**Design Techniques for Conformal Microstrip Antennas and Their Arrays**

Daniel B. Ferreira, Cristiano B. de Paula and Daniel C. Nascimento

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/53019

#### **1. Introduction**

Owing to their electrical and mechanical attractive characteristics, conformal microstrip an‐ tennas and their arrays are suitable for installation in a wide variety of structures such as aircrafts, missiles, satellites, ships, vehicles, base stations, etc. Specifically, these radiators can become integrated with the structures where they are mounted on and, consequently, do not cause extra drag and are less visible to the human eye; moreover they are lowweight, easy to fabricate and can be integrated with microwave and millimetre-wave cir‐ cuits [1,2]. Nonetheless, there are few algorithms available in the literature to assist their design. The purpose of this chapter is to present accurate design techniques for conformal microstrip antennas and arrays composed of these radiators that can bring, among other things, significant reductions in design time.

The development of efficient design techniques for conformal microstrip radiators, assist‐ ed by state-of-the-art computational electromagnetic tools, is desirable in order to estab‐ lish clear procedures that bring about reductions in computational time, along with high accuracy results. Nowadays, the commercial availability of high performance three-dimen‐ sional electromagnetic tools allows computer-aided analysis and optimization that replace the design process based on iterative experimental modification of the initial prototype. Software such as CST®, which uses the Finite Integration Technique (FIT), and HFSS®, based on the Finite Element Method (FEM), are two examples of analysis tools available in the market [3]. But, since they are only capable of performing the analysis of the struc‐ tures, the synthesis of an antenna needs to be guided by an algorithm whereby iterative

© 2013 Ferreira et al.; licensee InTech. This is an open access article 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. © 2013 Ferreira et al.; licensee InTech. This is a paper 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.

process of simulations, result analysis and model's parameters modification are conducted until a set of goals is satisfied [4].

sures that a determined number of sidelobes levels have the same value, so to get opti‐ mized array directivity. And, to obtain more accurate results, the radiation patterns of the array elements, which feed the developed procedure, are evaluated from the array fullwave simulation data. In this work, the CST® Version 2012 was used to get these data. The proposed design technique was coded in the Mathematica® package [13] to create a computer program capable of assisting the design of conformal microstrip arrays. Some examples are given in this section to illustrate the use and effectiveness of this computer

Design Techniques for Conformal Microstrip Antennas and Their Arrays

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5

Another concern for designing conformal microstrip arrays is how to implement a feed net‐ work that can impose appropriate excitations (amplitude and phase) on the array elements to synthesize a desired radiation pattern. Some microstrip arrays used in tracking systems, for example, employ the Butler Matrix [11] as a feed network. Nevertheless, this solution can just accomplish a limited set of look directions and cannot control the sidelobes levels. Hence, in this work, in order not to limit the number of radiation patterns that can be syn‐ thesized, an active circuit, composed of phase shifters and variable gain amplifiers, is adopt‐ ed to feed the array elements. Expressions for calculating the phase shifts and the gains of these components are addressed in Section 4, as well as some design examples are provided

The main property of the proposed ATLM is to allow the prediction of the impedance lo‐ cus determined in the antenna full-wave analysis when one of its geometric parameters is modified, for instance, the probe position, thereby replacing full-wave simulations in probe position optimization. It results in a dramatic computational time saving, since a circuital simulation is usually at least 1000 times faster than a full-wave one. In this sec‐ tion, the ATLM is described in detail and some design examples are provided to highlight

In order to describe the algorithm for the design of conformal microstrip antennas, for the sake of simplicity, let us first consider a probe-fed planar microstrip antenna with a gular patch of length *Lpa* and width *Wpa* , mounted on a dielectric substrate of thickness *hs* , relative permittivity ε*r* , and loss tangent tanδ, such as the one shown in Figure 1(a). The antenna feed probe is positioned *dp* apart from the patch centre. For the following analysis, it is adopted that the antenna resonant frequency *fr* is controlled by the length *Lpa* and once the probe is located along the *x*-axis, it excites the TM10 mode, whose main fringing field is also represented in Figure 1(a). Despite this geometry being of planar type, the same model pa‐ rameters are used to describe the conformal quasi-rectangular microstrip antennas illustrat‐

ed in Figure 1(b), 1(c) and 1(d), and consequently the algorithm is valid as well.

**2. Algorithm for conformal microstrip antennas design**

program.

its advantages.

**2.1. Algorithm description**

to demonstrate their applicability.

Generally, the design of a probe-fed microstrip antenna starts from an initial geometry de‐ termined by means of an approximate method such as the Transmission-line Model [5-7] or the Cavity Model [8]. Despite their numerical efficiency, i.e., they are not time-consum‐ ing and do not require a powerful computer to run on, these methods are not accurate enough for the design of probe-fed conformal microstrip antennas, leading to the need of antenna model optimization through the use of full-wave electromagnetic solvers in an iterative process. However, the full-wave simulations demand high computational efforts. Therefore, it is advantageous to have a design technique that employs full-wave electro‐ magnetic solvers for accuracy purposes, but requires a small number of simulations to ac‐ complish the design. Unfortunately, the approximated methods mentioned before provide no means for using the full-wave solution data in a feedback scheme, what precludes their integration in an iterative design process, hence restricting them just to the initial de‐ sign step. In this chapter, in order to overcome this drawback and to reduce the number of full-wave simulations required to synthesize a probe-fed conformal microstrip antenna with quasi-rectangular patch, a circuital model able to predict the antenna impedance lo‐ cus calculated in the full-wave electromagnetic solver is developed with the aim of replac‐ ing the full-wave simulations for the probe positioning. This is accomplished by the use of a transmission-line model with a set of parameters derived to fit its impedance locus to the one obtained in the full-wave simulation [4]. Since this transmission line model adapts its input impedance to fit the one from the full-wave simulation, at each algorithm itera‐ tion, it is an adaptive model per nature, so it was named ATLM – Adaptive Transmission Line Model. In Section 2, the ATLM is described in detail and some design examples are given to demonstrate its applicability.

Similar to what occurs with conformal microstrip antennas, the literature does not pro‐ vide a great number of techniques to guide the design of conformal microstrip arrays. Among these design techniques, there are, for example, the Dolph-Chebyshev design and the Genetic Algorithms [9]. However, the results provided by the Dolph-Chebyshev de‐ sign are not accurate for beam steering [10], once it does not take the radiation patterns of the array elements into account in its calculations, i.e., for this pattern synthesis technique, the array is composed of only isotropic radiators; hence it implies errors in the main beam position and sidelobes levels when the real patterns of the array elements are considered. On the other hand, the Genetic Algorithms can handle well the radiation patterns of the array elements and guarantee that the sidelobes assume a level better than a given specifi‐ cation *R* [9]. Nonetheless, to control the array directivity [11], it is important that all these sidelobes have the same level *R*, but to obtain this type of result Genetic Algorithms fre‐ quently requires a high number of iterations which increases the design time. Thus, in Section 3, an elegant procedure is employed, based on the solution of linearly constrained least squares problems [12], to the design of conformal microstrip arrays. Not only does this algorithm take the radiation pattern of each array element into account, but it also as‐ sures that a determined number of sidelobes levels have the same value, so to get opti‐ mized array directivity. And, to obtain more accurate results, the radiation patterns of the array elements, which feed the developed procedure, are evaluated from the array fullwave simulation data. In this work, the CST® Version 2012 was used to get these data. The proposed design technique was coded in the Mathematica® package [13] to create a computer program capable of assisting the design of conformal microstrip arrays. Some examples are given in this section to illustrate the use and effectiveness of this computer program.

Another concern for designing conformal microstrip arrays is how to implement a feed net‐ work that can impose appropriate excitations (amplitude and phase) on the array elements to synthesize a desired radiation pattern. Some microstrip arrays used in tracking systems, for example, employ the Butler Matrix [11] as a feed network. Nevertheless, this solution can just accomplish a limited set of look directions and cannot control the sidelobes levels. Hence, in this work, in order not to limit the number of radiation patterns that can be syn‐ thesized, an active circuit, composed of phase shifters and variable gain amplifiers, is adopt‐ ed to feed the array elements. Expressions for calculating the phase shifts and the gains of these components are addressed in Section 4, as well as some design examples are provided to demonstrate their applicability.

#### **2. Algorithm for conformal microstrip antennas design**

The main property of the proposed ATLM is to allow the prediction of the impedance lo‐ cus determined in the antenna full-wave analysis when one of its geometric parameters is modified, for instance, the probe position, thereby replacing full-wave simulations in probe position optimization. It results in a dramatic computational time saving, since a circuital simulation is usually at least 1000 times faster than a full-wave one. In this sec‐ tion, the ATLM is described in detail and some design examples are provided to highlight its advantages.

#### **2.1. Algorithm description**

process of simulations, result analysis and model's parameters modification are conducted

Generally, the design of a probe-fed microstrip antenna starts from an initial geometry de‐ termined by means of an approximate method such as the Transmission-line Model [5-7] or the Cavity Model [8]. Despite their numerical efficiency, i.e., they are not time-consum‐ ing and do not require a powerful computer to run on, these methods are not accurate enough for the design of probe-fed conformal microstrip antennas, leading to the need of antenna model optimization through the use of full-wave electromagnetic solvers in an iterative process. However, the full-wave simulations demand high computational efforts. Therefore, it is advantageous to have a design technique that employs full-wave electro‐ magnetic solvers for accuracy purposes, but requires a small number of simulations to ac‐ complish the design. Unfortunately, the approximated methods mentioned before provide no means for using the full-wave solution data in a feedback scheme, what precludes their integration in an iterative design process, hence restricting them just to the initial de‐ sign step. In this chapter, in order to overcome this drawback and to reduce the number of full-wave simulations required to synthesize a probe-fed conformal microstrip antenna with quasi-rectangular patch, a circuital model able to predict the antenna impedance lo‐ cus calculated in the full-wave electromagnetic solver is developed with the aim of replac‐ ing the full-wave simulations for the probe positioning. This is accomplished by the use of a transmission-line model with a set of parameters derived to fit its impedance locus to the one obtained in the full-wave simulation [4]. Since this transmission line model adapts its input impedance to fit the one from the full-wave simulation, at each algorithm itera‐ tion, it is an adaptive model per nature, so it was named ATLM – Adaptive Transmission Line Model. In Section 2, the ATLM is described in detail and some design examples are

Similar to what occurs with conformal microstrip antennas, the literature does not pro‐ vide a great number of techniques to guide the design of conformal microstrip arrays. Among these design techniques, there are, for example, the Dolph-Chebyshev design and the Genetic Algorithms [9]. However, the results provided by the Dolph-Chebyshev de‐ sign are not accurate for beam steering [10], once it does not take the radiation patterns of the array elements into account in its calculations, i.e., for this pattern synthesis technique, the array is composed of only isotropic radiators; hence it implies errors in the main beam position and sidelobes levels when the real patterns of the array elements are considered. On the other hand, the Genetic Algorithms can handle well the radiation patterns of the array elements and guarantee that the sidelobes assume a level better than a given specifi‐ cation *R* [9]. Nonetheless, to control the array directivity [11], it is important that all these sidelobes have the same level *R*, but to obtain this type of result Genetic Algorithms fre‐ quently requires a high number of iterations which increases the design time. Thus, in Section 3, an elegant procedure is employed, based on the solution of linearly constrained least squares problems [12], to the design of conformal microstrip arrays. Not only does this algorithm take the radiation pattern of each array element into account, but it also as‐

until a set of goals is satisfied [4].

4 Advancement in Microstrip Antennas with Recent Applications

given to demonstrate its applicability.

In order to describe the algorithm for the design of conformal microstrip antennas, for the sake of simplicity, let us first consider a probe-fed planar microstrip antenna with a gular patch of length *Lpa* and width *Wpa* , mounted on a dielectric substrate of thickness *hs* , relative permittivity ε*r* , and loss tangent tanδ, such as the one shown in Figure 1(a). The antenna feed probe is positioned *dp* apart from the patch centre. For the following analysis, it is adopted that the antenna resonant frequency *fr* is controlled by the length *Lpa* and once the probe is located along the *x*-axis, it excites the TM10 mode, whose main fringing field is also represented in Figure 1(a). Despite this geometry being of planar type, the same model pa‐ rameters are used to describe the conformal quasi-rectangular microstrip antennas illustrat‐ ed in Figure 1(b), 1(c) and 1(d), and consequently the algorithm is valid as well.

(c) Spherical microstrip antenna

(d) Conical microstrip antenna

Therefore, the standard set of control variables is composed of *Lpa* ,*R*(patch width to patch length ratio) and *Rp* (probe position to patch length ratio). The variables *Lpa* and *Rp* will be used in the algorithm to control its convergence and the variable *R* will be defined by speci‐ fication, based on the desired geometry (rectangular, square). Usually, *Wpa* is made 30%

In this work, it is considered that the resonant frequency *fr* occurs when the magnitude of

in which Γ*a* (*f*) is the reflection coefficient determined in the antenna full-wave analysis, *f*<sup>1</sup> and *f*<sup>2</sup> are the minimum and maximum frequencies that define the simulation domain [*f*1 ,*f*2]. For electrically thin radiators it is usually enough to choose *f*1 =0.95*f*0 and *f*2 =1.05*f*0, where *f*0 is the desired operating frequency, and whether the microstrip antenna is electrically thick, then *f*1 =0.80*f*0 and *f*2 =1.20*f*0, in order to locate *fr* between *f*1 and *f*2 in the first algorithm itera‐

Since the antennas design will be conducted in an iterative manner, the optimization process of the model needs to be evaluated against optimization goals in order to set a stop criterion.

> 0 1 *<sup>r</sup> <sup>f</sup> <sup>e</sup>*

and its maximum value specified as *emax*. It leads to the first optimization goal, that is,

where Γ*min* is a positive real number defined by specification. So, the maximum reflection co‐

Now that the main parameters of the design algorithm have been derived, let us focus on the Adaptive Transmission Line Model, depicted in Figure 2. As can be seen, this circuital model is composed of two microstrip lines, μ*S*1 and μ*S*2, whose widths are equal to *Wpa* , an

efficient magnitude observed at the resonant frequency needs to be lower than Γ*min* .

G=G Î *f f f ff* (3)

Design Techniques for Conformal Microstrip Antennas and Their Arrays

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7

*<sup>f</sup>* = - (4)

. *max e e* £ (5)

() , *a r min* G <G *f* (6)

the antenna reflection coefficient reaches its minimum value. Under this assumption,

1 2 ( ) min ( ) , for [ , ], *ar a <sup>f</sup>*

higher than *Lpa* , i.e., *R*=1.3 [14].

Therefore, let the frequency error be defined as

The second optimization goal is expressed by means of

tion.

 **Figure 1.** Microstrip antennas studied in this chapter

It is convenient to write both the probe position *dp* and patch width *Wpa* as functions of the patch length *Lpa* , to establish a standard set of control variables. Hence, the probe position is written as

$$d\_p = R\_p \, L\_{pa}, \; 0 < R\_p \le 0.5,\tag{1}$$

and the patch width as follows

$$\mathcal{W}\_{pa} = \mathcal{R}L\_{pa'} \ R \ge 1. \tag{2}$$

Therefore, the standard set of control variables is composed of *Lpa* ,*R*(patch width to patch length ratio) and *Rp* (probe position to patch length ratio). The variables *Lpa* and *Rp* will be used in the algorithm to control its convergence and the variable *R* will be defined by speci‐ fication, based on the desired geometry (rectangular, square). Usually, *Wpa* is made 30% higher than *Lpa* , i.e., *R*=1.3 [14].

In this work, it is considered that the resonant frequency *fr* occurs when the magnitude of the antenna reflection coefficient reaches its minimum value. Under this assumption,

$$\left|\Gamma\_a(f\_r)\right| = \min\_f \left|\Gamma\_a(f)\right|\_{\prime} \text{ for } f \in [f\_1, f\_2]\_{\prime} \tag{3}$$

in which Γ*a* (*f*) is the reflection coefficient determined in the antenna full-wave analysis, *f*<sup>1</sup> and *f*<sup>2</sup> are the minimum and maximum frequencies that define the simulation domain [*f*1 ,*f*2]. For electrically thin radiators it is usually enough to choose *f*1 =0.95*f*0 and *f*2 =1.05*f*0, where *f*0 is the desired operating frequency, and whether the microstrip antenna is electrically thick, then *f*1 =0.80*f*0 and *f*2 =1.20*f*0, in order to locate *fr* between *f*1 and *f*2 in the first algorithm itera‐ tion.

Since the antennas design will be conducted in an iterative manner, the optimization process of the model needs to be evaluated against optimization goals in order to set a stop criterion. Therefore, let the frequency error be defined as

$$e = \left| \frac{f\_r}{f\_0} - 1 \right| \tag{4}$$

and its maximum value specified as *emax*. It leads to the first optimization goal, that is,

$$e \le e\_{\text{max}}\,. \tag{5}$$

The second optimization goal is expressed by means of

written as

*Wpa*

6 Advancement in Microstrip Antennas with Recent Applications

**Figure 1.** Microstrip antennas studied in this chapter

and the patch width as follows

*Lpa*

(c) Spherical microstrip antenna

(a) Planar microstrip antenna (b) Cylindrical microstrip antenna

It is convenient to write both the probe position *dp* and patch width *Wpa* as functions of the patch length *Lpa* , to establish a standard set of control variables. Hence, the probe position is

(d) Conical microstrip antenna

, 0 0.5, *p p pa p d RL R* = <£ (1)

, 1. *W RL R pa pa* = ³ (2)

*Wpa*

*Lpa*

*Lpa*

*Wpa*

$$\left|\Gamma\_a(f\_r)\right| < \Gamma\_{\min},\tag{6}$$

where Γ*min* is a positive real number defined by specification. So, the maximum reflection co‐ efficient magnitude observed at the resonant frequency needs to be lower than Γ*min* .

Now that the main parameters of the design algorithm have been derived, let us focus on the Adaptive Transmission Line Model, depicted in Figure 2. As can be seen, this circuital model is composed of two microstrip lines, μ*S*1 and μ*S*2, whose widths are equal to *Wpa* , an ideal transmission line *TLp* – with characteristic impedance *Zp*and electrical length ∠*El* (in degrees) given by

$$
\angle E\_l = 360h\_s \left(\frac{c\_0}{f\sqrt{\varepsilon\_r}}\right)^{-1} \text{ .} \tag{7}
$$

of this parameters set is called ATLM synthesis and it is done with aid of a Gradient optimi‐ zation tool, usually available in circuit simulators such as Agilent ADS® [15], as follows.

\*

*Z Z* (9)

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\* *Zf Z c g* () , = (10)

\* = ( ), *Z Zf g a* (11)

Re{ } 0and Im{ } 0. *Z Z f f* > < (12)

, - G = + *L g*

*L g Z Z*

in which *ZL* is the load impedance and *Zg* is the generator impedance, with the superscript \* denoting the complex conjugate operator. Since for the ATLM the input voltage *vin* comes from a generator, it follows that *ZL*=*Zc* (*f*). By using a Gradient optimization tool with the

which is the generator impedance utilized during the ATLM synthesis. On the other hand, for the circuital simulation afterwards, *Zg*=*Z*0, where *Z*<sup>0</sup> is the characteristic impedance of the

Besides, to find a meaningful solution from a physical standpoint, the following two con‐

The complete probe-fed microstrip antenna design algorithm is depicted through the flow‐ chart in Figure 3, which can be summarized as follows: perform a full-wave antenna simula‐ tion for a given patch length and probe position at a certain frequency range (simulation domain), which results in accurate impedance locus data; synthesize the ATLM based on the most updated full-wave simulation data available; optimize the probe position in order to match the antenna to its feed network through circuital simulation and evaluate the reso‐ nant frequency; perform patch length scaling; update the full-wave model with the new val‐ ues of patch length and probe position; and repeat the whole process in an iterative manner

Consider the generalized load reflection coefficient [16] that is written as

*L*

goal Γ*L*=0 yields

after the optimization process.

antenna feed network.

until the goals are satisfied.

As we want to ensure that Γ*c* (*f*)=Γ*a* (*f*), i.e., *Zc* (*f*)=*Za* (*f*), yields

straints are ensured during the ATLM synthesis

where *c*<sup>0</sup> is the speed of the light in free-space –, a capacitor *C*, and two load terminations *Ls* . The ideal transmission line together with the capacitor *C* were included in the model to ac‐ count for the impedance frequency shift due to the feed probe. In order to fit the input impe‐ dance of this model to the one determined in the antenna full-wave analysis, the reflection coefficients at the terminals of the loads *Ls* are written as

0 1 ( ) 0 1 () ( ) , *jb bf <sup>f</sup> f a afe*- + G =+ (8)

in which Γ*f* (*f*) is the reflection coefficient of the equivalent slot of impedance *Zf* , and *a*0 , *a*1 , *b*0 , *b*1 as well as *Zp* and *C* are the set of parameters that determine the frequency response of the circuital model. It is worth mentioning that this ATLM is valid only if its variables *Lpa* and *Wpa* are kept identical to the ones used in the full-wave analysis.

**Figure 2.** Adaptive transmission line model – ATLM

Once the full-wave simulation Γ*a* (*f*) is known, the antenna input impedance *Za* (*f*) can be easily evaluated. The same is valid for the circuital model analysis in which the reflection coefficient is Γ*c* (*f*) and input impedance is *Zc* (*f*). It is important to point out that Γ*a* (*f*) data can be exported from the full-wave simulator to the circuit simulator in *Touchstone* format, so *Za* (*f*) can be utilized by the circuit simulator. The ATLM parameters set is calculated in order to have Γ*c* (*f*)=Γ*a* (*f*) over the simulation domain [*f*1 ,*f*2]. The process of finding the values of this parameters set is called ATLM synthesis and it is done with aid of a Gradient optimi‐ zation tool, usually available in circuit simulators such as Agilent ADS® [15], as follows.

Consider the generalized load reflection coefficient [16] that is written as

$$
\Gamma\_L = \frac{Z\_L - Z\_\mathbf{g}^\*}{Z\_L + Z\_\mathbf{g}},
\tag{9}
$$

in which *ZL* is the load impedance and *Zg* is the generator impedance, with the superscript \* denoting the complex conjugate operator. Since for the ATLM the input voltage *vin* comes from a generator, it follows that *ZL*=*Zc* (*f*). By using a Gradient optimization tool with the goal Γ*L*=0 yields

$$Z\_c(f) = Z\_g^\*,$$

after the optimization process.

ideal transmission line *TLp* – with characteristic impedance *Zp*and electrical length ∠*El*

<sup>0</sup> 360 , *l s*

*f* e

where *c*<sup>0</sup> is the speed of the light in free-space –, a capacitor *C*, and two load terminations *Ls* . The ideal transmission line together with the capacitor *C* were included in the model to ac‐ count for the impedance frequency shift due to the feed probe. In order to fit the input impe‐ dance of this model to the one determined in the antenna full-wave analysis, the reflection

0 1 () ( ) , *jb bf*

*b*0 , *b*1 as well as *Zp* and *C* are the set of parameters that determine the frequency response of the circuital model. It is worth mentioning that this ATLM is valid only if its variables *Lpa*

Once the full-wave simulation Γ*a* (*f*) is known, the antenna input impedance *Za* (*f*) can be easily evaluated. The same is valid for the circuital model analysis in which the reflection coefficient is Γ*c* (*f*) and input impedance is *Zc* (*f*). It is important to point out that Γ*a* (*f*) data can be exported from the full-wave simulator to the circuit simulator in *Touchstone* format, so *Za* (*f*) can be utilized by the circuit simulator. The ATLM parameters set is calculated in order to have Γ*c* (*f*)=Γ*a* (*f*) over the simulation domain [*f*1 ,*f*2]. The process of finding the values

in which Γ*f* (*f*) is the reflection coefficient of the equivalent slot of impedance *Zf*

and *Wpa* are kept identical to the ones used in the full-wave analysis.

*TLp*

1 2 *L R pa p* æ ö - ç ÷ è ø

<sup>1</sup> *S*

*<sup>c</sup> E h*

coefficients at the terminals of the loads *Ls* are written as

8 Advancement in Microstrip Antennas with Recent Applications

*Ls*

**Figure 2.** Adaptive transmission line model – ATLM

*vin C*

Ð = ç ÷

1

0 1 ( )

1 2 *L R pa p* æ ö <sup>+</sup> ç ÷ è ø

*Ls*

<sup>2</sup> *S*

*<sup>f</sup> f a afe*- + G =+ (8)

*r*


ç ÷ è ø

degrees) given by

(in

(7)

, and *a*0 , *a*1 ,

As we want to ensure that Γ*c* (*f*)=Γ*a* (*f*), i.e., *Zc* (*f*)=*Za* (*f*), yields

$$Z\_{\mathfrak{g}} = Z\_a^\star(f),\tag{11}$$

which is the generator impedance utilized during the ATLM synthesis. On the other hand, for the circuital simulation afterwards, *Zg*=*Z*0, where *Z*<sup>0</sup> is the characteristic impedance of the antenna feed network.

Besides, to find a meaningful solution from a physical standpoint, the following two con‐ straints are ensured during the ATLM synthesis

$$\text{Re}\,\langle Z\_f \rangle > 0 \\ \text{and} \\ \text{Im}\,\langle Z\_f \rangle < 0. \tag{12}$$

The complete probe-fed microstrip antenna design algorithm is depicted through the flow‐ chart in Figure 3, which can be summarized as follows: perform a full-wave antenna simula‐ tion for a given patch length and probe position at a certain frequency range (simulation domain), which results in accurate impedance locus data; synthesize the ATLM based on the most updated full-wave simulation data available; optimize the probe position in order to match the antenna to its feed network through circuital simulation and evaluate the reso‐ nant frequency; perform patch length scaling; update the full-wave model with the new val‐ ues of patch length and probe position; and repeat the whole process in an iterative manner until the goals are satisfied.

Generally, it is difficult to get the input impedance of the circuital model perfectly matched to the one obtained from full-wave simulation over the entire simulation domain [*f*1 ,*f*2] (i.e., *Zc* (*f*)≡*Za* (*f*)), so it is convenient to set the following goal in the Gradient optimizer,

$$\left|\Gamma\_{L}\right| \leq \begin{cases} -30\,\text{dB}, f \in \left[ (f\_{0} - \frac{f\_{2} - f\_{1}}{4}), (f\_{0} + \frac{f\_{2} - f\_{1}}{4}) \right] \\\\ -20\,\text{dB}, f \notin \left[ (f\_{0} - \frac{f\_{2} - f\_{1}}{4}), (f\_{0} + \frac{f\_{2} - f\_{1}}{4}) \right] \end{cases} \tag{13}$$

Regarding the probe position optimization, algorithm step 3b, it can be performed manually by means of a tuning process, a usual feature found in circuit simulators. Thus, *Rp* is tuned in order to minimize the magnitude of the input reflection coefficient of the circuital model. If desired, the optimization process can be performed employing an optimization tool, e.g., Gradient, Random, also available in circuit simulators. Usually, each circuital analysis takes no longer than 1 second using a simulator such ADS®. But, if one desires to create its own code for the ATLM circuital analysis and probe position optimization, a simple rithm can be implemented to seek the *Rp*that minimizes |Γ*c* (*f*)|, and the computational time will be great‐

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To illustrate the use of the technique proposed before, let us first consider the design of a cylindrical microstrip antenna (Figure 1(b)) with a quasi-rectangular metallic patch mounted on a cylindrical dielectric substrate with a thickness *hs*=0.762mm, relative permittivity ε*r*= 2.5 and loss tangent tan δ = 0.0022, which covers a copper cylinder (ground layer) with a 60.0 mm radius and 300.0-mm height. The patch centre is equidistant from the top and bottom of the copper cylinder. This radiator was designed to operate at *f*<sup>0</sup> = 3.5 GHz and the algorithm parameters were chosen as *emax*=0.1×10-2, Γ*min*=3.16×10-2 (return loss of 30dB), and *Wpa*=1.3*Lpa*. Once it is an electrically thin antenna, the simulation domain was given by *f*1 =0.95*f*0 and *f*<sup>2</sup>

Following the algorithm (Figure 3), a model was built (step 4a) in the CST® software with *Lpa*1 =27.11mm and *Rp*1 =0.25, and a first full-wave simulation was performed (step 5a). From the analysis of the obtained reflection coefficient Γ*a*(*f*), the determined resonant frequency was *fr*=3.384GHz (step 6a) and the reflection coefficient magnitude was -17dB, thus higher

Hence, at the first decision point of the algorithm, the reflection coefficient magnitude at res‐ onance is not lower than Γ*min*, so one must go to the step 1b. Then ATLM was synthesized for *Lpa*1 =27.11mm and *Rp*1 =0.25 and its parameters set was derived with the aid of the Gradient optimization tool of ADS®. After 55 iterations of the Gradient tool, the following parameters set was found: *Zp*=94Ω, *C*=0.87pF, *a*0 =-0.58, *a*1 =3.83×10-10s, *b*0 =-6.54, and *b*1 = 2.21×10-9 s. The full-wave impedance locus and the one obtained from circuital simulation of the synthe‐ sized ATLM are shown in Figure 4(a), and it can be seen that the locus determined though

With the circuital model available, the probe position was optimized through manual tuning of the variable *Rp*, and since for step 3b it is desired that the reflection coefficient magnitude at the resonance be below Γ*min* , *Rp* was tuned such as the ATLM impedance locus crossed the Smith Chart centre (Figure 4(a)), leading to *Rp*2 =0.21. The resonant frequency obtained from the circuital simulation with this probe position (step 4b) was *fr*=3.392GHz. Following the al‐ gorithm, the next step was the scaling of patch length (step 1c) leading to *Lpa*2 =26.28mm. Af‐ ter updating the full-wave model with these parameters, a full-wave simulation was executed (step 3c) resulting *fr*=3.480GHz with a reflection coefficient magnitude of -54dB (Figure 4(b)). Since |Γ*a*|<Γ*min* , the next step was step 1d where it was found that *e*=0.57×10-2,

than the desired maximum of -30 dB (Figure 4(b)).

circuital simulation fits very well the full-wave one.

ly reduced as well.

**2.2. Applications**

=1.05*f*0 .

The previous goal contributes to reduce the number of iterations required by the Gradient optimization tool to determine the set of parameters. It was found that, in general, the re‐ quired time for the synthesis of the ATLM is at most 5% of the time spent for one full-wave simulation.

**Figure 3.** Probe-fed microstrip antenna design algorithm; FWS – Full-Wave Simulation

Regarding the probe position optimization, algorithm step 3b, it can be performed manually by means of a tuning process, a usual feature found in circuit simulators. Thus, *Rp* is tuned in order to minimize the magnitude of the input reflection coefficient of the circuital model. If desired, the optimization process can be performed employing an optimization tool, e.g., Gradient, Random, also available in circuit simulators. Usually, each circuital analysis takes no longer than 1 second using a simulator such ADS®. But, if one desires to create its own code for the ATLM circuital analysis and probe position optimization, a simple rithm can be implemented to seek the *Rp*that minimizes |Γ*c* (*f*)|, and the computational time will be great‐ ly reduced as well.

#### **2.2. Applications**

Generally, it is difficult to get the input impedance of the circuital model perfectly matched to the one obtained from full-wave simulation over the entire simulation domain [*f*1 ,*f*2] (i.e.,

0 0

*ff ff ff f*

30dB, ( ),( ) 4 4 .

0 0

*ff ff ff f*

20dB, ( ),( ) 4 4

The previous goal contributes to reduce the number of iterations required by the Gradient optimization tool to determine the set of parameters. It was found that, in general, the re‐ quired time for the synthesis of the ATLM is at most 5% of the time spent for one full-wave

<sup>ï</sup> é ù - - - Ï- + <sup>ï</sup> ê ú <sup>î</sup> ë û

21 21

21 21

(1d) Evaluate *e*.

YES

*e* < *emax*?

YES

NO

(13)

*Zc* (*f*)≡*Za* (*f*)), so it is convenient to set the following goal in the Gradient optimizer,

<sup>ì</sup> é ù - - - Î- + <sup>ï</sup> ê ú ï ë <sup>û</sup> G £ <sup>í</sup>

*L*

10 Advancement in Microstrip Antennas with Recent Applications

(1b) Synthesize ATLM to fit Γ*a*(*f* ) using

() ? *a r min* G <G *f*

NO

Design finished

**Figure 3.** Probe-fed microstrip antenna design algorithm; FWS – Full-Wave Simulation

(1a) Set indexes *i* = 1, *n* = 1;

(6a) Evaluate *fr* from Γ*a*( *f* ).

*r*

(4a) Build model with *Rpn* and *Lpai*; (5a) Execute FWS and determine Γ*a*( *f* );

(2a) <sup>0</sup> <sup>0</sup> <sup>2</sup> *pai*

(3a) *Rpn* = 0.25;

*<sup>c</sup> <sup>L</sup> f* = e;

min ( ) ,for [ , ] *<sup>c</sup> min* 1 2 *<sup>f</sup>* G <G Î *f f ff* ;

0 *<sup>r</sup> pa i pa i <sup>f</sup> L L <sup>f</sup>* <sup>+</sup> <sup>=</sup> ; (2c) Update model using *Rpn* and

(3c) Execute FWS and determine

(4c) Evaluate *fr* from Γ*a*( *f* ); (5c) Increment *i*.

(4b) Evaluate *fr* from Γ*c*( *f* ).

(1c) 1

*Lpai+*1*;*

Γ*a*( *f* );

*Rpn* and *Lpai*; (2b) Increment *n*; (3b) Optimize *Rpn* such as

Start design

simulation.

To illustrate the use of the technique proposed before, let us first consider the design of a cylindrical microstrip antenna (Figure 1(b)) with a quasi-rectangular metallic patch mounted on a cylindrical dielectric substrate with a thickness *hs*=0.762mm, relative permittivity ε*r*= 2.5 and loss tangent tan δ = 0.0022, which covers a copper cylinder (ground layer) with a 60.0 mm radius and 300.0-mm height. The patch centre is equidistant from the top and bottom of the copper cylinder. This radiator was designed to operate at *f*<sup>0</sup> = 3.5 GHz and the algorithm parameters were chosen as *emax*=0.1×10-2, Γ*min*=3.16×10-2 (return loss of 30dB), and *Wpa*=1.3*Lpa*. Once it is an electrically thin antenna, the simulation domain was given by *f*1 =0.95*f*0 and *f*<sup>2</sup> =1.05*f*0 .

Following the algorithm (Figure 3), a model was built (step 4a) in the CST® software with *Lpa*1 =27.11mm and *Rp*1 =0.25, and a first full-wave simulation was performed (step 5a). From the analysis of the obtained reflection coefficient Γ*a*(*f*), the determined resonant frequency was *fr*=3.384GHz (step 6a) and the reflection coefficient magnitude was -17dB, thus higher than the desired maximum of -30 dB (Figure 4(b)).

Hence, at the first decision point of the algorithm, the reflection coefficient magnitude at res‐ onance is not lower than Γ*min*, so one must go to the step 1b. Then ATLM was synthesized for *Lpa*1 =27.11mm and *Rp*1 =0.25 and its parameters set was derived with the aid of the Gradient optimization tool of ADS®. After 55 iterations of the Gradient tool, the following parameters set was found: *Zp*=94Ω, *C*=0.87pF, *a*0 =-0.58, *a*1 =3.83×10-10s, *b*0 =-6.54, and *b*1 = 2.21×10-9 s. The full-wave impedance locus and the one obtained from circuital simulation of the synthe‐ sized ATLM are shown in Figure 4(a), and it can be seen that the locus determined though circuital simulation fits very well the full-wave one.

With the circuital model available, the probe position was optimized through manual tuning of the variable *Rp*, and since for step 3b it is desired that the reflection coefficient magnitude at the resonance be below Γ*min* , *Rp* was tuned such as the ATLM impedance locus crossed the Smith Chart centre (Figure 4(a)), leading to *Rp*2 =0.21. The resonant frequency obtained from the circuital simulation with this probe position (step 4b) was *fr*=3.392GHz. Following the al‐ gorithm, the next step was the scaling of patch length (step 1c) leading to *Lpa*2 =26.28mm. Af‐ ter updating the full-wave model with these parameters, a full-wave simulation was executed (step 3c) resulting *fr*=3.480GHz with a reflection coefficient magnitude of -54dB (Figure 4(b)). Since |Γ*a*|<Γ*min* , the next step was step 1d where it was found that *e*=0.57×10-2,

GHz and the algorithm parameters were chosen as *emax*=0.1×10-2, Γ*min*=3.16×10-2 (return loss of 30dB), and *Wpa*=1.3*Lpa*. By applying the developed algorithm, the ATLM parameters set found was *Zp*=104Ω, *C*=0.33pF, *a*0 =-0.26, *a*1 =3.01×10-10s, *b*0 =-4.01, *b*1 =1.53×10-9s, and the deter‐ mined patch parameters were *Rp*2 =0.23 and *Lpa*3 =26.18mm, which yielded a final frequency error *e* = 0.01×10-2 and 34-dB return loss at resonance, once again supporting the proposed design technique. Figure 5(b) presents the reflection coefficient magnitudes of the three full-

(a) (b)

**Figure 5.** Reflection coefficient magnitudes for each full-wave simulation required for the designs: (a) probe-fed

The previous section addressed a computationally efficient algorithm for assisting the de‐ sign of probe-fed conformal microstrip antennas with quasi-rectangular patches. In order to demonstrate its applicability, three conformal microstrip antennas were synthesized: a cylin‐ drical, a spherical and a conical one. According to what was observed, the algorithm con‐

Another concern in the design of conformal radiators is how to determine the current excita‐ tions of a conformal microstrip array to synthesize a desired radiation pattern, in which both the main beam position and the sidelobes levels can be controlled. This section is dedicated to the presentation of a technique employed for the design of conformal microstrip arrays. It is based on the iterative solution of linearly constrained least squares problems [12], so it has closed-form solutions and exhibits fast convergence, and, more important, it takes the radia‐ tion pattern of each array element into account in its code, what improves its accuracy. These radiation patterns are determined from the output data obtained through the confor‐ mal microstrip array analysis in a full-wave electromagnetic simulator, such as CST® and

**3. Radiation pattern synthesis of conformal microstrip arrays**

3350 3400 3450 3500 3550 3600 3650

Frequency (MHz)

spherical microstrip antenna, (b) probe-fed conical microstrip antenna

verges very fast, what expedites the antennas' design time.



G| *a*| (dB) -10

0



G| *a*| (dB) -10

0

Design Techniques for Conformal Microstrip Antennas and Their Arrays

3350 3400 3450 3500 3550 3600 3650

*Lpa*1 = 27.11 mm, *Rp*1 = 0.25 *Lpa*2 = 26.23 mm, *Rp*2 = 0.23 *Lpa*3 = 26.18 mm, *Rp*2 = 0.23

http://dx.doi.org/10.5772/53019

13

Frequency (MHz)

wave simulations required to accomplish the conical microstrip antenna design.

*Lpa*1 = 27.11 mm, *Rp*1 = 0.25 *Lpa*2 = 26.20 mm, *Rp*2 = 0.20 *Lpa*3 = 26.06 mm, *Rp*2 = 0.20

**Figure 4.** Iterations of the algorithm for the probe-fed cylindrical microstrip antenna design: (a) impedance loci of the full-wave and circuital simulations, (b) reflection coefficient magnitude for the full-wave simulations

higher than *emax* , thus the algorithm went to step 1c, where a second patch length scaling was done leading to *Lpa*3 =26.13mm. A last full-wave simulation with *Rp*2 =0.21 and *Lpa*<sup>3</sup> =26.13mm was performed resulting in *e*=0.03×10-2 and return loss of 54dB at resonance, thus satisfying all specifications. This design required only three full-wave simulations in order to guarantee all specifications, what demonstrates the efficiency of the proposed design technique.

Now let us design a probe-fed spherical microstrip antenna, such as the one illustrated in Figure 1(c). A copper sphere (ground layer) of 120.0-mm radius is covered with a dielectric substrate of constant thickness *hs*=0.762mm, relative permittivity ε*r*=2.5 and loss tangent tanδ=0.0022. A quasi-rectangular patch with length *Lpa* and width *Wpa* is printed on the sur‐ face of the dielectric substrate. The design specifications were the same used previously and the steps of the algorithm followed a path similar to the one in the design of the cylindrical radiator. Once again, the algorithm took only three full-wave simulations to perform the de‐ sign, as observed in Figure 5(a). The ATLM parameter set found was *Zp*=91Ω, *C*=0.63 pF, *a*0 = 6.69×10-3, *a*1 = 2.32×10-10 s, *b*0 = -4.10, *b*1 = 1.54×10-9 s, and the resulting patch parameters were *Rp*2 =0.20 and *Lpa*3 =26.06mm, which led to a final frequency error *e*=0.03×10-2 and 35-dB return loss at resonance.

As a last example, let us consider the design of a conical microstrip antenna with a quasirectangular metallic patch, as shown in Figure 1(d). It is composed of a conical dielectric substrate of constant thickness *hs*=0.762mm that covers a 280.0-mm-high cone made of cop‐ per (ground layer) with a 40.0° aperture. The dielectric substrate has the same electromag‐ netic characteristics as the ones employed in the previous examples and the patch centre is located at the midpoint of its generatrix. This radiator was designed to operate at *f*0 = 3.5 GHz and the algorithm parameters were chosen as *emax*=0.1×10-2, Γ*min*=3.16×10-2 (return loss of 30dB), and *Wpa*=1.3*Lpa*. By applying the developed algorithm, the ATLM parameters set found was *Zp*=104Ω, *C*=0.33pF, *a*0 =-0.26, *a*1 =3.01×10-10s, *b*0 =-4.01, *b*1 =1.53×10-9s, and the deter‐ mined patch parameters were *Rp*2 =0.23 and *Lpa*3 =26.18mm, which yielded a final frequency error *e* = 0.01×10-2 and 34-dB return loss at resonance, once again supporting the proposed design technique. Figure 5(b) presents the reflection coefficient magnitudes of the three fullwave simulations required to accomplish the conical microstrip antenna design.

**Figure 5.** Reflection coefficient magnitudes for each full-wave simulation required for the designs: (a) probe-fed spherical microstrip antenna, (b) probe-fed conical microstrip antenna

#### **3. Radiation pattern synthesis of conformal microstrip arrays**

higher than *emax* , thus the algorithm went to step 1c, where a second patch length scaling was done leading to *Lpa*3 =26.13mm. A last full-wave simulation with *Rp*2 =0.21 and *Lpa*<sup>3</sup> =26.13mm was performed resulting in *e*=0.03×10-2 and return loss of 54dB at resonance, thus satisfying all specifications. This design required only three full-wave simulations in order to guarantee all specifications, what demonstrates the efficiency of the proposed design

**Figure 4.** Iterations of the algorithm for the probe-fed cylindrical microstrip antenna design: (a) impedance loci of the

3350 3400 3450 3500 3550 3600 3650

Frequency (MHz)

*Lpa*1 = 27.11 mm,

*Lpa*2 = 26.28 mm,

*Lpa*3 = 26.13 mm,

*Rp*1 = 0.25

*Rp*2 = 0.21

*Rp*2 = 0.21

(a) (b)

full-wave and circuital simulations, (b) reflection coefficient magnitude for the full-wave simulations



G| *a*| (dB) -10

0

Now let us design a probe-fed spherical microstrip antenna, such as the one illustrated in Figure 1(c). A copper sphere (ground layer) of 120.0-mm radius is covered with a dielectric substrate of constant thickness *hs*=0.762mm, relative permittivity ε*r*=2.5 and loss tangent tanδ=0.0022. A quasi-rectangular patch with length *Lpa* and width *Wpa* is printed on the sur‐ face of the dielectric substrate. The design specifications were the same used previously and the steps of the algorithm followed a path similar to the one in the design of the cylindrical radiator. Once again, the algorithm took only three full-wave simulations to perform the de‐ sign, as observed in Figure 5(a). The ATLM parameter set found was *Zp*=91Ω, *C*=0.63 pF, *a*0 = 6.69×10-3, *a*1 = 2.32×10-10 s, *b*0 = -4.10, *b*1 = 1.54×10-9 s, and the resulting patch parameters were *Rp*2 =0.20 and *Lpa*3 =26.06mm, which led to a final frequency error *e*=0.03×10-2 and 35-dB return

As a last example, let us consider the design of a conical microstrip antenna with a quasirectangular metallic patch, as shown in Figure 1(d). It is composed of a conical dielectric substrate of constant thickness *hs*=0.762mm that covers a 280.0-mm-high cone made of cop‐ per (ground layer) with a 40.0° aperture. The dielectric substrate has the same electromag‐ netic characteristics as the ones employed in the previous examples and the patch centre is located at the midpoint of its generatrix. This radiator was designed to operate at *f*0 = 3.5

technique.



Full-wave

0,5j

0,2j

0,2 0,5 1,0 2,0 5,0

1,0j

12 Advancement in Microstrip Antennas with Recent Applications


 Synthesized ATLM (*Rp*1= 0.25) Optimized probe position (*Rp*2= 0.21)



5,0j

2,0j

loss at resonance.

The previous section addressed a computationally efficient algorithm for assisting the de‐ sign of probe-fed conformal microstrip antennas with quasi-rectangular patches. In order to demonstrate its applicability, three conformal microstrip antennas were synthesized: a cylin‐ drical, a spherical and a conical one. According to what was observed, the algorithm con‐ verges very fast, what expedites the antennas' design time.

Another concern in the design of conformal radiators is how to determine the current excita‐ tions of a conformal microstrip array to synthesize a desired radiation pattern, in which both the main beam position and the sidelobes levels can be controlled. This section is dedicated to the presentation of a technique employed for the design of conformal microstrip arrays. It is based on the iterative solution of linearly constrained least squares problems [12], so it has closed-form solutions and exhibits fast convergence, and, more important, it takes the radia‐ tion pattern of each array element into account in its code, what improves its accuracy. These radiation patterns are determined from the output data obtained through the confor‐ mal microstrip array analysis in a full-wave electromagnetic simulator, such as CST® and HFSS®. Once those data are available, polynomial interpolation is utilized to write simple closed-form expressions that represent adequately the far electric field radiated by each ar‐ ray element, which makes the technique numerically efficient.

The developed design technique was implemented in the Mathematica® platform giving rise to a computer program – called CMAD (Conformal Microstrip Array Design) – capable of performing the design of conformal microstrip arrays. The Mathematica® package, an inte‐ grated scientific computer software, was chosen mainly due to its vast collection of built-in functions that permit implementing the respective algorithm in a short number of lines, in addition to its many graphical resources. At the end of the section, to illustrate the CMAD ability to synthesize the radiation pattern of conformal microstrip arrays, the synthesis of the radiation pattern of three conformal microstrip array topologies is considered. First, a microstrip antenna array conformed onto a cylindrical surface is analysed. Afterwards, a spherical microstrip array is studied. Finally, the synthesis of the radiation pattern of a coni‐ cal microstrip array is presented.

#### **3.1. Algorithm description**

The far electric field radiated by a conformal microstrip array composed of *N* elements and embedded in free space, assuming time-harmonic variations of the form *e j* ω*<sup>t</sup>*, can be written as

$$E = \mathbb{C} \frac{\epsilon^{\cdot \cdot j\_{0'}}}{r} I^{\ t} \cdot v(\Theta, \phi), \tag{14}$$

2† † | ( , )| [ ( , ) ( , )] , *<sup>t</sup>*

weight *w* and vector*v*(θ,ϕ).

*RMSE* less than 0.02.

subject to the constraints

where the complex weight *w* is equal to *I*\*, the superscript \* represents the complex conju‐ gate operator and † indicates the Hermitian transpose (complex conjugate transpose opera‐ tor). Therefore, the radiation pattern evaluation requires the knowledge of both complex

Once the array elements are chosen and their positions are predefined, to determine the vec‐ tor v (θ, ϕ) tor *v*(θ,ϕ) it is necessary to calculate the complex patterns *gn*(θ,ϕ), 1≤*n*≤*N*, of the array elements. For conformal microstrip arrays there are some well-known techniques to accomplish this [1], for example, the commonly used electric surface current method [17-19]. However, when this technique is employed to analyse cylindrical or conical microstrip ar‐ rays, for instance, it cannot deal with the truncation of the ground layer and the diffraction at the edges of the conducting surfaces that affect the radiation pattern. Moreover, the ex‐ pressions derived from this method for calculating the radiated far electric field frequently involve Bessel and Legendre functions. Nevertheless, as extensively reported in the litera‐ ture [20], the evaluation of these functions is not fast and requires good numerical routines. Hence, to overcome these drawbacks and to get more accurate results, in this chapter, the complex patterns *gn*(θ,ϕ) are determined from the data obtained through the conformal mi‐ crostrip array analysis in the CST® package. It is important to point out that other commer‐ cial 3D electromagnetic simulators, such as HFSS®, can also be used to assist the evaluation of the complex patterns *gn*(θ,ϕ), since they are able to take into account truncation of the

From the array full-wave simulation data, polynomial interpolation is applied to generate simple closed-form expressions that represent adequately the far electric field (amplitude and phase) radiated by each array element. In this work, the degree of the interpolation pol‐ ynomials is established from the analysis of the *RMSE* (root-mean-square error), which pro‐ vides a measure of similarity between the interpolated data and the ones given by CST®. For the following examples the interpolation polynomials' degrees are defined aiming at a

Considering the previous scenario, to synthesize a radiation pattern in a given plane, it just requires the determination of the current excitations *In* present in the complex weight *w*. Fig‐ ure 6 illustrates a typical specification of a radiation pattern containing information about the main beam direction α, the intervals intervals [θ*a*,θ*b*] and [θ*c*,θ*d*] where the sidelobes are

Based on (17) and following [12], a constrained least squares problem is established in order

*<sup>w</sup> w Aw* × × (18)

ground layer and diffraction at the edges of the conducting surfaces.

located as well as the maximum level *R* that can be assumed for them.

† min

to locate the main beam at the α direction,

*Iw w* × qf = × qf× qf × *v vv* (17)

Design Techniques for Conformal Microstrip Antennas and Their Arrays

http://dx.doi.org/10.5772/53019

15

where the constant ℂ is dependent on both the free-space electromagnetic characteristics, μ0 and ε0 , and the angular frequency ω, *k*0 =ω{μ0 ε0} 1/2 is the free-space propagation constant,

$$I^t = \begin{bmatrix} I\_1 & \cdots & I\_N \end{bmatrix} \tag{15}$$

with *In*,1 ≤ *n* ≤ *N*, representing the current excitation of the *n-*th array element and the super‐ script *t* indicates the transpose operator,

$$\mathbf{w}(\boldsymbol{\Theta}, \boldsymbol{\phi}) = \begin{bmatrix} \mathbf{g}\_1(\boldsymbol{\Theta}, \boldsymbol{\phi}) \\ \vdots \\ \mathbf{g}\_N(\boldsymbol{\Theta}, \boldsymbol{\phi}) \end{bmatrix}' \tag{16}$$

in which *gn*(θ,ϕ), 1 ≤ *n* ≤ *N*, denotes the complex pattern of the *n*-th array element evaluated in the global coordinate system. Boldface letters represent vectors throughout this chapter.

Based on (14), the radiation pattern of a conformal microstrip array can be promptly calcu‐ lated using the relation

$$\|I \cdot \mathbf{v}(\boldsymbol{\Theta}, \boldsymbol{\phi})\|^2 = \boldsymbol{w}^\dagger \cdot [\mathbf{v}(\boldsymbol{\Theta}, \boldsymbol{\phi}) \cdot \mathbf{v}^\dagger(\boldsymbol{\Theta}, \boldsymbol{\phi})] \cdot \boldsymbol{w} \,, \tag{17}$$

where the complex weight *w* is equal to *I*\*, the superscript \* represents the complex conju‐ gate operator and † indicates the Hermitian transpose (complex conjugate transpose opera‐ tor). Therefore, the radiation pattern evaluation requires the knowledge of both complex weight *w* and vector*v*(θ,ϕ).

Once the array elements are chosen and their positions are predefined, to determine the vec‐ tor v (θ, ϕ) tor *v*(θ,ϕ) it is necessary to calculate the complex patterns *gn*(θ,ϕ), 1≤*n*≤*N*, of the array elements. For conformal microstrip arrays there are some well-known techniques to accomplish this [1], for example, the commonly used electric surface current method [17-19]. However, when this technique is employed to analyse cylindrical or conical microstrip ar‐ rays, for instance, it cannot deal with the truncation of the ground layer and the diffraction at the edges of the conducting surfaces that affect the radiation pattern. Moreover, the ex‐ pressions derived from this method for calculating the radiated far electric field frequently involve Bessel and Legendre functions. Nevertheless, as extensively reported in the litera‐ ture [20], the evaluation of these functions is not fast and requires good numerical routines. Hence, to overcome these drawbacks and to get more accurate results, in this chapter, the complex patterns *gn*(θ,ϕ) are determined from the data obtained through the conformal mi‐ crostrip array analysis in the CST® package. It is important to point out that other commer‐ cial 3D electromagnetic simulators, such as HFSS®, can also be used to assist the evaluation of the complex patterns *gn*(θ,ϕ), since they are able to take into account truncation of the ground layer and diffraction at the edges of the conducting surfaces.

From the array full-wave simulation data, polynomial interpolation is applied to generate simple closed-form expressions that represent adequately the far electric field (amplitude and phase) radiated by each array element. In this work, the degree of the interpolation pol‐ ynomials is established from the analysis of the *RMSE* (root-mean-square error), which pro‐ vides a measure of similarity between the interpolated data and the ones given by CST®. For the following examples the interpolation polynomials' degrees are defined aiming at a *RMSE* less than 0.02.

Considering the previous scenario, to synthesize a radiation pattern in a given plane, it just requires the determination of the current excitations *In* present in the complex weight *w*. Fig‐ ure 6 illustrates a typical specification of a radiation pattern containing information about the main beam direction α, the intervals intervals [θ*a*,θ*b*] and [θ*c*,θ*d*] where the sidelobes are located as well as the maximum level *R* that can be assumed for them.

Based on (17) and following [12], a constrained least squares problem is established in order to locate the main beam at the α direction,

$$\min\_{w} w^{\dagger} \cdot A \cdot w$$

subject to the constraints

HFSS®. Once those data are available, polynomial interpolation is utilized to write simple closed-form expressions that represent adequately the far electric field radiated by each ar‐

The developed design technique was implemented in the Mathematica® platform giving rise to a computer program – called CMAD (Conformal Microstrip Array Design) – capable of performing the design of conformal microstrip arrays. The Mathematica® package, an inte‐ grated scientific computer software, was chosen mainly due to its vast collection of built-in functions that permit implementing the respective algorithm in a short number of lines, in addition to its many graphical resources. At the end of the section, to illustrate the CMAD ability to synthesize the radiation pattern of conformal microstrip arrays, the synthesis of the radiation pattern of three conformal microstrip array topologies is considered. First, a microstrip antenna array conformed onto a cylindrical surface is analysed. Afterwards, a spherical microstrip array is studied. Finally, the synthesis of the radiation pattern of a coni‐

The far electric field radiated by a conformal microstrip array composed of *N* elements and

where the constant ℂ is dependent on both the free-space electromagnetic characteristics, μ0

with *In*,1 ≤ *n* ≤ *N*, representing the current excitation of the *n-*th array element and the super‐

<sup>1</sup>(,)

(,) *<sup>N</sup>*

ê ú q f ë û M *g*

in which *gn*(θ,ϕ), 1 ≤ *n* ≤ *N*, denotes the complex pattern of the *n*-th array element evaluated in the global coordinate system. Boldface letters represent vectors throughout this chapter.

Based on (14), the radiation pattern of a conformal microstrip array can be promptly calcu‐

(,) ,

*g*

*v =*

é ù q f ê ú q f ê ú

<sup>1</sup> , *<sup>t</sup>*

, can be written as

(16)

*<sup>r</sup> <sup>I</sup> <sup>t</sup>* <sup>⋅</sup>*v*(*θ*, *<sup>ϕ</sup>*), (14)

*<sup>N</sup> II I* é ù *=* ë û L (15)

1/2 is the free-space propagation constant,

embedded in free space, assuming time-harmonic variations of the form *e j* ω*<sup>t</sup>*


*<sup>E</sup>* <sup>=</sup><sup>ℂ</sup> *<sup>e</sup>*

and ε0 , and the angular frequency ω, *k*0 =ω{μ0 ε0}

script *t* indicates the transpose operator,

lated using the relation

ray element, which makes the technique numerically efficient.

14 Advancement in Microstrip Antennas with Recent Applications

cal microstrip array is presented.

**3.1. Algorithm description**

**Figure 6.** Typical specification of a radiation pattern in a given plane

$$\mathbf{v}\_s^\dagger \cdot \varpi = \mathbf{1},\tag{19}$$

Re{ } Im{ } , *<sup>t</sup> w ww* <sup>=</sup> é ù ë û % (24)

Design Techniques for Conformal Microstrip Antennas and Their Arrays

http://dx.doi.org/10.5772/53019

17

% (25)

<sup>ˆ</sup> , *<sup>C</sup> ssd* <sup>=</sup> é ù ë û % *vvv* % % (26)

100 , *<sup>t</sup> <sup>f</sup>* <sup>=</sup> é ù ë û % (27)

*s ss* = é ù ë û *v vv* % (28)

*s ss* = -é ù ë û *v vv* (29)

*d dd* = é ù ë û *v vv* % (30)

( ) <sup>1</sup> 1 1 , *<sup>t</sup> w A CCA C f* - - - = ×× × × × % % %% % % % (31)

*ww w* ¬ +D . (32)

D × ×D (33)

Re{ } Im{ } , Im{ } Re{ } *A A <sup>A</sup> A A* é ù - <sup>=</sup> ê ú ë û

Re{ } Im{ } , *<sup>t</sup>*

Re{ } Im{ } . *<sup>t</sup>*

After solving the problem (18)-(20) the main beam is located at the α-direction. Neverthe‐ less, it cannot be assured that the sidelobes levels are below the threshold *R*. In order to get

A constrained least squares problem, similar to (18)-(20), that ensures the sidelobes levels, is

it, the complex weight *w* is updated by residual complex weights Δ*w*, as follows:

set up for the purpose of calculating the residual complex weights Δ*w*, that is,

D

† min*<sup>w</sup> wAw*

ˆ Im{ } Re{ } , *<sup>t</sup>*

The closed-form solution to the problem (22) and (23) is

from which the complex weight *w* is promptly evaluated.

with

$$\text{Re}\{\mathbf{v}\_d^\dagger \cdot \boldsymbol{w}\} = \mathbf{0} \,, \tag{20}$$

in which *vs*=*v*(α,ϕ'), *vd*=∂*v*(θ,ϕ)/∂θ|(θ , ϕ) = (α , ϕ') , ϕ' is the ϕ coordinate of the plane where the pattern is being synthesized, and

$$A = \frac{1}{2} \sum\_{\ell=1}^{L} \mathbf{v}(\boldsymbol{\theta}\_{\ell'} \boldsymbol{\phi}') \cdot \mathbf{v}^{\dagger}(\boldsymbol{\theta}\_{\ell'} \boldsymbol{\phi}') , \tag{21}$$

with the angles θ*ℓ*, *ℓ*=1,2,…,*L*, uniformly sampled in the sidelobes intervals [θ*a*,θ*b*] and [θ*c*,θ*d*]. In the next examples the adopted step size between consecutive θ*ℓ* is equal to 0.1° (for each of the sidelobes intervals).

In order to find a closed-form solution to the problem defined by (18) to (20), we determine its real counterpart [21], that is,

$$\min\_{\tilde{w}} \tilde{w}^t \cdot \tilde{A} \cdot \tilde{w} \tag{22}$$

subject to the following linear constraints

$$
\tilde{C} \cdot \tilde{w} = \tilde{f},
\tag{23}
$$

where

Design Techniques for Conformal Microstrip Antennas and Their Arrays http://dx.doi.org/10.5772/53019 17

$$
\tilde{w} = \begin{bmatrix} \operatorname{Re} \{w\} & \operatorname{Im} \{w\} \end{bmatrix}^t,\tag{24}
$$

$$
\tilde{A} = \begin{bmatrix}
\operatorname{Re}\{A\} & -\operatorname{Im}\{A\} \\
\operatorname{Im}\{A\} & \operatorname{Re}\{A\}
\end{bmatrix}'\tag{25}
$$

$$
\tilde{\mathbf{C}} = \begin{bmatrix} \tilde{\mathbf{v}}\_s & \hat{\mathbf{v}}\_s & \tilde{\mathbf{v}}\_d \end{bmatrix} \tag{26}
$$

$$
\tilde{f} = \begin{bmatrix} 1 & 0 & 0 \end{bmatrix}^t \tag{27}
$$

with

† 1, *<sup>v</sup><sup>s</sup>* × = *<sup>w</sup>* (19)

q

† Re{ } 0 , *<sup>v</sup><sup>d</sup>* × = *<sup>w</sup>* (20)

*v v* (21)

% % % (22)

, *<sup>t</sup> Cw f* × = % % % (23)

in which *vs*=*v*(α,ϕ'), *vd*=∂*v*(θ,ϕ)/∂θ|(θ , ϕ) = (α , ϕ') , ϕ' is the ϕ coordinate of the plane where the

†

<sup>1</sup> ( , ') ( , '), <sup>2</sup>

with the angles θ*ℓ*, *ℓ*=1,2,…,*L*, uniformly sampled in the sidelobes intervals [θ*a*,θ*b*] and [θ*c*,θ*d*]. In the next examples the adopted step size between consecutive θ*ℓ* is equal to 0.1°

In order to find a closed-form solution to the problem defined by (18) to (20), we determine

= qf× qf å l l

1,0

*R*

q*<sup>a</sup>* q*<sup>b</sup>* q*<sup>c</sup>* q*<sup>d</sup>*

Relative field strength

1

min *<sup>t</sup> w*

*w Aw* × × %

=

l

*L*

*A*

**Figure 6.** Typical specification of a radiation pattern in a given plane

16 Advancement in Microstrip Antennas with Recent Applications

pattern is being synthesized, and

(for each of the sidelobes intervals).

subject to the following linear constraints

its real counterpart [21], that is,

where

$$
\tilde{\boldsymbol{\nu}}\_s = \left[ \operatorname{Re} \{ \boldsymbol{\nu}\_s \} \quad \operatorname{Im} \{ \boldsymbol{\nu}\_s \} \right]^t,\tag{28}
$$

$$
\hat{\boldsymbol{\nu}}\_s = \begin{bmatrix} -\operatorname{Im}\{\boldsymbol{\nu}\_s\} & \operatorname{Re}\{\boldsymbol{\nu}\_s\} \end{bmatrix}^t,\tag{29}
$$

$$
\tilde{\boldsymbol{\nu}}\_d = \begin{bmatrix} \operatorname{Re}\{\boldsymbol{\nu}\_d\} & \operatorname{Im}\{\boldsymbol{\nu}\_d\} \end{bmatrix}^t. \tag{30}
$$

The closed-form solution to the problem (22) and (23) is

$$
\tilde{w} = \tilde{A}^{-1} \cdot \tilde{\mathbf{C}} \cdot \left( \tilde{\mathbf{C}}^{\dagger} \cdot \tilde{A}^{-1} \cdot \tilde{\mathbf{C}} \right)^{-1} \cdot \tilde{f},
\tag{31}
$$

from which the complex weight *w* is promptly evaluated.

After solving the problem (18)-(20) the main beam is located at the α-direction. Neverthe‐ less, it cannot be assured that the sidelobes levels are below the threshold *R*. In order to get it, the complex weight *w* is updated by residual complex weights Δ*w*, as follows:

$$
\pi w \leftarrow w + \Delta w.\tag{32}
$$

A constrained least squares problem, similar to (18)-(20), that ensures the sidelobes levels, is set up for the purpose of calculating the residual complex weights Δ*w*, that is,

$$\min\_{\Delta w} \Delta w^{\dagger} \cdot A \cdot \Delta w \tag{33}$$

subject to the constraints

$$
\mathbf{v}\_s^\dagger \cdot \Delta \mathbf{z} \mathbf{v} = \mathbf{0},\tag{34}
$$

time is diminished. In the following three sections, examples of radiation pattern synthesis

To illustrate the described pattern synthesis technique, let us first consider the design of a five-element cylindrical microstrip array, such as the one shown in Figure 7(a). For this ar‐ ray, the cylindrical ground layer is made out of copper cylinder with a 60.0-mm radius and a 300.0-mm height. The employed dielectric substrate has a relative permittivity ε*<sup>r</sup>* = 2.5, a loss tangent tan δ = 0.0022 and its thickness is *hs* = 0.762 mm. The array patches are identical to the one designed in Section 2.2 to operate at 3.5 GHz. The five elements are fed by 50-ohm coaxial probes positioned 5.49 mm apart from the patches' centres and the interelement spacing was chosen to be λ0 / 2 = 42.857 mm (λ0 is the free-space wavelength at 3.5 GHz).

0°

Design Techniques for Conformal Microstrip Antennas and Their Arrays

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19

180°

210°

330°

30°

150°

60°

 CMAD CST®

120°

90°

are provided to demonstrate the capability of the developed CMAD program.

(a) (b)

0


Normalized radiation pattern (dB)



270°

240°

**Figure 7.** (a)Five-element cylindrical microstrip array, (b) *E*θ radiation pattern: *xz*-plane, α = 60°, *R* = -20 dB, and *f* = 3.5 GHz

It is important to point out that the elements close to the ends of the ground cylinder have significantly different radiation patterns than those close to the centre of this cylinder; how‐ ever, the technique developed in this chapter can handle well this aspect, different from the common practice that assumes the elements' radiation patterns are identical [22]. To clarify this difference among the patterns, Figure 8 shows the radiation patterns of the elements number 1 and 5. In Figure 8(a) they were evaluated in CST® and in Figure 8(b) they were determined from the interpolation polynomials. As observed, there is an excellent agree‐ ment between the radiation patterns described by the interpolation polynomials and the ones provided by CST®, even in the back region, where the radiation pattern exhibits low

300°



0

**3.2. Cylindrical microstrip array**

**5**

**4**

**1**

**2**

**3**

$$\operatorname{Re}\{\mathbf{v}\_d^\dagger \cdot \Delta w\} = 0,\tag{35}$$

$$\mathbf{v}\_{i}^{\dagger} \cdot \Delta \mathbf{w} = f\_{i}, i = 1, 2, \dots, m\_{\prime} \tag{36}$$

in which *v<sup>i</sup>* =*v*(θ*<sup>i</sup>* ,ϕ'), with θ*<sup>i</sup>* denoting the θ coordinate of the *i*-th sidelobe, *m* is the number of sidelobes whose levels are being modified (the maximum *m* is equal to *N*–2), and the complex function *fi* can be evaluated through

$$\mathbf{f}\_i = (\mathbf{R} - \lVert \mathbf{c}\_i \rVert) \frac{\mathbf{c}\_i}{\lVert \mathbf{c}\_i \rVert} \tag{37}$$

where

$$\boldsymbol{\mathcal{L}}\_{i} = \boldsymbol{\mathfrak{w}}^{\dagger} \cdot \boldsymbol{\mathfrak{v}}\_{i} \,. \tag{38}$$

It is important to point out that the constraints (34) and (35) retain the main beam located at the α-direction, and the ones in (36) are responsible for conducting the sidelobes levels to the threshold *R*. A closed-form solution to the problem (33)-(36) is also determined from its real counterpart, analogous to the solution to the problem (18)-(20). The problem (33)-(36) is iteratively solved until the sidelobes levels reach the desired value *R*. Notice that at each iteration the maximum number of sidelobes whose levels are controlled is equal to *N* – 2, i.e., if the array radiation pattern has more than *N* – 2 sidelobes, we choose the *N* – 2 side‐ lobes with the highest levels to apply the constraints (36).

The radiation pattern synthesis technique described before was implemented in the Mathe‐ matica® platform with the aim of developing a CAD – called CMAD – capable of performing the design of conformal microstrip arrays. The inputs required to start the design procedure in the CMAD program are the Text Files (.txt extension) containing the points that describe the complex patterns of each array element – obtained from the conformal microstrip array simulation in CST® package –, the look direction α, the maximum sidelobes level *R*, and the starting and ending points of the intervals [θ*a*,θ*b*] and [θ*c*,θ*d*] where they are located. As a result, the CMAD returns the current excitations and the synthesized pattern. It is worth mentioning that the use of interpolation polynomials to describe the complex patterns expe‐ dites the evaluation of both vector *v*(θ,ϕ) and its derivative; consequently, the CMAD's run time is diminished. In the following three sections, examples of radiation pattern synthesis are provided to demonstrate the capability of the developed CMAD program.

#### **3.2. Cylindrical microstrip array**

subject to the constraints

in which *v<sup>i</sup>*

where

complex function *fi*

=*v*(θ*<sup>i</sup>*

,ϕ'), with θ*<sup>i</sup>*

18 Advancement in Microstrip Antennas with Recent Applications

can be evaluated through

lobes with the highest levels to apply the constraints (36).

† 0 , *<sup>v</sup><sup>s</sup>* ×D = *<sup>w</sup>* (34)

† Re{ } 0 , *<sup>v</sup><sup>d</sup>* ×D = *<sup>w</sup>* (35)

*<sup>c</sup>* = - (37)

† . *i i c w*= × *<sup>v</sup>* (38)

† , 1,2, ... , , *<sup>v</sup>i i* ×D = = *w fi m* (36)

denoting the θ coordinate of the *i*-th sidelobe, *m* is the number

of sidelobes whose levels are being modified (the maximum *m* is equal to *N*–2), and the

( | |) , | | *i*

It is important to point out that the constraints (34) and (35) retain the main beam located at the α-direction, and the ones in (36) are responsible for conducting the sidelobes levels to the threshold *R*. A closed-form solution to the problem (33)-(36) is also determined from its real counterpart, analogous to the solution to the problem (18)-(20). The problem (33)-(36) is iteratively solved until the sidelobes levels reach the desired value *R*. Notice that at each iteration the maximum number of sidelobes whose levels are controlled is equal to *N* – 2, i.e., if the array radiation pattern has more than *N* – 2 sidelobes, we choose the *N* – 2 side‐

The radiation pattern synthesis technique described before was implemented in the Mathe‐ matica® platform with the aim of developing a CAD – called CMAD – capable of performing the design of conformal microstrip arrays. The inputs required to start the design procedure in the CMAD program are the Text Files (.txt extension) containing the points that describe the complex patterns of each array element – obtained from the conformal microstrip array simulation in CST® package –, the look direction α, the maximum sidelobes level *R*, and the starting and ending points of the intervals [θ*a*,θ*b*] and [θ*c*,θ*d*] where they are located. As a result, the CMAD returns the current excitations and the synthesized pattern. It is worth mentioning that the use of interpolation polynomials to describe the complex patterns expe‐ dites the evaluation of both vector *v*(θ,ϕ) and its derivative; consequently, the CMAD's run

*i*

*i i*

*<sup>c</sup> f Rc*

To illustrate the described pattern synthesis technique, let us first consider the design of a five-element cylindrical microstrip array, such as the one shown in Figure 7(a). For this ar‐ ray, the cylindrical ground layer is made out of copper cylinder with a 60.0-mm radius and a 300.0-mm height. The employed dielectric substrate has a relative permittivity ε*<sup>r</sup>* = 2.5, a loss tangent tan δ = 0.0022 and its thickness is *hs* = 0.762 mm. The array patches are identical to the one designed in Section 2.2 to operate at 3.5 GHz. The five elements are fed by 50-ohm coaxial probes positioned 5.49 mm apart from the patches' centres and the interelement spacing was chosen to be λ0 / 2 = 42.857 mm (λ0 is the free-space wavelength at 3.5 GHz).

 **Figure 7.** (a)Five-element cylindrical microstrip array, (b) *E*θ radiation pattern: *xz*-plane, α = 60°, *R* = -20 dB, and *f* = 3.5 GHz

It is important to point out that the elements close to the ends of the ground cylinder have significantly different radiation patterns than those close to the centre of this cylinder; how‐ ever, the technique developed in this chapter can handle well this aspect, different from the common practice that assumes the elements' radiation patterns are identical [22]. To clarify this difference among the patterns, Figure 8 shows the radiation patterns of the elements number 1 and 5. In Figure 8(a) they were evaluated in CST® and in Figure 8(b) they were determined from the interpolation polynomials. As observed, there is an excellent agree‐ ment between the radiation patterns described by the interpolation polynomials and the ones provided by CST®, even in the back region, where the radiation pattern exhibits low level and oscillatory behaviour. It validates the use of polynomial interpolation functions to represent the far electric field radiated by the conformal array elements.

**3.3. Spherical microstrip array**

strate surface.

**5**

**4**

**1**

**2**

**3**

Another conformal microstrip array topology used to demonstrate the CMAD's ability to synthesize radiation patterns is the five-element spherical microstrip array, which operates at 3.5 GHz, illustrated in Figure 9(a). For this array, the selected ground layer is a copper sphere with a radius of 120.0 mm. A typical microwave substrate (ε*<sup>r</sup>* = 2.5, tan δ = 0.0022 and *hs* = 0.762 mm) covers all the ground sphere and the array patches are the same as the ones designed in Section 2.2. The angular interelement spacing in the θ-direction was chosen to be 20.334°, which corresponds to an arc length of λ0 / 2 onto the external microwave sub‐

(a) (b)

**Figure 9.** (a) Five-element spherical microstrip array, (b) *E*θ radiation pattern: *xz*-plane, α = 55°, *R* = -20 dB, and *f* = 3.5 GHz

In this case, the synthesized radiation pattern in the *xz*-plane must have its main beam locat‐ ed at α = 55.0° direction and the maximum sidelobe level cannot exceed -20 dB. After enter‐ ing these requirements in the CMAD program, it outputs the normalized current excitations (Table 2) and the synthesized radiation pattern (Figure 9(b)). To verify these results, the nor‐ malized current excitations were loaded into the spherical microstrip array simulation con‐ ducted in the CST® software. The radiation pattern obtained is also shown in Figure 9(b) for comparisons purposes. As seen, the radiation pattern given by the CMAD program and the one determined in CST® show a very good agreement, thus supporting the proposed radia‐ tion pattern synthesis technique. It is important to point out that the interelement spacing

could be varied if the array directivity needs to be altered.


Normalized radiation pattern (dB)



0

270°

240°

300°



0

0°

180°

210°

330°

Design Techniques for Conformal Microstrip Antennas and Their Arrays

30°

http://dx.doi.org/10.5772/53019

150°

60°

 CMAD CST®

21

120°

90°

For this cylindrical array, let us consider that the radiation pattern in the *xz*-plane must have the main beam located at α = 60° and the maximum sidelobe level allowed is *R* = -20 dB. By using the CMAD program, we get both the array normalized current excitations, depicted in Table 1, and the synthesized radiation pattern, shown in Figure 7(b). In order to validate these results, we provide the normalized current excitations (Table 1) for the array simula‐ tion in CST®. The radiation pattern evaluated in CST® is also represented in Figure 7(b). Ac‐ cording to what is observed, there is an excellent agreement between the radiation pattern given by the CMAD and the one calculated in CST®, thus validating the developed techni‐ que to design cylindrical microstrip arrays.

**Figure 8.** *E*θ radiation patterns – elements number 1 and 5: *xz*-plane and *f* = 3.5 GHz. (a) CST® and (b) interpolation polynomials


**Table 1.** Cylindrical microstrip array: normalized current excitations

#### **3.3. Spherical microstrip array**

level and oscillatory behaviour. It validates the use of polynomial interpolation functions to

For this cylindrical array, let us consider that the radiation pattern in the *xz*-plane must have the main beam located at α = 60° and the maximum sidelobe level allowed is *R* = -20 dB. By using the CMAD program, we get both the array normalized current excitations, depicted in Table 1, and the synthesized radiation pattern, shown in Figure 7(b). In order to validate these results, we provide the normalized current excitations (Table 1) for the array simula‐ tion in CST®. The radiation pattern evaluated in CST® is also represented in Figure 7(b). Ac‐ cording to what is observed, there is an excellent agreement between the radiation pattern given by the CMAD and the one calculated in CST®, thus validating the developed techni‐

(a) (b)

1 1.0∠0.0° 0.800∠-82.394° 0.360∠6.211° 0.781∠-90.315° 0.617∠172.593°


Normalized radiation pattern (dB)



0

270°

240°

**Normalized Current Excitation**

300°



0

0°

180°

210°

330°

30°

150°

and (b) interpolation

60°

 #1 #5

120°

90°

represent the far electric field radiated by the conformal array elements.

que to design cylindrical microstrip arrays.

20 Advancement in Microstrip Antennas with Recent Applications

0°

180°

**Table 1.** Cylindrical microstrip array: normalized current excitations

210°

330°

30°

150°

**Figure 8.** *E*θ radiation patterns – elements number 1 and 5: *xz*-plane and *f* = 3.5 GHz. (a) CST®

**Element Number**

60°

 #1 #5

120°

90°


Normalized radiation pattern (dB)



0

polynomials

270°

240°

300°



0

Another conformal microstrip array topology used to demonstrate the CMAD's ability to synthesize radiation patterns is the five-element spherical microstrip array, which operates at 3.5 GHz, illustrated in Figure 9(a). For this array, the selected ground layer is a copper sphere with a radius of 120.0 mm. A typical microwave substrate (ε*<sup>r</sup>* = 2.5, tan δ = 0.0022 and *hs* = 0.762 mm) covers all the ground sphere and the array patches are the same as the ones designed in Section 2.2. The angular interelement spacing in the θ-direction was chosen to be 20.334°, which corresponds to an arc length of λ0 / 2 onto the external microwave sub‐ strate surface.

**Figure 9.** (a) Five-element spherical microstrip array, (b) *E*θ radiation pattern: *xz*-plane, α = 55°, *R* = -20 dB, and *f* = 3.5 GHz

In this case, the synthesized radiation pattern in the *xz*-plane must have its main beam locat‐ ed at α = 55.0° direction and the maximum sidelobe level cannot exceed -20 dB. After enter‐ ing these requirements in the CMAD program, it outputs the normalized current excitations (Table 2) and the synthesized radiation pattern (Figure 9(b)). To verify these results, the nor‐ malized current excitations were loaded into the spherical microstrip array simulation con‐ ducted in the CST® software. The radiation pattern obtained is also shown in Figure 9(b) for comparisons purposes. As seen, the radiation pattern given by the CMAD program and the one determined in CST® show a very good agreement, thus supporting the proposed radia‐ tion pattern synthesis technique. It is important to point out that the interelement spacing could be varied if the array directivity needs to be altered.


Figure 11. The phase shifters play a role in controlling the phases of the current excitations, as well as the variable gain amplifiers that are responsible for settling their amplitudes. In this section, expressions for calculating the phase shifts ϕ*n* and the gains *Gn*, in terms of the array current excitations and their electrical characteristics, including the self and mutual impedances, are derived. It is worth mentioning that the evaluated expressions take into ac‐ count the mismatches between the array elements' driving impedances and the characteris‐

At the end of this section, to illustrate the synthesis of the proposed active feed network (Figure 11), the design of the active beamformers of the three conformal microstrip arrays (cylindrical, spherical and conical) that appear along the chapter is described. Furthermore, to validate the phase shifts and gains calculated, the designed feed networks are analysed in

(a) (b)

**Figure 10.** (a) Four-element conical microstrip array, (b) *E*θ radiation pattern: *xz*-plane, α = 70°, *R* = -20 dB, and *f* = 3.5 GHz

1 0.574∠-7.835°

2 0.875∠0.149°

3 1.0∠0,0°

4 0.625∠-6.561°

240°

300°


Normalized radiation pattern (dB)



0

**Element Number**

**Table 3.** Conical microstrip array: normalized current excitations

270°



0

0°

Design Techniques for Conformal Microstrip Antennas and Their Arrays

180°

210°

**Normalized Current Excitation**

330°

30°

150°

60°

 CMAD CST®

http://dx.doi.org/10.5772/53019

23

120°

90°

tic impedance *Z*0 of the lines, what improves their accuracy.

the ADS® package.

**1**

**2**

**3**

**4**

**Table 2.** Spherical microstrip array: normalized current excitations

#### **3.4. Conical microstrip array**

Finally, let us consider the radiation pattern synthesis of the four-element conical microstrip array presented in Figure 10(a). For this array, the ground layer is a 280.0-mm-high cone made of copper with a 40.0° aperture. This cone is covered with a dielectric substrate of con‐ stant thickness *hs* = 0.762 mm, relative permittivity ε*r* = 2.5 and loss tangent tan δ = 0.0022. The array elements are identical to the one designed in Section 2.2, so they have a length of 26.18 mm in the generatrix direction, an average width of 34.03 mm in the ϕ-direction, and the 50-ohm coaxial probes are located 6.02 mm apart from the patches' centres toward the ground cone basis. The interelement spacing in the generatrix direction is of 42.857 mm (= λ0 / 2) as well as the centre of the element #1 is 110.0 mm apart from the cone apex in this same direction.

The radiation pattern specifications for this synthesis are: main beam direction α = 70° and maximum sidelobe level *R* = -20 dB, both in the *xz*-plane. By using the CMAD program, we derive the normalized current excitations, shown in Table 3, and the synthesized radiation pattern in the frequency 3.5 GHz, illustrated in Figure 10(b). Also in Figure 10(b) the array radiation pattern calculated in CST®, considering the normalized current excitations of Table 3, is presented. As observed, the radiation pattern obtained with CMAD matches the one de‐ termined in CST®, once again supporting the proposed design approach.

#### **4. Active feed circuit design**

As can be seen, the radiation pattern synthesis technique presented in the previous section is suitable for applications that require electronic radiation pattern control, for example. How‐ ever, it only provides the array current excitations, i.e., to complete the array design it is still necessary to synthesize its feed network. A simple active circuit topology dedicated to feed those arrays can be composed of branches having a variable gain amplifier cascaded to a phase shifter, both controlled by a microcontroller, and a 1 : *N* power divider, as depicted in Figure 11. The phase shifters play a role in controlling the phases of the current excitations, as well as the variable gain amplifiers that are responsible for settling their amplitudes. In this section, expressions for calculating the phase shifts ϕ*n* and the gains *Gn*, in terms of the array current excitations and their electrical characteristics, including the self and mutual impedances, are derived. It is worth mentioning that the evaluated expressions take into ac‐ count the mismatches between the array elements' driving impedances and the characteris‐ tic impedance *Z*0 of the lines, what improves their accuracy.

**Element Number**

**Table 2.** Spherical microstrip array: normalized current excitations

22 Advancement in Microstrip Antennas with Recent Applications

**3.4. Conical microstrip array**

**4. Active feed circuit design**

same direction.

**Normalized Current Excitation**

1 0.680∠264.460°

2 0.252∠-6.059°

3 0.160∠156.639°

5 0.728∠-36.758°

4 1.0∠0.0°

Finally, let us consider the radiation pattern synthesis of the four-element conical microstrip array presented in Figure 10(a). For this array, the ground layer is a 280.0-mm-high cone made of copper with a 40.0° aperture. This cone is covered with a dielectric substrate of con‐ stant thickness *hs* = 0.762 mm, relative permittivity ε*r* = 2.5 and loss tangent tan δ = 0.0022. The array elements are identical to the one designed in Section 2.2, so they have a length of 26.18 mm in the generatrix direction, an average width of 34.03 mm in the ϕ-direction, and the 50-ohm coaxial probes are located 6.02 mm apart from the patches' centres toward the ground cone basis. The interelement spacing in the generatrix direction is of 42.857 mm (= λ0 / 2) as well as the centre of the element #1 is 110.0 mm apart from the cone apex in this

The radiation pattern specifications for this synthesis are: main beam direction α = 70° and maximum sidelobe level *R* = -20 dB, both in the *xz*-plane. By using the CMAD program, we derive the normalized current excitations, shown in Table 3, and the synthesized radiation pattern in the frequency 3.5 GHz, illustrated in Figure 10(b). Also in Figure 10(b) the array radiation pattern calculated in CST®, considering the normalized current excitations of Table 3, is presented. As observed, the radiation pattern obtained with CMAD matches the one de‐

As can be seen, the radiation pattern synthesis technique presented in the previous section is suitable for applications that require electronic radiation pattern control, for example. How‐ ever, it only provides the array current excitations, i.e., to complete the array design it is still necessary to synthesize its feed network. A simple active circuit topology dedicated to feed those arrays can be composed of branches having a variable gain amplifier cascaded to a phase shifter, both controlled by a microcontroller, and a 1 : *N* power divider, as depicted in

termined in CST®, once again supporting the proposed design approach.

At the end of this section, to illustrate the synthesis of the proposed active feed network (Figure 11), the design of the active beamformers of the three conformal microstrip arrays (cylindrical, spherical and conical) that appear along the chapter is described. Furthermore, to validate the phase shifts and gains calculated, the designed feed networks are analysed in the ADS® package.

**Figure 10.** (a) Four-element conical microstrip array, (b) *E*θ radiation pattern: *xz*-plane, α = 70°, *R* = -20 dB, and *f* = 3.5 GHz


**Table 3.** Conical microstrip array: normalized current excitations

**Figure 11.** Active feed network

#### **4.1. Design equations**

For the analysis conducted here the phase shifters are considered perfectly matched to the input and output lines and produce zero attenuation. Based on these assumptions the scat‐ tering matrix (*S pf* ) *n* of the *n*-th phase shifter, 1≤*n*≤*N*, assumes the form

$$(\mathbf{S}\_{pf})\_n = \begin{pmatrix} 0 & e^{j\phi\_n} \\ e^{j\phi\_n} & 0 \end{pmatrix}' \tag{39}$$

Let us examine the operation of the *n*-th circuit branch. The input power *Pn* at the terminals

<sup>1</sup> <sup>2</sup> Re{ }| | ,

where *Zinn* is the driving impedance at the terminals of the *n*-th array element and can be

1

in which *Zn*<sup>κ</sup> is the *n*-th array element self-impedance, if *n*=κ, and the mutual impedance be‐ tween the *n*-th and κ-th array elements, if *n* ≠ κ. In this chapter the self and mutual impedan‐ ces will be determined from the array simulation data. However, those impedances could also be obtained from the measurements conducted in the array prototype, what certainly

Alternatively, the input power at the terminals of the *n*-th array element can be expressed in

2

0 0 . *<sup>n</sup>*

2

*n*

*n Z Z in in Z Z in*

Combining (41) and (43) results in an expression to evaluate the incident power at the termi‐

terms of the incident power *P*0*<sup>n</sup>* and the reflection coefficient Γ*inn* at the terminals as

*n*


0 2 Re{ }| | , 2(1 | | ) *n n*

which is equal to the *n*-th variable gain output power, disregarding the losses in the lines.

Based on (45), an equation to determine the gain of the *n*-th variable gain amplifier is de‐

*Z I in <sup>P</sup>*

*n*

*n*

k k

*N n n*

*<sup>I</sup> Z Z in <sup>I</sup>*

k=

<sup>2</sup> *n nn P ZI* <sup>=</sup> *in* (41)

Design Techniques for Conformal Microstrip Antennas and Their Arrays

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25

<sup>=</sup> å (42)

<sup>0</sup> (1 | | ), *nn n P P* = -G*in* (43)

<sup>+</sup> (44)

*in* <sup>=</sup> - G (45)

of the *n*-th array element can be calculated by

would lead to a more accurate feed network design.

evaluated using

with

rived:

nals of the *n*-th array element

with ϕ*<sup>n</sup>* (0≤ϕ*n*<2π) representing the phase shift produced by the *n*-th phase shifter. Notice that the matching requirement can be met to within a reasonable degree of approximation for commercial IC (Integrated Circuit) phase shifters, however those devices frequently ex‐ hibit moderate insertion loss. So, to take the insertion loss into account in our analysis mod‐ el, the gains *Gn* are either decreased or increased (to compensate the insertion losses).

The variable gain amplifiers are also considered perfectly matched to the input and output lines and they are unilateral devices, i.e., *s*12*<sup>n</sup>*=0. Hence, the scattering matrix (*S a* ) *n* of the *n*-th variable gain amplifier is given by

$$(S\_a)\_n = \begin{pmatrix} 0 & 0 \\ s\_{21n} & 0 \end{pmatrix}' \tag{40}$$

in which *s*21*<sup>n</sup>* denotes the gain (linear magnitude) of the *n*-th variable gain amplifier. It is worth mentioning that lots of commercial IC variable gain amplifiers have input and output return loss better than 10 dB and exhibit high directivity, therefore, the preceding assump‐ tions are reasonable. More precise results using the scattering parameters of commercial var‐ iable gain amplifiers and phase shifters are presented in [23].

Let us examine the operation of the *n*-th circuit branch. The input power *Pn* at the terminals of the *n*-th array element can be calculated by

<sup>1</sup> <sup>2</sup> Re{ }| | , <sup>2</sup> *n nn P ZI* <sup>=</sup> *in* (41)

where *Zinn* is the driving impedance at the terminals of the *n*-th array element and can be evaluated using

$$Z\dot{m}\_n = \sum\_{\kappa=1}^{N} Z\_{m\kappa} \frac{I\_\kappa}{I\_n} \tag{42}$$

in which *Zn*<sup>κ</sup> is the *n*-th array element self-impedance, if *n*=κ, and the mutual impedance be‐ tween the *n*-th and κ-th array elements, if *n* ≠ κ. In this chapter the self and mutual impedan‐ ces will be determined from the array simulation data. However, those impedances could also be obtained from the measurements conducted in the array prototype, what certainly would lead to a more accurate feed network design.

Alternatively, the input power at the terminals of the *n*-th array element can be expressed in terms of the incident power *P*0*<sup>n</sup>* and the reflection coefficient Γ*inn* at the terminals as

$$P\_n = P\_{0n} (1 - |\Gamma \| \mathbf{n}\_n|^2) \, , \tag{43}$$

with

*G*<sup>1</sup> f<sup>1</sup>

1

*N*

(39)

*...*

Power Divider 1:*N*

tering matrix (*S pf* ) *n* of the *n*-th phase shifter, 1≤*n*≤*N*, assumes the form

*In*

24 Advancement in Microstrip Antennas with Recent Applications

**Figure 11.** Active feed network

**4.1. Design equations**

variable gain amplifier is given by

*GN* f*<sup>N</sup>*

For the analysis conducted here the phase shifters are considered perfectly matched to the input and output lines and produce zero attenuation. Based on these assumptions the scat‐

> 0 ( ) ,

*pf n j <sup>e</sup> <sup>S</sup> e*

*n*

with ϕ*<sup>n</sup>* (0≤ϕ*n*<2π) representing the phase shift produced by the *n*-th phase shifter. Notice that the matching requirement can be met to within a reasonable degree of approximation for commercial IC (Integrated Circuit) phase shifters, however those devices frequently ex‐ hibit moderate insertion loss. So, to take the insertion loss into account in our analysis mod‐

The variable gain amplifiers are also considered perfectly matched to the input and output lines and they are unilateral devices, i.e., *s*12*<sup>n</sup>*=0. Hence, the scattering matrix (*S a* ) *n* of the *n*-th

> 0 0 () , <sup>0</sup> *a n n*

in which *s*21*<sup>n</sup>* denotes the gain (linear magnitude) of the *n*-th variable gain amplifier. It is worth mentioning that lots of commercial IC variable gain amplifiers have input and output return loss better than 10 dB and exhibit high directivity, therefore, the preceding assump‐ tions are reasonable. More precise results using the scattering parameters of commercial var‐

è ø (40)

21

*s* æ ö <sup>=</sup> ç ÷

*S*

iable gain amplifiers and phase shifters are presented in [23].

f æ ö = ç ÷ ç ÷ è ø

el, the gains *Gn* are either decreased or increased (to compensate the insertion losses).

0 *n*

*j*

f

$$\Gamma \dot{m}\_n = \frac{Z \dot{m}\_n - Z\_0}{Z \dot{m}\_n + Z\_0}. \tag{44}$$

Combining (41) and (43) results in an expression to evaluate the incident power at the termi‐ nals of the *n*-th array element

$$P\_{0n} = \frac{\text{Re}\{Z\dot{m}\_n\} \|I\_n\|^2}{\text{2}\{1 - \|\Gamma \dot{m}\_n\|^2\}}\,\text{}\,\text{}\,\tag{45}$$

which is equal to the *n*-th variable gain output power, disregarding the losses in the lines.

Based on (45), an equation to determine the gain of the *n*-th variable gain amplifier is de‐ rived:

$$\log G\_n = \frac{P\_{0n}}{P\_{0m}} = \frac{\text{Re}\{Zin\_n\}}{\text{Re}\{Zin\_m\}} \frac{1 - \|\Gamma \dot{m}\_m\|^2}{1 - \|\Gamma \dot{m}\_n\|^2} \frac{\|I\_n\|^2}{\|I\_m\|^2}. \tag{46}$$

The expressions for evaluating the gains *Gn* (46) and phase shifts ϕ*<sup>n</sup>* (49) were incorporated into the developed computer program CMAD to generate a new module devoted to design active feed networks, such as the one illustrated in Figure 11. The inputs required to start the circuit design are the array current excitations and the *Touchstone* File (.sNp extension) containing the array scattering parameters – obtained from the conformal microstrip array simulation in a full-wave electromagnetic simulator, for example. In the next section, to demonstrate the capability of this new CMAD feature, the feed networks of the three confor‐

Design Techniques for Conformal Microstrip Antennas and Their Arrays

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27

The normalized current excitations found in Tables 1 to 3 and the scattering parameters of the three conformal microstrip arrays synthesized in this chapter (evaluated in CST®) were provided to the CMAD. As results, it returned the gains and phase shifts of the active feed networks that implement the radiation patterns shown in Figures 7(b), 9(b) and 10(b). These

To verify the validity of the results found in Table 4, the designed active feed networks were analysed in the ADS® package. As an example, Figure 12 shows the simulated feed network for the conical microstrip array. In this circuit, the array is represented through a 4-port mi‐ crowave network, whose scattering parameters are the same as the ones used by the CMAD, it is fed by a 30-dBm power source with a 50-ohm impedance, and there are four current probes to measure the currents at the terminals of the 4-port microwave network, which cor‐ respond to the array current excitations. Table 5 summarizes the current probes readings for the three analysed feed networks. The comparison between the currents given in Table 5 and the ones presented in Tables 1 to 3 shows that these currents are in agreement, thereby

> **Cylindrical Array Spherical Array Conical Array Gain (dB) Phase Shift (deg) Gain (dB) Phase Shift (deg) Gain (dB) Phase Shift (deg)**

1 7.4 351.1 11.1 114.6 0.0 0.0

2 5.7 267.6 3.8 205.0 4.2 7.0

3 0.0 0.0 0.0 0.0 5.4 4.1

4 4.9 260.6 14.0 210.3 1.5 356.6

5 2.4 164.0 10.9 173.0 – –

mal microstrip arrays previously synthesized will be designed.

**4.2. Examples**

**Branch Number**

values are listed in Table 4.

validating the design equations derived before.

**Table 4.** Gains and phase shifts of the designed active feed networks

Notice that to evaluate (46) it is necessary to choose one of the circuit branches as a refer‐ ence, i.e., the gain of the *m*-th variable gain amplifier is set equal to 1.0.

It is important to highlight that this formulation has relevant importance for arrays whose mutual coupling among elements is strong [23], since it takes this effect into account. For ar‐ rays whose mutual coupling among elements is weak and the array elements self-impedan‐ ces are close to *Z*0 , (46) is approximated by

$$\mathcal{G}\_n \cong \frac{\|I\_n\|^2}{\|I\_m\|^2}.\tag{47}$$

Now, to determine the phase shifts ϕ*n*, let us consider the current *In* at the terminals of the *n*th array element, that is,

$$I\_n = I\_{0n} e^{j\phi\_n} (1 - \Gamma i n\_n) \, , \tag{48}$$

in which *I*0*<sup>n</sup> <sup>e</sup> <sup>j</sup>ϕ<sup>n</sup>* is the incident current wave at the terminals of the *n*-th array element.

Once the currents *In* are provided by the algorithm described in the last section, to calculate ϕ*n* the phases of the left and right sides of (48) are enforced to be equal. Then,

$$
\boldsymbol{\phi}\_{n} = \boldsymbol{\delta}\_{nm} - \arg\{\mathbf{1} - \boldsymbol{\Gamma}\boldsymbol{m}\_{n}\} + \arg\{\mathbf{1} - \boldsymbol{\Gamma}\boldsymbol{m}\_{m}\},
\tag{49}
$$

with

$$\delta\_{nm} = \arg\{I\_n\} - \arg\{I\_m\}.\tag{50}$$

Also for the determination of the phase shift ϕ*n*, the *m*-th circuit branch was taken as a refer‐ ence, i.e., its phase shifter does not introduce any phase shift (ϕ*m*=0°) in the signal.

For arrays whose mutual coupling among elements is weak and the array elements self-im‐ pedances are close to *Z*0 , the phase shift ϕ*n* (49) reduces to

$$
\Phi\_n \cong \delta\_{nm}.\tag{51}
$$

The expressions for evaluating the gains *Gn* (46) and phase shifts ϕ*<sup>n</sup>* (49) were incorporated into the developed computer program CMAD to generate a new module devoted to design active feed networks, such as the one illustrated in Figure 11. The inputs required to start the circuit design are the array current excitations and the *Touchstone* File (.sNp extension) containing the array scattering parameters – obtained from the conformal microstrip array simulation in a full-wave electromagnetic simulator, for example. In the next section, to demonstrate the capability of this new CMAD feature, the feed networks of the three confor‐ mal microstrip arrays previously synthesized will be designed.

#### **4.2. Examples**

2 2

2 2


@ (47)

*nn n I Ie in* <sup>f</sup> = -G (48)

arg{1 } arg{1 }, *n nm <sup>n</sup> <sup>m</sup>* f =d - -G + -G *in in* (49)

arg{ } arg{ }. *nm n <sup>m</sup>* d= - *I I* (50)

. *n nm* f @d (51)

Re{ } 1 | | | | . Re{ } 1| || | *n n mn*

*m m n m*

Notice that to evaluate (46) it is necessary to choose one of the circuit branches as a refer‐

It is important to highlight that this formulation has relevant importance for arrays whose mutual coupling among elements is strong [23], since it takes this effect into account. For ar‐ rays whose mutual coupling among elements is weak and the array elements self-impedan‐

> 2 2 | | . | | *n*

Now, to determine the phase shifts ϕ*n*, let us consider the current *In* at the terminals of the *n*-

<sup>0</sup> (1 ), *<sup>n</sup> <sup>j</sup>*

Once the currents *In* are provided by the algorithm described in the last section, to calculate

Also for the determination of the phase shift ϕ*n*, the *m*-th circuit branch was taken as a refer‐

For arrays whose mutual coupling among elements is weak and the array elements self-im‐

ence, i.e., its phase shifter does not introduce any phase shift (ϕ*m*=0°) in the signal.

pedances are close to *Z*0 , the phase shift ϕ*n* (49) reduces to

is the incident current wave at the terminals of the *n*-th array element.

*m*

*n*

ϕ*n* the phases of the left and right sides of (48) are enforced to be equal. Then,

*<sup>I</sup> <sup>G</sup> I*

*PZ I in in <sup>G</sup> P Zin in I*

0

0

ence, i.e., the gain of the *m*-th variable gain amplifier is set equal to 1.0.

*n*

26 Advancement in Microstrip Antennas with Recent Applications

ces are close to *Z*0 , (46) is approximated by

th array element, that is,

in which *I*0*<sup>n</sup> <sup>e</sup> <sup>j</sup>ϕ<sup>n</sup>*

with

The normalized current excitations found in Tables 1 to 3 and the scattering parameters of the three conformal microstrip arrays synthesized in this chapter (evaluated in CST®) were provided to the CMAD. As results, it returned the gains and phase shifts of the active feed networks that implement the radiation patterns shown in Figures 7(b), 9(b) and 10(b). These values are listed in Table 4.

To verify the validity of the results found in Table 4, the designed active feed networks were analysed in the ADS® package. As an example, Figure 12 shows the simulated feed network for the conical microstrip array. In this circuit, the array is represented through a 4-port mi‐ crowave network, whose scattering parameters are the same as the ones used by the CMAD, it is fed by a 30-dBm power source with a 50-ohm impedance, and there are four current probes to measure the currents at the terminals of the 4-port microwave network, which cor‐ respond to the array current excitations. Table 5 summarizes the current probes readings for the three analysed feed networks. The comparison between the currents given in Table 5 and the ones presented in Tables 1 to 3 shows that these currents are in agreement, thereby validating the design equations derived before.


**Table 4.** Gains and phase shifts of the designed active feed networks


**Table 5.** Current probes readings (in ampere)

#### **5. Conclusion**

In summary, a computationally efficient algorithm capable of assisting the design of probefed conformal microstrip antennas with quasi-rectangular patches was discussed. Some ex‐ amples were provided to illustrate its use and advantages. As seen, it can result in significant reductions in design time, since the required number of full-wave electromagnet‐ ic simulations, which are computationally intensive – especially for conformal radiators –, is diminished. For instance, the proposed designs could be performed with only three fullwave simulations. Also in this chapter, an accurate design technique to synthesize radiation patterns of conformal microstrip arrays was introduced. The adopted technique takes the ra‐ diation pattern of each array element into account in its code through the use of interpola‐ tion polynomials, different from the common practice that assumes the elements' radiation patterns are identical. Hence, the developed technique can provide more accurate results. Besides, it is able to control the sidelobes levels, so that optimized array directivity can be achieved. This design technique was coded in the Mathematica® platform giving rise to a computer program, called CMAD, that evaluates the array current excitations responsible for synthesizing a given radiation pattern. To show the potential of the CMAD program, the design of cylindrical, spherical and conical microstrip arrays were exemplified. Finally, an active feed network suitable for applications that require electronic radiation pattern con‐ trol, like tracking systems, was addressed. The expressions derived for the synthesis of this circuit take into account the mutual coupling among the array elements; therefore they are also suited for array configurations in which the mutual coupling among the elements is strong. These design equations were incorporated into the CMAD code adding to it one more project tool. In order to validate this new CMAD feature, the feed networks of the three conformal microstrip arrays described along the chapter were designed. The obtained results were validated through the feed networks' simulations in the ADS® software.

**Figure 12.** Simulated feed network for the conical microstrip array

The authors would like to acknowledge the support given to this work, developed under the project "Adaptive Antennas and RF Modules for Wireless Broadband Networks Applied to Public Safety", with the support of the Ministry of Communications' FUNTTEL (Brazilian Fund for the Technological Development of Telecommunications), under Grant No.

and Daniel C. Nascimento2

Design Techniques for Conformal Microstrip Antennas and Their Arrays

http://dx.doi.org/10.5772/53019

29

[1] Wong KL. Design of Nonplanar Microstrip Antennas and Transmission Lines. New

01.09.0634.00 with the Financier of Studies and Projects - FINEP / MCTI.

, Cristiano B. de Paula1

1 CPqD - Telecommunications R&D Foundation, Brazil

2 ITA - Technological Institute of Aeronautics, Brazil

York: John Wiley & Sons, Inc.; 1999.

**Acknowledgements**

**Author details**

Daniel B. Ferreira1

**References**

**Figure 12.** Simulated feed network for the conical microstrip array

#### **Acknowledgements**

**Branch**

**Table 5.** Current probes readings (in ampere)

28 Advancement in Microstrip Antennas with Recent Applications

**5. Conclusion**

**Number Cylindrical Array Spherical Array Conical Array**

1 0.160∠-10.37° 0.249∠113.2° 0.106∠-9.417°

2 0.128∠-92.76° 0.092∠-157.3° 0.161∠-1.432°

3 0.058∠-4.156° 0.059∠5.375° 0.184∠-1.581°

4 0.125∠-100.7° 0.366∠-151.3° 0.115∠-8.141°

In summary, a computationally efficient algorithm capable of assisting the design of probefed conformal microstrip antennas with quasi-rectangular patches was discussed. Some ex‐ amples were provided to illustrate its use and advantages. As seen, it can result in significant reductions in design time, since the required number of full-wave electromagnet‐ ic simulations, which are computationally intensive – especially for conformal radiators –, is diminished. For instance, the proposed designs could be performed with only three fullwave simulations. Also in this chapter, an accurate design technique to synthesize radiation patterns of conformal microstrip arrays was introduced. The adopted technique takes the ra‐ diation pattern of each array element into account in its code through the use of interpola‐ tion polynomials, different from the common practice that assumes the elements' radiation patterns are identical. Hence, the developed technique can provide more accurate results. Besides, it is able to control the sidelobes levels, so that optimized array directivity can be achieved. This design technique was coded in the Mathematica® platform giving rise to a computer program, called CMAD, that evaluates the array current excitations responsible for synthesizing a given radiation pattern. To show the potential of the CMAD program, the design of cylindrical, spherical and conical microstrip arrays were exemplified. Finally, an active feed network suitable for applications that require electronic radiation pattern con‐ trol, like tracking systems, was addressed. The expressions derived for the synthesis of this circuit take into account the mutual coupling among the array elements; therefore they are also suited for array configurations in which the mutual coupling among the elements is strong. These design equations were incorporated into the CMAD code adding to it one more project tool. In order to validate this new CMAD feature, the feed networks of the three conformal microstrip arrays described along the chapter were designed. The obtained

results were validated through the feed networks' simulations in the ADS® software.

5 0.099∠162.2° 0.267∠172.0° –

The authors would like to acknowledge the support given to this work, developed under the project "Adaptive Antennas and RF Modules for Wireless Broadband Networks Applied to Public Safety", with the support of the Ministry of Communications' FUNTTEL (Brazilian Fund for the Technological Development of Telecommunications), under Grant No. 01.09.0634.00 with the Financier of Studies and Projects - FINEP / MCTI.

#### **Author details**

Daniel B. Ferreira1 , Cristiano B. de Paula1 and Daniel C. Nascimento2


#### **References**

[1] Wong KL. Design of Nonplanar Microstrip Antennas and Transmission Lines. New York: John Wiley & Sons, Inc.; 1999.

[2] Josefsson L, Persson P. Conformal Array Antenna Theory and Design. Hoboken: John Wiley & Sons, Inc.; 2006.

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[21] Tseng CY. Minimum Variance Beamforming with Phase-Independent Derivative

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[23] Ferreira DB, de Paula CB, Nascimento DC. Design of an Active Feed Network for Antenna Arrays. In: MOMAG 2012, 5-8 Aug. 2012, Joao Pessoa, Brazil. (in Portu‐

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[13] Mathematica. Wolfram Research. http://www.wolfram.com/products/mathematica/

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**Chapter 2**

**Bandwidth Optimization of**

Additional information is available at the end of the chapter

microstrip antenna with wide range of work.

antenna bandwidth [5].

Marek Bugaj and Marian Wnuk

http://dx.doi.org/10.5772/54661

**1. Introduction**

**Aperture-Coupled Stacked Patch Antenna**

The microstrip antennas have been one of the most innovative fields of antenna techniques for the last three decades. Microstrip antennas have several advantages such as lightweight, smallvolume, and that they can be made conformal to the host surface. In addition, these antennas are manufactured using printed-circuit technology, so that mass production can be achieved at a low cost. Microstrip antennas, which are used for defense and commercial applications, are replacing many conventional antennas [1]. However, the types of applications of microstrip antennas are restricted by the narrow bandwidth (BW). Accordingly, increasing the BW of the microstrip antennas has been a primary goal of research for many years. This is reflected in the large number of papers on the subject published in journals and conference proceedings. In fact, several broadband microstrip antennas configurations have been reported in the last few decades. They have additional advantages: simplicity of production, small weight, narrow section, easiness of integration of radiators with feeding system. However, this construction also has the following disadvantages: narrow band, limited power capacity, not sufficient efficiency of radiation. Still ongoing search for solutions to obtain a broad range of work in the microstrip antenna. The aim of this study is to demonstrate that it is possible to build a

The basic configuration of microstrip antenna consists of metallic strip printed on thin earthed dielectric base. The feeding is accomplished through concentric cable, it runs perpendicularly through a substrate or a strip line runs on a substrate in the plane of aerial[15]. The aperture coupling feed was proposed by Pozar and it has many advantages over other types of feeds. These include shielding of the antenna from spurious feed radiating, the use of suitable substrates for feed structure and the antenna, and the use of thick substrates for increasing the

> © 2013 Bugaj and Wnuk; licensee InTech. This is an open access article 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.

> © 2013 Bugaj and Wnuk; licensee InTech. This is a paper 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.

### **Chapter 2**

### **Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna**

Marek Bugaj and Marian Wnuk

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/54661

#### **1. Introduction**

The microstrip antennas have been one of the most innovative fields of antenna techniques for the last three decades. Microstrip antennas have several advantages such as lightweight, smallvolume, and that they can be made conformal to the host surface. In addition, these antennas are manufactured using printed-circuit technology, so that mass production can be achieved at a low cost. Microstrip antennas, which are used for defense and commercial applications, are replacing many conventional antennas [1]. However, the types of applications of microstrip antennas are restricted by the narrow bandwidth (BW). Accordingly, increasing the BW of the microstrip antennas has been a primary goal of research for many years. This is reflected in the large number of papers on the subject published in journals and conference proceedings. In fact, several broadband microstrip antennas configurations have been reported in the last few decades. They have additional advantages: simplicity of production, small weight, narrow section, easiness of integration of radiators with feeding system. However, this construction also has the following disadvantages: narrow band, limited power capacity, not sufficient efficiency of radiation. Still ongoing search for solutions to obtain a broad range of work in the microstrip antenna. The aim of this study is to demonstrate that it is possible to build a microstrip antenna with wide range of work.

The basic configuration of microstrip antenna consists of metallic strip printed on thin earthed dielectric base. The feeding is accomplished through concentric cable, it runs perpendicularly through a substrate or a strip line runs on a substrate in the plane of aerial[15]. The aperture coupling feed was proposed by Pozar and it has many advantages over other types of feeds. These include shielding of the antenna from spurious feed radiating, the use of suitable substrates for feed structure and the antenna, and the use of thick substrates for increasing the antenna bandwidth [5].

© 2013 Bugaj and Wnuk; licensee InTech. This is an open access article 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. © 2013 Bugaj and Wnuk; licensee InTech. This is a paper 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.

The methods of analysis and projection of microstrip antennas have developed simultaneously with the development of aerials. Nowadays several methods of analyzing the antennas on dielectric surface are used, however, the most commonly used ones are the full wave model based on Green's function and the method of moments where analysis relies on solution of integral equation, concerning electric field, with regard to unknown currents flowing through elements of the antenna and its feeding system [7].

to the dominant mode of the patch and the microstrip line occurs because the slot interrupts

Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna

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35

For an analyzed planar structure activity of the antenna is more important than surrounding space, so the analyzed area is not to large. But it is large enough so that the results would reflect analyzed area precisely and strictly, taking into account limited computing power of a computer. One of the most important parameters, which will be calculated, is bandwidth whose value is dependent from parameters of antenna. The described aerial is structure multi

Choice of laminates and other materials for the implementation of the antenna and antenna system is one of the most important steps in the process of designing microstrip antennas. Planar microstrip antenna can be built with the theoretically infinite number of layers. This solution, unfortunately, leads to a reduction in antenna efficiency and leads to excitation of surface waves. In order to provide the required bandwidth efficiency of the antenna work and

the longitudinal current flow in them[3].

**Figure 1.** An aperture coupled microstrip patch antenna.

**3. Optimization**

resonance.

Millimeter wave printed antennas can take on many forms, including microstrip patch elements and a variety of proximity coupled printed radiators. The microstripline-fed printed slot and the aperture coupled patch are examples of the latter type and may be useful in certain planar array applications [2].

The paper presents the model of the antenna on which the influence of parameters on antenna bandwidth simulation was conducted (the influence of changes permittivity and thickness of every layer). One of the most important parameters which have been calculated is the band‐ width. Its value depends on antenna parameters (thickness and permittivity of every layer). The paper shows that as a result of optimization which has been demonstrated we can create a planar antenna with wide range of work. The analysis process of multilayer microstrip antennas is complex and time consuming[4,11].

One of the main problems associated with the use of planar antennas in radio links is their relatively narrow frequency band of operation, it has been indicated at the outset of this chapter. This problem has been described in literature, in books such as monographs [6] or [9, ch. 3 and 6] and in paper such as [8]. The next literature is worth noting the work of Borowiec and Słobodzian, who described [10] a method of increasing bandwidth of planar antennas. Unfortunately, the bandwidth of the antenna work, which was obtained only at 15-18 %. Increasing the frequency band planar antenna work can be done through the use of:


#### **2. Analyzed antenna**

Aperture coupling antenna feeding method was first suggested in 1985 by David.M. Pozar [9]. Using this method of feeding antenna we have hope to obtain a wide operating bandwidth B, which has tried to prove, by various authors [9]. The basic condition for obtaining satisfactory results is to optimize the parameters of multilayer antennas.

An exploded view of this type antenna is shown in Figure 1. The antenna consists of four layers with two radiators. Radiators are microstrip patches; they are on layers of h2 and h4. The microstrip patch is feed by microstrip line trough slot in the common ground plane. The width microstrip line is W and is printed on a substrate described by h1 and ε1. Coupling of the slot

to the dominant mode of the patch and the microstrip line occurs because the slot interrupts the longitudinal current flow in them[3].

For an analyzed planar structure activity of the antenna is more important than surrounding space, so the analyzed area is not to large. But it is large enough so that the results would reflect analyzed area precisely and strictly, taking into account limited computing power of a computer. One of the most important parameters, which will be calculated, is bandwidth whose value is dependent from parameters of antenna. The described aerial is structure multi resonance.

**Figure 1.** An aperture coupled microstrip patch antenna.

#### **3. Optimization**

The methods of analysis and projection of microstrip antennas have developed simultaneously with the development of aerials. Nowadays several methods of analyzing the antennas on dielectric surface are used, however, the most commonly used ones are the full wave model based on Green's function and the method of moments where analysis relies on solution of integral equation, concerning electric field, with regard to unknown currents flowing through

Millimeter wave printed antennas can take on many forms, including microstrip patch elements and a variety of proximity coupled printed radiators. The microstripline-fed printed slot and the aperture coupled patch are examples of the latter type and may be useful in certain

The paper presents the model of the antenna on which the influence of parameters on antenna bandwidth simulation was conducted (the influence of changes permittivity and thickness of every layer). One of the most important parameters which have been calculated is the band‐ width. Its value depends on antenna parameters (thickness and permittivity of every layer). The paper shows that as a result of optimization which has been demonstrated we can create a planar antenna with wide range of work. The analysis process of multilayer microstrip

One of the main problems associated with the use of planar antennas in radio links is their relatively narrow frequency band of operation, it has been indicated at the outset of this chapter. This problem has been described in literature, in books such as monographs [6] or [9, ch. 3 and 6] and in paper such as [8]. The next literature is worth noting the work of Borowiec and Słobodzian, who described [10] a method of increasing bandwidth of planar antennas. Unfortunately, the bandwidth of the antenna work, which was obtained only at 15-18 %.

Aperture coupling antenna feeding method was first suggested in 1985 by David.M. Pozar [9]. Using this method of feeding antenna we have hope to obtain a wide operating bandwidth B, which has tried to prove, by various authors [9]. The basic condition for obtaining satisfactory

An exploded view of this type antenna is shown in Figure 1. The antenna consists of four layers with two radiators. Radiators are microstrip patches; they are on layers of h2 and h4. The microstrip patch is feed by microstrip line trough slot in the common ground plane. The width microstrip line is W and is printed on a substrate described by h1 and ε1. Coupling of the slot

results is to optimize the parameters of multilayer antennas.

Increasing the frequency band planar antenna work can be done through the use of:

elements of the antenna and its feeding system [7].

34 Advancement in Microstrip Antennas with Recent Applications

antennas is complex and time consuming[4,11].

**•** Tuning frequency planar radiators,

**•** Dual frequency transmitters,

**•** Multilayer structures.

**2. Analyzed antenna**

planar array applications [2].

Choice of laminates and other materials for the implementation of the antenna and antenna system is one of the most important steps in the process of designing microstrip antennas. Planar microstrip antenna can be built with the theoretically infinite number of layers. This solution, unfortunately, leads to a reduction in antenna efficiency and leads to excitation of surface waves. In order to provide the required bandwidth efficiency of the antenna work and we need to limit the number of layers to this, to obtain both wide bandwidth operation and high efficiency.

In this case the optimization is folded, since all possible combinations of parameters will be examined. This optimization is time-consuming and complex process. In Figure 2 an algorithm of the optimization was presented. Bandwidth planar antenna can be expressed using the equation (1):

$$B = \frac{VSWR - 1}{\frac{c\sqrt{\varepsilon\_e}}{4f\_0h}}\tag{1}$$

and permittivity (Figure 3). On each of graphs optimum areas marked on the color red. Layer

Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna

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37

The object of the study is primarily broadband properties of the antenna input impedance and directional properties, which determine the further use of the model. Particular attention is

h3 has the optimum area smallest of all examined layers.

**5. The results of the optimization process**

**Figure 2.** Algorithm of the optimization

where:

*Q* - quality factor

*f* <sup>0</sup> - center frequency of band

*εe* - permittivity

*h* - thickness of antenna

Optimization parameters:


In order to optimize the iterative method was used. It is time consuming but allowed us to investigate the effect of dielectric parameters of the antenna operating band (fig.3). In the optimization process the following steps of changes of input parameters were accepted:


#### **4. Limitations of the optimization**

Permeability and thickness of each layer are limited typical values offered by various manu‐ facturers such as ROGERS, ARLON, etc. Different companies offer dielectrics with very similar structural parameters. Therefore, the values of h and εr values are limited discrete values occurring in the family.

As a result of computational series this way conducted for every of layers three-dimensional graphs giving the full image and the inspection of all possible combinations to the thickness Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna http://dx.doi.org/10.5772/54661 37

**Figure 2.** Algorithm of the optimization

we need to limit the number of layers to this, to obtain both wide bandwidth operation and

In this case the optimization is folded, since all possible combinations of parameters will be examined. This optimization is time-consuming and complex process. In Figure 2 an algorithm of the optimization was presented. Bandwidth planar antenna can be expressed using the

0

In order to optimize the iterative method was used. It is time consuming but allowed us to investigate the effect of dielectric parameters of the antenna operating band (fig.3). In the optimization process the following steps of changes of input parameters were accepted:

Permeability and thickness of each layer are limited typical values offered by various manu‐ facturers such as ROGERS, ARLON, etc. Different companies offer dielectrics with very similar structural parameters. Therefore, the values of h and εr values are limited discrete values

As a result of computational series this way conducted for every of layers three-dimensional graphs giving the full image and the inspection of all possible combinations to the thickness

4 *e*


*VSWR <sup>B</sup> c f h* e

1

(1)

high efficiency.

36 Advancement in Microstrip Antennas with Recent Applications

equation (1):

where:

*Q* - quality factor

*εe* - permittivity

*f* <sup>0</sup> - center frequency of band

*h* - thickness of antenna

Optimization parameters:

**•** Layers permittivity: ε1, ε2, ε3, ε<sup>4</sup>

**•** Layers thickness: h1, h2, h3, h4 (Fig.1)

**•** electric penetrability of layers (*ε*1, *ε*2, *ε*3, *ε*4) – 0.05

**•** thickness of layers (h1, h2, h3, h4) – 0.05 [mm]

**4. Limitations of the optimization**

occurring in the family.

and permittivity (Figure 3). On each of graphs optimum areas marked on the color red. Layer h3 has the optimum area smallest of all examined layers.

#### **5. The results of the optimization process**

The object of the study is primarily broadband properties of the antenna input impedance and directional properties, which determine the further use of the model. Particular attention is paid to the bandwidth of the work, which was the basic parameter determining the final construction of the structure. Using the current state of knowledge should lead to the use of dielectrics with relatively lowest values of electrical permittivity. Optimization was carried out by examining the every of the layers in structure. The results to optimize were presented on the graphs below. The optimization process was as follows: for each layer has been studied sufficiently large set of combinations of thickness and permeability, and for each of them determined the bandwidth of operation. As a result of a series of calculations for each of the layers was formed three-dimensional graphs which give a complete picture and review all possible combinations of thickness and permeability. On each of the graphs obtained areas with the best bandwidth - in the diagrams shown in red. As can be seen in the following analysis for each layer there is at least some optimum combinations. A limitation of choosing the right laminate is the availability of mass-produced laminates of sufficient thickness and permeabil‐ ity. Laminates as well as other electronic components such as resistors and capacitors are produced in the so-called series with typical values, with defined thicknesses and permittivity. This is some major difficulty for designers. The process of optimization and testing of all parameters of the antenna was carried out using IE3D software (Zeland Software) based on the method of moments. In order to verify the correctness of their analysis before the construction of physical model of antenna we one more time made calculations the VSWR and radiation characteristics of the final model using a different calculation method (fig.10 and 11). To perform calculations in order to verify the selected software CST Microwave Studio based on FDTD method. Smith chart of wideband multilayer antenna is show in figure 9.

Figure 9. Smith chart of wideband multilayer antenna. **Figure 3.** Results of optimization for the parameters of the four layers of the aperture-coupled microstrip antenna

that despite these changes the antenna VSWR <2.

Figure 10.Figure 10. Verification of model with using CST.

Input impedance of the antenna in operating band varies in the range of 30 to 70 [Ω]. This input impedance makes full use of the antenna in the whole operating band. Such changes in the impedance is a side effect for maximum bandwidth . It should be noted

The results also show how little room for maneuver there is for choosing the right laminate structure. For some structures may unfortunately find that the physical realization is impos‐ sible because in our area of interest is not in any laminate. Then we would look for a solution by changing the dimensions of the radiating elements so as to be able to use existing laminates.

Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna

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39

The thickness of layers in a multilayer structure is one of the more important elements affecting directly on the bandwidth of the work the whole structure of radiation. Analysis the impact of the thickness the layers on the bandwidth in the structure consisted of the cyclic change in thickness (in steps of 0.05 mm) layer and setting the bandwidth (VSWR <2) when the other elements in the construction of the antenna in the same state. Maintaining other elements of the antenna can be sure that the effect is obtained only from changes in thickness. The analysis was performed for all layers occurring in the structure. For obtained in the optimization

The first was analyzed h4 layer. It is located at the top of the antenna. The results are illustrated in Figure 4. The results can be concluded that the bandwidth of the work at a level above 50% can be achieved by changes in the thickness of this layer in the range from 0.008 to 0.062λ0.

As a result of optimization selected the following dielectrics:

**6. Influence of dielectric parameters on antenna bandwidth**

process the parameters of laminates determined parameters of the antenna.

h1=1,57 mm, ε1 =2.2 - Rogers-RT/duroid 5880

h4 =0,25mm, ε4 =3.50 - Rogers/RO3035

**Figure 4.** Influence thickness of h4 layer on bandwidth

h2 =3,048 mm, ε2 =2.6 -Rogers-RT/ULTRALAM 2000 h3 =3 mm, ε3 =1.07- polymethacrylamid hard foam.

The radiation pattern of antenna has stable shape in the whole operating band. In the whole frequency range the gain of antenna

(calculated) is around 5 [dBi]. The width of the radiation characteristics (- 3dB) is around 100 °.

The results also show how little room for maneuver there is for choosing the right laminate structure. For some structures may unfortunately find that the physical realization is impos‐ sible because in our area of interest is not in any laminate. Then we would look for a solution by changing the dimensions of the radiating elements so as to be able to use existing laminates.

As a result of optimization selected the following dielectrics:

The process of optimization and testing of all parameters of the antenna was carried out using IE3D software (Zeland Software) h1=1,57 mm, ε1 =2.2 - Rogers-RT/duroid 5880 h2 =3,048 mm, ε2 =2.6 -Rogers-RT/ULTRALAM 2000 h3 =3 mm, ε3 =1.07- polymethacrylamid hard foam. h4 =0,25mm, ε4 =3.50 - Rogers/RO3035

paid to the bandwidth of the work, which was the basic parameter determining the final construction of the structure. Using the current state of knowledge should lead to the use of dielectrics with relatively lowest values of electrical permittivity. Optimization was carried out by examining the every of the layers in structure. The results to optimize were presented on the graphs below. The optimization process was as follows: for each layer has been studied sufficiently large set of combinations of thickness and permeability, and for each of them determined the bandwidth of operation. As a result of a series of calculations for each of the layers was formed three-dimensional graphs which give a complete picture and review all possible combinations of thickness and permeability. On each of the graphs obtained areas with the best bandwidth - in the diagrams shown in red. As can be seen in the following analysis for each layer there is at least some optimum combinations. A limitation of choosing the right laminate is the availability of mass-produced laminates of sufficient thickness and permeabil‐ ity. Laminates as well as other electronic components such as resistors and capacitors are produced in the so-called series with typical values, with defined thicknesses and permittivity.

FDTD method. Smith chart of wideband multilayer antenna is show in figure 9.

based on the method of moments. In order to verify the correctness of their analysis before the construction of physical model of

Input impedance of the antenna in operating band varies in the range of 30 to 70 [Ω]. This input impedance makes full use of the antenna in the whole operating band. Such changes in the impedance is a side effect for maximum bandwidth . It should be noted

The radiation pattern of antenna has stable shape in the whole operating band. In the whole frequency range the gain of antenna

(calculated) is around 5 [dBi]. The width of the radiation characteristics (- 3dB) is around 100 °.

This is some major difficulty for designers.

38 Advancement in Microstrip Antennas with Recent Applications

Figure 9. Smith chart of wideband multilayer antenna.

**Figure 3.** Results of optimization for the parameters of the four layers of the aperture-coupled microstrip antenna

that despite these changes the antenna VSWR <2.

Figure 10.Figure 10. Verification of model with using CST.

#### antenna we one more time made calculations the VSWR and radiation characteristics of the final model using a different calculation method (fig.10 and 11). To perform calculations in order to verify the selected software CST Microwave Studio based on **6. Influence of dielectric parameters on antenna bandwidth**

The thickness of layers in a multilayer structure is one of the more important elements affecting directly on the bandwidth of the work the whole structure of radiation. Analysis the impact of the thickness the layers on the bandwidth in the structure consisted of the cyclic change in thickness (in steps of 0.05 mm) layer and setting the bandwidth (VSWR <2) when the other elements in the construction of the antenna in the same state. Maintaining other elements of the antenna can be sure that the effect is obtained only from changes in thickness. The analysis was performed for all layers occurring in the structure. For obtained in the optimization process the parameters of laminates determined parameters of the antenna.

**Figure 4.** Influence thickness of h4 layer on bandwidth

The first was analyzed h4 layer. It is located at the top of the antenna. The results are illustrated in Figure 4. The results can be concluded that the bandwidth of the work at a level above 50% can be achieved by changes in the thickness of this layer in the range from 0.008 to 0.062λ0. Figure 4. Influence thickness of h4 layer on bandwidth

area of the upper frequencies.

0.25<sup>0</sup> (fig.6)

When we increase the thickness of the layer above the limit then the range bandwidth is narrows in the area of the upper frequencies. The first was analyzed h4 layer. It is located at the top of the antenna. The results are illustrated in Figure 4. The results can be concluded that the bandwidth of the work at a level above 50% can be achieved by changes in the thickness of this layer in the range from 0.008 to 0.0620. When we increase the thickness of the layer above the limit then the range bandwidth is narrows in the

Figure 5. VSWR for values outside of the optimal range (a) thickness >0.062<sup>0</sup> (b) thickness <0.008<sup>0</sup> **Figure 5.** VSWR for values outside of the optimal range (a) thickness >0.062λ0 (b) thickness <0.008λ<sup>0</sup>

Using the same calculation process, we determined the influence of thickness h3 to h1 on the bandwidth of the antenna. **7. Study the impact of the total thickness of the antenna operating bandwidth** Using the same calculation process, we determined the influence of thickness h3 to h1 on the bandwidth of the antenna.

Using the results obtained during the optimization and additional numerical calculations can be concluded that the multilayer

**Figure 6.** Bandwidth as a function of thickness of the multilayer structure due to the change in thickness of each layer.

Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna

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41

For optimized model antenna the electrical parameters were determined: VSWR, impedance, characteristic of radiation. Figure 6 shows the VSWR of optimal single patch antenna. How‐ ever, the input impedance is shown in Figures 7 (reactance and resistance). Resistance in the range of work fluctuates around the value of 50Ω. the reactance value fluctuates around the

**8. Calculation of parameters for optimum model**

value of the 0.

**Figure 7.** VSWR of optimal single patch antenna.

#### structure achieves the highest bandwidth for the measured quantity of work, as the ratio of thickness of the antenna to the wavelength and containing in the range of 0.21-0.27 0. When the thickness of the structure has a value outside this range is rapidly declining bandwidth operation. For all layers of optimum thickness ratio of the total structure to the radiated wave length (center frequency 8.27 GHz antenna operation) at which it achieves the greatest band of operation is in all cases very close to the value of **7. Study the impact of the total thickness of the antenna operating bandwidth**

Mistake how we can make when selecting layer h1 and h2 is the smallest of all the layers, both in terms of thickness and permeability. Minor deviations from the optimum value (due to the bandwidth of operation) the effect of limiting the bandwidth of operation well below 50%. For working bandwidth> 50% of the thickness and permittivity of each layer should contain, respectively, in the intervals: - layer h1: thickness from 0.041 to 0.062 <sup>0</sup> and permittivity εr1 from 1.78 to 2.62; - layer h2: thickness from 0.084 to 0.121 <sup>0</sup> and permittivity εr2 from 2.28 to 2.77; Using the results obtained during the optimization and additional numerical calculations can be concluded that the multilayer structure achieves the highest bandwidth for the measured quantity of work, as the ratio of thickness of the antenna to the wavelength and containing in the range of 0.21-0.27 λ0. When the thickness of the structure has a value outside this range is rapidly declining bandwidth operation. For all layers of optimum thickness ratio of the total structure to the radiated wave length (center frequency 8.27 GHz antenna operation) at which it achieves the greatest band of operation is in all cases very close to the value of 0.25λ0 (fig.6)



**Figure 6.** Bandwidth as a function of thickness of the multilayer structure due to the change in thickness of each layer.

#### **8. Calculation of parameters for optimum model**

When we increase the thickness of the layer above the limit then the range bandwidth is

Using the same calculation process, we determined the influence of thickness h3 to h1 on the bandwidth of the antenna.

Using the same calculation process, we determined the influence of thickness h3 to h1 on the

Using the results obtained during the optimization and additional numerical calculations can be concluded that the multilayer structure achieves the highest bandwidth for the measured quantity of work, as the ratio of thickness of the antenna to the wavelength and containing in the range of 0.21-0.27 0. When the thickness of the structure has a value outside this range is rapidly declining bandwidth operation. For all layers of optimum thickness ratio of the total structure to the radiated wave length (center frequency 8.27 GHz antenna operation) at which it achieves the greatest band of operation is in all cases very close to the value of

Mistake how we can make when selecting layer h1 and h2 is the smallest of all the layers, both in terms of thickness and permeability. Minor deviations from the optimum value (due to the bandwidth of operation) the effect of limiting the bandwidth of operation well below 50%. For working bandwidth> 50% of the thickness and permittivity of each layer should contain,

Using the results obtained during the optimization and additional numerical calculations can be concluded that the multilayer structure achieves the highest bandwidth for the measured quantity of work, as the ratio of thickness of the antenna to the wavelength and containing in the range of 0.21-0.27 λ0. When the thickness of the structure has a value outside this range is rapidly declining bandwidth operation. For all layers of optimum thickness ratio of the total structure to the radiated wave length (center frequency 8.27 GHz antenna operation) at which it achieves the greatest band of operation is in all cases very close to the value of 0.25λ0 (fig.6)

Mistake how we can make when selecting layer h1 and h2 is the smallest of all the layers, both in terms of thickness and permeability. Minor deviations from the optimum value (due to the bandwidth of operation) the effect of limiting the bandwidth of operation well below 50%. For working bandwidth> 50% of the thickness and permittivity of each layer should contain,

**•** layer h1: thickness from 0.041 to 0.062 λ0 and permittivity εr1 from 1.78 to 2.62;

**•** layer h2: thickness from 0.084 to 0.121 λ0 and permittivity εr2 from 2.28 to 2.77;

**•** layer h4: thickness from 0.008 to 0.062 λ0 and permittivity εr4 from 2.05 to 4.62;

**•** layer h3: thickness from 0.077 to 0.176 λ0 and permittivity εr3 from 1 to 1.36;

**7. Study the impact of the total thickness of the antenna operating bandwidth**

**7. Study the impact of the total thickness of the antenna operating**

**Figure 5.** VSWR for values outside of the optimal range (a) thickness >0.062λ0 (b) thickness <0.008λ<sup>0</sup>

The first was analyzed h4 layer. It is located at the top of the antenna. The results are illustrated in Figure 4. The results can be concluded that the bandwidth of the work at a level above 50% can be achieved by changes in the thickness of this layer in the range from 0.008 to 0.0620. When we increase the thickness of the layer above the limit then the range bandwidth is narrows in the

narrows in the area of the upper frequencies.

40 Advancement in Microstrip Antennas with Recent Applications

Figure 5. VSWR for values outside of the optimal range (a) thickness >0.062<sup>0</sup> (b) thickness <0.008<sup>0</sup>





Figure 4. Influence thickness of h4 layer on bandwidth

area of the upper frequencies.

0.25<sup>0</sup> (fig.6)

**bandwidth**

respectively, in the intervals:

respectively, in the intervals:

bandwidth of the antenna.

For optimized model antenna the electrical parameters were determined: VSWR, impedance, characteristic of radiation. Figure 6 shows the VSWR of optimal single patch antenna. How‐ ever, the input impedance is shown in Figures 7 (reactance and resistance). Resistance in the range of work fluctuates around the value of 50Ω. the reactance value fluctuates around the value of the 0.

**Figure 7.** VSWR of optimal single patch antenna.

**Figure 8.** Reactance and resistance of optimal single patch antenna.

The resultant input impedance allows the full use of the antenna in the whole range of work. As a result of optimizing the working range was achieved 62.5% (VSWR<2).

**Figure 9.** Smith chart of wideband multilayer antenna.

Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna

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43

**Figure 10.** Figure 10. Verification of model with using CST.

The process of optimization and testing of all parameters of the antenna was carried out using IE3D software (Zeland Software) based on the method of moments. In order to verify the correctness of their analysis before the construction of physical model of antenna we one more time made calculations the VSWR and radiation characteristics of the final model using a different calculation method (fig.10 and 11). To perform calculations in order to verify the selected software CST Microwave Studio based on FDTD method. Smith chart of wideband multilayer antenna is show in figure 9.

Input impedance of the antenna in operating band varies in the range of 30 to 70 [Ω]. This input impedance makes full use of the antenna in the whole operating band. Such changes in the impedance is a side effect for maximum bandwidth. It should be noted that despite these changes the antenna VSWR <2.

The radiation pattern of antenna has stable shape in the whole operating band. In the whole frequency range the gain of antenna (calculated) is around 5 [dBi]. The width of the radiation characteristics (- 3dB) is around 100 °.

Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna http://dx.doi.org/10.5772/54661 43

**Figure 9.** Smith chart of wideband multilayer antenna.

**Figure 8.** Reactance and resistance of optimal single patch antenna.

42 Advancement in Microstrip Antennas with Recent Applications

multilayer antenna is show in figure 9.

changes the antenna VSWR <2.

characteristics (- 3dB) is around 100 °.

The resultant input impedance allows the full use of the antenna in the whole range of work.

The process of optimization and testing of all parameters of the antenna was carried out using IE3D software (Zeland Software) based on the method of moments. In order to verify the correctness of their analysis before the construction of physical model of antenna we one more time made calculations the VSWR and radiation characteristics of the final model using a different calculation method (fig.10 and 11). To perform calculations in order to verify the selected software CST Microwave Studio based on FDTD method. Smith chart of wideband

Input impedance of the antenna in operating band varies in the range of 30 to 70 [Ω]. This input impedance makes full use of the antenna in the whole operating band. Such changes in the impedance is a side effect for maximum bandwidth. It should be noted that despite these

The radiation pattern of antenna has stable shape in the whole operating band. In the whole frequency range the gain of antenna (calculated) is around 5 [dBi]. The width of the radiation

As a result of optimizing the working range was achieved 62.5% (VSWR<2).

**Figure 10.** Figure 10. Verification of model with using CST.

Figure 11.Radiations pattern of multilayer antenna-simulations **Figure 11.** Radiations pattern of multilayer antenna-simulations

Selection of components of the antenna (thickness and permeability layers) gives the value of VSWR<2. The antenna's radiating patch has very similar level and distribution of currents. The main radiating element is side edges of the patches are the same as in single-layer structures. The distribution of currents guarantees consistent with the direction of the feed line. Selection of components of the antenna (thickness and permeability layers) gives the value of VSWR<2. The antenna's radiating patch has very similar level and distribution of currents. The main radiating element is side edges of the patches are the same as in single-layer structures. The distribution of currents guarantees consistent with the direction of the feed line.

Figure 12.Current distribution in antanna elements

**9. Physical model of the antenna**

**Figure 12.** Current distribution in antanna elements

Figure 13.Layers of antenna and model of antenna.

**Figure 13.** Layers of antenna and model of antenna.

Figure 14.Dimension of h1 layer

by the h1 and ε1.

impedance are a side effect for a maximum bandwidth of work.

changes of parameters of the aerial in (checked in measurements).

aerial in.

In the figure 13 shows the antenna layers. First from left is put layer h1 with coupling slot. Holes in layers of the antenna were carried out intentionally with a view to precise connecting with oneself layers, they aren't bringing changes of parameters of the

Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna

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In Figure 13 a ready model of the aerial was described, the structure of aerials is coated with foamed PCV. They aren't bringing

Obtained in a multi-layer band work is not possible in single layer antennas [2]. In the whole range of work input impedance of the antenna is stable. Antenna input impedance in the band of work is changing in the range of 36 to 67 []. Such changes in the

The result for the physical model confirms the correctness of the analysis and calculations obtained using the calculation method based on the method of moments. Three of the four laminates used in its construction include teflon, and one of the layers is made of polimethacrylamid foam. This caused some difficulties in the technological process of joining them together and generates small

The resulting optimization model of the antenna is shown in Figures 9, 10 and 11. The antenna is a multi-layered structure having in its construction of two radiating elements in the form of "patches" located on successive layers of the dish. Patch located in the h2 layer is fed by a line through a gap made in the plane of the masses. Above it there is another patch that by using the resonance (of another already in the structure) greatly improves the bandwidth of operation. The power supply line located on the layer defined

inaccuracies in the contact of subsequent layers. This gave slight differences between calculations and measurements.

#### **9. Physical model of the antenna**

In the figure 13 shows the antenna layers. First from left is put layer h1 with coupling slot. Holes in layers of the antenna were carried out intentionally with a view to precise connecting with oneself layers, they aren't bringing changes of parameters of the aerial in.

In Figure 13 a ready model of the aerial was described, the structure of aerials is coated with foamed PCV. They aren't bringing changes of parameters of the aerial in (checked in measurements).

In Figure 13 a ready model of the aerial was described, the structure of aerials is coated with foamed PCV. They aren't bringing **Figure 12.** Current distribution in antanna elements

changes of parameters of the aerial in (checked in measurements).

Figure 11.Radiations pattern of multilayer antenna-simulations

**Figure 11.** Radiations pattern of multilayer antenna-simulations

44 Advancement in Microstrip Antennas with Recent Applications

**9. Physical model of the antenna**

measurements).

[dBi]

Selection of components of the antenna (thickness and permeability layers) gives the value of VSWR<2. The antenna's radiating patch has very similar level and distribution of currents. The main radiating element is side edges of the patches are the same as in

[dBi] [dBi]

single-layer structures. The distribution of currents guarantees consistent with the direction of the feed line.

Selection of components of the antenna (thickness and permeability layers) gives the value of VSWR<2. The antenna's radiating patch has very similar level and distribution of currents. The main radiating element is side edges of the patches are the same as in single-layer structures.

In the figure 13 shows the antenna layers. First from left is put layer h1 with coupling slot. Holes in layers of the antenna were carried out intentionally with a view to precise connecting

In Figure 13 a ready model of the aerial was described, the structure of aerials is coated with foamed PCV. They aren't bringing changes of parameters of the aerial in (checked in

The distribution of currents guarantees consistent with the direction of the feed line.

with oneself layers, they aren't bringing changes of parameters of the aerial in.

Obtained in a multi-layer band work is not possible in single layer antennas [2]. In the whole range of work input impedance of the antenna is stable. Antenna input impedance in the band of work is changing in the range of 36 to 67 []. Such changes in the

The result for the physical model confirms the correctness of the analysis and calculations obtained using the calculation method based on the method of moments. Three of the four laminates used in its construction include teflon, and one of the layers is made of polimethacrylamid foam. This caused some difficulties in the technological process of joining them together and generates small

The resulting optimization model of the antenna is shown in Figures 9, 10 and 11. The antenna is a multi-layered structure having in its construction of two radiating elements in the form of "patches" located on successive layers of the dish. Patch located in the h2 layer is fed by a line through a gap made in the plane of the masses. Above it there is another patch that by using the resonance (of another already in the structure) greatly improves the bandwidth of operation. The power supply line located on the layer defined

inaccuracies in the contact of subsequent layers. This gave slight differences between calculations and measurements.

Figure 13.Layers of antenna and model of antenna. **Figure 13.** Layers of antenna and model of antenna.

Figure 14.Dimension of h1 layer

by the h1 and ε1.

impedance are a side effect for a maximum bandwidth of work.

Obtained in a multi-layer band work is not possible in single layer antennas [2]. In the whole range of work input impedance of the antenna is stable. Antenna input impedance in the band of work is changing in the range of 36 to 67 [Ω]. Such changes in the impedance are a side effect for a maximum bandwidth of work.

The result for the physical model confirms the correctness of the analysis and calculations obtained using the calculation method based on the method of moments. Three of the four laminates used in its construction include teflon, and one of the layers is made of polimetha‐ crylamid foam. This caused some difficulties in the technological process of joining them together and generates small inaccuracies in the contact of subsequent layers. This gave slight differences between calculations and measurements.

**Figure 15.** Dimension of h2 and h4 layers

**10. Result of measurements**

**•** Standing wave ratio VSWR

**•** Input impedance Z

**•** Radiation patterns

articles[12,13,14].

**•** Resistance R

**•** Reactance X

measured results in the frequency range (5,5-11,5 GHz) for :

h3 and h4.

The h2 layer is made of foam, which cannot be applied metallization. Therefore, the patch was placed on the bottom layer of h4. In result the radiating patch will be located between the layers

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Measurement of parameters and antenna characteristics were carried out at the Laboratory for Electromagnetic Compatibility of the Electronics Department of the Military Technical Academy equipped with an anechoic chamber. A prototype is made and the following

Figure 16 shows the model of antenna VSWR during measurements. In the next Figure 17 shows the results of measurements of VSWR, which reaches a value of less than 2 in frequency range from 5.8 GHz to 10.15 GHz. during the measurement parameters and antenna charac‐ teristics of dielectric parameters was also studied based on the methodology described in the

**Figure 14.** Dimension of h1 layer

The resulting optimization model of the antenna is shown in Figures 9, 10 and 11. The antenna is a multi-layered structure having in its construction of two radiating elements in the form of "patches" located on successive layers of the dish. Patch located in the h2 layer is fed by a line through a gap made in the plane of the masses. Above it there is another patch that by using the resonance (of another already in the structure) greatly improves the bandwidth of operation. The power supply line located on the layer defined by the h1 and ε1.

**Figure 15.** Dimension of h2 and h4 layers

Obtained in a multi-layer band work is not possible in single layer antennas [2]. In the whole range of work input impedance of the antenna is stable. Antenna input impedance in the band of work is changing in the range of 36 to 67 [Ω]. Such changes in the impedance are a side effect

The result for the physical model confirms the correctness of the analysis and calculations obtained using the calculation method based on the method of moments. Three of the four laminates used in its construction include teflon, and one of the layers is made of polimetha‐ crylamid foam. This caused some difficulties in the technological process of joining them together and generates small inaccuracies in the contact of subsequent layers. This gave slight

The resulting optimization model of the antenna is shown in Figures 9, 10 and 11. The antenna is a multi-layered structure having in its construction of two radiating elements in the form of "patches" located on successive layers of the dish. Patch located in the h2 layer is fed by a line through a gap made in the plane of the masses. Above it there is another patch that by using the resonance (of another already in the structure) greatly improves the bandwidth of

operation. The power supply line located on the layer defined by the h1 and ε1.

for a maximum bandwidth of work.

46 Advancement in Microstrip Antennas with Recent Applications

**Figure 14.** Dimension of h1 layer

differences between calculations and measurements.

The h2 layer is made of foam, which cannot be applied metallization. Therefore, the patch was placed on the bottom layer of h4. In result the radiating patch will be located between the layers h3 and h4.

#### **10. Result of measurements**

Measurement of parameters and antenna characteristics were carried out at the Laboratory for Electromagnetic Compatibility of the Electronics Department of the Military Technical Academy equipped with an anechoic chamber. A prototype is made and the following measured results in the frequency range (5,5-11,5 GHz) for :


Figure 16 shows the model of antenna VSWR during measurements. In the next Figure 17 shows the results of measurements of VSWR, which reaches a value of less than 2 in frequency range from 5.8 GHz to 10.15 GHz. during the measurement parameters and antenna charac‐ teristics of dielectric parameters was also studied based on the methodology described in the articles[12,13,14].

**Figure 16.** Model of antenna during VSWR measurmeants.

**Figure 18.** Measured input impedance of optimal single patch antenna.

**Figure 19.** Photos of the antenna during measurments in the anechoic chamber.

Figure 18 shows the measured values of resistance and reactance of antenna model. The meas‐ ured resistance value ranges from 35 to 55 ohms. Reactance varies in the range from -10 to 5 ohms.

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**Figure 17.** Measured VSWR of optimal single patch.

Obtained in the measurement bandwidth of the work is:

$$B = \frac{2(f\_{\text{max}} - f\_{\text{min}})}{f\_{\text{max}} + f\_{\text{min}}} \cdot 100\% = \frac{2(10150 - 5800)}{(10150 + 5800)} \cdot 100\% = \frac{2 \cdot 4350}{15950} \cdot 100\% \approx 55\% \tag{2}$$

Figure 18 shows the measured values of resistance and reactance of antenna model.

**Figure 18.** Measured input impedance of optimal single patch antenna.

Figure 18 shows the measured values of resistance and reactance of antenna model. The meas‐ ured resistance value ranges from 35 to 55 ohms. Reactance varies in the range from -10 to 5 ohms.

**Figure 19.** Photos of the antenna during measurments in the anechoic chamber.

**Figure 17.** Measured VSWR of optimal single patch.

**Figure 16.** Model of antenna during VSWR measurmeants.

48 Advancement in Microstrip Antennas with Recent Applications

max min max min

*f f <sup>B</sup> f f*

Obtained in the measurement bandwidth of the work is:

2( ) 2(10150 5800) 2 4350 100% 100% 100% 55% ) (10150 5800) 15950

Figure 18 shows the measured values of resistance and reactance of antenna model.


The subject carried out by the author toprimarily study broadening the antenna bandwidth properties, which confirm the elimination of the problem of narrowband in the structures of planar antennas and directional properties. Particular attention is paid to the impedance properties defined by examining the standing wave ratio (VSWR) in the bandwidth of the antenna, the ratio was determined relative to a standard value of impedance 50Ώ. Radiation characteristics was investigated for frequencies from 5.5 GHz to 11.5 GHz in steps of 1 GHz. The paper presents the characteristics for a center frequency band operation (7.6 GHz) and for two frequencies distant by about 1 GHz bandwidth from the ends of the work, the frequency of 6.5 GHz and 9.5 GHz. For the same frequency were also determined and presented in the work sheet in the computer simulations. Figure 19.Photos of the antenna during measurments in the anechoic chamber. The subject carried out by the author toprimarily study broadening the antenna bandwidth properties, which confirm the elimination of the problem of narrowband in the structures of planar antennas and directional properties. Particular attention is paid to the impedance properties defined by examining the standing wave ratio (VSWR) in the bandwidth of the antenna, the ratio was determined relative to a standard value of impedance 50Ώ. Radiation characteristics was investigated for frequencies from 5.5 GHz to 11.5 GHz in steps of 1 GHz. The paper presents the characteristics for a center frequency band operation (7.6 GHz) and for

Figure 20 shows the far field radiation characteristics of the antenna at the center frequency (7.6 GHz) and at 6.5 and 9.5 GHz two frequencies distant by about 1 GHz bandwidth from the ends of the work, the frequency of 6.5 GHz and 9.5 GHz. For the same frequency were also determined and presented in the work sheet in the computer simulations.

Figure 20 shows the far field radiation characteristics of the antenna at the center frequency (7.6 GHz) and at 6.5 and 9.5 GHz

Width of the main lobe at the level of -3 [dB] in the whole operating band is approximately

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Width of the main lobe at the level of -3 [dB] in the whole operating band is approximately 140 °. Radiation pattern has a stable

Antenna gain is in the range from 4 dBi to 5.7 dBi. For multilayer structure with a bandwidth

Presented in a multi-layer structure despite the complex structure can be used to construct the antenna array, thereby increasing antenna gain. For this purpose, designed four element array,

Antenna gain is in the range from 4 dBi to 5.7 dBi. For multilayer structure with a bandwidth greater than 50% this is considered to

Presented in a multi-layer structure despite the complex structure can be used to construct the antenna array, thereby increasing

Parameters and characteristics of the antenna array were also measured in the anechoic chamber (fig.21). For the model was made the following we measured in this same frequency range (5,5-11,5 GHz) following parameters: standing wave ratio VSWR, input

impedance Z, resistance R, reactance X, radiation patterns. Measurement results are shown in Figures 23 and 24.

140 °. Radiation pattern has a stable shape in the frequency domain.

**Figure 21.** Measured antenna gain versus frequency.

shape in the frequency domain.

whose design is shown in Figure 21.

Figure 23.Antenna array during measurments in anechoic chamber.

be very good gain values.

Figure 22.Antenna array.

**Figure 22.** Antenna array.

Figure 21.Measured antenna gain versus frequency.

greater than 50% this is considered to be very good gain values.

antenna gain. For this purpose, designed four element array, whose design is shown in Figure 21.

Figure 20.Radiation paterrns(H - plane). **Figure 20.** Radiation paterrns(H - plane).

Width of the main lobe at the level of -3 [dB] in the whole operating band is approximately 140 °. Radiation pattern has a stable shape in the frequency domain.

**Figure 21.** Measured antenna gain versus frequency.

The subject carried out by the author toprimarily study broadening the antenna bandwidth properties, which confirm the elimination of the problem of narrowband in the structures of planar antennas and directional properties. Particular attention is paid to the impedance properties defined by examining the standing wave ratio (VSWR) in the bandwidth of the antenna, the ratio was determined relative to a standard value of impedance 50Ώ. Radiation characteristics was investigated for frequencies from 5.5 GHz to 11.5 GHz in steps of 1 GHz. The paper presents the characteristics for a center frequency band operation (7.6 GHz) and for two frequencies distant by about 1 GHz bandwidth from the ends of the work, the frequency of 6.5 GHz and 9.5 GHz. For the same frequency were also determined and presented in the

Figure 19.Photos of the antenna during measurments in the anechoic chamber.

Figure 20 shows the far field radiation characteristics of the antenna at the center frequency

5.8 GHz 6.5 GHz

7.6 GHz 9.6 GHz

frequency were also determined and presented in the work sheet in the computer simulations.

The subject carried out by the author toprimarily study broadening the antenna bandwidth properties, which confirm the elimination of the problem of narrowband in the structures of planar antennas and directional properties. Particular attention is paid to the impedance properties defined by examining the standing wave ratio (VSWR) in the bandwidth of the antenna, the ratio was determined relative to a standard value of impedance 50Ώ. Radiation characteristics was investigated for frequencies from 5.5 GHz to 11.5 GHz in steps of 1 GHz. The paper presents the characteristics for a center frequency band operation (7.6 GHz) and for two frequencies distant by about 1 GHz bandwidth from the ends of the work, the frequency of 6.5 GHz and 9.5 GHz. For the same

Figure 20 shows the far field radiation characteristics of the antenna at the center frequency (7.6 GHz) and at 6.5 and 9.5 GHz

work sheet in the computer simulations.

50 Advancement in Microstrip Antennas with Recent Applications

Figure 20.Radiation paterrns(H - plane).

**Figure 20.** Radiation paterrns(H - plane).

(7.6 GHz) and at 6.5 and 9.5 GHz

Antenna gain is in the range from 4 dBi to 5.7 dBi. For multilayer structure with a bandwidth greater than 50% this is considered to be very good gain values. Figure 21.Measured antenna gain versus frequency.

Presented in a multi-layer structure despite the complex structure can be used to construct the antenna array, thereby increasing antenna gain. For this purpose, designed four element array, whose design is shown in Figure 21. Antenna gain is in the range from 4 dBi to 5.7 dBi. For multilayer structure with a bandwidth greater than 50% this is considered to be very good gain values. Presented in a multi-layer structure despite the complex structure can be used to construct the antenna array, thereby increasing

antenna gain. For this purpose, designed four element array, whose design is shown in Figure 21.

impedance Z, resistance R, reactance X, radiation patterns. Measurement results are shown in Figures 23 and 24.

Parameters and characteristics of the antenna array were also measured in the anechoic chamber (fig.21). For the model was made the following we measured in this same frequency range (5,5-11,5 GHz) following parameters: standing wave ratio VSWR, input

Figure 22.Antenna array. **Figure 22.** Antenna array.

Figure 23.Antenna array during measurments in anechoic chamber.

shape in the frequency domain.

Figure 21.Measured antenna gain versus frequency.

be very good gain values.

Parameters and characteristics of the antenna array were also measured in the anechoic cham‐ ber (fig.21). For the model was made the following we measured in this same frequency range (5,5-11,5 GHz) following parameters: standing wave ratio VSWR, input impedance Z, resist‐ ance R, reactance X, radiation patterns. Measurement results are shown in Figures 23 and 24. Figure 22.Antenna array. Parameters and characteristics of the antenna array were also measured in the anechoic chamber (fig.21). For the model was made

Width of the main lobe at the level of -3 [dB] in the whole operating band is approximately 140 °. Radiation pattern has a stable

Antenna gain is in the range from 4 dBi to 5.7 dBi. For multilayer structure with a bandwidth greater than 50% this is considered to

Presented in a multi-layer structure despite the complex structure can be used to construct the antenna array, thereby increasing

the following we measured in this same frequency range (5,5-11,5 GHz) following parameters: standing wave ratio VSWR, input

Figure 24.Impedance of antenna array- measurmeants.

**[Ω]**

Figure 25.Radiation paterrns of array.

**Figure 26.** VSWR – simualtions and measurments.

**Figure 25.** Radiation paterrns of array.

well as the FDTD method.

**11. Comparison of simulations and measurements**

**11. Comparison of simulations and measurements**

10,5 GHz 5,8 GHz

The most important parameter in view of the article is the course of VSWR as a function of frequency. The result obtained for the physical model confirms the correctness of the analysis and calculations obtained using the calculation method based on the method of moments, as

method of moments, as well as the FDTD method.

The most important parameter in view of the article is the course of VSWR as a function of frequency. The result obtained for the physical model confirms the correctness of the analysis and calculations obtained using the calculation method based on the

4 5 6 7 8 9 10 11 12 13 14

**Frequency [GHz]**

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impedance Z, resistance R, reactance X, radiation patterns. Measurement results are shown in Figures 23 and 24.

antenna gain. For this purpose, designed four element array, whose design is shown in Figure 21.

Figure 23.Antenna array during measurments in anechoic chamber.

**Figure 23.** Antenna array during measurments in anechoic chamber.

**Figure 24.** Impedance of antenna array- measurmeants.

**Frequency [GHz]** Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna http://dx.doi.org/10.5772/54661 53

4 5 6 7 8 9 10 11 12 13 14

Figure 25.Radiation paterrns of array. **Figure 25.** Radiation paterrns of array.

Parameters and characteristics of the antenna array were also measured in the anechoic cham‐ ber (fig.21). For the model was made the following we measured in this same frequency range (5,5-11,5 GHz) following parameters: standing wave ratio VSWR, input impedance Z, resist‐ ance R, reactance X, radiation patterns. Measurement results are shown in Figures 23 and 24.

Figure 23.Antenna array during measurments in anechoic chamber.

6,5 GHz

shape in the frequency domain.

Figure 21.Measured antenna gain versus frequency.

be very good gain values.

Figure 22.Antenna array.

52 Advancement in Microstrip Antennas with Recent Applications

**Figure 23.** Antenna array during measurments in anechoic chamber.

**Figure 24.** Impedance of antenna array- measurmeants.

Width of the main lobe at the level of -3 [dB] in the whole operating band is approximately 140 °. Radiation pattern has a stable

Antenna gain is in the range from 4 dBi to 5.7 dBi. For multilayer structure with a bandwidth greater than 50% this is considered to

Presented in a multi-layer structure despite the complex structure can be used to construct the antenna array, thereby increasing

antenna gain. For this purpose, designed four element array, whose design is shown in Figure 21.

#### The most important parameter in view of the article is the course of VSWR as a function of frequency. The result obtained for the **11. Comparison of simulations and measurements**

method of moments, as well as the FDTD method.

**11. Comparison of simulations and measurements**

Figure 24.Impedance of antenna array- measurmeants.

**[Ω]**

The most important parameter in view of the article is the course of VSWR as a function of frequency. The result obtained for the physical model confirms the correctness of the analysis and calculations obtained using the calculation method based on the method of moments, as well as the FDTD method.

physical model confirms the correctness of the analysis and calculations obtained using the calculation method based on the

Reduction of bandwidth in the upper-frequency of band (as confirmed by further simulations and calculations exploring the effects of precision interfaces between layers of the antenna on its parameters), the inaccuracy of the interfaces between layers of the dish. Three of the four laminates used in its construction include Teflon, and one of the layers is made of foam polimethacrylamid. This causes some technological difficulties in the process of connecting them together and produce a minimum of contact inaccuracy of subsequent layers. The simulations confirm the situation.

layer substrates and they parameters. Calculations show how difficult it is to choose optimal value for laminates when we want to obtain wide band. Permittivity and thickness are equally important for bandwidth antenna. The analysis of the antenna was done by the usage of IE3D - Zeland Software (method of moments - MoM). The method has been applied to the micro‐ strip-fed slot antenna and to the aperture coupled antenna with a good result when compared

Bandwidth Optimization of Aperture-Coupled Stacked Patch Antenna

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55

The model of antenna allows use of all the positive properties of planar antennas with simultaneous work in a wide frequency range, which so far has been the main element to eliminate this type of the antenna of use in many designs. Given the trend for miniaturization of antenna devices and the development of radio technology and integrated systems presented in the paper of construction seems to be very prospective. The design of this antenna is a modern solution to the antenna, which is especially important in the use of the moving objects. The results of experimental studies measuring fully confirm the possibility of constructing planar antenna with wide bandwidth operation. In addition, ease of implementation of antenna arrays using planar antennas opens up new possibilities in the use of this construction. Designed antenna operates in X-band and certainly could be an interesting alternative to the

currently used antenna antennas operating in this band.

\*Address all correspondence to: marek.bugaj@wat.edu.pl

Faculty of Electronics, Military University of Technology, Warsaw, Poland

[1] Turker, N, Gunes, F, & Yildirim, T. Artificial Neural Design of Microstrip Antennas",

[2] Kumar, G, & Ray, K. P. Broadband Microstrip Antennas" Artech House, (2003).

[3] Garg, R. pp. Bhartia, I. Bahl "Microstrip antenna design handbook" Artec Hause,

[4] Bi, Z, & Wu, K. Ch. Wu, J. Litva "And dispersive boundary condition handicap mi‐ crostrip component analysis using the FDTD method", IEEE Trans. Antennas and

and Marian Wnuk

Turk J Elec Engin, (2006). , 14(3)

Propagation, (1992). , 40, 774-777.

1-58053-244-6

INC

with measured data.

**Author details**

Marek Bugaj\*

**References**

**Figure 27.** Radiation paterrns of antenna measurments (a) and simualtions (b).

#### **12. Conclusion**

This article presents issues related to the theory and technique of multilayer planar antennas fed by the slot. This paper describes multilayer configuration to increase the BW of the antenna. This configuration has many advantages, including wide BW, reduction in spurious feed network radiation, and a symmetric radiation pattern with low cross-polarization. The antenna configuration with a resonant aperture yields wide BW by proper optimization of the coupling between the patch and the resonant slot. The basic characteristics and the effects of various parameters on the overall antenna performance are discussed.

The results of the study are satisfactory. The paper describes a clear advantage of multilayer antennas over monolayer ones, where the bandwidth is significantly narrower. The coupling aperture antenna after optimization can result in a considerable increase of bandwidth. The bandwidth of aerial is the outcome of the way feed as well as the utilization to build the multilayer substrates and they parameters. Calculations show how difficult it is to choose optimal value for laminates when we want to obtain wide band. Permittivity and thickness are equally important for bandwidth antenna. The analysis of the antenna was done by the usage of IE3D - Zeland Software (method of moments - MoM). The method has been applied to the micro‐ strip-fed slot antenna and to the aperture coupled antenna with a good result when compared with measured data.

The model of antenna allows use of all the positive properties of planar antennas with simultaneous work in a wide frequency range, which so far has been the main element to eliminate this type of the antenna of use in many designs. Given the trend for miniaturization of antenna devices and the development of radio technology and integrated systems presented in the paper of construction seems to be very prospective. The design of this antenna is a modern solution to the antenna, which is especially important in the use of the moving objects. The results of experimental studies measuring fully confirm the possibility of constructing planar antenna with wide bandwidth operation. In addition, ease of implementation of antenna arrays using planar antennas opens up new possibilities in the use of this construction. Designed antenna operates in X-band and certainly could be an interesting alternative to the currently used antenna antennas operating in this band.

#### **Author details**

Reduction of bandwidth in the upper-frequency of band (as confirmed by further simulations and calculations exploring the effects of precision interfaces between layers of the antenna on its parameters), the inaccuracy of the interfaces between layers of the dish. Three of the four laminates used in its construction include Teflon, and one of the layers is made of foam polimethacrylamid. This causes some technological difficulties in the process of connecting them together and produce a minimum of contact inaccuracy of subsequent layers. The

(a) (b)

This article presents issues related to the theory and technique of multilayer planar antennas fed by the slot. This paper describes multilayer configuration to increase the BW of the antenna. This configuration has many advantages, including wide BW, reduction in spurious feed network radiation, and a symmetric radiation pattern with low cross-polarization. The antenna configuration with a resonant aperture yields wide BW by proper optimization of the coupling between the patch and the resonant slot. The basic characteristics and the effects of various

The results of the study are satisfactory. The paper describes a clear advantage of multilayer antennas over monolayer ones, where the bandwidth is significantly narrower. The coupling aperture antenna after optimization can result in a considerable increase of bandwidth. The bandwidth of aerial is the outcome of the way feed as well as the utilization to build the multi-

**Figure 27.** Radiation paterrns of antenna measurments (a) and simualtions (b).

parameters on the overall antenna performance are discussed.

simulations confirm the situation.

54 Advancement in Microstrip Antennas with Recent Applications

**12. Conclusion**

Marek Bugaj\* and Marian Wnuk

\*Address all correspondence to: marek.bugaj@wat.edu.pl

Faculty of Electronics, Military University of Technology, Warsaw, Poland

#### **References**


[5] Kin-Lu WongCompact and bradband miccrostrip antennas", (2002). by John Wiley & Sons, Inc., New York, 0-47122-111-2

**Chapter 3**

**Full-Wave Spectral Analysis of Resonant Characteristics**

During the last decades, superconducting antenna was one of the first microwave compo‐ nents tobedemonstratedas anapplicationofhigh-temperature superconductingmaterial[1-3]. High *Tc* superconducting microstrip antennas (HTSMA) are becoming popular and getting increased attention in both theoretical research and engineering applications due to their excellent advantages. Various patch configurations implemented on different types of substrates have been tested and investigated. In the design of microstrip antennas, anisotrop‐ ic substances have been increasingly popular. Especially the effects of uniaxial type anisotro‐ py have been investigated due to availability of this type of substances. These structures characterized by their low profile, small size, light weight, low cost and ease of fabrication, which makes them very suitable for microwave and millimeter-wave device applications [4-6]. HTSMA structures have shown significant superiority over corresponding devices fabricated with normal conductors such as gold, silver, or copper. Major property of superconductor is very low surface resistance; this property facilitates the development of microstrip antennas with better performance than conventional antennas. Compared to other patch geometries, the circular and annular ring microstrip patches printed on a uniaxial anisotropic substrate, have been more extensively studied for a long time by a number of investigators [7-11]. Circular microstrip patch can be used either as radiating antennas or as oscillators and filters in microwave integrated circuits (MIC's). The inherent advantage of an annular ring antenna is: first, the size of an annular ring for a given mode of operation is smaller than that of the circular disc resonating at the same frequency. Second, The presence of edges at the inner and outer radii causes more fringing than in the case of a circular microstrip antenna, in which fringing occurs only at the outer edge, and this implies more radiation from these edges, that leads to

> © 2013 Barkat; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2013 Barkat; licensee InTech. This is a paper 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.

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

**and Radiation Patterns of High Tc Superconducting**

**Circular and Annular Ring Microstrip Antennas**

Additional information is available at the end of the chapter

Ouarda Barkat

**1. Introduction**

http://dx.doi.org/10.5772/54665

