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In this chapter, 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.
3.2 Microstrip Patch Antenna
In its most basic form, a Microstrip patch antenna consists of a radiating patch on one side of a dielectric substrate which has a ground plane on the other side as shown in figure 3.1. The patch is generally made of conducting material such as copper or gold and can take any possible shape. The radiating patch and the feed lines are usually photo etched on the dielectric substrate. High RF PCB laminates such as the ArlonÂ® DiClad880 referenced in this dissertation need not be exposed to UV light during the etching process. This PCB does not come with a resist layer on top of the surface. On the contrary, the resist must be manually drawn (or printed in industrial scale production) on the PCB surface by using appropriate resist pens.
Fig.3.1 - Basic Structure of an MPA
In order to simplify analysis and performance prediction, the patch is generally square, rectangular, circular, triangular, elliptical or some other common shape as shown in figure 3.2 . For a rectangular patch, the length L of the patch is usually 0.3333Î»o < L < 0.5Î»o, where Î»o is the free-space wavelength. The patch is selected to be very thin such that t << Î»o (where t is the patch thickness). The height h of the dielectric substrate is usually 0.003Î»o â‰¤ h â‰¤ 0.05Î»o. The dielectric constant of the substrate (Îµr) is typically in the range 2.2 â‰¤ Îµr â‰¤12.
Fig.3.2 - Basic MPA Shapes
Microstrip patch antennas radiate primarily because of the fringing fields between the patch edge and the ground plane. For good antenna performance, a thick dielectric substrate having a low dielectric constant is desirable since this provides better efficiency, larger bandwidth and better radiation . 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 a narrower bandwidth. Hence a compromise must be reached between the antenna dimensions and the antenna performance.
3.2.2 Advantages and Disadvantages of an MPA
Microstrip patch antennas are increasing in popularity for use in wireless applications due to their low-profile structure. Therefore they are extremely compatible with embedded antennas in handheld wireless devices such as smart mobile phones. Some of their principal advantages discussed by  and  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 polarisation.
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 of their major disadvantages discussed by  and  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 large Q leads to narrow bandwidth and low efficiency. Q can be reduced by increasing the thickness of the dielectric substrate. But as the thickness increases, an increasing fraction of the total power delivered by the source goes into a surface wave. This surface wave contribution can be 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 can be minimised by use of photonic bandgap structures as discussed by . Other problems such as lower gain and lower power handling capacity can be overcome by using an array configuration for the elements.
3.3 Various Antenna Feed Techniques
Microstrip patch antennas can be fed by a variety of methods. These methods can be classified into two categories- contacting and non-contacting. In the contacting method, the RF power is fed directly to the radiating patch using a connecting element such as a microstrip line. In the non-contacting scheme, electromagnetic field coupling is done to transfer power between the microstrip line and the radiating patch . The four most popular feed techniques used are the microstrip line, coaxial probe (both contacting schemes), aperture coupling and proximity coupling (both non-contacting schemes).
3.3.1 Microstrip Line Feed
In this type of feed technique, a conducting strip is connected directly to the edge of the microstrip patch as shown in figure 3.3. The conducting strip is smaller in width as compared to the patch and this kind of feed arrangement has the advantage that the feed can be etched on the same substrate to provide a planar structure.
Fig.3.3 - Microstrip line feed
The purpose of the inset cut in the patch is to match the impedance of the feed line to the patch without the need for any additional matching element. This is achieved by properly controlling the inset position. Hence this is an easy feeding scheme, since it provides ease of fabrication and simplicity in modeling as well as impedance matching. However as the thickness of the dielectric substrate being used increases, surface waves and spurious feed radiation also increases, which hampers the bandwidth of the antenna . The feed radiation also leads to undesired cross polarised radiation.
3.3.2 Coaxial Feed
The Coaxial feed or probe feed is a very common technique used for feeding Microstrip patch antennas. As seen from figure 3.4, the inner conductor of the coaxial connector extends through the dielectric and is soldered to the radiating patch, while the outer conductor is connected to the ground plane. This is the method employed in this dissertation.
Fig.3.4 - Probe feed
The main advantage of this type of feeding scheme is that the feed can be placed at any desired location inside the patch in order to match with its input impedance. This feed method is easy to fabricate and has low spurious radiation. However, its major disadvantage is that it provides narrow bandwidth and is difficult to model since a hole has to be drilled in the substrate and the connector protrudes outside the ground plane, thus not making it completely planar for thick substrates ( h > 0.02Î»o ). Also, for thicker substrates, the increased probe length makes the input impedance more inductive, leading to matching problems . It is seen from above that for a thick dielectric substrate, which provides broad bandwidth, the microstrip line feed and the coaxial feed suffer from numerous disadvantages. The non-contacting feed techniques which are discussed below, solve these problems.
3.3.3 Aperture Coupled Feed
In this type of feed technique, the radiating patch and the microstrip feed line are
separated by the ground plane as shown in figure 3.5. Coupling between the patch and the feed line is made through a slot or an aperture in the ground plane.
Fig.3.5 - Aperture-coupled feed
The coupling aperture is usually centered under the patch, leading to lower cross polarisation due to the symmetry of the configuration. The amount of coupling from the feed line to the patch is determined by the shape, size and location of the aperture. Since the ground plane separates the patch and the feed line, spurious radiation is minimised. Generally, a high dielectric material is used for the bottom substrate and a thick, low dielectric constant material is used for the top substrate to optimise radiation from the patch . The major disadvantage of this feed technique is that it is difficult to fabricate due to multiple layers, which also increases the antenna thickness. This feeding scheme also provides narrow bandwidth.
3.3.4 Proximity Coupled Feed
This type of feed technique is also called as the electromagnetic coupling scheme. As shown in figure 3.6, two dielectric substrates are used such that the feed line is between the two substrates and the radiating patch is on top of the upper substrate. The main advantage of this feed technique is that it eliminates spurious feed radiation and provides very high bandwidth (as high as 13%) , due to the overall increase in the thickness of the microstrip patch antenna. This scheme also provides choices between two different dielectric media, one for the patch and one for the feed line to optimise the individual performances.
Fig.3.6 - Proximity-coupled feed
Matching can be achieved by controlling the length of the feed line and the width-to-line ratio of the patch. The major disadvantage of this feed scheme is that it is difficult to fabricate because of the two dielectric layers which need proper alignment. Also, there is an increase in the overall thickness of the antenna.
Table 3.1 below summarises the characteristics of the different feed techniques.
Poor due to
Table 3.1 Comparing the different feed techniques 
3.4 Methods of Analysis
The most popular models for the analysis of Microstrip patch antennas are the transmission line model, cavity model, and full wave models  such as MOM and FDTD. The Software design tool used in this dissertation uses a precursor of the FDTD as described in the following sections.
The transmission line model is the simplest of all and it gives good physical insight but it is less accurate.
The cavity model is more accurate and gives good physical insight but is complex in nature.
The full wave models are extremely accurate, versatile and can treat single elements, finite and infinite arrays, stacked elements, arbitrary shaped elements and coupling. These give less insight as compared to the two models mentioned above and are far more complex in nature.
3.4.1 Transmission Line Model
This model represents the microstrip antenna by two slots of width W and height h, separated by a transmission line of length L. The microstrip is essentially a nonhomogeneous line of two dielectrics, typically the substrate and air.
Fig.3.7 - Microstrip line Antenna
Fig.3.8 - Electric Field Lines emanating from the Antenna
Hence, as seen from figure 3.8, most of the electric field lines reside in the substrate and parts of some lines in air. As a result, this transmission line cannot support pure transverse electric-magnetic (TEM) mode of transmission, since the phase velocities would be different in the air and the substrate. Instead, the dominant mode of propagation would be the quasi-TEM mode. Hence, an effective dielectric constant (Îµreff) must be obtained in order to account for the fringing and the wave propagation in the line. The value of Îµreff is slightly less then Îµr because the fringing fields around the periphery of the patch are not confined in the dielectric substrate but are also spread in the air as shown in figure 3.8 above. The expression for Îµreff is given by ,  and  as:
where Îµreff = Effective dielectric constant
Îµr = Dielectric constant of substrate
h = Height of dielectric substrate
W = Width of the patch
Considering figure 3.9 below, this shows a rectangular microstrip patch antenna of length L, width W on a substrate of height h. The co-ordinate axis is selected such that the length is along the x direction, width is along the y direction and the height is along the z direction.
Fig.3.9 - Microstrip Patch Antenna
In order to operate in the fundamental TM10 mode, the length of the patch must be slightly less than Î»/2 where Î» is the wavelength in the dielectric medium and is equal to Î»o /âˆšÎµreff where Î»o is the free space wavelength. The TM10 mode implies that the field varies one Î»/2 cycle along the length, and there is no variation along the width of the patch. In figure 3.10 shown below, the microstrip patch antenna is represented by two slots, separated by a transmission line of length L and open circuited at both the ends. Along the width of the patch, the voltage is maximum and current is minimum due to the open ends. The fields at the edges can be resolved into normal and tangential components with respect to the ground plane.
Fig.3.10 - Microstrip Patch Antenna plan view
Fig.3.11 - Microstrip Patch Antenna side view
As seen from figure 3.11 the normal components of the electric field at the two edges along the width are in opposite directions and thus out of phase since the patch is Î»/2 long and hence they cancel each other in the broadside direction. The tangential components (seen in Figure 3.11), which are in phase, means that the resulting fields combine to give maximum radiated field normal to the surface of the structure. Hence the edges along the width can be represented as two radiating slots, which are Î»/2 apart and excited in phase and radiating in the half space above the ground plane. The fringing fields along the width can be modeled as radiating slots and electrically the patch of the microstrip antenna looks greater than its physical dimensions. The dimensions of the patch along its length have now been extended on each end by a distance Î”L, which is given empirically by , ,  and  as:
The effective length of the patch Leff now becomes  and :
For a given resonance frequency o f , the effective length is given by  and  as:
For a rectangular Microstrip patch antenna, the resonance frequency for any mn TM mode is given by  as:
where m and n are modes along L and W respectively.
For efficient radiation, the width W is given by  as:
The Antenna design of this dissertation was initially compiled using the transmission line model and the design was fine tuned using the full wave model provided by CST.
3.4.2 Cavity Model
Although the transmission line model discussed in the previous section is easy to use, it has some inherent disadvantages. Specifically, it is useful for patches of rectangular design and it ignores field variations along the radiating edges. These disadvantages can be overcome by using the cavity model. A brief overview of this model is given below.
In this model, the interior region of the dielectric substrate is modeled as a cavity bounded by electric walls on the top and bottom. The basis for this assumption is the following observations for thin substrates ( h << Î» ) .
Since the substrate is thin, the fields in the interior region do not vary much in the z direction, i.e. normal to the patch.
The electric field is z directed only, and the magnetic field has only the transverse components H x and H y in the region bounded by the patch metallisation and the ground plane. This observation provides for the electric walls at the top and the bottom.
Fig.3.12 - Charge distribution and current density creation
on the microstrip patch Antenna
Considering figure 3.12 shown above, when the microstrip patch is provided power, a charge distribution is seen on the upper and lower surfaces of the patch and at the bottom of the ground plane. This charge distribution is controlled by two mechanisms which are an attractive mechanism and a repulsive mechanism as discussed by . The attractive mechanism is between the opposite charges on the bottom side of the patch and the ground plane, which helps in keeping the charge concentration intact at the bottom of the patch. The repulsive mechanism is between the like charges on the bottom surface of the patch, which causes pushing of some charges from the bottom, to the top of the patch. As a result of this charge movement, currents flow at the top and bottom surface of the patch.
The cavity model assumes that the height to width ratio (i.e. height of substrate and width of the patch) is very small and as a result of this the attractive mechanism dominates and causes most of the charge concentration and the current to be below the patch surface. Much less current would flow on the top surface of the patch and as the height to width ratio further decreases, the current on the top surface of the patch would be almost equal to zero, which would not allow the creation of any tangential magnetic field components to the patch edges. Hence, the four sidewalls could be modeled as perfectly magnetic conducting surfaces. This implies that the magnetic fields and the electric field distribution beneath the patch would not be disturbed.
However, in practice, a finite width to height ratio would be there and this would not make the tangential magnetic fields to be completely zero, but they being very small, the side walls could be approximated to be perfectly magnetic conducting .
Since the walls of the cavity, as well as the material within it are lossless, the cavity would not radiate and its input impedance would be purely reactive. Hence, in order to account for radiation and a loss mechanism, one must introduce a radiation resistance Rr and a loss resistance RL. A lossy cavity would now represent an antenna and the loss is taken into account by the effective loss tangent Î´eff which is given as:
QT is the total antenna quality factor and has been expressed by  in the form:
Qd represents the quality factor of the dielectric and is given as:
where Ï‰r is the angular resonant frequency.
WT is the total energy stored in the patch at resonance.
Pd is the dielectric loss.
tanÎ´ is the loss tangent of the dielectric.
Qc represents the quality factor of the conductor and is given as:
where Pc is the conductor loss.
Î” is the skin depth of the conductor.
h is the height of the substrate.
Qr represents the quality factor for radiation and is given as:
where Pr is the power radiated from the patch.
Substituting equations (2.37), (2.38), (2.39) and (2.40) in equation (2.36), we get
Thus, equation (2.41) describes the total effective loss tangent for the microstrip patch antenna.
3.4.3 Full Wave Solutions
220.127.116.11 Finite Integration Technique (FIT), Perfect Boundary ApproximationÂ® (PBA) technique & Thin Sheet Techniqueâ„¢ (TST).
CST MICROWAVE STUDIOÂ® is a general-purpose electromagnetic simulator based on the Finite Integration Technique (FIT), first proposed as stated in . This numerical method provides a universal spatial discretisation scheme, applicable to various electromagnetic problems, ranging from static field calculations to high frequency applications in time or frequency domain .
The FIT formulation is a very general method and therefore can be applied to all frequency ranges, from DC to high frequencies. All electromagnetic field regimes are already covered by CST's software package MAFIAÂ®, whose development started as stated in . Based on this long experience, the "STUDIO"-family development started in 1997. Several improvements concerning user interface, visualisation and solver performance were integrated. However, the most fundamental change is the new mesh strategy, the Perfect Boundary ApproximationÂ® (PBA) technique, particularly extended by the Thin Sheet Techniqueâ„¢ (TST) .
With respect to Cartesian grids, the FIT formulation can be rewritten in time domain to yield standard Finite Difference Time Domain methods (FDTD). However, whereas classical FDTD methods are limited to staircase approximations of complex boundaries, the mentioned PBAÂ® technique applied to the FIT algorithm maintains all the advantages of structured Cartesian grids, while allowing an accurate modeling of curved structures .
CST MWS actually has several solvers available. The standard is a Finite Integral Technique (FIT) solver, which is basically FDTD with integration instead of differentiation. It also has a direct MoM, iterative MLFMM, and eigenmode solvers .
18.104.22.168 Transient Solver
The CST MICROWAVE STUDIOÂ® transient solver allows the simulation of a structure's behavior in a wide frequency range in just a single computation run. Consequently this is an efficient solver for most driven problems (i.e. with nonzero sources), especially for devices with open boundaries or large dimensions.
22.214.171.124 Error Sources / Sources of Inaccuracy
Every method, which tries to describe a real world problem using a numerical model, conceals the danger of introducing errors, either because the model itself is not identical with the real world, or because the numerical simulation is subject to errors.
This section gives an overview about the most important error sources. Many of them may be negligible in practice, but should always be aware of them in order to make sure that the results are reliable .
126.96.36.199.1 Simulation Model is not in Agreement with Reality
Geometric dimensions are wrong or geometric details have been neglected. This happens quite often and can only be avoided by comparing the model carefully with the drawing and the real structure. The influence of small details can be studied by carrying out the same simulation with and without details.
Material parameters are wrong, either because they are unknown and had to be chosen somehow, or because a value taken is valid for another frequency band but not for the band of interest. It might be necessary, especially when investigating a broader band, to enter the correct frequency dependency of
the material values. For example, for some dielectrics a constant tan Î´ ï€ is an appropriate choice rather than a constant conductivity.
The source of excitation was not chosen correctly, e.g. a perfectly matched microstrip port instead of a coax fed microstrip with normalised impedance. Furthermore for open ports such as microstrips or coplanar lines, the port size has to be chosen sufficiently large in order to avoid a truncation of the propagating modes. Discrete ports are typically not perfectly matched, even when they have the same impedance as the waveguide.
The same considerations are valid for output ports, for which a simulation model that fits best to the measurement structure should be found.
Sometimes the environment is not considered correctly. Objects that are placed
near the measured structure may influence the result and in this case should be included in the simulation model.
188.8.131.52.2 Inaccuracies due to the Simulation
Discretisation error: To ensure accurate results, the electromagnetic fields have
to be sampled sufficiently in space. Generally, the accuracy of the field solution increases with a finer mesh and it can be proven that convergence is ensured by the FI method. CST MICROWAVE STUDIOÂ® supports convergence studies by automatic adaption of the mesh density parameters and by visualisation of the convergence progress.
Truncation error: If the calculation is stopped before the time-domain signals have decayed down to zero, a so-called "truncation error" is introduced.
The geometry error is the deviation between the entered CAD structure and the simulation model. Some methods that are based on orthogonal grids convert rounded structures into so-called staircase models before starting the simulation. In Finite Element meshes, rounded structures are replaced by piecewise straight objects. With the employed PBA technique (Perfect Boundary Approximationâ„¢), the geometry error becomes very small or even negligible especially for rounded conductors. However, if an object becomes small compared to the size of the mesh cells, the geometry error may not always be neglected.
Some inaccuracy may be introduced through boundary conditions. In the case of radiating structures, the open space is simulated by so-called open boundaries. The employed PML technique (Perfectly Matched Layer) is well tested and very accurate even when the structure is near to the object. CST MICROWAVE STUDIOÂ® chooses automatically the optimum size of the surrounding simulation box but in some rare cases it may be worthwhile checking the sensitivity of the result to changes of this box.
Waveguide ports have a specific open boundary technique in which the waves
are separated into their mode patterns. This technique allows even higher accuracies than the PML boundary condition for the surroundings. In cases of
inhomogeneous ports such as microstrip lines, combined with very broadband
excitations, it might be necessary to adjust special parameters in order to keep the error below -50 or -60 dB. As mentioned before, the size of the waveguide port also has to be defined large enough.
Even if the field values are calculated correctly, interpolation errors may still occur, e.g. when deriving secondary field quantities or when calculating the field values at locations other than the grid edges.
Numerical errors may be caused by the finite representation of numbers, but can typically be neglected for the explicit algorithm in time-domain. However, in case of the eigenmode or frequency domain solver a numerical error may arise when the correspondent matrix system is solved.