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					          Degree Project




Design and Simulation of Microstrip Phase Array Antenna using ADS



                       Supervisor: Prof. Sven-Erik Sandström

              Department of Computer Science, Physics and Mathematics




             Submitted for the degree of Master in Electrical Engineering

               Specialized in Signal Processing and Wave Propagation




          Muhammad Kamran Khattak            Osama Siddique             Waqar Ahmed
          2011-05-17
          Subject: Master Thesis
          Level: Second
          Course code: 5ED06E
                                    Acknowledgement

We would like to thank our supervisor Dr. Sven-Erik Sandström for his kind support, patient
guidance and co-operation in making this work possible. We would like to thank the Department
of Computer Science, Physics and Mathematics, Linnaeus University, Sweden, for providing
best educational facilities. We would like to thank the Swedish government for providing free
education, education facilities and co-operation. We would like to thank all our friends and
siblings whose company will always be cherished. And last, we would like to thank our parents
who are the source of our very existence. Without their support, accomplishing this goal was
never possible. We thank our parents from heart and soul.




                                               ii
                                           Abstract
The aim of this project is to design a microstrip phase array antenna in ADS (Advance Design
System) Momentum. The resonant frequency of which is 10 GHz. Two circular patches with a
radius of 5.83 mm each are used in designing the array antenna. RT-DURROID 5880 is used as a
substrate for this microstrip patch array design. These circular patches are excited using coaxial
probe feed and transmission lines of particular lengths and widths. These transmission lines
perfectly match the impedance of the circular patches. Various parameters, for example the S-
parameters, two dimensional and three dimensional radiation patterns, excitation models, gain,
directivity and efficiency of the designed antenna are obtained from ADS Momentum.




Key words: Microstrip phase array antenna, Circular patch antenna, ADS Momentum.




                                                iii
Table of Contents
1 Introduction ................................................................................................................................................................1
    1.1 Thesis Approach ..................................................................................................................................................1
    1.2 Objective .............................................................................................................................................................1
    1.3 Thesis Organization .............................................................................................................................................2
2. Literature Review ....................................................................................................................................................3
    2.1 Basic Antenna Terminology ................................................................................................................................3
        2.1.1 Radiation Pattern..........................................................................................................................................3
        2.1.2 Radiation Pattern of a dipole antenna ..........................................................................................................4
        2.1.3 Directivity ....................................................................................................................................................4
        2.1.4 Gain..............................................................................................................................................................4
        2.1.5 Aperture Efficiency ......................................................................................................................................5
        2.1.6 Beamwidth ...................................................................................................................................................5
        2.1.7 Input Impedance...........................................................................................................................................6
        2.1.8 Polarization ..................................................................................................................................................6
        2.1.9 Antenna Efficiency ......................................................................................................................................6
        2.1.10 Beam Efficiency.........................................................................................................................................6
        2.1.11 Bandwidth ..................................................................................................................................................7
        2.1.12 Antenna Radiation Efficiency ....................................................................................................................7
        2.1.13 Return Loss ................................................................................................................................................7
    2.2 Basics of Transmission Line Theory ...................................................................................................................7
        2.2.1 Wave propagation on a transmission line ....................................................................................................8
        2.2.2 Phase velocity ..............................................................................................................................................8
        2.2.3 Voltage reflection coefficient (Г) .................................................................................................................8
        2.2.4 Standing wave ratio (VSWR) ......................................................................................................................8
        2.2.5 Transmission lines with some special lengths..............................................................................................9
        2.2.6 Charactereristic Impedence ..........................................................................................................................9
        2.2.7 The Smith Chart ......................................................................................................................................... 10
        2.2.8 S-parameters .............................................................................................................................................. 11
    2.4 Antenna Arrays ................................................................................................................................................. 12
        2.4.1 Broadside Array ........................................................................................................................................ 13
        2.4.2 End-Fire Array ........................................................................................................................................... 13
        2.5 Mutual Coupling in Antenna Array .............................................................................................................. 14
    2.6 Microstrip Antennas .......................................................................................................................................... 15
        2.6.1 Introduction ................................................................................................................................................ 15

                                                                                       iv
        2.6.2 Rectangular Patch ...................................................................................................................................... 16
        2.6.3 Feed Models ............................................................................................................................................... 18
        2.6.4 Microstrip Line Feed .................................................................................................................................. 18
        2.6.5 Coaxial Probe Feed .................................................................................................................................... 18
        2.6.6 Aperture- coupled Feed .............................................................................................................................. 19
    2.7 Photonic crystals in microstrip antenna substrates ............................................................................................ 22
3. ADS Momentum Overview ..................................................................................................................................... 23
    3.1 Introductions to ADS Momentum ..................................................................................................................... 23
    3.2 Applications of Momentum ............................................................................................................................... 23
    3.3 Method of Calculation ....................................................................................................................................... 24
    3.4 Working with ADS Momentum ........................................................................................................................ 25
    3.5 Theory of Operation for Momentum ................................................................................................................. 27
    3.6 Method of Moment Technology ........................................................................................................................ 28
    3.7 Simulation Techniques Used in ADS ................................................................................................................ 31
    3.8 Block Diagram of ADS Momentum Simulation ............................................................................................... 32
4. Design and Analysis ................................................................................................................................................ 33
    4.1 Design of a Rectangular Patch Antenna ............................................................................................................ 33
    4.2 Gain and Directivity .......................................................................................................................................... 35
    4.3 Design of the Circular Patch.............................................................................................................................. 37
        4.3.1 Resonant Frequency ................................................................................................................................... 37
        4.3.2 Radius of the Patch .................................................................................................................................... 38
        4.3.3 Feed Point Location ................................................................................................................................... 38
    4.4 Proposed Design of a Single Circular Patch Antenna ....................................................................................... 39
        4.4.1 Gain and Directivity: .................................................................................................................................. 40
        4.4.2 S11 Parameters: ........................................................................................................................................... 41
        4.4.3 Efficiency ................................................................................................................................................... 43
    4.5 Proposed Design for the Circular Patch Array Antenna .................................................................................... 43
        4.5.1 Directivity and Gain ................................................................................................................................... 45
        4.5.2 S11 Parameters ............................................................................................................................................ 47
5. Conclusion ............................................................................................................................................................... 50
    5.1 Conclusion Summary ........................................................................................................................................ 50
    5.2 Future work ....................................................................................................................................................... 50
References ................................................................................................................................................................... 51




                                                                                       v
Table of Figures
Figure 1: Radiation pattern of a Dipole antenna. ............................................................................ 3
Figure 2: Antenna Beamwidth. ....................................................................................................... 5
Figure 3: The Smith chart. ............................................................................................................ 10
Figure 4: Mutual Coupling Mechanism. ....................................................................................... 14
Figure 5: Different shapes of microstrip patch. ............................................................................ 16
Figure 6: Rectangular microstrip patch antenna. .......................................................................... 16
Figure 7: Fringing effects in the microstrip patch antenna. .......................................................... 17
Figure 8: Microstrip feed line designed in ADS. .......................................................................... 18
Figure 9: Coaxial probe feed......................................................................................................... 19
Figure 10: Aperture-coupled feed. ................................................................................................ 20
Figure 11: Proximity-coupled feed. .............................................................................................. 20
Figure 12: Types of feed. .............................................................................................................. 21
Figure 13: Stepwise simulation of ADS Momentum. ................................................................... 24
Figure 14: Layout window of ADS Momentum. .......................................................................... 25
Figure 15: Different parameters in ADS Momentum. .................................................................. 26
Figure 16: Output S-parameter curves. ......................................................................................... 27
Figure 17: Discretization of the surface current using rooftop basis function. ............................. 29
Figure 18: Mesh representation in the form of L and C. .............................................................. 30
Figure 19: Block diagram of ADS Momentum simulation. ......................................................... 32
Figure 20: Rectangular patch designed in ADS Momentum layout. ............................................ 33
Figure 21: Magnitude of S11 in dB. ............................................................................................... 34
Figure 22: S11-parameter shown in Smith chart ............................................................................ 35
Figure 23: Gain and Directivity of the rectangular patch. ............................................................ 36
Figure 24: 3D graph of the far field radiation. .............................................................................. 36
Figure 25: Design of single circular patch antenna in ADS Momentum. ..................................... 39
Figure 26: Excitation of circular patch antenna in ADS Momentum. .......................................... 40
Figure 27: Gain and Directivity of single circular patch antenna in ADS Momentum. ............... 40
Figure 28: 3D view of the directivity of the single circular patch simulated in ADS Momentum.
....................................................................................................................................................... 41
Figure 29: Magnitude vs Frequency graph of input reflection coefficient. .................................. 42
Figure 30: S11-parameter of a single circular patch antenna on a Smith chart. ............................ 42
Figure 31: Efficiency of single circular patch antenna simulated by ADS Momentum. .............. 43
Figure 32: Circular patch phase array antenna designed in ADS Momentum. ............................ 43
Figure 33: 3D view of circular patch microstrip phase array antenna. ......................................... 45
Figure 34: Gain and Directivity graphs of circular patch microstrip phase array antenna. .......... 45
Figure 35: 3D Directivity of circular patch microstrip phase array antenna. ............................... 46
Figure 36: 3D radiation pattern shown by EMDS. ....................................................................... 47
Figure 37: Magnitude vs Frequency graph of S11 parameter. ....................................................... 47
Figure 38: Phase vs Frequency graphs of S11 parameter. ............................................................. 48

                                                                           vi
Figure 39: S11 parameter plotted on the Smith chart..................................................................... 48
Figure 40: Efficiency of the circular patch microstrip phase array antenna. ................................ 49
Figure 41: Radiated power of the circular patch microstrip phase array antenna. ....................... 49




                                                            vii
1 Introduction
1.1 Thesis Approach

The thesis comprises design of a microstrip phase array antenna using circular patches. This
antenna will have the main beam in the broadside direction with a specified beam width. The
designed antenna consists of an array antenna with two circular patches. These two circular
patches are connected to the quarter-wave transmission line through two transmission lines with
specified length and width depending on the impedance of the circular patches. A coaxial probe
is connected to the quarter-wave transmission line which will excite the system i.e. the antenna.
The design is implemented and analyzed in ADS Momentum. ADS Momentum is a 2.5D
simulator which is used to solve complex electromagnetic circuits. It can build passive
electromagnetic circuits and the simulation shows the S-parameters of the designed system. ADS
Momentum takes care of the electromagnetic coupling effect. It also provides 2D and 3D visuals
of output parameters, for example the radiation pattern and the directivity of the antenna.


1.2 Objective

      Design and simulate a microstrip phase array antenna in ADS Momentum with a main
       beam in the broadside direction with specified beam width. It operates at 10 GHz
       (Resonant Frequency) with RT-DURROID 5880 as a substrate.
      The array antenna will consist of two circular patches in a linear fashion, having radius of
       5.49 mm each. The height of each of the patch is 17.4 µm. The thickness of the substrate
       is 0.787 mm for both the patches.
      Two transmission lines are used to connect these patches to quarter-wave transmission
       lines. The impedance of each transmission line is required to be 200 Ω. The length of
       each transmission line is 462 mil (11.72 mm) and the width of each transmission line is
       2.39 mil (0.06095 mm). The electrical length of each line is 180º.
      A quarter-wave transmission line is used to match the impedance of the system. The
       impedance of the line is 50 Ω. The length calculated to get 50 Ω impedance is 5.428 mm
       (213.70 mil) and the width is 2.419 mm (95.23 mil). The electrical length of the quarter
       wave transmission line is 90º.

                                                 1
       This corporate feed network is excited by coaxial probe feed. A 50 Ω coaxial probe is
        connected to the quarter wave transmission line.
       The antenna is designed and simulated in ADS Momentum.




    1.3 Thesis Organization

Chapter 1 consists of an introduction and the objectives of the thesis. Chapter 2 represents a
literature review and the prerequisite knowledge required in the design and simulation of the
antenna. Chapter 3 gives a short overview of ADS Momentum. Chapter 4 is related to the design
of the microstrip phase array antenna. Chapter 5 concludes and suggests future work that can be
done in this field.




                                                2
2. Literature Review
2.1 Basic Antenna Terminology

Antennas radiate and receive electromagnetic waves which are converted into current after
reception. Some of the basic characteristics of antennas are discussed below.

2.1.1 Radiation Pattern
The antenna radiation pattern, or antenna pattern, is defined as ``a mathematical function or a
graphical representation of the radiation properties of antenna as a function of space
coordinates”. Radiation properties include power flux density, radiation intensity, field strength,
directivity, phase or polarization. A trace of received electric or magnetic field at a constant
radius is called amplitude patten. A graph of the spatial variation of the power density along a
constant radius is called an amplitude power pattern [1]. The radiation pattern can be presented
in two forms :

                             Azimuth Pattern
                             Elevation Pattern

The top view of the energy radiated by an antenna is known as Azimuth Pattern while the
graphical side view is called an Elevation. The combination of these two terms is known as 2D
pattern of the field produced [1]. The basic radiation pattern of a dipola antenna is shown in Fig.
1.




                           Figure 1: Radiation pattern of a Dipole antenna.




                                                  3
2.1.2 Radiation Pattern of a dipole antenna
Following are some important terms for an antenna [1]:

      Field Pattern (in linear scale) represents a plot of the magnitude of the electric or
       magnetic field as a function of angular space.
      Power Pattern (in linear) typically represents a plot of the square of the magnitude of the
       elecrtric or magnetic field as a function of the angular space.
      Power Pattern (in decibels) represents the magnitude of the electric or magnetic field in
       decibels, as sa function of the angular space.

2.1.3 Directivity
The ratio of the radiation intensity in a given direction to the radiation intensity avreaged over all
directions [1]. Mathematically directivity can be expressed as

                                                                                                      (1)

The directivity of a non-isotropic source is equal to the ratio of the its radiation intensity in a
given direction over that of isotropic source

                                                                                                      (2)


The partial directivity of an antenna for a given polarization is, the part of the radiation intensity
corresponding to that polarization, divided by the total radiation intensity averaged over all
directions.

2.1.4 Gain
The gain of the antenna is related to the directivity of the antenna. Gain takes into account the
directional capabilities as well as the efficiency of the antenna [1].

The gain of an antenna (in a given direction) is defined as “the ratio of the intensity, in a given
direction, to the radiation intensity that would result if the power fed to the antenna were radiated
isotropically”. The radiation intensity corresponding to the isotropically radiated power is equal
to the power from the generator, to the antenna divided by 4π [1].



                                                  4
Mathematically this can be expressed as

                          radiation intensity          (    )
        Gain = 4π                               = 4π               (dimensionless)    (3)
                    total input (accepted)power



2.1.5 Aperture Efficiency
The ratio of the maximum effective area to the physical area.

2.1.6 Beamwidth
The beamwidth involves a trade-off because the side lobe level increases as the beamwidth
decreases and vice versa. The beamwidth is also used to describe the capability of the antenna to
distinguish between two adjacent radiating sources or radar targets [1].

The beamwidth of an antenna is defined as the angular separation between two identical points
on opposite sides of the pattern maximum. There are a number of beamwidths in the antenna
pattern. One of the most widely used beamwidths is the Half-Power Beamwidth (HPBW) [1].




                                    Figure 2: Antenna Beamwidth.




                                                 5
2.1.7 Input Impedance
The impedance presented by an antenna at its terminals or the ratio of the voltage to current at a
pair of terminals [1].

                                      ZA = RA + jXA                                               (5)

RA is the real part and XA is the imaginary part. The resistive part relates to the power
dissipation, while the imaginary (reactive) part relates to power stored in the near field of the
antenna.

2.1.8 Polarization
The polarization is the orientation of the electric field far from the source [2]. It describes the
time-varying direction and relative magnitude of the electric field vector. Polarization for an
antenna in a given direction is defined as the polarization of the E-field transmitted (radiated) by
the antenna. When the direction is not stated the polarization is taken to be the polarization in the
direction of maximum gain. The polarization of a wave radiated by an antenna, in a specified
direction, at a point in the far field, is defined as the polarization of the plane wave which is used
to represent the radiated wave at that point [1]. Polarization may be classified as linear, circular,
elliptical, circular left hand, circular right hand, elliptical right and elliptical left hand.

2.1.9 Antenna Efficiency
The total antenna efficiency eo is used to take into account losses at the input terminals of the
antenna. Such losses may be caused by:

       Reflections because of the mismatch between transmission line and antenna.
       I2R losses (conductive and dielectric).

In general, overall efficiency can be written as:

                                                                                                  (6)

eo = total efficiency, er = reflection mismatch efficiency, ec = conduction efficiency,
ed = dielectric efficiency.

2.1.10 Beam Efficiency
A parameter used to judge the quality of transmitting and receiving antennas is the beam
efficiency [1].

                                                     6
                                                 (               )
                                                         (           )
                                                                                                  (7)


����1 is the half angle of the cone in the above equation.

2.1.11 Bandwidth
The bandwidth of an antenna is defined as “the range of frequencies within which the
performance of the antenna, with respect to some characteristics, conforms to a specified
standard”. The bandwidth can be considered to be the range of frequencies on either side of the
center frquency where the antenna characteristics are close to those at the center frequency [1].

2.1.12 Antenna Radiation Efficiency
The conduction dielectric efficiency is defined as the ratio of the power delivered to the radiation
resistance Rr, to the power delivered to Rr and RL. The resistance RL is used to represent the
conduction-dielectric losses [1].

2.1.13 Return Loss
The characterization of the input and output signal can be shown in a more convenient way in the
form of return loss when a load is mismatched [3]. This means that all the source power is not
delivered to the load. This loss of power is known as “return loss” and can be represented as:

                                             | |(            )                                   (8a)

Where                         | |                                                                (8b)


| Г|= Magnitude of reflection coefficient, Vo = Reflected voltage, Vin = Incident voltage, ZL and
Zo are the load and characteristic impedances.


2.2 Basics of Transmission Line Theory
Transmission lines and waveguides are conduits for transporting RF signals between elements of
a system. For example transmission lines are used between an exciter output and transmitter
input, between the transmitter input and its output and between the transmitter output and the
antenna [4]. Transmission lines are complex networks containing the equivalent of all the three



                                                     7
basic electrical components: resistance, capacitance, and inductance. Hence, transmission lines
must be analyzed in terms of an RLC network [4].

2.2.1 Wave propagation on a transmission line
The wavelength of the travelling waves is defined as the distance between two successive points
of equal phase on the line at a fixed instant of time [4].

                                                                                              (9)


2.2.2 Phase velocity
The phase velocity of the wave is defined as the speed at which a constant phase point travels
down the line.

                                                                                            (10)

2.2.3 Voltage reflection coefficient (Г)
The amplitude of the reflected voltage wave, normalized to the amplitude of the incident voltage
wave, is defined as the voltage reflection coefficient [1].

                                                                                            (11)


The average power flow is constant at along the line and the total power delivered to the load is
the difference between incident power and the reflected power. If Г =0, maximum power is
delivered to the load while no power is delivered for Г =1 (all the incident power is reflected
back from the load) [1].

2.2.4 Standing wave ratio (VSWR)
When a tranmission line is not matched to its load some of the energy is absorbed by the load
and some is reflected back down the line towards the source. The intereference of the incident
and reflected wave creates standing waves on the transmission line [4]. As the magnitude of the
reflection coefficient Γ increases, the ratio of Vmax to Vmin also increases. A measure of the
mismatch of the line is called the standing wave ration (SWR), also know as the volatage
standing wave ratio (VSWR) [1].




                                                  8
                                                                                                        (12)


One has, 1<VSWR<∞ , where 1 implies a matched load.

2.2.5 Transmission lines with some special lengths
There are some special transmission lines. For example:

                                        l=     /2,          Zin = ZL

This means that half a wavelength of the transmission line does not alter or transform the
impedance regardless of the characteristic impedance of the line.

If the line is a quarter wavelength long i.e. l=        /4 +n      /2, for n = 1,2,3...N, the input impedance
is given by,

                                             Zin=           / ZL                                        (13)

Such a line is called quarter wave transformer because it has the effect of inverting the load
impedance [1].

2.2.6 Charactereristic Impedence
The charactereristic impedence for a specific type of line is a function of the conductor size, the
conductor spacing, the conductor geometry and the dielectric constant of the insulating material
used between the conductors [4]. The transmission line is an RLC network with a charactereristic
impdence Z0. Z0 is a function of line per unit lenght parameters, resistance R, conductance G,
inductance L, capacitance C.


                                         Z0 = √                                                       (14a)

                   If X>>R


                                                    √                                                  (14b)




                                                        9
2.2.7 The Smith Chart
The mathematics of transmission lines becomes cumbersome at times, especially when dealing
with complex impedances and nonstandard situations. In 1939, Phillip H. Smith published a
graphical device for solving these problems, the Smith Chart. It consists of a series of
overlapping orthogonal circles that intersect each other at right angles. These sets of orthogonal
circles make up the basic structure of the Smith chart and are shown in Fig. 3. The following is a
brief description of the Smith chart and how it works [4].




                                     Figure 3: The Smith chart.

                                                10
2.2.7.1 The normalized  impedance line
A baseline bisects the Smith chart outer circle and forms the reference of measurements made on
the chart. The Complex impedance contains both resistance and reactance and is expressed
mathematically as:

                                                  Z= R    jX                                    (15)

R is the resistive component of the impedance and X is the reactive component of the impedance
[4].

The pure resistance circle represents the situation where X=0, and the impedance is therefore
equal to the resistive component only. To make the Smith chart universal, the impedances along
the pure resistance line are normalized with reference to system impedance (Z0). The actual
impedance it is divided by the system impedance. The pure resistance line is structured such that
the system standard impedance is at the center of the chart and has a normalized value of 1.0 [4].

2.2.7.2 The constantresistance circles
The isoresistance circles, also called the constant resistance circles represent points of equal
resistance. These circles are all tangent to the point at the right hand extreme of the pure
resistance line and are bisected by that line.

2.2.7.3 The constantreactance circles
The circles above the pure resistance line represent the inductive reactance (+X) while the circles
below the pure resistance line represent capacitive reactance (-X). The outermost circle is called
the pure reactance circle. Points along this circle represent reactance only.

2.2.8 S-parameters
The S-parameters are very important in microwave design for describing the behavior of
electrical devices. Most of the electrical properties i.e. gain, return loss, power, VSWR etc relates
to the S-parameters. The S-parameters can be observed by sending a signal through an input port
and observing the response on an output port. The term impedance is of great importance while
calculating the S-parameters because the system should be matched properly, otherwise
reflection which will give rise to standing waves and the system will not produce the desired
output. The S-parameters S11 and S22 represent input and output reflection while S21 is the
forward transmission coefficient (gain) and S12 is the reverse transmission coefficient (isolation).

                                                 11
2.4 Antenna Arrays

Usually the radiation pattern of a single element is relatively wide, and each element provides
low values of directivity (gain). In many applications, it is necessary to design antennas with
very high directive characterristics (very high gain) to meet the demands of long distance
communication. This can only be accomplished by increasing the electrical size of the antenna
[1]. Enlarging the dimensions of single elements often leads to more directive characteristics.
Another way to enlarge the dimensions of the antenna, without increasing the size of individual
element, is to form an assembly of radiating elements in an electrical and geometrical
configuration. This new antenna antenna formed is referred to as an array [1].

The antenna arrays are of vast importance and are widely used nowadays for various purposes
like military, missiles and satellite communication. There are different forms of antenna arrays
linear, circular, planar etc. The radiation pattern of an array antenna is mostly considered in the
far field, where the field depends on two parameters. One is the distance r of the reciever and the
other deals with the spherical coordinates θ and φ. The radiation pattern of an antenna can be
calculated by :

                          Array Pattern = Array element pattern * Array factor(AF)            (16)

The array factor determines the overall radiation pattern of the array while the element pattern
describes radiation pattern of the individual element [5]. The array factor can also be defined as
“The function of the total number of elements, their spacing and the phase difference between
each element” [6]. The array factor for a uniform antenna can be written mathematicaly as:

                                                          ⁄
                                                      ⁄
                                                                                              (17)


One may normalise the array factor so that the maximum value is equal to unity.

                                                              ⁄
                                         (   )                ⁄
                                                                                              (18)




                                                 12
Antenna array design involves two broader concepts:

                          Broadside Array
                          End-Fire Array

2.4.1 Broadside Array
In a broadside array, the radiators are along a straight line producing a beam perpendicular to the
line [5]. For an optimal design, the maxima of the single element as well as of the array should
be directed toward θ= 900 and the phase angle        is zero.

                                                 (      ⁄       )
                                  (    )               ⁄
                                                                                                 (19)
                                                  (             )


Where          and

The requirements for the single element can be met by a judicious choice of the radiators, and
those of the array factor by the proper separation and excitation of the individual radiators [1].

2.4.2 End-Fire Array
A linear array whose direction of maximum radiation is along the axis of the array. It may either
be unidirectional or birectional. The main beam will either be at θo= 0o or 180o.

                                                                                                 (20)

For θo= 0o or 180o

                                                                                                 (21)

Which gives

                                                  (             )                                (22)



                                                 (      ⁄   (       )
                                  (    )               ⁄
                                                                                                 (23)
                                                  (         (       )




                                                 13
2.5 Mutual Coupling in Antenna Array
One of the basic characteristics of an antenna array appears when two or more elements are
located near to each other and effect each other [1]. The amount of coupling depends on the
following:

      Radiation characteristics.
      Actual separation between elements .
      Relative orientation of elements.

The mutual coupling between two radiating elements depends upon the distance between them.
If they are close to each other the mutual coupling will be greater. Thus energy is transferred
between elements and this is called mutual coupling. One can say that the electromagnetic
coupling between the elements is mutual [7].

The transmitting mode coupling can be shown with the help of Fig. 4. Two antennas, A and B
are placed relative to each other. Antenna A is excited by a source and radiates. When this
radiation reaches antenna B, it excites antenna B and rescatteres some the energy back to antenna
A. Antenna A recieves the energy again and so on. The total contribution that an element makes
to the far field pattern does not depend on its own excitation from the generator only, but also
upon the total parasitic excitation due to which coupling is introduced to other generators [8].
The mutual coupling phenomenon is reciprocal in nature. If one antenna is used as a transmitter
and the other as a reciever or vice versa. Both is the same.




                        A                                 B


                       Figure 4: Mutual Coupling Mechanism.




                                                     14
Since mutual coupling in phased array antennas can affect the radiation pattern so consideration
should be given to this mechanism.




2.6 Microstrip Antennas

2.6.1 Introduction
For applications where size, weight, cost, performance, ease of installation and aerodynamics are
constraints, low profile antennas are needed. Aircraft, spacecraft, satellite and missile
applications and recently mobile radio and wireless communications demands this [1]. To meet
these requirements microstrip antennas can be used. These antennas are low profile, suited to
planar and non planar surfaces, simple and inexpensive to manufacture, mechanically robust
when mounted on rigid surfaces, compatible with MMIC designs, and when the particular patch
shape and mode are selected, they are very versatile in terms of resonant frequency, polarization,
pattern and impedance [1].

Major operational disadvantages of microstrip antennas are their low efficiency, low power, high
Q, poor polarization purity, poor scan performance, spurious feed radiation and narrow
frequency bandwidth which is typically only a fraction of a percent or at most, a few percent [1].
Microstrip antennas also exhibit large electromagnetic signatures at certain frequencies outside
the operating band and are rather large physically at VHF and possibly UHF frequencies. In large
arrays there is a trade-off between bandwidth and scan volume [1].

The idea of the microstrip antenna was introduced in 1953 by G.A Deschamps and it received
considerable attention by 1973. In 1970, Howell and Munson defined a transmission model for
microstrip antennas. Microstrip antenna patch elements are the most common form of printed
antennas. These antennas are quite cheap, light weight and give good results. The microstrip
patch can have different shapes like circular, rectangular or square as shown in Fig. 5.




                                                15
                            Figure 5: Different shapes of microstrip patch.

2.6.2 Rectangular Patch
The rectangular patch is by far the most widely used configuration. A basic form of rectangular
patch is shown in the Fig. 6.




                           Figure 6: Rectangular microstrip patch antenna.

The patch of a microstrip antenna is usually made of a conducting material. The patch is parallel
to the ground plane. In between the patch and the ground plane there is substrate with a dielectric
constant whose value depends on the substrate used. The inside of the rectangular patch is shown
in Fig. 7.




                                                  16
                        Figure 7: Fringing effects in the microstrip patch antenna.

Because the dimensions of the patch are finite, the fields at the edges of the patch undergo
fringing [1]. The amount of fringing is a function of the dimensions of the patch and the height
of the substrate. For the principal E-plane (xy-plane), fringing is a function of the ratio of the
length of the patch L to the height h of the substrate (L/h), and the dielectric constant ϵ r of the
substrate [1]. Most of the electric field lines reside in the substrate and parts of some line exist in
air. As W/h >> 1 and εr >> 1, the electric field lines concentrate to the substrate. Fringing in this
case makes the microstrip line look wider electrically compared to its physical dimensions [1].
The resonant length can be calculated using:



                                                                √

L is resonant lenght,    is the wavelength in printed circuit board,          is wavelenght in free space
and εr is the dielectric constant. The effective dielectric constant can be calculated by the
formula:


                                                      *          +                                  (22)

Some of the electric field rests inside the substrate while some extends outwards due to fringing.
Because of the fringing field between the edge of the patch and the ground plane, the patch
radiates. To make antennas efficient, thick dielectric substrates with low dielectric constant are
suitable. This gives larger bandwidth efficiency and desirable radiation. Due to large bandwidth,
the size of the antenna will be very large, which is not wanted. To get rid of this problem, a thin
dielectric substrate with high     reduces the bandwidth but a trade-off has to be made.



                                                    17
2.6.3 Feed Models
There are many configurations that can be used to feed microstrip antennas. The four most
popular feed models are microstrip line, coaxial probe, aperture coupling and proximity coupling
[1].

2.6.4 Microstrip Line Feed
The microstrip feed line is also a conducting strip, usually of much smaller width compared to
the patch. The microstrip feed line is easy to fabricate, simple to match by controlling the inset
position and rather simple to model [1]. However, as the substrate thickness increases, surface
waves and spurious feed radiation increases which for practical designs limit the bandwidth [1].




                            Figure 8: Microstrip feed line designed in ADS.



2.6.5 Coaxial Probe Feed
The inner conductor of the coax is attached to the radiation patch and the outer conductor is
connected to the ground plane [1]. The coaxial probe feed is also easy to fabricate and match,
and has low spurious radiation. However, it also has narrow bandwidth and it is more difficult to
model, especially for thick substrates [1].




                                                  18
                                    Figure 9: Coaxial probe feed.




2.6.6 Aperture- coupled Feed

The most difficult technique to fabricate is the aperture coupled feed. Having a narrow
bandwidth, it is however somewhat easier to model and has moderate spurious radiation [1]. The
aperture coupling consists of two substrates separated by a ground plane. On the bottom side of
the lower substrate there is a microstrip feed line whose energy is coupled to the patch through a
slot in the ground plane separating the two substrates. This arrangement allows independent
optimization of the feed mechanism and the radiating element. Typically a high dielectric
material is used for the bottom substrate, and a thick low dielectric constant material is used for
the top substrate [1].




                                                 19
                                  Figure 10: Aperture-coupled feed.



The main disadvantage of such a design is that it requires complex multiple layers.



2.6.7 Proximity-coupled Feed

Proximity-coupled Feed is sometimes called an electromagnetic coupling scheme. It consists of
two layers on top of each other. There is no ground plane in such an antenna. The microstrip feed
line is in between the two substrates and the radiation patch is on the top of the substrate as show
in Fig. 11. Of the four feeding models, the proximity coupling has the largest bandwidth and it is
fairly easy to model, having low spurious radiation [1]. However, its fabrication is more difficult.
The length of the feeding stub and the width- to-line ratio of the patch can be used to control the
match [1].




                                  Figure 11: Proximity-coupled feed.


                                                 20
2.6.8 Arrays and Feed Networks

Arrays are very versatile and are used, among other things, to synthesize a required pattern that
cannot be achieved with a single element. In addition, they are used to scan the beam of an
antenna system, increase directivity, and perform various other functions which would be
difficult with any one single element [1]. The elements can be fed by a single line called the
series-feed network or by multiple lines called corporate-feed network [1]. Among all the
feeding techniques, corporate feed is mostly used in scanning, phased multiple beam or shaped-
beam arrays. With this method, the designer has more control of the feed of each element
(amplitude and phase) and it is ideal for scanning phased arrays, multiple beam arrays, or
shaped-beam arrays [1]. While designing an array, the feed point and the distance between each
patch is kept constant in order to provide equal phase patch excitation. A series feed network is
easy to fabricate and implement as compared to corporate feed network. The disadvantage of
using series feed is that it gives phase delay and hence it is not preferred for the phase scanning
arrays [9]. These phase shifts are frequency dependant due to which beam scanning is dependent
on the frequency [9]. Corporate feed networks provide flexible phase control of each array
element. It is suitable for phase scanning as it is less affected by the frequency scan [9]. The most
common form of corporate feed network is the Wilkinson Power divider rule.




                       (a) Series Feed.                                 (b) Corporate Feed.



                                          Figure 12: Types of feed.




                                                     21
2.7 Photonic crystals in microstrip antenna substrates

During the past decade, a new technology has emerged which has become the key to developing
ultra-wideband microstrip antennas. This technology manipulates the substrate in such a way that
the surface waves are completely forbidden from forming, hence resulting in improvements in
the antenna efficiency and bandwidth, while reducing the side lobes and electromagnetic
interference levels. These substrates contain so called photonic crystals [10].

The patch antennas on high ԑ substrates are not efficient radiators due to losses. The patch
antenna having a narrow frequency bandwidth results in reduced gain and efficiency at high
frequencies. Patch antennas also have an unacceptably high level of cross polarization and
mutual coupling within the array environment. Therefore, much effort has been made recently to
realize high efficiency patch antennas on high permittivity substrates at high frequencies [11].

A PGB crystal is a periodic structure that forbids the propagation of electromagnetic waves
within a particular frequency band, called the band gap, thus permitting controls of the behavior
of the electromagnetic waves other than the conventional guiding and filtering structures [10].

The photonic crystals are a class of periodic metallic, dielectric or composite structures that
exhibit a forbidden band (band gap) of frequencies in which waves, incident at various directions
interfere destructively and thus are unable to propagate [12]. Based on the spatial periodicity of
the crystal structure, the band gaps can be in one, two or three-dimensional planes, with a level
of complexity that increases with the number of dimensions. The three-dimensional nature of
the band gap rejects incident energy from all directions around a unite sphere like a high
efficiency reflector or mirror. In a 2-D photonic crystal fiber the band gap exists only within a
plane, thereby allowing propagation along one axis only. This is the ideal scenario for microstrip
antenna design, since the rejection plane could be in the plane of the patch and thus prevent
surface wave formation [12].




                                                 22
3. ADS Momentum Overview
3.1 Introductions to ADS Momentum

Momentum is a part of Advance Design System and it provides the simulation tools required to
evaluate and design products of modern communication systems. Momentum is an
electromagnetic solver in the form of a simulator that computes the S-parameters for general
planar circuits which includes microstrip, slotline, stripline, coplanar waveguides and many other
topologies. Multilayer communication circuits and printed circuit boards can also be simulated in
ADS Momentum with accurate results. Momentum is a complete tool for prediction of the
performance of high frequency circuit boards, antennas and integrated circuits [13].

The ADS Momentum optimization tool extends Momentum capability to a real design
automation tool. The Momentum Optimization process varies geometry parameters
automatically to help in achieving the optimal structure that for the circuit or device performance
goals. Momentum optimizations can be done by using layout components (parameterized) from
the schematic page.

One of the great advantages that Momentum possesses is the 3-dimensional interface that it
provides for the user during simulations and results. Momentum is a 2.5D solver that can do both
2D and 3D computations. For example while computing the antenna parameters, Momentum
provides both 2D and 3D graphs of the directivity and the far-field radiation patterns of the
antenna.


3.2 Applications of Momentum

ADS Momentum can be used as follows [13].

      ADS Momentum is applicable when no analytical model exists for the circuit.
       Momentum co-simulates with ADS and performs the required tasks.
      ADS Momentum can be used to determine coupling effects.
      ADS Momentum can calculate narrow resonances within the circuit model which cannot
       be found with analytical models.



                                                23
     ADS Momentum can be used to display the radiation patterns and far field radiation plots
      for antennas etc.
     ADS Momentum can show the current pattern and current densities within the circuit.
     Momentum can be used for the CPW (Co Planar Waveguides) results with no slot mode.
     Momentum can be used to optimize or modify the geometry of the passive layouts to
      achieve the desired results.


3.3 Method of Calculation

  The method of simulation that is used by ADS Momentum is called the Method of Moments
  which is based on the integral formulation of Maxwell’s equations, simulating the circuit
  with matrix equations. Fig. 13 shows the stepwise simulation of a circuit by ADS
  Momentum. Where a known circuit is first simulated and then divided into mesh strip, wires
  with rectangles and triangles (arbitrary surface meshes). The next step is to model the surface
  current in each current cell i.e. linear distribution. The final step is to solve a mesh matrix
  equation and calculate S-parameters.




                          Figure 13: Stepwise simulation of ADS Momentum.




                                                24
3.4 Working with ADS Momentum

A short literature on how one should start using ADS Momentum is given below. As with every
simulator, working with the ADS Momentum is a stepwise process. Some of the steps are given
below.

Step 1:

Step 1 shows the startup of the ADS Momentum. Momentum starts in the ADS layout window
as shown in Fig. 14.




                            Figure 14: Layout window of ADS Momentum.

A number of options can be seen on the task and menu bar. We can use different kinds of
microwave components depending on our requirement. Fig. 14 shows the mapping of microstrip
patches of varying lengths in the ADS layout window. Ports are connected on both sides of the
circuit, making it a two port network for the S-parameter calculation.




                                                25
Step 2:

The Microstrip patch antennas cannot be designed without a substrate. In order to define a
particular substrate we can create our own substrate or we can use the built in substrates defined
in ADS momentum.




                         Figure 15: Different parameters in ADS Momentum.

Fig. 15 shows the different parameters which need to be set before simulating any design in the
ADS Momentum layout. After substrate definition, we will use ports calibration. Port is
necessary in the optimization of any design because it serves as an input to the system. The next
parameter in the list is Mesh setting. We can change the mesh frequency in order to synchronize
it with the input resonant frequency. Design cannot work if the mesh frequency is not
synchronized with the input resonant frequency.

Step 3:

The final step is to calculate the S-parameters. Depending on the number of ports used in the
network, ADS Momentum will provide the related S-parameters. Fig. 16 shows an example of
output curves of S-parameters calculated by ADS Momentum.




                                               26
                               Figure 16: Output S-parameter curves.




3.5 Theory of Operation for Momentum
Momentum is based on a numerical discretization technique called the Method of Moments. This
technique is used to solve the Maxwell equations for planar structures embedded in multilayer
dielectric substrates. Momentum uses two different modes of simulation which are based on the
Method of Moments. The first one is the microwave, or full wave, mode of simulation and the
second one is the RF, or quasi-static, mode of simulation. The application and formulation of the
Green’s function is the main difference between these two methods.

Momentum, or the full wave simulation mode, uses the full wave Green’s function. The Full
wave Green’s function is frequency dependant and it fully characterizes the substrate without
making any further approximations. This formulation results in the L and C elements that are
complex and frequency dependant as shown in Fig. 13. The RF, or quasi-static, mode uses a


                                                27
frequency independent Green’s function which results in L and C elements which are complex
but frequency independent. As this mode is not frequency dependant, the quasi-static mode only
approximates the solution of the network (L and C) for the first frequency simulation point and
hence the RF mode runs much faster than the Momentum mode. The simulations also show that
the quasi-static mode should be used for structures that are smaller than half a wavelength [13].

Both the engine modes use the star-loop basis function that ensures a stable solution at all
frequencies. Both the modes use the mesh reduction algorithm which helps in reducing the
number of unknowns when dividing the design into polygonal meshes. This function can be
turned on or off [13].

Excitation of the networks is fed through the input port. The currents in the equivalent network
model are given by unknown amplitudes in the rooftop expansion model. The amplitudes are
obtained by solving for the unknowns in the rooftop expansion. The S-parameters are extracted
with the help of the port calibration process.




3.6 Method of Moment Technology

The method of moments (MoM) was first applied by R.F. Harrington who worked extensively on
the method and successfully applied it to electromagnetic field problems. It is based on the
theory of weighted residuals and variational calculus. In the MoM, Maxwell’s equations are
transformed into integral equations before discretization.

Momentum uses the mixed potential integral equation (MPIE) formulation [14]. This method
expresses the electric and magnetic fields with a combination of the scalar and the vector
potential. The electric and magnetic surface currents in the design network are the unknowns in
the planar circuit. From electromagnetics one has the integral equation,




                               ∬       ⃡( ⃗ ⃗ )⃗⃗( ⃗ )   ⃗⃗⃗⃗⃗( ⃗)                         (23)




                                                 28
Here, ⃗( ⃗) represents the unknown surface current and ⃗⃗ ( ⃗) represents the known excitation of
the problem. The Green’s dyadic of the layered medium acts as an integral kernel. The unknown
surface currents are discretized by meshing the planar metallization pattern and applying an
expansion in a finite number of sub-sectional basis functions B1( ⃗)…., BN( ⃗) [14]:




                                ⃗( ⃗) = ∑      ⃗⃗ ( ⃗)                                          (24)




The rooftop functions are used in planar EM simulators. These standard basis functions are
defined over rectangular, triangular and polygonal cells in the mesh. Each rooftop is associated
with one edge of the mesh and represents current with continuous density as shown in Fig. 17. Ij,
determine the current elements that corresponds to the edges of the mesh [14].




              Figure 17: Discretization of the surface current using rooftop basis functions.




Eq. 23 is discretized by inserting the rooftop expansion of Eq. 24. We can write:




                                                    29
                                      =∑          j(r)      or ZI = V                                (25)


                                        ∬        ⃗⃗ ( ⃗) ∬              ⃡ ( ⃗ ⃗ ) ⃗⃗ ( )              (26)


                                         ∬       ⃗⃗⃗⃗( ⃗)     ⃗⃗ ( ⃗)                                   (27)




The matrix Z is known as the interaction matrix since the elements in this matrix describe the
electromagnetic interaction between the rooftop basis functions. The vector V represents the
discretized contribution of the excitation applied at the ports of the circuit [14].

The final values of L and C in the network can be written as:

                                        ∬       ⃗⃗⃗⃗( ⃗) ∬              ⃡⃗⃗⃗⃗⃗( ⃗ ⃗ ) ⃗⃗ ( ⃗ )

(28)

                                        ∬           ⃗⃗⃗⃗( ⃗) ∬            ⃡⃗⃗⃗⃗( ⃗ ⃗ )   ⃗⃗⃗⃗(⃗⃗⃗)     (29)


Eq. (28) and Eq. (29) gives a physical interpretation to the interaction matrix, as shown in Fig.
18.




                         Figure 18: Mesh representation in the form of L and C.




The whole discussion is explained diagrammatically in Fig. 17.




                                                  30
3.7 Simulation Techniques Used in ADS
In addition to the “auto-select mode”, ADS uses three different matrix solution techniques which
are explained as following.

   1. Direct Dense.
   2. Iterative Dense.
   3. Direct Compressed.




3.7.1 Direct Dense Method

In this method, the matrix N is stored in a dense matrix format which requires memory space of
order N2. This matrix is then solved by the direct matrix factorization technique. This method
requires N3 order for solution (computer time). The direct dense matrix solver has a
predetermined number of operations. The main disadvantage of this method is that it requires
cubic computer time to solve dense matrices of the order N. Hence it requires larger time for
complex problems [13].


3.7.2 Iterative Dense Method

In this method, the matrix N is stored in a dense matrix format which requires N2 memory space
while the matrix N is solved using iterative matrix solver technology. This solution method
requires N2 order to solve the matrix, hence scaling the computer time to quadratic (N2) from
cubic (in the direct dense method). This yields shorter simulation time for larger problem sizes
[13].

Convergence of the iterative technique is the main drawback of this method of simulation
because iterative methods do not converge quickly in large and complex problems. ADS
monitors the convergence rate and automatically jumps to the direct dense method of simulation
when it detects stagnancy in the convergence [13].


3.7.3 Direct Compressed Method

Direct compressed method (DCM) is one of the latest techniques used for matrix solution. DCM
is also known as the FMM (Fast Multipole method) and is considered to be one of the top ten

                                               31
algorithms of the 20th century. In this method, the matrix is stored in a compressed matrix form
which requires NlogN memory space while it is solved using direct compressed matrix
factorization technique. The direct compressed factorization technique requires (NlogN)1.5
computer time [20].

The computer time that this method requires is linear logarithmic with matrix size N which
makes this method most useful for the solution of large and complex problems. This method
reduces both the simulation speed and the memory allocation space required for the simulation
[13].

All these three type of methods are available in ADS. Generally the default settings of the ADS
are set to auto-mode but user can change the type of simulation manually. ADS is sensitive to the
type of problem and chooses proper simulation method according to the problem, so the
preferable way to use ADS is to keep the settings on auto-mode.


3.8 Block Diagram of ADS Momentum Simulation

The Block diagram in Fig. 20 shows how ADS Momentum simulates its designs and provides
the outputs.




                       Figure 19: Block diagram of ADS Momentum simulation.




                                               32
4. Design and Analysis
Before going into the details of the project, it is useful to perform a simple test with the ADS
Momentum to validate the simulations of ADS Momentum with known results. For this purpose,
an example from the book of “Antenna Theory” [1] was simulated in ADS momentum. All the
results were calculated mathematically and then fed to the ADS Momentum design guide to get
the visuals of the far field and other graphical results.


4.1 Design of a Rectangular Patch Antenna

A rectangular patch with TMX010 mode is designed in ADS Momentum. The length of the patch
is 0.906 cm, the width of the patch is 1.186 cm and the height of the patch is 0.1588 cm.
Permittivity of the substrate is 2.2 and the resonance frequency is 10 GHz. RT Durroid 5880 is
used as a substrate with a substrate height of 0.787 µm. The rectangular patch was energized
using coaxial probe feed. The mathematical solution is available in [1].

This patch was designed in ADS Momentum. After design, the patch was simulated in ADS
Momentum to get the directivity, the gain curves along with the 3D visuals of the far field
radiation and the 3D view of the designed antenna patch. Fig. 20 shows the design of the single
rectangular patch in ADS Momentum environment.




                    Figure 20: Rectangular patch designed in ADS Momentum layout.




                                                  33
Fig. 21 and Fig. 22 show the shows the simulation results of the rectangular patch in ADS
Momentum. Fig. 21 shows the behavior of the S11 parameter or the input reflection coefficient
over a range of frequencies. It is clear from the figure that the patch resonates at 10 GHz and has
minimum loss at the resonant frequency i.e. -3 dB.


                             m1
                             freq=10.35GHz
                             dB(example_14_1_mom_a..S(1,1))=-3.077
                             Min
                                                 S11
                                         0


                                         -1
                             Mag. [dB]




                                         -2

                                                                       m1
                                         -3


                                         -4
                                              0   2   4   6        8   10   12   14   16
                                                          Frequency




                                          Figure 21: Magnitude of S11 in dB.



Fig. 22 shows the same input reflection coefficient (S11) result in the Smith chart. We can see
from the Smith chart that the impedance of the system is also resistive at the input. The marker
shows the impedance of the system at the resonant frequency.




                                                              34
                            Figure 22: S11-parameter shown in Smith chart




4.2 Gain and Directivity

One of the main features of the ADS Momentum is that it can give us both the 2D and 3D graphs
of the gain and directivity of the system. Fig. 23 shows the gain and directivity of the rectangular
patch simulated in ADS Momentum. The lower graph line, the Gain of the system is
approximately -20 dB while the upper line, the directivity of the system, is approximately 10 dB.




                                                 35
                                   Power
                                           Gain                              Directivity
                                    20


                                     0


                      Mag. [dB]    -20


                                   -40


                                   -60
                                         -100

                                                -80

                                                      -60

                                                            -40

                                                                  -20

                                                                         0

                                                                             20

                                                                                  40

                                                                                           60

                                                                                                80

                                                                                                     100
                                                                        THETA




                                  Figure 23: Gain and Directivity of the rectangular patch.

Similarly ADS Momentum simulates the three dimensional view of the directivity, or the far
field radiation pattern, of the rectangular patch microstrip antenna as shown in Fig. 24. It can be
seen that the far field radiation is not broad side but almost isotropic. As it is a single patch
antenna, it does not possess great directivity.




                                         Figure 24: 3D graph of the far field radiation.




                                                                   36
4.3 Design of the Circular Patch

The design of the circular patch requires some constraints. Following are some design
parameters which should be calculated while designing the circular patch.

4.3.1 Resonant Frequency
The resonant frequency of the circular patch can be analyzed with the cavity model. The cavity
model consists of the electrical conductors above and below the cavity while a perfect magnetic
conductor having cylindrical shape and radius a in between the two electrical conductors
represents the value of the cavity [1, 9, 15].

The resonant frequency for TMzmn0 mode is:


                       (fr)mn0 =
                                     (   )
                                                 (    )                                     (30)


     in Eq. (30) is the nth zero of the Bessel function Jm(X) which determines the resonant
frequency that is different for different modes of operation. Following are values of the      [1].

                                                     = 1.1841

                                                     = 3.0542

                                                     = 3.8318

                                                     = 4.2012

With the values of the zeros of the Bessel function in Eq. (30) we can show,


                         (fr)mn0 =                                                           (31)
                                             √

For the mode that is used in the design one has,


                         (fr)110 =                                                           (32)
                                         √

Eq. (32) gives the resonant frequency for the circular patch in the cavity model. Here ae is the
radius of the patch while c is the velocity of light in vacuum.


                                                      37
4.3.2 Radius of the Patch
In designing a rectangular patch, we account for the length and width of the patch. Changing
these two parameters will change the mode of operation of the rectangular patch. In the circular
patch, we have only one degree of freedom and that is the radius of the patch. To calculate the
radius of the patch we have to include fringing in the circular patch. Fringing is the effect which
makes the patch electrically larger than geometrical patch. Due to this phenomenon, the effective
radius ae is introduced. Eq. 33 shows the expression for effective radius for the circular patch [1,
2, 15].




                         ae = a√,             * ( )                +-                        (33)

Here the original radius a is given by


               a=                                                                            (34)
                    √,         * (   )            +-



                F=                                                                            (35)
                         √

4.3.3 Feed Point Location
In the design and excitation of the circular patch, the feed point location is one of the most
important parameters [15]. The impedance of the circular patch antenna is almost zero at the
center of the patch while it is about 200-300 ohms at the edges of the patch. Impedance matching
can only be obtained by locating the feed point so that the overall system impedance equals 50
ohms. According to Karmakar [9], the mathematical expression for the feed point location for the
TM110 is given below:

                                            = a/3                                            (36)


 Eq. (36) is the location of the feed point.


                                                       38
4.4 Proposed Design of a Single Circular Patch Antenna

To design a circular patch antenna in ADS Momentum, we need to know all the parameter
values [15, 16, 17]. All the needed design parameters were calculated using the known equations.
RT DURROID 5880 was used as a substrate with relative permittivity ԑ equal to 2.2. The height
of the substrate H is equal to 0.787µm. The loss tangent for this substrate is equal to 0.0009.

The radius of the circular patch calculated using Eq. 33 was equal to 5.83 mm. The feed point
distance from the center of the circle is equal to 1.83 mm. We used coaxial probe feed to excite
the circular patch antenna with the input impedance equal to 50 ohms. Fig. 25 shows the design
of this circular patch in ADS Momentum.




                 Figure 25: Design of single circular patch antenna in ADS Momentum.



After designing the circular patch in the ADS Momentum environment, the patch was simulated
to check the performance of the patch. Figures (26a) and (26b) shows the three dimensional
design of the circular patch antenna before and after excitation, respectively.




                                                 39
(a): Circular Patch before excitation                       (b) Circular patch after excitation



                     Figure 26: Excitation of circular patch antenna in ADS Momentum.




4.4.1 Gain and Directivity:
Fig. 27 shows the gain and directivity curves of the single circular patch antenna simulated by
ADS momentum.




            Figure 27: Gain and Directivity of single circular patch antenna in ADS Momentum.

The lower curve in Fig. 27 represents gain while the upper curve represents the directivity of the
patch. As visible from the figure, the gain of the single circular patch antenna is 5 dB
approximately while the directivity of the patch is approximately 8 dB.


                                                   40
ADS Momentum can also simulate the three-dimensional graph of the single circular patch
antenna along with two dimensional graphs as shown in Fig. 27. Fig. 28 shows the 3D graph of
the far field radiation of the antenna.




       Figure 28: 3D view of the directivity of the single circular patch simulated in ADS Momentum.

From Fig. 28, it is clearly visible that the single circular patch antenna has the main beam in the
90º to 270º range i.e. Perpendicular to the axis of the patch. The single circular patch antenna is
not an efficient antenna so the main lobe is wide.

4.4.2 S11 Parameters:
ADS Momentum simulations help us in gathering information about the reflection coefficients of
the antenna. We are using only one probe, so all the coefficients of the S-matrix will be zero
accept the S11 parameter which is the input reflection coefficient [1]. We can easily understand
the performance of the circular patch antenna from the S11 Parameter graph. Fig. 29 shows the
graph of S11 parameter simulated by ADS Momentum.




                                                    41
                Figure 29: Magnitude vs Frequency graph of input reflection coefficient.



Fig. 29 clearly indicates that the single circular patch antenna resonates at 9.875 GHz having a
minimum magnitude of approximately -5 dB.

ADS Momentum also simulates the graph for the input reflection coefficient on the smith chart
as shown in Fig. 30. The single circular patch antenna resonates at 10 GHz with minimum
impedance at that particular point which is also indicated by the m2 marker on the Smith chart.




              Figure 30: S11-parameter of a single circular patch antenna on a Smith chart.


                                                   42
4.4.3 Efficiency
       Fig. 31 shows the efficiency of the single circular patch antenna simulated by ADS.




           Figure 31: Efficiency of single circular patch antenna simulated by ADS Momentum.




4.5 Proposed Design for the Circular Patch Array Antenna

Fig. 32 shows our final project design. The array consists of two circular patches excited with
coaxial probe feed, designed and simulated in ADS Momentum.




              Figure 32: Circular patch phase array antenna designed in ADS Momentum.




                                                  43
Each of the circular patches has the radius of 5.83 mm. The separation between the two circular
patches is 12 mm from center to center. The impedance of the circular patch is 200-300 ohms at
the edge of the patch while this impedance decreases to zero towards the center of the patch. The
two circular patches are excited with a coaxial probe feed through the corporate feed method i.e.
The Wilkinson power divider rule. The patches are connected to the coaxial probe via two
transmission lines. These two transmission lines are terminated by a quarter wave transmission
line.

In order to make the circular patch array antenna radiate, the impedance of the system should be
matched and it should not exceed 50 ohms [13, 15]. For this purpose the length and width of the
transmission lines were calculated with the software called Line Calc, which is available in ADS.
For a 200 ohms transmission line, the length is equal to 11.72 mm and the width is equal to
0.06096 mm. Both these transmission lines are terminated on the 100 ohms termination point on
the quarter wave transmission line. The length of the quarter wave transmission line is equal to
5.428 mm and the width of the quarter wave transmission line is equal to 2.419 mm. The 50
ohms coaxial probe is connected to the other termination point of the quarter wave transmission
line. With these arrangements, the impedance of the system is matched to approximately 50
ohms.

RT-Durroid 5880 is used as the substrate for the circular patch microstrip phase array antenna.
This substrate is used worldwide for the design of the microstrip phase array antenna. The
thickness of the substrate is very important in the design of the microstrip antenna because the
beamwidth changes with the thickness of the substrate [16, 18, 19]. For a 10 GHz resonating
frequency, the thickness of the substrate is 0.787 mm while the thickness of the circular patches
is 17.8 µm. The thickness of the patch should not exceed the thickness of the substrate.

The microstrip phase array antenna was simulated after design in ADS Momentum. Following
were the different simulation results of the proposed design.




                                                44
The 3D view of the design simulated by the ADS Momentum is shown in Fig. 33.




                  Figure 33: 3D view of circular patch microstrip phase array antenna.



4.5.1 Directivity and Gain
ADS Momentum provides both the 2D and 3D graphs of the gain and directivity of the
microstrip phase array antenna. The 2D graphs are shown in Fig. 34.




         Figure 34: Gain and Directivity graphs of circular patch microstrip phase array antenna.



From Fig. 34, it is clear that the magnitude of the gain and directivity of the system is
approximately 5 dB. Maximum results are obtained from 60º to 120º.

The 3D graph of the radiation pattern of the designed antenna is shown in Fig. 35.




                                                   45
               Figure 35: 3D Directivity of circular patch microstrip phase array antenna.



Fig. 35 shows an accurate three dimensional graph of the radiation pattern of the microstrip
phase array antenna. The antenna is radiating broadside i.e. Perpendicular to the axis of the
patch. The main beam is sharp in between 90º and 270º. This graph shows that the design is
working well and that it has achieved the desired results.

A more advanced 3D curve is obtained from the ADS Momentum using a feature called the
Electro Magnetic Design Solver showing a different presentation method of the 3D curves. The
Graph obtained by EMDS is shown in Fig. 36.




                                                   46
                          Figure 36: 3D radiation pattern shown by EMDS.

EMDS in Fig. 36 shows main lobes on 90 º and 270 º with nulls at 0 º and 180 º.

4.5.2 S11 Parameters
As we have used only one probe feed in our design, we will find only the input reflection
coefficients or the S11 parameters of the micro strip phase array antenna. The simulation results
of the ADS Momentum are shown in Fig. 37.




                     Figure 37: Magnitude vs Frequency graph of S11 parameter.




                                                47
                        Figure 38: Phase vs Frequency graphs of S11 parameter.




                         Figure 39: S11 parameter plotted on the Smith chart.

Figures 37, 38, and 39 give us clear information about the performance of our design. In Fig. 37
we can see that the designed antenna resonates at the desired frequency which is 10 GHz. At the
resonant frequency the input reflection coefficient has the minimum magnitude which is about
-16 dB.

In Fig. 39, the input reflection coefficient is shown on the Smith chart where the marker clearly
indicates that the microstrip phase array antenna resonates at 10 GHz having the minimum
impedance over the straight resistance line at the resonating frequency. The graphs in the three
figures verify the performance of the designed antenna to a great extent.


                                                 48
The efficiency of this antenna is shown in the Fig. 40. The efficiency of array antenna is far
better than the efficiency of single circular patch antenna. The efficiency of the array antenna is
90% while the efficiency of single circular patch antenna was 60%.




               Figure 40: Efficiency of the circular patch microstrip phase array antenna.




The power radiated by the designed antenna is shown in Fig. 41.




             Figure 41: Radiated power of the circular patch microstrip phase array antenna.




                                                   49
5. Conclusion
5.1 Conclusion Summary

All the simulation results show that the microstrip phase array antenna performs better then the
single circular patch or the single rectangular patch antenna. The radiation pattern of the
microstrip array antenna is far better than the single circular or the single rectangular patch. The
main beam is in the broadside direction between 90º and 270º with nulls at 0º and 180º. Similarly
the efficiency, directivity and gain of the array patch antenna is better than the single patch. All
these simulations lead to the conclusion that the number of patches in an array is directly
proportional to the efficiency, directivity and gain of the antenna. If we increase the number of
elements in the array, the radiation pattern will improve further.

Another important conclusion that was deduced from all the experiments that were made during
the design of this antenna was that impedance matching is very important. Effic ient results were
only obtained when the impedance of the system was perfectly matched to 50 Ω.

5.2 Future work
Antenna technology is a vast field. Every day new research is published. A few design
parameters were taken into consideration while designing this antenna. Further improvements
can be made in the following areas.

      The gain, directivity, radiation pattern and efficiency can be improved by using 2n array
       elements in the microstrip phase array antenna. We have used only two circular patches.
      The beam of the circular patch phase array antenna can be steered using phase shifters in
       the design.
      Recent research involves the use of photonic band gap crystals in the substrate to improve
       the band width of the antenna.
      Instead of the ADS Momentum, the HFSS simulator can be used for design and
       simulation.




                                                50
References
 [1] C. A. Balanis, Antenna Theory, 3rd edition, John Wiley, New York, 2005.
 [2] N. J. Kolias, R. C. Compton, J. P. Fitch and D. M. Pozar, Antenna, CRC Press, 2000.
 [3] M. K. A. Rahim, A. Asrokin, M. H. Jamaluddin, M. R. Ahmad, T. Masril and M. Z. A.
    Abdul Aziz, “Microstrip Patch Antenna Array at 5.8 GHz for Point to Point
    Communication,” International RF and Microwave Conference Proceedings, pp. 216-219,
    Malaysia, September 2006.
 [4] J. J. Carr, Practical Antenna Handbook, fourth edition, McGraw-Hill, New York, 2001.
 [5] S. N. Makarov, Antenna and EM Modeling with MATLAB, John Wiley, New York, 2002.
 [6] R. Iwata and S. Chen, “Mutual Coupling Effects in Microstrip Patch Phased Array
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 [7] L. Allen and L. Diamond, “A Simple Model for Mutual Coupling Effects on Patterns of
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 [8] N. Misran and M. T. Islam, “Broadband E-H Shaped Microstrip Patch Antenna for
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 [9] N. C. Karmakar, “Investigations into a Cavity-Backed Circular Patch Antenna,” IEEE AP-
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 [10] Y. Qian, R. Cocciolo, D. Sievebpiper, V. Radisic, E. Yablonovitch, “A microstrip patch
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 [11] G.P. Gauthier, A. Courtay and G.M. Rebeiz, “Microstrip Antennas on Synthesized Low
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 [12] Agi and Malloy, “Integration of a Microstrip Patch Antenna with a Two-Dimensional
    Photonic Crystal Substrate,” Electromagnetics, Vol. 19, 1999
 [13] ADS built in manuals and online help.
 [14] R. F. Harrington, Field computation by Moment Methods, Maxillan, New York, 1968.
 [15] T. F. Lai, W. N. Mahadi and N. Soin, “Circular Patch Microstrip Array Antenna for KU-
    band,” World Academy of Science, Engineering and Technology. Vol. 48, pp. 298-302,
    2008.


                                              51
[16] S. L. Mallikarjun, R. G. Madhuri, S. A. Malipatil and P. M. Hdalgi, “Development of
   microstrip array antenna for wide band and multiband applications,” Indian Journal of
   Radio and Space Physics, Vol. 38, pp. 289-294, October 2009.
[17] A. Keshtkar, Ah. Keshtkar and A.R. Dastkhosh, “Circular Microstrip Patch Array
   Antenna for C-Band Altimeter System,” International Journal of Antennas and
   Propagation, Hindawi Publishing Corporation, Vol. 2008, pp. 01-07, 2008.
[18] H. Iizuka, K. Sakakibara, T. Wantanabe, K. Sato, “Millimeter-Wave Microstrip Array
   Antenna with High Efficiency for Automotive Radar System,” R&D Review of Toyota
   CRDL, Vol. 37, No. 2, pp. 7-12, April 23, 2002.
[19] M. Mahfuzul, M. R. Sonchoy and M. Osman Goni, “Design and Performance Analysis of
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   Proceedings, pp. 1837-1842, Moscow, August 21, 2009.
[20] R. Caifman, V. Rokhlin and S. Wandzura, “The Fast Multipole Method for the Wave
   Equation: A Pedestrian Prescription,” IEEE AP-35, pp 1-12, June 1993.




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