*k* = 1, 8 12, 16, 24, 32, 40, 48, 56, 64) and the comparison of measured |S11| parameter, with prototype images. The proposed of bio‐inspired patch antennas is based on a circle patch antenna with displaced microstrip line feed, and quarter‐wave transformer, with dimensions calculated accordingly [7, 9].

**Figure 4** shows the |S11| parameters measured of the polar antennas to *k* = 8, 16, and 24. We noted that the increase of the patch perimeter by use of polar interaction provides a reduction of the resonant frequencies, similar to the fractal comportment.

**Figure 5** shows the use of polar transformer in development of the array patch antenna with 4 petals, *k* = 8 interactions. The polar array presented good response, with simulated and measured results closed, and loss return less than −45 dB, bandwidth of 101 MHz, cover the WLAN band in 2.4 GHz.

**Figure 4.** Interactions of bio‐inspired polar microstrip patch antenna: (a) prototypes; (b) resonant frequency vs inter‐ actions and (c) return loss for k = 8, 16 and 24.

**Figure 5.** Polar microstrip patch antenna 1×2 array.

#### **3.3. Leaf‐shaped antennas from Gielis superformula**

#### *3.3.1. Tulip flower–shaped antenna*

presents the image generated by MATLAB® using turtle algorithm. **Figure 3(c)** and **(d)** show

As observed in **Figure 3(e)**, the antenna presents an UWB behavior operating between the C‐ Band (4–8 GHz) and X‐Band (8–12 GHz), with measured bandwidth of 5.95 GHz (5.9–1.85 GHz), and good relationship between simulated and measured results, with difference in bandwidth

**Figure 4** shows frequency resonance of bio‐inspired polar microstrip antenna for *k*‐interac‐ tions (*k* = 1, 8 12, 16, 24, 32, 40, 48, 56, 64) and the comparison of measured |S11| parameter, with prototype images. The proposed of bio‐inspired patch antennas is based on a circle patch antenna with displaced microstrip line feed, and quarter‐wave transformer, with dimensions

**Figure 4** shows the |S11| parameters measured of the polar antennas to *k* = 8, 16, and 24. We noted that the increase of the patch perimeter by use of polar interaction provides a reduction

**Figure 5** shows the use of polar transformer in development of the array patch antenna with 4 petals, *k* = 8 interactions. The polar array presented good response, with simulated and measured results closed, and loss return less than −45 dB, bandwidth of 101 MHz, cover the

*a*)

0

*b*) *c*)

**Figure 4.** Interactions of bio‐inspired polar microstrip patch antenna: (a) prototypes; (b) resonant frequency vs inter‐

Resonant frequency

k 8 16 32 48 64

Frequency, GHz 2.3 2.4 2.5 2.6 2.7

k = 8 k =16 k =24

the top and bottom layers of the prototype built, respectively.

of the resonant frequencies, similar to the fractal comportment.

**3.2. Bio‐inspired polar microstrip antennas**

calculated accordingly [7, 9].

94 Trends in Research on Microstrip Antennas

WLAN band in 2.4 GHz.

Frequency, GHz

actions and (c) return loss for k = 8, 16 and 24.

3 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.8

of 17%.

The image of the tulip flower with three petals was generated by the Gielis superformula using the software MATLAB®, with values: *m* = 2, *n*1 = 400, *n*2 and *n*3 =1200, *a* and *b* = 1. In **Figure 6** are shown the dimensions of the petals, the design simulated, and the prototype antenna.

The radiation element is composed of one central petal and two lateral petals with an inclina‐ tion of 25°. The antenna was designed for a first resonance frequency at 2.1 GHz, with wave‐ length of λ ≈ 13 mm, which was used as approximated dimension between the edge and the center of the structure.

**Figure 7** presents the comparison of simulated and measured |S11| parameter of the tulip flower–shaped antenna. In **Table 5**, it can be observed the measured and simulated values of

**Figure 6.** Tulip flower–shaped antenna for UWB applications: (a) petals exported in DXF format; (b) simulated structure top and bottom and (c) prototype.

**Figure 7.** Comparison between simulated and measured return loss of the tulip flower–shaped antenna.

**Table 5.** Measured and simulated values of resonant frequencies and bandwidth of the bio‐inspired antenna.

resonant frequencies and bandwidth of the bio‐inspired antenna. It can be noted that both anten‐ nas comply with the FCC parameters with a bandwidth greater than 7.5 GHz (3.1–10.6 GHz).

The 3D radiation patterns simulated for the frequencies of 6.3 and 8.6 GHz can be observed in **Figure 8(a)** and **(b)**. The 2D radiation patterns simulated for the same frequencies can be observed in **Figure 8(c)** and **(d)** with radiation pattern measured in semi‐anechoic chamber for *Phi* = 90°. The results cover the FCC parameters, with omnidirectional radiation pattern, half power beam width (HPBW) greater than 60°, maximum gain in broadside direction, and current density of 6 A/m2 .

#### *3.3.2. Jasmine flower–shaped antenna*

Based on a circular planar monopole antenna (PMA) with a radius of 10.71 mm, a bio‐inspired printed monopole antenna with the geometry of jasmine flower with 10 petals was designed. The image of the jasmine flower with 10 petals with 1 mm long was generated by Gielis super‐ formula using the software MATLAB®, with values: *m* = 10, *n*1 = −2, *n*2 and *n*3 = 1.2, *a* and *b* = 1, and the parameters: *m* = 10, *n*1 = 8, *n*2 and *n*3 = −0.6, *a* and *b* = 1 for petals with 7 mm long.

**Figure 8.** Radiation pattern: (a) far‐field 3D with gain in dBi and current density in A/m2 at 6.3 GHz; (b) far‐field 3D with gain in dBi and current density in A/m2 at 8.6 GHz; (c) 2D, E‐plane (*φ* = 0°) and H‐plane (*φ* = 90°) with HPBW indication at 6.3 GHz; (d) 2D, E‐plane (*φ* = 0°) and H‐plane (*φ* = 90°) with HPBW indication at 8.6 GHz.

In **Figure 9** are shown the shapes generated, simulated structures with dimensions, and pro‐ totypes of the proposed antennas. The use of the bio‐inspired geometry provided a reduction of 11.3% in comparison with the classical PMA.

resonant frequencies and bandwidth of the bio‐inspired antenna. It can be noted that both anten‐ nas comply with the FCC parameters with a bandwidth greater than 7.5 GHz (3.1–10.6 GHz).

**Frequency, GHz**  1 2 3 4 5 6 7 8 9 10 11 12 13 13.5

**Table 5.** Measured and simulated values of resonant frequencies and bandwidth of the bio‐inspired antenna.

*1*

 **(GHz)** *f2*

 **(GHz)**

*Antenna* **BW (GHz)** *f*

1 Simulated 9.45 1.37 10.82 2 Measured 9.56 2.77 12.33

**Figure 7.** Comparison between simulated and measured return loss of the tulip flower–shaped antenna.

*Simulated Measured*

*UWB, 3.1 to 10.6 GHz*

The 3D radiation patterns simulated for the frequencies of 6.3 and 8.6 GHz can be observed in **Figure 8(a)** and **(b)**. The 2D radiation patterns simulated for the same frequencies can be observed in **Figure 8(c)** and **(d)** with radiation pattern measured in semi‐anechoic chamber for *Phi* = 90°. The results cover the FCC parameters, with omnidirectional radiation pattern, half power beam width (HPBW) greater than 60°, maximum gain in broadside direction, and

Based on a circular planar monopole antenna (PMA) with a radius of 10.71 mm, a bio‐inspired printed monopole antenna with the geometry of jasmine flower with 10 petals was designed. The image of the jasmine flower with 10 petals with 1 mm long was generated by Gielis super‐

= −2, *n*2

= −0.6, *a* and *b* = 1 for petals with 7 mm long.

and *n*3

= 1.2, *a* and *b* = 1,

current density of 6 A/m2

**|S 11|, dB**

0

96 Trends in Research on Microstrip Antennas

*3.3.2. Jasmine flower–shaped antenna*

and the parameters: *m* = 10, *n*1

.

formula using the software MATLAB®, with values: *m* = 10, *n*1

= 8, *n*2

and *n*3

As seen in **Figure 10**, for the circular PMA, measured and simulated results are close, indicat‐ ing convergence between the designed and built prototypes.

**Figure 9.** Jasmine flower–shaped antenna: (a) shapes exported in DXF format; (b) simulated structures, top and bottom; (c) prototypes.

**Figure 10.** Comparison between simulated and measured results for designed circular printed monopole antenna.

In order to validate the simulations, two prototypes of bio‐inspired PMA were built with petal lengths of 1 and 7 mm. The comparisons between simulated and measured results are shown in **Figures 11** and **12**.

It can be seen, from the **Figures 11** and **12**, that increasing the length defining the petals allows a reduction in the radius of the patch element in 11.30% and promotes the modification of the resonance frequency. The antenna with 7 mm presented an operating range within the range of the X‐Band frequency. The measurements of the return loss of the circular PMA and the bio‐ inspired antenna with a petal length of 7 mm present a higher bandwidth than the simulation.

**Figure 11.** Comparison between simulated and measured results for jasmine flower PMA with petal length of 1 mm.

**Figure 12.** Comparison between simulated and measured results for jasmine flower PMA with petal length of 7 mm.

In order to validate the simulations, two prototypes of bio‐inspired PMA were built with petal lengths of 1 and 7 mm. The comparisons between simulated and measured results are shown

**Figure 10.** Comparison between simulated and measured results for designed circular printed monopole antenna.

**Frequency, G H z** 123 456 7 8 9 10 11 12 13 13.5

*Circular PMA Simulated Circular PMA Measured UWB, 3.1 to 10.6 GHz*

It can be seen, from the **Figures 11** and **12**, that increasing the length defining the petals allows a reduction in the radius of the patch element in 11.30% and promotes the modification of the resonance frequency. The antenna with 7 mm presented an operating range within the range of the X‐Band frequency. The measurements of the return loss of the circular PMA and the bio‐ inspired antenna with a petal length of 7 mm present a higher bandwidth than the simulation.

> *Jasmine 1 mm Simulated Jasmine 1 mm Measured UWB, 3.1 to 10.6 GHz*

**Frequency, G H z** 1 2 3 4 5 6 7 8 9 10 11 12 13 13.5

**Figure 11.** Comparison between simulated and measured results for jasmine flower PMA with petal length of 1 mm.

in **Figures 11** and **12**.

**|S 11|, dB**

**| S 11| ,**

0

**d**

**B**

0

98 Trends in Research on Microstrip Antennas

The bio‐inspired antenna with a petal length of 1 mm presents a bandwidth 11% lower com‐ pared to simulations, but still cover the UWB range.

The bio‐inspired geometry of a jasmine flower increases the perimeter of the antenna com‐ pared to a classical PMA and consequently the frequency behavior. The perimeter of the antenna is bigger without changing its size. In the case of petal, length of 7 mm is possible to change the resonance frequency and bandwidth to operate in the X‐band range (8–12 GHz).

The **Figure 13** shows the measured values of the circular PMA and the bio‐inspired antennas with petal length of 1 and 7 mm.

**Figure 13.** Comparison between measurements of |S11| for built printed monopole antennas: circular and jasmine flowers (1 and 7 mm).

The difference between the resonance frequencies and bandwidth of the built antennas is presented in **Table 6**.

**Figure 14** shows the 3D simulated radiation patterns of the circular PMA and the bio‐inspired antennas with petal length of 1 mm and 7 mm. The radiation patterns at 7.13 GHz of the cir‐ cular PMA, at 7.06 GHz, of the jasmine flower with petal length of 1 mm and at 9.25 GHz of the jasmine flower with petal length of 7 mm are presented in **Figure 14(a)**–**(c)**, respectively. The antennas presented maximum gain in the broadside direction close to 6 dBi and omnidi‐ rectional radiation pattern.

## *3.3.3. Wearable ginkgo biloba leaf‐shaped antenna*

The ginkgo biloba is a plant of Chinese origin; its name means silver apricot and can be found on all continents. The leaves of this plant have interesting characteristics, such as good ratio between its length and width, and a geometry with a larger perimeter than Euclidean geome‐ tries. Those characteristics, in a PMA, provide a broadband antenna, with reduced dimensions, covering the lower frequency bands. This feature allows a compact antenna design and the

**Table 6.** Comparison of frequency response and bandwidth.

**Figure 14.** 3D simulated radiation patterns: (a) PMA at 7.13 GHz, (b) 1 mm jasmine flower at 7.06 GHz, (c) 7 mm jasmine flower at 9.25 GHz.

possibility of use in different frequency bands. From the determination of the perimeter, the use of geometry of ginkgo biloba leaf was applied to a broadband antenna structure, in which it was possible to run the project for an antenna that covers the frequencies of the technologies 2G, 3G and 4G.

The image of the ginkgo biloba leaf used for the proposed antenna was generated using the software MATLAB®, with values: *m* = 4, *n*1 = −0.1*, n*2 = 0.14, *a* = 0.1 and *b* = 1.

In **Figure 15** are shown the shape generated and the simulated structure with dimensions and, in **Figure 16**, the prototype of the proposed antenna.

**Figure 15.** Simulated structure of the textile PMA ginkgo biloba.

The difference between the resonance frequencies and bandwidth of the built antennas is

**Figure 14** shows the 3D simulated radiation patterns of the circular PMA and the bio‐inspired antennas with petal length of 1 mm and 7 mm. The radiation patterns at 7.13 GHz of the cir‐ cular PMA, at 7.06 GHz, of the jasmine flower with petal length of 1 mm and at 9.25 GHz of the jasmine flower with petal length of 7 mm are presented in **Figure 14(a)**–**(c)**, respectively. The antennas presented maximum gain in the broadside direction close to 6 dBi and omnidi‐

The ginkgo biloba is a plant of Chinese origin; its name means silver apricot and can be found on all continents. The leaves of this plant have interesting characteristics, such as good ratio between its length and width, and a geometry with a larger perimeter than Euclidean geome‐ tries. Those characteristics, in a PMA, provide a broadband antenna, with reduced dimensions, covering the lower frequency bands. This feature allows a compact antenna design and the

*1*

11.00 2.50 13.50

8.45 3.75 12.20

4.25 8.00 12.25

3.44 9.25 11.69

presented in **Table 6**.

100 Trends in Research on Microstrip Antennas

rectional radiation pattern.

3 Jasmine 7 mm

4 Jasmine 7 mm

5 Jasmine 1 mm

6 Jasmine 1 mm

simulated

measured

simulated

measured

**Table 6.** Comparison of frequency response and bandwidth.

5.95 0.87 -6.05 -0.12 -0.19 -0.26 -0.33 -0.40

flower at 9.25 GHz.

*3.3.3. Wearable ginkgo biloba leaf‐shaped antenna*

7.13 Gain, dBi

*a*)

5.78 1.45 -4.45 -0.10 -0.16 -0.22 -0.28 -0.33

*Antenna* **BW (GHz)** *f*

1 Circular simulated 7.38 2.31 9.69 2 Circular measured 10.69 2.81 13.50

Gain, dBi GHz GHz GHz

**Figure 14.** 3D simulated radiation patterns: (a) PMA at 7.13 GHz, (b) 1 mm jasmine flower at 7.06 GHz, (c) 7 mm jasmine

*b*) c)

7.06 Gain, dBi 9.25 5.95 0.87 -6.04 -0.12 -0.20 -0.25 -0.34 -0.41

 **(GHz)** *f2*

 **(GHz)**

**Figure 16.** Textile PMA ginkgo biloba prototype.

In **Figure 17** is shown the comparison of the values of the parameter |S11| measured and simulated of the PMA ginkgo biloba. As noted, the measurement and simulation show simi‐ lar results, indicating convergence between the simulation and the prototype.

In **Figure 18**, the parameter |S11| measured of the PMA ginkgo biloba in the pocket can be seen, close of the head and hand at distance of 20 mm. As noted, the antenna used close to the body suffers interference, which promotes the shift of the frequency and bandwidth of the antenna. In **Table 7**, the measured and simulated values, resonant frequencies, and band‐ width of the bio‐inspired antenna can be observed. The resonance frequencies have difference <4,2%, the first frequency and bandwidth covering 2G (1850–1900 MHz), 3G (1920–1975 MHz) and 4G (LTE; 2500–2690 MHz) bands.

**Figure 17.** Simulated and measured |S11| parameter of the PMA ginkgo biloba.

**Figure 18.** Simulated and measured |S11| parameter of the PMA ginkgo biloba with body interferences.

In **Figure 17** is shown the comparison of the values of the parameter |S11| measured and simulated of the PMA ginkgo biloba. As noted, the measurement and simulation show simi‐

In **Figure 18**, the parameter |S11| measured of the PMA ginkgo biloba in the pocket can be seen, close of the head and hand at distance of 20 mm. As noted, the antenna used close to the body suffers interference, which promotes the shift of the frequency and bandwidth of the antenna. In **Table 7**, the measured and simulated values, resonant frequencies, and band‐ width of the bio‐inspired antenna can be observed. The resonance frequencies have difference <4,2%, the first frequency and bandwidth covering 2G (1850–1900 MHz), 3G (1920–1975 MHz)

> **Frequency ,**  1 1.5 2 2.5 3 3.5 4 4.5 5

**Frequency ,** 1 1.5 2 2.5 3 3.5 4 4.5 5

**Figure 17.** Simulated and measured |S11| parameter of the PMA ginkgo biloba.

*Simulated Measured*

*GHz*

**Figure 18.** Simulated and measured |S11| parameter of the PMA ginkgo biloba with body interferences.

*Measured Free On the Hand In the Pocket On the Head*

*GHz*

*2G, 3G and 4G, 1.8 to 2.69 GH z*

*2G, 3G and 4G, 1.8 to 2.69 GH z*

lar results, indicating convergence between the simulation and the prototype.

and 4G (LTE; 2500–2690 MHz) bands.

102 Trends in Research on Microstrip Antennas

**|S 11|, dB**

**|S 11|, dB**

The measurements, using the antenna nearly the head, hand, and in the pocket, showed different resonant frequencies and bandwidths. The biggest difference in the resonance frequency was observed nearly the hand, with a difference of 13.68%. The biggest dif‐ ference in bandwidth was detected at the antenna close to the head, with a difference of 72.96%.

The **Figure 19** shows the 2D and 3D radiation patterns of the PMA textile ginkgo biloba at 2.12 GHz, with a maximum gain 3.16 dBi in the broadside direction. The 2D radiation pattern measured for *Phi* = 90° was performed in semi‐anechoic chamber. It can be observed that the half‐power beam width (HPBW) in (*φ* = 90) E‐plane is ~120° with an omnidirectional radiation pattern. By presenting equivalent power distribution and omnidirectional radiation diagram, this antenna can be used in applications that require direct communication between devices, in which the transmitter/receiver can take various positions.

**Figure 19.** 2D and 3D radiation pattern of the antenna proposed.

## *3.3.4. Wearable Bidens pilosa leaf‐shaped antenna*

The Bidens pilosa is native to the Americas, but it is known widely as an introduced species of other regions. The use of geometry of Bidens pilosa with three leaves was applied to a broad‐ band antenna structure, in which it was possible to run the project for an antenna that covers the WLAN range at 2.40 GHz (2.40–2.4835 GHz).

Based on the perimeter of a classical circular antenna, it is possible to design the bio‐inspired textile patch antenna with three elliptical leaves using the Gielis formula. Thus, the leaves are generated by the parameters *n*1 = 2, *m* = 400, *n*2 and *n*3 = 1200, a and *b* = 1. The final structure obtained total perimeter of 143.3 mm.

In **Figure 20** are shown the circular patch simulated, the dimensions of the single leaf used, the simulated dimensions of the bio‐inspired array antenna and the prototype, respectively. In the simulation and the prototype, the under leaf was inclined at 20°, and the down leaves were inclined at 40° in relation to the geometry of Bidens pilosa, in order to provide fine‐tun‐ ing of the resonance frequency.

**Figure 21** shows a comparison between the simulated |S11| parameter for the circular patch antenna and the bio‐inspired textile antenna. The circular patch antenna obtains a bandwidth of 140 MHz and the bio‐inspired wearable patch antenna of 130 MHz. Both antennas have bandwidth that fully covers the required frequency range for WLAN technology. However, the bio‐inspired array patch antenna presents a reduction of total length in 33.61% and width in 52.01% compared to the circular patch antenna.

**Figure 22** shows a comparison between the simulated and measured |S11| parameter for the bio‐inspired wearable textile patch antenna proposed. As it can be observed, the simulated and measured prototypes show a convergent behavior. The measured bandwidth is 8.33% narrower than the simulated values, but still fully covering the WLAN band.

**Figure 20.** (a) Circular patch simulated (b) leaves array of *Bidens pilosa*, (c) single elliptical leaf, (d) bio‐inspired patch antenna simulated, (e) bio‐inspired prototype.

**Figure 21.** Comparison between |S11| parameter of the circular patch and the bio‐inspired textile antenna.

*3.3.4. Wearable Bidens pilosa leaf‐shaped antenna*

the WLAN range at 2.40 GHz (2.40–2.4835 GHz).

in 52.01% compared to the circular patch antenna.

*a*) *b*) *c*)

13.30 mm 13.30

mm

4.80 mm

antenna simulated, (e) bio‐inspired prototype.

1,25 mm

24.80 mm

10,25mm

generated by the parameters *n*1

104 Trends in Research on Microstrip Antennas

ing of the resonance frequency.

obtained total perimeter of 143.3 mm.

The Bidens pilosa is native to the Americas, but it is known widely as an introduced species of other regions. The use of geometry of Bidens pilosa with three leaves was applied to a broad‐ band antenna structure, in which it was possible to run the project for an antenna that covers

Based on the perimeter of a classical circular antenna, it is possible to design the bio‐inspired textile patch antenna with three elliptical leaves using the Gielis formula. Thus, the leaves are

In **Figure 20** are shown the circular patch simulated, the dimensions of the single leaf used, the simulated dimensions of the bio‐inspired array antenna and the prototype, respectively. In the simulation and the prototype, the under leaf was inclined at 20°, and the down leaves were inclined at 40° in relation to the geometry of Bidens pilosa, in order to provide fine‐tun‐

**Figure 21** shows a comparison between the simulated |S11| parameter for the circular patch antenna and the bio‐inspired textile antenna. The circular patch antenna obtains a bandwidth of 140 MHz and the bio‐inspired wearable patch antenna of 130 MHz. Both antennas have bandwidth that fully covers the required frequency range for WLAN technology. However, the bio‐inspired array patch antenna presents a reduction of total length in 33.61% and width

**Figure 22** shows a comparison between the simulated and measured |S11| parameter for the bio‐inspired wearable textile patch antenna proposed. As it can be observed, the simulated and measured prototypes show a convergent behavior. The measured bandwidth is 8.33%

53,39°

**Figure 20.** (a) Circular patch simulated (b) leaves array of *Bidens pilosa*, (c) single elliptical leaf, (d) bio‐inspired patch

**20o 40o**

83,51°

**4.80 mm**

4,60 mm

25,30mm

**25.50 mm**

38,44 mm

**38.50 mm**

*d*) *e*)

narrower than the simulated values, but still fully covering the WLAN band.

8,74 mm

**8.80 mm**

22,01 mm

**22 mm**

and *n*3

= 1200, a and *b* = 1. The final structure

= 2, *m* = 400, *n*2

**Figure 22.** Comparison of |S11| parameter simulated and measured of *Bidens pilosa* patch antenna.

In **Figure 23** is illustrated the radiation pattern in 3D and 2D with the half power beam width and relative front‐to‐back (F/B) for the simulated bio‐inspired textile array antenna. The 2D radi‐ ation pattern measured for *Phi* = 90° was performed in semi‐anechoic chamber. It can be noted that the antenna presents an end‐fire direction with maximum gain of 6.71 dBi, HPBW = 90° (indicated by the letters 'A' and 'B') and F/B = 21 dB.

In **Figure 24** is shown the simulated current density of the bio‐inspired textile antenna and the circular antenna at 2.43 GHz. It can be observed that the surface current is more distributed on the edges than on the center of the patch. The current density of the circular patch is 5.86 A/m2 , and the bio‐inspired is 40.06 A/m2 . Therefore, the bio‐inspired antenna presents a higher con‐ centration of the surface current in a smaller physical area of the antenna.

**Figure 23.** Radiation pattern of the bio‐inspired textile antenna: (a) 3D with antenna structure, (b) 2D with HPBW and relative F/B.

**Figure 24.** Current density distribution: (a) circular patch antenna, (b) bio‐inspired textile patch antenna.

## **4. Conclusion**

In this chapter, we have described some trends for design innovative bio‐inspired microstrip antennas. The methods of analysis, manufacturing, and measurement have presented con‐ sidering different dielectric materials (rigid and flexible) for the manufacture of the antennas. The unique properties of space filling and self similarity naturally result in more compact and multiband behavior antennas. Consequently, these antennas have their gain reduced, which in many wireless applications are undesirable characteristics. On the other hand, as observed on the last case, the bio‐inspired antenna presents a higher concentration of the surface current in a smaller physical area compared to classical geometries with esthetic appeal. The bio‐inspired microstrip antennas have few design variables and smooth responses in the region of interest of these design variables, which facilitates all steps of the design methodology. These charac‐ teristics open a vast research field for wearable embedded antennas.

## **Author details**

Alexandre Jean René Serres1 \*, Georgina Karla de Freitas Serres1 , Paulo Fernandes da Silva Júnior1 , Raimundo Carlos Silvério Freire1 , Josiel do Nascimento Cruz1 , Tulio Chaves de Albuquerque1 , Maciel Alves Oliveira1 and Paulo Henrique da Fonseca Silva2

\*Address all correspondence to<EMAIL_ADDRESS>
1 Electrical Engineering – COPELE, Federal University of Campina Grande – UFCG, Campina Grande, Brazil

2 Electrical Engineering, Federal Institute of Paraiba – IFPB, Paraiba, Brazil

## **References**

**4. Conclusion**

5.86 5.62 5.27 4.91 4.56 4.20 3.85 3.50 3.14 2.79

relative F/B.

**Gain, dBi**

**6.72 2.43 -3.41 -9.27 -1.51 -2.68 -3.26 -3.85 -4.43 -5.02 -5.60 -6.19 -6.78**

106 Trends in Research on Microstrip Antennas

In this chapter, we have described some trends for design innovative bio‐inspired microstrip antennas. The methods of analysis, manufacturing, and measurement have presented con‐ sidering different dielectric materials (rigid and flexible) for the manufacture of the antennas. The unique properties of space filling and self similarity naturally result in more compact and multiband behavior antennas. Consequently, these antennas have their gain reduced, which in many wireless applications are undesirable characteristics. On the other hand, as observed on the last case, the bio‐inspired antenna presents a higher concentration of the surface current in

*a b*) )

**Figure 24.** Current density distribution: (a) circular patch antenna, (b) bio‐inspired textile patch antenna.

48.08 46.12 43.21 40.30 37.39 34.48 31.57 28.66 25.75 22.84

**Figure 23.** Radiation pattern of the bio‐inspired textile antenna: (a) 3D with antenna structure, (b) 2D with HPBW and

89,82°

**H P H P**

**92º**

**B W B W**

Density Current, A/m2 Density Current, A/m2

*a*) *b*)

**2.42 GHz Measur ed Phi = 0º Simulated Phi = 90º Measur ed Phi = 0º 9**

[11] Falko Dressler and Ozgur B. Akan. A survey on bio‐inspired networking. Computer

[12] J.A. Flint. A biomimetic antenna in the shape of a bat's ear. IEEE Antennas and Wireless

[13] Nader Behdad, Mudar A. Al‐Joumayly and Meng Li. Biologically Inspired Electrically Small Antenna Arrays With Enhanced Directional Sensitivity. IEEE Antennas and Wireless Propagation Letters . 2011;**10**:361‐364. DOI: 10.1109/LAWP.2011.2146223 [14] Khabat Ebnabbasi. A Bio‐Inspired Printed‐Antenna Transmission‐Range Detection System. IEEE Antennas and Propagation Magazine. 2013;**55**(3):193‐200.  Electronics

[16] Xiao‐Feng Bai, Shun‐Shi Zhong and Xian‐Ling Liang. Leaf‐shaped monopole antenna with extremely wide bandwidth. Microwave and Optical Technology Letters. 2006;

[17] Soh Fujita, Manabu Yamamoto and Toshio Nojima. A study of a leaf‐shaped bowtie slot antenna for UWB applications. In: IEEE, editor. International Symposium on Antennas

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[21] P. F. Silva Júnior, P. H. da F. Silva, A. J. R. Serres, J. C. Silva and R. C. S. Freire. Bio‐ inspired design of directional leaf‐shaped printed monopole antennas for 4G 700 MHz band. Microwave and Optical Technology Letters. 2016;**58**(7):1529‐1533. DOI: 10.1002/

[22] D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method. New York: Wiley:

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108 Trends in Research on Microstrip Antennas

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**Provisional chapter**

## **Printed Planar Antenna Designs Based on Metamaterial Unit-Cells for Broadband Wireless Communication Systems Unit-Cells for Broadband Wireless Communication Systems**

**Printed Planar Antenna Designs Based on Metamaterial**

DOI: 10.5772/intechopen.68600

Mohammad Alibakhshikenari, Mohammad Naser-Moghadasi, Ramazan Ali Sadeghzadeh, Bal Singh Virdee and Ernesto Limiti Mohammad Naser-Moghadasi, Ramazan Ali Sadeghzadeh, Bal Singh Virdee and Ernesto Limiti Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68600

Mohammad Alibakhshikenari,

#### **Abstract**

With the continuing development of mobile communications, the communication standards, which include operating frequencies and protocols, are also evolving. In order to accommodate these and future changes, antennas with characteristics of wideband and multiband are becoming a necessity. Hence, wireless communications industries are now demanding broadband antennas that are low-profile and low-volume structures. Conventional planar microstrip antennas are the most common form of printed antennas that have been used for many years. This is because these antennas offer advantages of low cost, conformability, and ease of manufacturing; however, the bandwidth of these types of antennas is highly restricted. Among different types of planar antennas, the slotted structure that offers the simplest structure is compact and radiates omnidirectionally; these features make it an excellent candidate for broadband applications.

**Keywords:** planar slotted antennas, metamaterials, composite right-/left-handed transmission lines, traveling-wave antenna, wireless communications systems

## **1. Introduction**

Printed planar antennas such as patch antennas are favored over other types of antennas as they are low profile, light weight, and can be easily manufactured using low-cost PCB techniques. These types of antennas are constructed using microstrip integrated circuit technology, where a metal

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

layer is separated from the ground-plane by a dielectric substrate [1, 2]. The thickness of the metal layer is much smaller than the operating wavelength. Such antennas are conventionally excited through a feed-line with a voltage between the patch and the ground plane. This excites a current on the patch, and hence, a vertical electric field between the patch and the ground plane [3]. The patch element resonates when its width or diameter is near λg /2, leading to relatively large current and field amplitudes, and the radiation mechanism occurs from the fringing fields between the edge of the microstrip and the ground plane. Printed planar antennas essentially radiate energy in a direction perpendicular to the plane of the antenna substrate with moderately high gain [3–5].

The choice of the substrate used is important (dielectric constant, thickness, and loss tangent). There are various shapes of patch antennas (circular being the most common) [4]; however, the principles of operation are essentially the same. Circular patches offer advantages over other geometries for applications such as arrays and can also be easily modified to produce a range of impedance values and radiation patterns.

Microstrip patch antennas enjoy many advantages when compared to other types of antennas; they are relatively small, low profile, low cost, light weight, and can be integrated to other circuits or active devices which can possibly result in a single-board solution, unlike wire, waveguide, or horn antennas for example. This also allows this type of antenna to be easily mounted on objects, such as computers or flying bodies, and can be easily employed for array design.

The most common disadvantage of microstrip antennas is the inherent narrow impedance bandwidth, which is due to the thickness, which is normally thin. The easiest and most well-known method of moderately improving the bandwidth is by increasing the height of the substrate [4], which has the effect of increasing the radiation conductance. However, this is not a desirable option as it leads to introducing surface waves and power loss, but usually works well for bandwidths up to 4–6% [6]. Other disadvantages of microstrip patch patch antenna are low efficiency, low power, and poor polarization purity [5, 7]. To overcome this drawback, various metamaterial (MTM) structures, including split-ring resonator (SRR) [8], spiral, rod, omega, S-shape, and symmetric rings, etc., have been explored in literature [9, 10].

This chapter presents the design and measured performance of compact planar slotted antennas based on unique MTM structures for application in broadband wireless communication systems. Typical realization of MTM transmission line (TL) is based on quasi-lumped TL with elementary cells consisting of a series capacitor and a shunt inductor. In reality, the loss associated with the MTM structure introduces series parasitic inductance in the capacitor, and parasitic shunt capacitance in the inductor; thus, the resulting MTM structure is more accurately represented by a composite right/left-handed (CRLH) transmission-line structure. The optimized "d-shaped" antenna presented in the chapter is shown to operate over a wideband from 0.75 to 4.5 GHz with a peak gain of 3.5 dBi and efficiency of 60% at 2 GHz. Moreover, the antenna is compact and easy to fabricate using standard PCB techniques. In addition, an "X-shaped" antenna, which is also presented here, is shown to operate from 0.4 to 4.7 GHz with a gain of 2 dBi and radiates energy with an efficiency of 65% at 2.5 GHz.

## **2. Metamaterial traveling-wave antenna**

layer is separated from the ground-plane by a dielectric substrate [1, 2]. The thickness of the metal layer is much smaller than the operating wavelength. Such antennas are conventionally excited through a feed-line with a voltage between the patch and the ground plane. This excites a current on the patch, and hence, a vertical electric field between the patch and the ground plane [3]. The

and field amplitudes, and the radiation mechanism occurs from the fringing fields between the edge of the microstrip and the ground plane. Printed planar antennas essentially radiate energy in a direction perpendicular to the plane of the antenna substrate with moderately high gain [3–5].

The choice of the substrate used is important (dielectric constant, thickness, and loss tangent). There are various shapes of patch antennas (circular being the most common) [4]; however, the principles of operation are essentially the same. Circular patches offer advantages over other geometries for applications such as arrays and can also be easily modified to produce a

Microstrip patch antennas enjoy many advantages when compared to other types of antennas; they are relatively small, low profile, low cost, light weight, and can be integrated to other circuits or active devices which can possibly result in a single-board solution, unlike wire, waveguide, or horn antennas for example. This also allows this type of antenna to be easily mounted on objects, such as computers or flying bodies, and can be easily employed

The most common disadvantage of microstrip antennas is the inherent narrow impedance bandwidth, which is due to the thickness, which is normally thin. The easiest and most well-known method of moderately improving the bandwidth is by increasing the height of the substrate [4], which has the effect of increasing the radiation conductance. However, this is not a desirable option as it leads to introducing surface waves and power loss, but usually works well for bandwidths up to 4–6% [6]. Other disadvantages of microstrip patch patch antenna are low efficiency, low power, and poor polarization purity [5, 7]. To overcome this drawback, various metamaterial (MTM) structures, including split-ring resonator (SRR) [8], spiral, rod, omega, S-shape, and symmetric rings, etc., have been explored in

This chapter presents the design and measured performance of compact planar slotted antennas based on unique MTM structures for application in broadband wireless communication systems. Typical realization of MTM transmission line (TL) is based on quasi-lumped TL with elementary cells consisting of a series capacitor and a shunt inductor. In reality, the loss associated with the MTM structure introduces series parasitic inductance in the capacitor, and parasitic shunt capacitance in the inductor; thus, the resulting MTM structure is more accurately represented by a composite right/left-handed (CRLH) transmission-line structure. The optimized "d-shaped" antenna presented in the chapter is shown to operate over a wideband from 0.75 to 4.5 GHz with a peak gain of 3.5 dBi and efficiency of 60% at 2 GHz. Moreover, the antenna is compact and easy to fabricate using standard PCB techniques. In addition, an "X-shaped" antenna, which is also presented here, is shown to operate from 0.4 to 4.7 GHz with a gain of 2 dBi and radiates energy with an efficiency of 65%

/2, leading to relatively large current

patch element resonates when its width or diameter is near λg

112 Trends in Research on Microstrip Antennas

range of impedance values and radiation patterns.

for array design.

literature [9, 10].

at 2.5 GHz.

In this section, a traveling-wave planar antenna is implemented using composite right/lefthanded structures. The antenna is constructed using a unique metamaterial unit cell implemented by etching "X-shaped" slots inside a rectangular patch. The patch is inductively terminated to the ground plane through a via-hole, as shown in **Figure 1**. The proposed antenna is henceforth referred to as "X-shaped" antenna. The resulting structure displays negative permittivity and permeability characteristics over a given frequency range. The aperture of the antenna can be increased by simply cascading together a number of these metamaterial unit cells, as shown in **Figure 1**. Hence, the antenna's gain and radiation efficiency are improved with negligible effect on its fractional bandwidth, which is contrary to what is observed in traditional antennas.

The antenna was designed and fabricated on Rogers RT/Duroid®5880 substrate, which is a glass microfiber reinforced PTFE composite with dissipation factor tanδ = 0.0009, dielectric constant *εr* = 2.2, and height *h* = 1.6 mm. The proposed antenna structure essentially acts as a guiding structure for traveling waves; thus, the traveling wave forms the main radiating mechanism. The antenna is excited on the left-hand side at port#1, and is terminated on the right-hand side at port#2 with a matched 50 Ω load, i.e., SMD1206, which is terminated to ground. Surface currents associated with the RF signal travel over the antenna structure in one direction from port#1 to the termination port#2. This is in contrast to conventional standing wave or resonant antennas, such as the monopole or dipole antennas. The nonresonating traveling-wave antenna, shown in **Figure 1**, exhibits a wide operating bandwidth.

The equivalent electrical circuit representing the metamaterial unit cell is shown in **Figure 2(a)**.  Unavoidable parasitic effects in the unit cell are generated by gaps between patch and ground plane and the current flows over the patch. The parasitic anomalies are represented by the shunt right-handed (RH) capacitance (*C*R) and the series RH inductance (*L*R). Loss in the structure is modeled by the resistance (*R*R, *R*L) and conductance (*G*R, *G*L). Components *R*R and *G*R represent right-handed loss, and *R*L and *G*L represent left-handed loss. Important characteristics of the metamaterial unit cell were obtained from the analysis of the loss-less equivalent circuit as described in Ref. [10]. At low frequencies, *L*R and *C*R can be considered short-circuited and open-circuited, respectively, so that the equivalent circuit can be essentially reduced to a series-*C*L/shunt-*L*L circuit, which is left-handed since it has antiparallel phase and group velocities. The resulting left-handed circuit has a high-pass nature; therefore, a left-handed stopband is presented below a certain cut-off frequency. At high frequencies, *C*L and *L*L can be considered as short-circuited and opencircuited, respectively, so that the equivalent circuit can be reduced to the series-*L*R/shunt-*C*R circuit, which is right-handed since it has parallel phase and group velocities. This left-handed circuit has a low-pass nature; therefore, a right-handed stopband is presented above a certain cut-off frequency. The analysis in Ref. [10] shows that the left-handed structure exhibits negative permeability and permittivity. Unlike conventional or normal right-handed unit cell-based structures, the distinguishing feature of a LH structure is its dimensions; in particular, its length is independent of the guided wavelength, which makes the structure significantly smaller.

**Figure 1.** Antenna layout, (a) top layer, (b) isometric view of the simulation model, and (c) the fabricated prototype.

Dispersion diagram of the metamaterial unit cell structure, shown in **Figure 2(b)**, was obtained by substituting the S-parameters, which were obtained with ANSYS HFSS™ (high frequency structure simulator), in Eq.(1) as described in Ref. [10]:

Printed Planar Antenna Designs Based on Metamaterial Unit-Cells for Broadband Wireless... http://dx.doi.org/10.5772/intechopen.68600 115

**Figure 2.** (a) Equivalent circuit model of the unit-cell and (b) the dispersion diagram of the loss-less CRLH unit cell.

$$\beta = \cos^{-1}\left(\frac{1 - S\_{\text{i1}}S\_{\text{i2}} + S\_{\text{i2}}S\_{\text{i1}}}{2S\_{\text{i1}}}\right) / l \tag{1}$$

The dispersion diagram shows the range of left-handed characteristics (i.e., 0.65–2.25 GHz) and the range of right-handed characteristics (i.e., 2.25–4.4 GHz). The slow-wave and fast-wave regions have been indicated in **Figure 2(b)**. The expression of Air-line, which separates the

Dispersion diagram of the metamaterial unit cell structure, shown in **Figure 2(b)**, was obtained by substituting the S-parameters, which were obtained with ANSYS HFSS™ (high frequency