**2.2 Microstrip antenna design methodology**

In this section, a microstrip antenna design methodology using PCB technology is presented, and preliminary results are presented. After choosing a type of MSA, its design had been done in order to meet the application criteria. Often, design requirements are conflicting, for example, when a small-volume antenna with a wide bandwidth and high gain is desired.

The design of conventional patch antennas (with square, rectangular, circular shapes) is already well established [6]. In general, the initial patch dimensions are given by analytical expressions obtained from approximated models, for example, the cavity model [6].

After initial design phase, an accurate analysis of the resonant and radiation antenna properties is made through computer simulation of a full-wave method: MoM, FDTD, FEM, etc. At this step, the initial dimensions of an antenna (radiator, feed line, ground plane, etc.) can be adjusted by designer for fine tuning of resonant frequency, bandwidth, and gain, among other parameters.

A trend in the development of microstrip devices involves an intensive use of computational resources available in the application of CAD tools, computational electromagnetic analysis methods, as well as computational intelligence tools for modeling and optimization [22, 23]. **Figure 2** shows a block diagram with the main steps of the methodology used in the development of microstrip antenna prototypes.

In this design approach considered, the microstrip antennas built on single dielectric layer are fed by microstrip lines. Computational simulations of microstrip antennas were done with the use of commercial software ANSYS Designer®. A developed FDTD-3D method also is applied for antenna analysis.

MSA manufacture was performed using two PCB techniques: corrosion with iron perchloride and with a milling machine, model LPKF ProtoMat S103. **Figure 3(a)**

**153**

**Figure 4.**

**Figure 3.**

*Fractal and Polar Microstrip Antennas and Arrays for Wireless Communications*

tric material parameters addressed in this work is presented in **Table 2**.

*(a) Images of PCB results; (b) ceramic characterization with dielectric probe 85,070.*

*DRA: (a) measured ceramic material parameter; (b) compact and broadband 2.45 GHz.*

shows enlarged images of microstrip bends and T-junctions made using chemical corrosion and milling machine, whose manufacturing results are more accurate. Measured values of antenna parameters were obtained using a vector network

Relative dielectric permittivity and loss tangent of dielectric materials can be obtained by the following methods: coaxial probe, free space, resonant cavities, and capacitive methods [24]. The characterization of the dielectric materials (ceramic, polyamide, and denim) was performed by probe method using E5071C VNA (300 kHz–20 GHz) and Dielectric Probe 85,070 program, **Figure 3(b)**. **Figure 4(a)** shows results for ceramic dielectric. **Figure 4(b)** shows results of a compact and broadband inset-feed DRA antenna for operation in 2.4 GHz band. A list of dielec-

*DOI: http://dx.doi.org/10.5772/intechopen.83401*

analyzer (model S5071C, Agilent Technologies).

**Figure 2.** *Design methodology for microstrip antennas.*

*Fractal and Polar Microstrip Antennas and Arrays for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.83401*

shows enlarged images of microstrip bends and T-junctions made using chemical corrosion and milling machine, whose manufacturing results are more accurate. Measured values of antenna parameters were obtained using a vector network analyzer (model S5071C, Agilent Technologies).

Relative dielectric permittivity and loss tangent of dielectric materials can be obtained by the following methods: coaxial probe, free space, resonant cavities, and capacitive methods [24]. The characterization of the dielectric materials (ceramic, polyamide, and denim) was performed by probe method using E5071C VNA (300 kHz–20 GHz) and Dielectric Probe 85,070 program, **Figure 3(b)**. **Figure 4(a)** shows results for ceramic dielectric. **Figure 4(b)** shows results of a compact and broadband inset-feed DRA antenna for operation in 2.4 GHz band. A list of dielectric material parameters addressed in this work is presented in **Table 2**.

**Figure 3.**

*Wireless Mesh Networks - Security, Architectures and Protocols*

Gielis formula have also been proposed [21].

**2.2 Microstrip antenna design methodology**

wide bandwidth and high gain is desired.

the cavity model [6].

Fractal antennas have a natural multiband behavior and compact design and can be used as a reconfigurable microstrip antenna [17–19]. Optimized fractal antennas in size and performance are suitable for wireless applications [20]. Currently, fractal antennas have several commercial applications, and international companies such as Fractal Antenna Systems, Fractus, Rayspan, and Ficosa International, among others, explore the unique properties of fractals for the manufacture of commercial antennas. Recently, polar shape commercial antennas inspired by the

In this section, a microstrip antenna design methodology using PCB technology is presented, and preliminary results are presented. After choosing a type of MSA, its design had been done in order to meet the application criteria. Often, design requirements are conflicting, for example, when a small-volume antenna with a

The design of conventional patch antennas (with square, rectangular, circular shapes) is already well established [6]. In general, the initial patch dimensions are given by analytical expressions obtained from approximated models, for example,

After initial design phase, an accurate analysis of the resonant and radiation antenna properties is made through computer simulation of a full-wave method: MoM, FDTD, FEM, etc. At this step, the initial dimensions of an antenna (radiator, feed line, ground plane, etc.) can be adjusted by designer for fine tuning of reso-

A trend in the development of microstrip devices involves an intensive use of computational resources available in the application of CAD tools, computational electromagnetic analysis methods, as well as computational intelligence tools for modeling and optimization [22, 23]. **Figure 2** shows a block diagram with the main steps of the methodology used in the development of microstrip antenna prototypes. In this design approach considered, the microstrip antennas built on single dielectric layer are fed by microstrip lines. Computational simulations of microstrip antennas were done with the use of commercial software ANSYS Designer®. A

MSA manufacture was performed using two PCB techniques: corrosion with iron perchloride and with a milling machine, model LPKF ProtoMat S103. **Figure 3(a)**

nant frequency, bandwidth, and gain, among other parameters.

developed FDTD-3D method also is applied for antenna analysis.

**152**

**Figure 2.**

*Design methodology for microstrip antennas.*

*(a) Images of PCB results; (b) ceramic characterization with dielectric probe 85,070.*

**Figure 4.** *DRA: (a) measured ceramic material parameter; (b) compact and broadband 2.45 GHz.*


**Table 2.** *List of dielectric materials.*

**Figure 5.**

*Microstrip patch antenna analysis: (a) FDTD, uniform mesh; (b) MoM, tetrahedral mesh; (c) Ez-field propagation in the time domain; (d) comparison between simulation results.*

**Figure 5** shows analysis results for a benchmark patch antenna proposed by Sheen [25]: using a homemade FDTD-3D method, developed according to [26], and using Ansys Designer (MoM). Sheen's antenna geometry is illustrated in **Figure 5(a)** superimposed by the rectangular uniform FDTD mesh; MoM tetrahedral mesh is shown in **Figure 5(b)**.

The FDTD simulation makes it possible to observe the electromagnetic fields in the time domain. The Ez-field propagation in dielectric layer of an incident Gaussian pulse is illustrated in **Figure 5(c)**. After the occurrence of multiple reflections in the patch contours, the reflected wave back through the microstrip line is used to compute the reflection coefficient. In **Figure 5(d)** the obtained analysis results in the frequency domain are compared. The simulation time of each method depends on the computational mesh, and in this example run, it is about 15–30 minutes, which is a computing time lower than that spent in 1990 by Sheen, 12 hours [25].

**Figure 6** illustrates the square patch antennas designed to operate at 2.45 GHz considering different types of microstrip line feeding techniques (direct, quarter-wave transformer, inset-fed). A combination of these feeding techniques also proposed for impedance matching of patch antenna, **Figure 6(d)**. In addition, spurline filter can be inserted into the microstrip line feed for harmonic rejection with minimum degradation of the antenna radiation pattern, **Figure 6(e)**.

**155**

patch antenna.

**Figure 7.**

*coefficient.*

**Figure 6.**

*hybrid with double-arm spurline filter.*

**3. Fractal and polar transformations**

**3.1 Types and applications**

*Fractal and Polar Microstrip Antennas and Arrays for Wireless Communications*

The inset-feed and QWT techniques have been combined to obtain a hybrid impedance matching with wider microstrip line section. We insert the spurline band-stop filter in QWT microstrip line section in order to suppress high-order patch resonances. **Figure 7(a)** shows layout and dimensions of such antenna considering low-cost FR-4 fiberglass dielectric substrate (see **Table 2**). **Figure 7(b)** shows simulated and measured results for proposed single-band 2.45 GHz square

*(a) Layout of 2.45 GHz single-band square patch antenna, (b) simulated and measured results for reflection* 

*Square patch antennas and microstrip line feed techniques: (a) direct, (b) QWT, (c) inset-feed, (d) hybrid, (e)* 

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 [27]. Fractal geometry is the study of sets with these properties, which are too irregular to be described by calculus or traditional Euclidian geometry language [27, 28].

*DOI: http://dx.doi.org/10.5772/intechopen.83401*

*Fractal and Polar Microstrip Antennas and Arrays for Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.83401*

**Figure 6.**

*Wireless Mesh Networks - Security, Architectures and Protocols*

**Figure 5** shows analysis results for a benchmark patch antenna proposed by Sheen [25]: using a homemade FDTD-3D method, developed according to [26], and using Ansys Designer (MoM). Sheen's antenna geometry is illustrated in **Figure 5(a)** superimposed by the rectangular uniform FDTD mesh; MoM tetrahedral mesh is

*Microstrip patch antenna analysis: (a) FDTD, uniform mesh; (b) MoM, tetrahedral mesh; (c) Ez-field* 

*propagation in the time domain; (d) comparison between simulation results.*

The FDTD simulation makes it possible to observe the electromagnetic fields in the time domain. The Ez-field propagation in dielectric layer of an incident Gaussian pulse is illustrated in **Figure 5(c)**. After the occurrence of multiple reflections in the patch contours, the reflected wave back through the microstrip line is used to compute the reflection coefficient. In **Figure 5(d)** the obtained analysis results in the frequency domain are compared. The simulation time of each method depends on the computational mesh, and in this example run, it is about 15–30 minutes, which is a computing time lower than that spent in 1990 by Sheen,

**Figure 6** illustrates the square patch antennas designed to operate at 2.45 GHz considering different types of microstrip line feeding techniques (direct, quarter-wave transformer, inset-fed). A combination of these feeding techniques also proposed for impedance matching of patch antenna, **Figure 6(d)**. In addition, spurline filter can be inserted into the microstrip line feed for harmonic rejection with minimum degradation of the antenna radiation pattern, **Figure 6(e)**.

**154**

shown in **Figure 5(b)**.

**Figure 5.**

**Table 2.**

*List of dielectric materials.*

12 hours [25].

*Square patch antennas and microstrip line feed techniques: (a) direct, (b) QWT, (c) inset-feed, (d) hybrid, (e) hybrid with double-arm spurline filter.*

**Figure 7.**

*(a) Layout of 2.45 GHz single-band square patch antenna, (b) simulated and measured results for reflection coefficient.*

The inset-feed and QWT techniques have been combined to obtain a hybrid impedance matching with wider microstrip line section. We insert the spurline band-stop filter in QWT microstrip line section in order to suppress high-order patch resonances. **Figure 7(a)** shows layout and dimensions of such antenna considering low-cost FR-4 fiberglass dielectric substrate (see **Table 2**). **Figure 7(b)** shows simulated and measured results for proposed single-band 2.45 GHz square patch antenna.
