Antennas are a fundamental element of all wireless communication systems. An antenna is the component of a wireless communication system that transmits/receives electromagnetic waves. There are different types of antennas as Wire antennas, Aperture antennas, Microstrip antennas, Reflector antennas, Horn antennas, etc.
The microstrip antennas consists in a metallic patch printed on top of a thin substrate placed above a ground plane. In resume, this antenna can be divided into four parts patch, ground plane, substrate and feeding, as presented in figure XXXX.
The metallic patch can have different shapes, shown in Figure XXXX. However, the most common are the rectangular and circular since they are the easiest to fabricate and analyse.
Microstrip antennas have an important feature in these days due the constants decrease in size of the communications systems due to a greater integration of electronics, so there is a need of more compact antennas. Microstrip can answer these demand from technology since they are “low profile, conformable to planar and nonplanar sur- faces, simple and inexpensive to manufacture using modern printed-circuit technology, mechanically robust when mounted on rigid surfaces, compatible with MMIC designs, and when the particular patch shape and mode are selected, they are very versa- tile in terms of resonant frequency, polarization, pattern, and impedance”. However, these type of antennas presents some disadvantages as low efficiency, low gain, narrow bandwidth, low power handling capacity, poor scan performance, poor polarization purity and spurious feed radiation. To overcome some of these disadvantages (for example the gain) the microstrip patch antennas can be used in arrays, this will be discuss further on.
METHODS of ANALISYS
There are several models to analyse a microstrip patch antenna. This models were developed to achieve an estimation of the parameters of these antennas, such as input impedance, bandwidth and others.
The analysis is an important step in the design process. The antenna analysis allows the understanding of the operating principles, this is useful to recognize which are the modifications need on the antenna parameter to an archive a desired configuration, it reduce the number of trial and error during the design process and is helpful to carry out the conclusion of the antenna performance.
The simplest and popular models are the transmission-line and cavity. This two models will be briefly discussed in the following sections.
Transmission model: Lê apartir daqui
A rectangular patch and a microstrip transmission line present a similar physical shape. Therefore, this model is one of the most simple and intuitive, but it can only be applied to the mention shaped structures. 
The transmission line models consider a rectangular microstrip patch antenna as two radiating slots with a length of W. Each radiating slot will be represented by a parallel equivalent admittance that is separated by a transmission line with a length equal to L and open circuited at both ends. A schematic of it is presented in figXXXX. The characteristic impedance and propagation constant of the transmission line are imposed by the patch size (W, L) and the substrate parameters. , 
The transmission line model takes into account the impact of the fringing effects.
The microstrip antenna presents finite dimensions (L ,W). Therefore, the field that arises from the radiating edges of the patch undergoes fringing, as figFRIN illustrates. The fringing field depends on the antenna parameters (W,L,h,er and fr).
As it can be observed in figureFRIN, the propagation of the fringing field is not just enclosed in the substrate, it also goes through the air. This implies the calculation of the Effective dielectric constant, that considers the fringing effects on the wave propagation in the line. The effective dielectric constant is the dielectric constant of the uniform dielectric material immerse in a homogeneous environment so that identical electrical characteristics are presented when the same material is immerse in a non-homogeneous environment.
The value of the effective dielectric constant is closer to the dielectric constant of the substrate when εr>1 and if the operating frequency is high, since most of the electric field is concentrated in the substrate.
According to Balanis, the effective dielectric constant is obtained by the flowing expression:
Due to the fringing effects, the electrical length of the patch is greater than the physical length. The half of the difference between them is known as Length extension. It depends on the effective dielectric constant and the width-to-height ratio.
For the dominant mode TM010 the resonant frequency of the microstrip antenna is a function of its length, then the effective length of the patch is given by:
Since the length extension occurs in each side of the patch, the physical length of the patch is given by:
In the dominant mode TM010 there are no fringing fields along the width of the patch, therefore for an efficient radiation the width is approximately
where fr is the resonant frequency and c the speed of light. 
The transmission line model can determine the input impedance of the patch antenna along the central line. This is a crucial parameter, to obtain a good impedance matching between the feedline and the feed point.
As mentioned before, each radiating slot is represented by the transmission line model as parallel equivalent admittance. The model is presented in the following figure.
A priori it is known that both slots are similar. The conductance of a single slot can be obtained by the field expression of the cavity model.
In an ideal design, the slots would be separated by L=ʎ/2. However, due to the mentioned fringing effects, the separation between the slot is less than the ideal. If the length reduction is well selected (0.48ʎ<L<0.49ʎ), the equivalent admittance of the second slot is transformed to its conjugate.
Then, it is easy to understand that the input impedance, considering the mutual effects between the slots, is given by the following expression.
However, the expression (numero) just performed the input impedance in the edge of the patch antenna and, as mentioned before, it is possible to obtain the input impedance along the central line. A priori it is known that the current is low at the edge and increases when moving towards the centre of the patch, the opposite occurs with the voltage. Therefore it is possible to conclude that the impedance at the edge is high and low at the centre. ,,
Observing the figure (number) it is possible to see that the variation of the impedance follows a square cosine, depending on the length of the patch and the distance from the edge to the centre (d). , 
There are many methods to feed microstrip patch antennas, the most popular are the coaxial probe, microstrip line, aperture coupling and proximity coupling.  These methods can be divided into two categories, contact and non-contact feed. Contact feed methods have narrow bandwidth and are more sensitive to dimensional from the etching process. On the other hand, they are more simple to manufacture. 
Each feeding method has its own characteristics, advantages and disadvantages.
Coaxial probe feed:
The coaxial probe is widely used since it is easy and cheap to implement. As it can be observed in figure(COAX), the inner conductor of the coax passes through the substrate and the ground plane, without any contact by making a hole on them, and is attached directly to the radiating. The outer conductor is connected to the ground. , 
This feeding method has as an advantage the impedance matching that is obtained by simply selecting the feed location that provides the desired impedance, and has low spurious radiations, since the probe is directly attached to the radiating patch and isolated from the patch. On the other hand, it is difficult to model, provides a narrow bandwidth (1-5%) and the probe is a radiating element causing cross-polarization. , ,  PORHIFEN… latex
The microstrip line or edge feed is a simple and the mostly used feeding method, since the microstrip line is directly attached to the edge of the radiating patch. The radiating patch and the microstrip line are coplanar as it can be observed in figure(MICRO). Therefore, the fabrication process is easy, it is well suited for arrays and it is easy to apply a method of impedance matching as a quarter-wavelength transformer or by simply controlling the inset position., 
This method has some drawbacks, the feed line is also a radiating element which leads to undesired radiation that will increase the cross-polarization level since the radiating patch and the feed line are in the same plane. In summary, this method suffers from surface wave losses, spurious radiation feed and has low bandwidth (2–5%); these disadvantages are more evident when is used a thicker substrate., , 
Aperture coupled feed:
The aperture coupled feed is composed by two dielectric substrates, the patch substrate placed above the ground plane and the feed line substrate under it, figure(APERTURE). The patch and the feed line are coupled through a slot/aperture created on the ground plane , the slot is centered with the patch to achieve maximum coupling and low cross polarization.
Typically, the patch substrate presents a low dielectric constant to improve the radiation of the patch and the feed line substrate with a high dielectric to improve the transmission in the feed line. 
As advantages, the aperture coupled provides a large number of parameters that can be adjusted to achieve the intended performance (shape of the slot aperture, dielectric of the substrate, slot aperture can be resonant or not (a resonant aperture creates another resonance into the one from the patch increasing the bandwidth, on the other hand it increases the back radiation )); the ground plane between the radiating patch and the feedline minimizes the spurious radiations and increases the polarization purity and it is possible to achieve a wide bandwidth., , 
On the other hand, the aperture coupled feed is a multi-layer feeding method that implies difficulties on the fabrication process.
An electromagnetic wave, as it can be observed in Figure WAVEelectromagnetic, is composed by the electric and the magnetic fields that are perpendicular to each other and to the direction of propagation.
Polarization is a property of electromagnetic waves that describes the relative magnitude and direction of the electric-field vector in function of the time. Polarization is a curve formed by the instantaneous electric-field vector.
Polarization of an antenna is the polarization of the electromagnetic wave radiated by the antenna in a given direction. When its direction is not stated the polarization is assumed to be in the direction of its maximum gain.
To achieve a better performance in the wireless communication link, maximum power transfer, the transmitting and receiving antennas should have the same polarization.
The polarization can be defined in terms of the radiated or received wave by an antenna to a given direction.
According to Balanis, the polarization of the radiated wave is defined as “the polarization of the (locally) plane wave which is used to represent the radiated wave at that point. At any point in the far field of an antenna the radiated wave can be represented by a plane wave whose electric-field strength is the same as that of the wave and whose direction of propagation is in the radial direction from the antenna. As the radial distance approaches infinity, the radius of curvature of the radiated wave’s phase front also approaches infinity and thus in any specified direction the wave appears locally as a plane wave.” And the polarization of the received wave is defined as the “polarization of a plane wave, incident from a given direction and having a given power flux density, which results in maximum available power at the antenna terminals.”
The geometric figure traced by the instantaneous vector of the electric field defines the type of polarization. The rotation of the field defines if it is a right-hand or left-hand polarization. The polarization can be elliptical, circular or linear; where the circular and linear polarization are a special case of the elliptical polarization., 
The linear polarization is simple to obtain since the electric field varies along the same straight line. This happens when the field vector presents just one component, or two orthogonal linear components that are in time phase or multiples of 180º out-of-phase.
There are two types of linear polarization that are presented in Figure Polarization Linear. Vertical polarization occurs when the electrical field is perpendicular to the surface of the earth, and horizontal polarization occurs when the electrical field is parallel to the surface of the earth.
Figure polarization Linear
Circular polarization is the most used in the wireless communication system since it presents some important advantages over the linear polarization. An antenna circularly polarized radiates power in all planes in the propagation axes, therefore the receiving and transmitting antenna does not have to present the same orientation, is more robust to signal degradation and is able to minimize the propagation anomalies.
In circular polarization the electric-field vector traces a circle around the propagation axes in function of the time. To achieve it the electric field has to be composed by two orthogonal linear components with the same magnitude and present a time-phase difference of 90º between them.
Figura CIRCULAR 
In microstrip antennas is rather simple to achieve circular polarization by simply feeding the patch antenna at two different points to excite two orthogonal propagation methods. The time-phase difference can be obtained by using powers dividers, as the Hybrid. It also can be obtained by a single feed. This will be studied further in this work.
The axial ratio is a parameter that quantifies the wave polarization quality of an antenna. Typically, an antenna radiates an electromagnetic wave that presents elliptical polarization. The axial ratio of the radiated wave is the ratio between the major axis and minor axis (the two orthogonal components of the field) as presented in the following figure.
Ar=(major axis(OA))/(minor axis(OB))
Typically, the axial ratio is expressed in dB as
For an elliptical polarized antenna, the axial ration is greater than one and less than infinity.
For a linear polarized antenna, the axial ratio is infinity since one of the components of the field is zero.
For a circular polarized antenna, the axial ratio is 1 (0 dB) since the field components have the same magnitude. In practice, for a good circular polarization the axial ratio should be below 3 dB where 0 dB is the optimal case.
Inicio do capitulo:
This chapter will be focused in microstrip antennas. Therefore, the fundamental antenna parameters will not be addressed in this work since they are already well covered in the literature regarding antennas. The following antenna parameters are exposed books such as Balanis.
As mentioned before an single element presents low gain and directivity, a wide radiation diagram, specially microstrip antennas that are not capable to provide more than 10 dB of gain. 
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