In this chapter, an introduction to the Microstrip Patch Antenna is followed by its advantages and disadvantages. Next, some feed modeling techniques are discussed. Finally, a detailed explanation of Microstrip patch antenna analysis and its theory are discussed, and also the working mechanism is explained
The concept of microstrip patch antennas dates back to 1950s but it was not until 1970 that serious attention was paid to development of printed circuit technology, photolithographic technique and the substrate with low loss tangent. The basic configuration of a microstrip patch antenna is a thin metallic patch on a thin grounded dielectric substrate as shown in Figure 2.1
Figure 2.1. Structure of microstrip patch antenna
In order to simplify analysis and performance, the patch is generally considered as square, rectangular, circular, triangular, and elliptical or some other common shape as shown in Figure 2.2.Microstrip patch antennas are able to radiate primarily because of the fringing fields between the patch edge and the ground plane. For good antenna
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Fig 2.2 Common Shapes of microstrip patch antenna
performance, a thick dielectric substrate having a low dielectric constant is desirable since this provides better efficiency, larger bandwidth and better radiation [balanis book]. However, such a configuration leads to a larger antenna size. In order to design a compact Microstrip patch antenna, higher dielectric constants must be used which are less efficient and result in narrower bandwidth. Hence a compromise must be reached between antenna dimensions and antenna performance. The pattern of a single patch antenna is relatively wide and provides low gain. In many applications it is necessary to have high directive characteristics to meet communication system requirements. This can only be accomplished by using antenna arrays.
Microstrip patch antennas are now increasingly being used for wireless applications due to their low-profile structure. Therefore they are extremely compatible for embedded antennas in handheld wireless devices such as cellular phones, pagers etc.. The telemetry and communication antennas on missiles need to be thin and conformal and are nowadays most often Microstrip patch antennas. Another area where they have been used successfully is in Satellite communication. Some of their principal advantages discussed by [balanis] and Kumar and Ray are given below:
Light weight and low volume.
Low profile planar configuration which can be easily made conformal to host surface.
Low fabrication cost, hence can be manufactured in large quantities.
Supports both, linear as well as circular polarization.
Can be easily integrated with microwave integrated circuits (MICs).
Capable of dual and triple frequency operations.
Mechanically robust when mounted on rigid surfaces.
Microstrip patch antennas suffer from a number of disadvantages as compared to conventional antennas. Some are given below:
Extraneous radiation from feeds and junctions
Poor end fire radiator except tapered slot antennas
Low power handling capacity.
Surface wave excitation
Microstrip patch antennas have a very high antenna quality factor (Q). Q represents the losses associated with the antenna and a high Q results in narrow bandwidth and low efficiency. Q can be reduced by increasing the thickness (h) of the substrate. But as the thickness increased, an increasing fraction of the total power delivered to the patch by the source goes into surface waves. This surface wave contribution is counted as an unwanted power loss since it is ultimately scattered at the dielectric bends and causes degradation of the antenna characteristics. However, surface waves are minimized by use of photonic bandgap structures as discussed by Qian ET. Other problems such as lower gain and lower power handling capacity can be overcome by using an array configuration for the elements.
2.3 Microstrip patch Antenna
There are a variety of substrates that can be used for the design of microstrip patch antennas and their relative dielectric constants are in the range of 2.2< É›< 12.We would prefer thick substrates with low dielectrics as they result in better efficiency, broader bandwidth and lousy bound fields for radiation into space(Pozar,1987). Many configurations can be used to excite microstrip patch antennas:
Transmission Line Feed: The simplest possibility to feed a patch is by connecting it directly with a microstrip line as it is shown in Fig. 2.1. In this case, the feed circuit and the antenna are on the same substrate.
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Coaxial Feed: The patch is feed through a coaxial probe that is set perpendicular to the ground plane (Fig. 2.3). The center probe extends across the dielectric substrate and is connected to the patch. This structure allows using two different substrates for the feed structure and the patch. Optimal performance can be reached for both the circuit and the radiation characteristics. Brachat and Sabatier  have constructed a sophisticated antenna of this feed type and achieved a measured bandwidth of 52% (for a VSWR â‰¤ 2). But coaxial feeds are difficult to realize in practice because it requires careful handling and the mechanical control of the connection is difficult, especially for very high frequencies.
Fig 2.3 Coaxial Feed
Coupled feed: The feed line is put parallel to an edge of the patch on the same substrate. But it does not touch the resonator (Fig. 2.4a). Coupling takes place continuously along the edge of the patch.
Fig 2.4 a) Coupled Feed b) Proximity coupling
Fig 2.5 Aperture Coupled Feed
Proximity coupling: Proximity coupling of the patch to the feed line is also obtained by placing the patch and the feed at different levels (Fig. 2.4b). By using a thin substrate of high-permittivity dielectric for the substrate of the feed line, its radiation can be reduced considerably. The line and the patch can be optimized separately to a certain extent.
Slot Feed or Aperture Coupled Feed: With this design type, the two functions of radiation and guided transmission are completely separated by placing the ground plane between the radiating patch and the feed system as shown in Fig. 2.5. A slot in the ground plane provides coupling between the two sides. The dielectrics can be chosen with the goal directed to optimize separately radiation from the patch and significantly with this technique by choosing a proper form of the slot and the feed line. Shin and Kim  present a wideband and high-gain one-patch microstrip antenna coupled with H-shape aperture with very good performance. The measurement shows a maximum gain of 10.4 dBi at 2.05 GHz with a 3 dB gain bandwidth of 24% at the center frequency of 2.17 GHz. The impedance bandwidth is increased up to 56.2% (VSWR â‰¤ 2). In addition, the cross-polarization level is below -18.2 dB at the E-plane and below -25.7 dB at the H-plane. Jang  has designed a wideband printed annular slot antenna with cross shaped feed line. The measured bandwidth is 108.4% (VSWR â‰¤ 2) and a cross-polarization of less than -13 dB for both (E&H) planes at the center frequency of 3.76 GHz.
The rectangular patch antenna is the most widely used configuration and is easy to analyze using both transmission line and cavity model. For the rectangular patch as shown in Fig 2.1 the lowest frequency (Æ’rc) 010 for the dominant mode TM010 is given by
Where C is the speed of light in free space, Î¼o =4Ð» Ã-10-7 is the permeability of free space, É›o is the permittivity of free space ,L is the length of patch, W is the width of patch, h is the height of substrate, Leff is the effective length of the patch ,Î”L is the extended incremental length due to fringing effects, q is the fringe factor ,É›eff and É›r is the effective and relative dielectric constant, respectively.
The transmission line theory is employed to model the patch as two parallel radiating slots. The resonant input impedance Zin at the edge is obtained as
Where G1 is the conductance of slot 1, and G12 is the mutual conductance between slots 1 and 2. The plus (+) is sued for odd modes or antisymmetric voltage distribution beneath the patch and between the slots while the minus (-) sign is for even modes or symmetric resonant voltage distribution. The conductance of slot 1 and mutual conductance between slot 1 and 2 can be evaluated as
Where 0r is the number or propagation constant of free space,Î»0 is the free space wavelength, f is the operating frequency in Hz,J0 is the Bessel Function of the first kind of order zero. The typical values of the input impedance feeding at the edge are in the range of 150-300 ohms.
The far field radiation of a rectangular patch operating in the dominant TM010 is broad in both E and H planes. For the patch shown in Fig 2.1 the pattern over a large ground plane may be calculated by using the cavity model as two parallel magnetic line sources of length W separated by a distance Leff along the y direction. The fare field radiated by each slot are Er â‰ˆ EÉµ â‰ˆ0, and
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Where V0 is the slot voltage across the radiating edges. The x-y plane (Éµ=90,0â‰¤Ï†â‰¤90,and 270â‰¤Éµâ‰¤360) is the principle E plane for the microstrip antenna and the calculated radiated field Eq. 2.6 becomes
The principle H plane for the microstrip patch is y-z plane (Ï†=0,0â‰¤Ï†â‰¤180) and the expression of the radiated fields Eq.2.6 can be written as
Where = is the intrinsic impedance.
Polarization of the radiated wave is defined as the property of an electromagnetic wave defining the time varying direction and relative magnitude of the electric-field vector. Polarization of an antenna in a given direction is defined as the polarization of the wave transmitted by the antenna. A time harmonic wave is linearly polarized at a given point in space if the electric field vector at that point is always oriented along a straight line at every instant of time. A time harmonic wave is circularly polarized at a given point in space if the electric field vector at that point traces a circle as a function of time. The sense of rotation for circularly polarized field is determined by observing the field rotation as the wave is viewed as it moves away from the observer. If the rotation is clockwise the wave is right hand circularly polarized (RHCP).If the rotation is anti clock wise the wave is left hand circularly polarized (LHCP).however linear and circular polarization are only special cases of elliptical polarization. For elliptical polarization the ration of major axis to minor axis of the curves traced at a given position is referred to as AR (axial ratio).
Fig 2.6 Corner truncated circularly polarized antenna
Both square and rectangular patches radiate primarily linearly polarized waves if conventional feeds are used with no modifications. However circular and elliptical polarization can be obtained by using different feeds and slight modification to the elements. For example circular polarization can be achieved if two orthogonal modes are excited with a time-phase difference of 900 are excited by changing physical dimensions of the patch or using two feeds. The circular polarization with only one feed can be achieved by a square patch with truncated ends on two opposite sides as in Fig 2.6. The antenna is fed along a center line as with linearly polarized patch. If fed from the side as shown in the figure the polarization will be right-hand circularly polarized. When fed from the adjacent side, it will be left hand circularly polarized.
2.3 Array Theory
The total field of an array is determined by the vector addition of the field radiated by each element. To provide very directive patterns it is necessary that field from the elements interfere constructively in the desired direction and interfere destructively in remaining space. In an array of identical elements, there are five parameters to determine the overall pattern of the antenna: the geometrical configuration of the array (linear, circular, rectangular, spherical etc), the relative displacement between the elements, the excitation amplitude, the excitation phase, the relative pattern of the individual element.
A two element array is first considered to simplify the presentation and give a better physical interpretation. An array of two infinitesimal horizontal dipoles as shown in Fig.2.7 (a) is positioned along the z-axis, and the total field radiated is equal to the sum of two given by
In the y-z plane where aÉµa is the unit vector along Éµa direction, k = 2Ð»/Î» is the wave number ,Î» is the wavelength ,Io is the current of the dipole, l is the length of the dipole ,Î² is difference in phase excitation between the elements. The magnitude of the radiators is identical .Assume far filed observation as shown in Fig 2.7(b).
for amplitude variations (2.12)
and Eq.(2.9) can be reduced to
It is apparent that the far field of the array is equal to field of the single element positioned at the origin multiplied by a factor, referred to as array factor (AF) and is given by
Fig 2.7 a)Two infinitesimal dipoles ,b) Far field observations
in the normalized form. The total field can be written in the form as
The array factor, in general is a function of number of elements, the geometrical arrangement, relative magnitudes, relative phases and spacing's. It will be simpler from if the elements have identical amplitudes, phases and spacing's.
An array of identical elements all of identical magnitudes and each with a progressive phase are referred to as a uniform array. For a uniform array of N elements as shown in Fig. 2.8 assume all elements have identical amplitudes but each succeeding element has a Î² progressive phase lead current excitation relative to the proceeding one. The total field can be calculated by multiplying the array factor of the single element as in Eq. 2.15.The array factor is given by
Where Ïˆ=kdcosÉµ+Î² and Eq. 2.16 can be written as
The maximum value of Eq.2.17 is equal to N. The normalized form is
And the directivity (maximum gain) of the array factor
In addition to placing antenna along a line, individual radiators can be positioned along a rectangular grid to form a planar array.planar array provide additional variables to control and shape the pattern of the array .planar array are more versatile and can provide more symmetrical patterns with low side lobes. Consider M elements are placed along x-axis to
Fig .No. 2.9 planar array
form a linear array as shown in Fig .2.8 with the spacing and progressive phase shift between the elements represented by dx and Î²x .If N such elements are placed next to each othere in the y axis with a distance of dy and a progressive Î²y , a planar array will be formed as shown in Fig 2.8. The array factor for the entire array can be written as
According to Eq. (2.17-2.18) ,Eq.2.20 can be reduced and written in the normalized form as
Where Ïˆx=kdx sinÉµcosÏ†+Î²x and Ïˆy=kdy sinÉµsinÏ†+Î²y .The directivity is given by (Elliott , 1964 )
Where and are the directivities of the each linear array.
Arrays can be analyzed using above theory .However such an approach does not take into account mutual coupling effects, which can be significant in microstrip antennas. There fore foe more accurate results analysis of the total filed may be performed.
An array is in the series feed network where all the elements are deed by a single line as shown in Fig 2.9 (a) or in the corporate feed network as shown in Fig 2.9(b) to provide power splits 2n such as quarter wave length impedance transformers. Corporate feed network is more general, versatile and hence ideal for scanning applications. Both Cooperate and series feed networks can be fabricated using photolithography.
In this chapter the basic concept of microstrip patch antenna and array theory are introduced. In order increases directivity of the patch antenna array are necessary. By means of antenna array the direction of maximum radiation can be controlled. Design analysis and experiment on microstrip patch antenna will be presented in the following chapters.
 Martin Windlin, Microstrip Patch Antenna at 10.5 GHz for Automobile Obstacle