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    CHAPTER 1: INTRODUCTION

    1.1 INTRODUCTION OF ANTENNAAntennas are a very important component of communication systems. By definition,

    an antenna is a device used to transform an RF signal, travelling on a conductor, into an

    electromagnetic wave in free space. Antennas demonstrate a property known as reciprocity,

    which means that an antenna will maintain the same characteristics regardless if it is

    transmitting or receiving. Most antennas are resonant devices, which operate efficiently over

    a relatively narrow frequency band. An antenna must be tuned to the same frequency band of

    the radio system to which it is connected; otherwise the reception and the transmission will

    be impaired. When a signal is fed into an antenna, the antenna will emit radiation distributed

    in space in a certain way. A graphical representation of the relative distribution of the

    radiated power in space is called a radiation pattern.

    A current flowing in a wire of a length related to the RF produces an electromagnetic

    field. This field radiates from the wire and is set free in space. The principles of radiation of

    electromagnetic energy are based on two laws.

    (i) A moving electric field creates a magnetic (H) field.

    (ii) A moving magnetic field creates an electric (E) field.

    1.2 CLASSIFICATION OF ANTENNASThere are many different types of antenna. Some of them are listed below.

    (i) Wire antenna(a)Short dipole antenna(b)Dipole antenna(c)Monopole antenna(d)Folded dipole antenna(e)Small loop antenna

    (ii) Microstrip antenna(a)

    Rectangular Microstrip (Patch) antenna

    (b)Planner inverted-F antenna

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    (iii) Reflector antenna(a)Corner reflector(b)Parabolic reflector (Dish antenna)

    (iv) Travelling antenna(a)Helical antenna(b)Yagi-Uda antenna

    (v) Aperture antenna(a)Slot antenna(b)Lens antenna(c)

    Cavity-backed slotted antenna

    (d)Slotted waveguide antenna(e)Horn antenna

    (i) INTRODUCTION TO WIRE ANTENNAA dipole antenna is a straight electrical conductor measuring wavelength from end

    to end and connected at the center to a radio-frequency (RF) feed line. This antenna, also

    called a doublet, is one of the simplest types of antenna, and constitutes the main RF radiating

    and receiving element in various sophisticated types of antennas. The dipole is inherently a

    balanced antenna, because it is bilaterally symmetrical.

    Ideally, a dipole antenna is fed with a balanced, parallel-wire RF transmission line.

    However, this type of line is not common. An unbalanced feed line, such as coaxial cable,

    can be used, but to ensure optimum RF current distribution on the antenna element and in the

    feed line, an RF transformer called a balun (contraction of the words "balanced" and

    "unbalanced") should be inserted in the system at the point where the feed line joins the

    antenna. For best performance, a dipole antenna should be more than wavelengths above

    the ground, the surface of a body of water, or other horizontal, conducting medium such as

    sheet metal roofing. The element should also be at least several wavelengths away from

    electrically conducting obstructions such as supporting towers, utility wires, guy wires, and

    other antennas. Dipole antennas can be oriented horizontally, vertically, or at a slant. The

    polarization of the electromagnetic field (EM) radiated by a dipole transmitting antenna

    corresponds to the orientation of the element. When the antenna is used to receive RF signals,

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    it is most sensitive to EM fields whose polarization is parallel to the orientation of the

    element. The RF current in a dipole is maximum at the center (the point where the feed line

    joins the element), and is minimum at the ends of the element. The RF voltage is maximum at

    the end and is minimum at the center.

    (ii) INTRODUCTION TO MICROSTRIP ANTENNAA patch antenna is a wafer-like directional antenna suitable for covering single-floor

    small offices, small stores and other indoor locations where access points cannot be placed

    centrally. Patch antennas produce hemispherical coverage, spreading away from the mount

    point at a width of 30 to 180 degrees.

    Patch antennas are also known as panel, flat panel or microstrip antennas. They are

    formed by overlaying two metallic plates, one larger than the other, with a dielectric sheet in

    the middle. This type of antenna is usually encased in white or black plastic, not only to

    protect the antenna, but also to make it easy to mount. Because they are flat, thin and

    lightweight, patch antennas are often hung on walls or ceilings where they remain visually

    unobtrusive and blend easily into the background.

    (iii) INTRODUCTION TO REFLECTOR ANTENNAA dish antenna, also known simply as a dish, is common in microwave systems. This

    type of antenna can be used for satellite communication and broadcast reception, space

    communications, radio astronomy, and radar.

    A dish antenna consists of an active, or driven, element and a passive parabolic or

    spherical reflector. The driven element can be a dipole antenna or a horn antenna. If a horn is

    used, it is aimed back at the center of the reflecting dish. The reflector has a diameter of at

    least several wavelengths. As the wavelength increases (and the frequency decreases), the

    minimum required dish diameter becomes larger. When the dipole or horn is properly

    positioned and aimed, incoming electromagnetic bounce off the reflector and the energy

    converges on the driven element. If the horn or dipole is connected to a transmitter, the

    element emits electromagnetic waves that bounce off the reflector and propagate outward in a

    narrow beam. A dish antenna is usually operated with an unbalanced feed line. For satellite

    television reception, coaxial cable is used. In applications such as radar where a high-powersignal is transmitted, a feed system is preferred.

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    (iv) INTRODUCTION TO TRAVELLING ANTENNAA helical antenna is a specialized antenna that emits and responds to electromagnetic

    fields with rotating (circular) polarization. These antennas are commonly used at earth-based

    stations in satellite communications systems. This type of antenna is designed for use with an

    unbalanced feed line such as coaxial. The center conductor of the cable is connected to the

    helical element, and the shield of the cable is connected to the reflector. To the casual

    observer, a helical antenna appears as one or more "springs" or helixes mounted against a flat

    reflecting screen. The length of the helical element is one wavelength or greater. If the helix

    or reflector is too small (the frequency is too low), the efficiency is severely degraded.

    Maximum radiation and response occur along the axis of the helix.

    Helical antennas are commonly connected together in so-called bays of two, four, or

    occasionally more elements with a common reflector. The entire assembly can be rotated in

    the horizontal (azimuth) and vertical (elevation) planes, so the system can be aimed toward a

    particular satellite. If the satellite is not in a geostationary orbit, the azimuth and elevation

    rotators can be operated by a computerized robot that is programmed to follow the course of

    the satellite across the sky.

    Yagi antenna, also known as a Yagi-Uda array or simply a Yagi, is a

    unidirectional antenna commonly used in communications when a frequency is above

    10 MHz this type of antenna is popular among Amateur Radio and Citizens Band radio

    operators. It is used at some surface installations in satellite communications systems. A basic

    Yagi consists of two or three straight elements, each measuring approximately 1/2

    electrical wavelengths. The antenna can be balanced or unbalanced. The Yagi is inherently a

    balanced antenna, but it can be fed with coaxial and a device called a balun at the point where

    the feed line joins the driven element.

    The driven element of a Yagi is the equivalent of a center-fed, half-wave dipole

    antenna. Parallel to the driven element, are straight rods or wires

    called reflectors and directors. A reflector is placed behind the driven element and a director

    is placed in front of the driven element. A typical Yagi has one reflector and one or more

    directors. The antenna propagates electromagnetic field energy in the direction running from

    the driven element toward the director(s), and is most sensitive to incoming electromagnetic

    field energy in this same direction.

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    (v) INTRODUCTION TO APERTURE ANTENNAAn aperture antenna contains some sort of opening through which electromagnetic

    waves are transmitted or received. Examples of aperture antennas include slots, waveguides,

    horns, reflectors and lenses. The analysis of aperture antennas is typically quite different than

    the analysis of wire antennas. Rather than using the antenna current distribution to determine

    the radiated fields, the fields within the aperture are used to determine the antenna radiation

    patterns. Aperture antennas are commonly used in aircraft or spacecraft applications. The

    aperture can be mounted flush with the surface of the vehicle, and the opening can be covered

    with a dielectric which allows electromagnetic energy to pass through.

    A horn antenna is used for the transmission and reception of microwave signals. Itderives its name from the characteristic flared appearance. The flared portion can be square,

    rectangular, or conical. The maximum radiation and response corresponds with the axis of the

    horn. In this respect, the antenna resembles an acoustic horn. It is usually fed with a

    waveguide.

    In order to function properly, a horn antenna must be a certain minimum size relative

    to the wavelength of the incoming or outgoing electromagnetic. Horn antennas are commonly

    used as the active element in a dish antenna. The horn is pointed toward the center of the dish

    reflector. The use of a horn, rather than a dipole antenna or any other type of antenna, at the

    focal point of the dish minimizes loss of energy (leakage) around the edges of the dish

    reflector. It also minimizes the response of the antenna to unwanted signals not in the favored

    direction of the dish. Horn antennas are used all by themselves in short-range radar systems,

    particularly those used by law-enforcement personnel to measure the speeds of approaching

    or retreating vehicles.

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    1.3 THESIS OUTLINEThe outline of this thesis is as follows.

    Chapter 2: This chapter serves to review the important developments in the design and

    modeling of different horn antennas since its origin. Developments in corrugation for satellite

    and radar antenna, and recent development over the Gaussian profiled horn antenna.

    Chapter 3: It presents the basic theory of waveguides, horn antenna and the corrugated horn

    antenna. Furthermore the concept of how to generate the hybrid mode by mixturing the TE 11

    and TM11 mode, and the design calculation equations for the mode converter (corrugated

    horn antenna)

    Chapter 4: This chapter describes the simulation software HFSS. Designing process of

    circular waveguide and the conical horn antenna using HFSS and results are presented in this

    chapter.

    Chapter 5: This chapter describes the simulation software HFSS. Designing process of

    conical corrugated horn antenna using HFSS and results are presented in this chapter.

    Chapter 6: This chapter is the conclusion of the project and also included the Future work

    for the Conical Corrugated Horn Antenna.

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    CHAPTER 2: LITERATURE REVIEW

    2.1 INTRODUCTION

    Waveguide is an excellent microwave transmission line, with low loss and predictable

    performance, usable at any frequency by choosing the proper dimensions. Circular corrugated

    horn antennas can be analyzed as the cascade of step-type discontinuities in waveguide.

    High-performance microwave communication, radar, remote-sensing and plasma heating

    systems often use an antenna horn as transmitter. This horn is a key component. It must

    match the microwave power from the source to the free space with minimum loss of energy

    and maximum efficiency. There are several designs for this horn, but for high performance-

    systems the best one is the corrugated horn. The corrugated wall presents the same boundary

    conditions to the electric and magnetic fields when it is capacitive (slots /4 to /2 deep).

    When excited in the transition between the smooth-wall waveguide and the corrugated-wall

    cone, the TE11 and TM11 waveguide modes, have equal phase velocities. The combination of

    these modes forms the hybrid mode HE11 when the mode phases are equal. When the modes

    are out of phase by 180, the hybrid mode is denoted EH11.

    Figure 2.1 Conical corrugated horn antenna

    There are three main reasons for the existence of corrugated horn antennas. Firstly,

    they exhibit radiation pattern symmetry, which offers the potential for producing reflector

    antennas with high gain and low spillover; secondly, they radiate with very low

    crosspolarisation, which is essential in dual polarisation systems and finally, they offer a wide

    bandwidth response. Now-a-days, in the age of the communications, horn antennas take a

    very important role in the development of the actual and future communications systems with

    high requirements in their radiations patterns. In fact, corrugated feeds are the best feeds ever

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    developed. A study on the principles of a pure mode horn will show why the corrugated horn

    is attractive for high-performance feeds. Pure mode horns are also known as single mode

    horns and with its characteristics in mind; a comprehensive comparison can be made between

    pure mode and corrugated horns.

    2.2 HISTORYIn the 1960s, the idea of corrugated horns was first considered by Kay

    [1], Simons and

    Kay[2]

    and Minnett and Thomas[3], [4]

    . This was due to the specific interest in achieving

    symmetric radiation patterns so that low-sidelobe and high efficiency reflector antennas could

    be produced. It was also realized in the 1970s by Parini, Clarricoats, and Olver[5]

    that

    corrugated horns radiate very low levels of crosspolarisation, which is essential for dual-

    polarisation operation or frequency re-use. This is the situation where two signal channels are

    transmitted on orthogonal polarisations at the same frequency, and no interaction takes place

    between the two channels. Therefore the channel capacity is doubled for a single antenna.

    2.3 RECENT TRENDSHowever, the use of corrugated horns was initially limited. The relatively high mass

    and volume were disadvantages that restricted applications. But the horns electrical

    advantages positively offset its mechanical disadvantages, and they were accepted and used

    as an ideal feed for a reflector in the 1980s. Different designs of the corrugated horn evolved

    and they are now a relatively mature antenna technology. Each system is different so the

    range of corrugated horn design keeps increasing.

    Ten to twenty years ago, corrugated horn antennas were restricted to be used in high

    performance applications, like being on board of satellites, earth station radio-telescopehorns, antenna measurement chambers and very few more applications. They were restricted

    to those applications for two main reasons: difficulties in the design and difficulties in the

    manufacture process of a corrugated feed. At present, the communication systems require

    really high performance antennas; sidelobe and crosspolar levels should be reduced in the

    radiation pattern as well as the size of the antenna. Low crosspolar levels are inherent to the

    corrugated horn antenna technology and this parameter has been conveniently improved

    during the last decades with the use of corrugated feeds. But sidelobe level of corrugated

    horns has got stuck and no improvements have been made till the last five years. Probably,

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    the improvement in sidelobe level has not been really necessary up to now. The incredible

    quantity of new communication systems that interact between them has made necessary to

    reduce the mutual interferences through sidelobes. In fact, the major benefits from the

    extremely low sidelobe interference characteristics are to reduce both operational costs and

    also the susceptibility to jamming or eavesdropping in military and secure applications. The

    manufacture process for corrugated feeds has been improved during the last years due to the

    massive use of numerical milling machines and the improvement made in computer

    technology to control those machines. Additionally, sometimes to implement mm-wave and

    submm-wave corrugated horns, expensive electroforming techniques are needed, especially

    where thin corrugations, small size and precision are required. Electroforming techniques

    have the disadvantage of the necessity to manufacture a mandrel for each antenna that will be

    destroyed afterwards becoming a very expensive manufacture method.

    Regarding to the global dimensions of corrugated horns, we can observe that its

    radiation aperture is almost determined for a given directivity; although a horn antenna can be

    shortened in its length. Shorter antenna profiles are really the preferred ones for practically all

    applications, satellites launching reduction of weight, lighter posts for base station antennas,

    and additionally they should be as well easier and cheaper to manufacture. Now-a-days,

    likely global market applications for corrugated feeds are: compact parabola feeds, covertsurveillance, secure communications, base station power saving, reduced interference.

    Guidelines for the design of rotationally symmetric circular waveguide mode

    converters are presented by Smain Amari and Jens Bornemann. The initial design shows very

    good performance which is further improved by using optimization techniques in connection

    with the coupled- integral-equations technique. The final design offers improved conversion

    efficiency and bandwidth and is verified by the CIET, MMT and HFSS.

    High quality corrugated feed horns at frequencies & 100 GHz are of great importance

    not only for industrial and telecommunications applications, but also for advanced

    fundamental scientific research (e.g. Letho, Tuovinen and Raisanen, 1990). Corrugated horns

    are used in fusion experiments as gaussian beam launchers and receivers for millimeter

    waves, both for plasma diagnostics and for low power testing of transmission lines in electron

    cyclotron heating experiments. Accurate observations of the Cosmic Microwave Background

    (CMB) require low-loss, low sidelobe antennas in the microwave to sub-millimeter range.

    Low sidelobe levels (

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    low return loss and insertion loss. Optimum designs for corrugated feed horns at high

    frequencies turn out to be critical for a reliable, accurate fabrication (e.g. Total et al., 1989).

    In optimized designs, the groove depth increases in the narrow throat section, where it should

    reach roughly /2 for optimal matching. 100 GHz the typical groove width is of the order of

    a fraction of a millimeter with depth more than 1 mm. Thus optimized feeds often cant be

    directly machined due to the lack of clearance for the cutting tool in the throat section. For

    best electrical performances, silver is the ideal material to be used due to its superior

    conductivity, although it may require passivation or coating. A first complete silver prototype

    has been produced at 120 150 GHz. Here we describe the feed design, the fabrication

    method and its measured performance.

    M. BERSANELLI have produced a prototype broadband, low-sidelobe conical

    corrugated feed horn suitable for measurements of the Cosmic Microwave Background

    (CMB) radiation in the frequency band 120150 GHz. The antenna is a first prototype for the

    Low Frequency Instrument array in ESAs PLANCK mission, a space project dedicated to

    CMB anisotropy measurements in the 30 900 GHz range. We describe the fabrication

    method, based on silver electro-formation, and present the two dimensional antenna beam

    pattern measured at 140 GHz with a millimeter-wave automated scalar test range. The beam

    has good symmetry in the E and H planes with a far sidelobe level approaching 60 dB atangles 80. An upper limit to the return loss was measured to be21 dB.

    Corrugated horns have been studied at large mainly for space applications. The work

    reported by Y. Bniguel, A. Berthon, K. Vant Klooster, L. Costes was intended to design a

    microwave source with less than 40 dB VSWR, less than 50 dB cross polarisation and

    low sidelobes over 20 % bandwidth. Additional constraints concern the beam width and the

    volume of the source. The results presented in this paper were obtained using the method of

    moment (MoM) technique based on the solution of integral equations, which is feasible

    because the symmetry of revolution allows reducing the problem to 1D integral equation.

    An evolutionary progranirnitzg (EP) algorithm is used by Vahraz Jamnejad, Ahmad

    Hoorfar, and Farzin Manshadi to optimize pattern of a corrugated circular horn subject to

    various constraints on return loss and antenna beam width and pattern circularity and low

    cross-polarization. The EP algorithm uses a Gaussian mutation operator. Examples on design

    synthesis of a 45 section corrugated horn, with a total of 90 optimization parameters, are

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    presented. The results show excellent and efficient optimization of the desired horn

    parameters

    The HE11 fundamental circular corrugated mode has been the ideal solution for a wide

    variety of applications where a high axial symmetry beam, low sidelobe levels and low

    crosspolar level were required. Nevertheless, a complex corrugated structure is needed, which

    transforms the fundamental smooth circular waveguide mode, TE11, to the fundamental

    circular corrugated waveguide HE11 mode. Usually, because nearly all of the implemented

    feeding systems are made in rectangular geometry, a rectangular to circular mode converter

    must be used. Thus, starting from a rectangular geometry if a mode with the same radiation

    characteristics as the circular corrugated waveguide HE11 mode could be generated, the

    rectangular to circular adapter could be eliminated.

    The paper by Prof. P.J.B. Clarricoats, Dr. R.F. Dubrovka and Prof. A.D. Olver

    described a novel compact corrugated horn with a wide bandwidth over which both the

    sidelobe level and crosspolarisation are low. The horn comprises three sections, an initial

    flare from the horn throat followed by two straight sections whose flare angles are chosen so

    that the final section leads to a plane aperture. By making an appropriate choice of the change

    in flare angle and the position of the change, the adverse influence of the higher order HE12

    mode can be greatly reduced, when it is excited at a change in flare angle. In the Conclusion

    had shown that the mode structure of an Omni Guide fiber had many similarities with that of

    a hollow metallic waveguide. They explained why these similarities exist, and they presented

    a simple model that accounts for the differences. They identified the TE01 mode as the

    lowest-loss mode in the dielectric waveguide, as it was the case for the metal waveguide.

    A dual-band feed for the Deep Space Network (DSN) large array is described by D. J.

    Hoppe1 and H. Reilly1. The feed covers the 8- to 9-GHz and 30- to 40-GHz bands using acoaxial configuration. A saturated corrugated horn controls the radiation pattern in the low

    frequency band, and a dielectric rod is used as the radiator in the high-frequency band. The

    major requirements for the feed are described, and a summary of several possible feed

    configurations was presented. The bulk of the article covers the mechanical configuration of

    the feed, measured radiation patterns, and measured scattering parameters.

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    2.4 GPHA

    Gaussian Profiled Horn Antennas (GPHAs) have demonstrated its feasibility as one

    of the best solutions by Jorge Teniente, Ramn Gonzalo and Carlos del-Ro. A corrugated

    gaussian horn antenna design with more than 40% bandwidth is proposed in this letter. The

    measured radiated far field patterns have a good agreement with the simulated ones. The

    measured results show a gaussian antenna with extremely wide bandwidth low sidelobes and

    low crosspolar levels.

    A parametric study is performed by A. A. Kishk and C.-S. Lim to the conical and

    Gaussian profiled horn antennas. Corrugations are added to these horns to further improve

    their radiation characteristics. The analyses are performed numerically using a body of

    revolution code, which uses the method of moments. The obtained numerical results are

    illustrated graphically to show the performance of the horns in terms of phase center, return

    loss, efficiency with parabolic reflector, directivity, and cross polarization of the horns.

    Results obtained conclude that the Gaussian profiled horns perform better than the existing

    conical horn antenna system. The Gaussian profiled horns provide higher efficiency, lower

    cross polarization, lower sidelobe levels as well as wider bandwidth.

    According to reference [7], corrugated horn antennas are supposed to provide a nearly

    perfect HE11 hybrid mode at its aperture while the contribution of any other hybrid modes as

    HE1n and EH1n (with n 2) should be reduced in order to obtain a low sidelobes and

    crosspolar levels. It is known that the addition of EH1n modes increases the crosspolar level

    of a corrugated horn antenna. Nevertheless, this paper shows that the idea of avoiding HE 1n

    modes to reduce sidelobes is not true. In fact, it proved that GPHAs provide a HE1n mode

    mixture at the aperture as function of the relation between aperture radius (R) and beam waist

    radius (0) of the fundamental gaussian beam to be generated.

    Ranajit Dey, Vijay Kumar Singh, Soumyabrata Chakrabarty and Rajeev Jyoti

    presented the design and analysis of compact asymmetric sine-squared profile corrugated

    horn at 2332 GHz. Using closed form equations, a code has been developed to compute the

    initial design dimensions of the horn. The computed initial design dimensions of the horn

    have been taken as input to another code based on mode matching technique which is more

    accurate. This mode matching technique based code has been used to further analyze andoptimize the horn to find out its final design dimensions. This code does full wave modal

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    analysis of the horn and accurately predicts electrical performance of the horn such as return

    loss, modal power and co-polar and cross-polar radiation patterns of the horn. Using the

    codes, a horn has been analyzed fabricated and tested for its performance.

    Figure 2.2 Corrugated Gaussian Profiled Horn Antenna, (corrugated GPHA)

    The design of a dual frequency corrugated horn, working at S- and X-band

    simultaneously, was presented by Jonas Flodin, Per-Simon Kildal and Ahmed Kishk. The

    horn was designed to feed the 20 m radio telescope at the Onsala Space Observatory (a

    classical Cassegrain), via two feed reflectors[8]

    and[9] The feed system is intended for

    geodetic measurements using Very Long Baseline Interferometry (VLBI). Large corrugated

    horns are nowadays mainly designed by using software based on mode matching. The

    Moment Method (MM) for Bodies of Revolution (BOR) has successfully been used to design

    small corrugated horns, see e.g.[10]

    . The design of large horn antennas using MM for BOR is

    difficult because of the large memory requirements. Internal resonances may also occur and

    give incorrect results. These resonances are difficult to distinguish from actual performance

    problems. However, the present paper shows that it is possible to identify the internal

    resonances by scanning the frequency and thereby it is possible to design even large horns,

    using the MM for BOR. The present design has been done by using the AKBOR code, which

    is based on[11]

    .

    The field matching technique was used for the modal analysis of a circular

    waveguide, which is corrugated to form discs between corrugations[12]

    . The dispersion

    relation of the structure has been derived considering all the harmonics of the traveling waves

    in the corrugation-free region and the stationary waves in the region of corrugation. Theresults have been validated against that reported earlier and also using HFSS, for azimuthally

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    symmetric modes, with particular reference to the modes TE01, TE02, and TE03. The mode

    TE01 and the axial periodicity of discs proved to be the most effective in controlling the

    dispersion characteristics of the structure for wideband performance of a gyro- TWT

    millimeter-wave amplifier.

    2.4.1 APPLICATIONS OF GPHA

    During the development of this report, many corrugated GPHA have been observed.

    In fact, the number of designed corrugated GPHAs was above one hundred and the number

    of manufactured ones above ten.

    The first corrugated GPHAs manufactured by means of electroforming and they were

    two millimeter wave horn antennas, one was a direct corrugated GPHA and the other a

    symmetrical corrugated GPHA. The measured results were very nice, validating our

    numerical design code, year 1996. At the same time, an antenna for the German company

    Reinhold Mhleisen (RM), was designed to work at 170 GHz and was integrated in a

    complete system for the Japan Atomic Research Institute. In 1997, manufactured and

    measured a high directivity corrugated GPHA to emulate the radiation of the TJ-II gyrotron

    and test a quasi-optical transmission line at low power in the CIEMAT in Madrid In 1998, the

    design of the Hispasat 1C satellite horn antenna was performed. At the beginning of this year

    it was managed to persuade the engineers of CASA/EADS to use, for one of the three horns

    to be on board of Hispasat 1C satellite, a new technology based on corrugated GPHAs, this

    satellite was launched on February 2000. The nice performance of this antenna was the

    reason to be also selected to be on board of the new Hispasat 1D satellite launched in

    September 2002 with a slightly different frequency band. The next antenna design to be

    manufactured had to be two years later. In the year 2000 the two sub-millimeter horn

    antennas of very high directivity and very low sidelobe level for the Rutherford Appleton

    Laboratory in England was designed. They manufactured them by means of high precision

    electroforming and will be a part of ESA funded MARSCHALS airborne system.

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    CHAPTER 3: CONICAL CORRUGATED

    HORN ANTENNA

    In this chapter, I am trying to design the mode-converter which is producing the

    hybrid mode HE11 from the TE11 mode. For that there are basically two main parts. First

    designing the waveguide for generating the transverse electric mode and the other one is

    designing the corrugated horn antenna. In moreover, here additional conical horn antenna is

    also designed.

    3.1 GENERATING THE WAVEGUIDE

    A circular waveguide is a tubular, circular conductor. A plane wave propagating

    through a circular waveguide results in a transverse electric mode (TE) or Transverse

    magnetic mode (TM).

    Circular waveguides offer implementation advantages over rectangular waveguide in

    that installation is much simpler when forming runs for turns and offsets, particularly when

    large radii are involved, and the wind loading is less on a round cross-section, meaning

    towers do not need to be as robust. Manufacturing is generally simpler, too, since only onedimension (the radius) needs to be maintained. Applications where differential rotation is

    required, like a rotary joint for a radar antenna, absolutely require a circular cross-section, so

    even if rectangular waveguide is used for the primary routing, a transition to circular and then

    possibly back to rectangular is needed.

    Every waveguide has a definite cut-off frequency for each allowed mode. If the

    frequency of the impressed signal is above the cut-off frequency for a given mode, the

    electromagnetic energy can be transmitted through the guide for the particular mode without

    attenuation. Otherwise the electromagnetic energy with a frequency below the cut off

    frequency for that particular mode will be attenuated to a negligible value in a relatively short

    distance. The dominant mode in a particular guide is the mode having the lowest cut-off

    frequency.

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    The equation for calculating the cut-off frequency is,

    For the TEnp mode is,

    Where is

    Table 3.1 values for for calculation of cut-off frequency in TEnp mode

    For the TMnp mode is,

    Where is

    Table 3.2 values for for calculation of cut-off frequency in TMnp mode

    Now here I am working for the X-band, which has a frequency range 8 GHz to the 12

    GHz. So for the TE11 mode the cut-off frequency for the working frequency band X can be

    calculated as,

    = 3.411 m

    n 0 3.832 7.016 10.174

    1 1.841 5.331 8.536

    2 3.054 6.706 9.970

    n 0 2.405 5.502 8.654

    1 3.832 7.016 10.174

    2 5.135 8.417 11.620

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    So the wavelength for the TE11 mode is 3.411 m. Which is further calculated for the

    frequency range is 8.79 GHz. Same way the cut-off frequency for the TM11 mode is 1.6388m.

    This is, 1.83 GHz, for frequency range.

    3.1.1 TEmn MODE IN CIRCULAR WAVEGUIDE,

    Here, considering that the waves in a circular waveguide are propagating in

    the positive z direction as shown in the figure. The TEnp modes in the circular waveguide are

    characterized by Ez = 0. This means that the z component of the magnetic field Hz must exist

    in the guide in order to have electromagnetic energy transmission.

    Figure: 3.1 coordinate of circular waveguide

    From the Maxwells and Helmholtz equation,

    The TEmn mode equation are expressed as,

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    Where ,

    3.1.2 TMmn MODE IN CIRCULAR WAVEGUIDE,

    The TMmn modes in a circular waveguide are characterized by Hz = 0. However, the z

    component of the electric field Ez must exist in order to have energy transmission in the

    guide.

    From the Maxwells and Helmholtz equation,

    The TMmn mode equation are expressed as,

    Where ,

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    Now the calculation for the other parameters,

    The cut-off wave number of a mode,

    Phase velocity,

    Now here is the field pattern for the TE11 and the TM11 mode,

    Figure: 3.2 field pattern for the TE11 and TM11 mode

    3.2 HORN ANTENNA

    Horns have a wide variety of uses, from small-aperture antennas to feed reflectors to

    large-aperture antennas used by themselves as medium-gain antennas. Horns can be excited

    in any polarization or combination of polarizations. The purity of polarization possible and

    the unidirectional pattern make horns good laboratory standards and ideal reflector feeds.

    Horns also closely follow the characteristics predicted by simple theories.

    Figure shows the general horn geometry. The input waveguide can be either

    rectangular or circular (elliptical). Wis the width of a rectangular aperture, and a is the radius

    of a circular aperture. The distance from the junction of the projected sides to the aperture is

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    the slant radiusR. The distance along the centreline from the aperture to the waveguide is the

    axial length. We derive the aperture field amplitude from the input waveguide mode while

    the phase distribution is approximately quadratic across the aperture.

    Figure3.3 general geometry of horn antenna

    Types of horn antenna

    (a)Pyramidal (Rectangular) horn antenna(b)Sectoral horn antenna(c)Conical horn antenna(d)Corrugated horn antenna(e)Ridged horn antenna(f) Septum horn antenna(g)Aperture-limited horn antenna

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    Pyramidal and conical horn antenna

    (a) (b)Figure: 3.4 (a) pyramidal horn antenna, (b) conical horn antenna

    Corrugated horn antenna

    Figure: 3.5 corrugated horn antenna

    Sectoral horn antenna

    Figure: 3.6 H-plane sectoral horn antenna

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    3.2.1 CONICAL HORN ANTENNA

    With a circular-aperture horn, we lose independent control of the beamwidths in the

    principal planes. The circular waveguide can support any orientation of the electric field and

    thereby allows any polarization in the horn. The cone of the horn projects to a point in the

    feed waveguide where we assume a point source radiating to the aperture. The aperture phase

    is approximately quadratic. The waveguide fields are given by

    Where J1 is the Bessel function, the radial component in the waveguide, the

    radius, and the cylindrical coordinate. (1.841) is the first zero of . Equation hasits maximum electric field directed along the plane.

    Figure: 3.7 general geometry of conical horn antenna

    The directivity (in dB) of a conical horn, with an aperture efficiency of andaperture circumference C, can be computed using,

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    Where a is the radius of the horn antenna at the aperture and

    3.3 DESIGNING THE CORRUGATION HORN ANTENNA

    3.3.1 CORRUGATION

    The general concept of the corrugation is Shaped into alternating parallel grooves

    and ridges. Its an iris in the parallel form.

    And for the corrugated conical horn antenna, it defined as, A horn antenna that has a

    circular cross section and a series of equally spaced ridges protruding from otherwise straight

    sides.

    3.3.2 WHY CORRUGATION NEEDED IN ANTENNA DESIGN?

    The basic question is arises is the why the corrugation is needed into the designing the

    antenna? So the answer is,

    First, it combines the both the modes, TE11 and TM11 mode, so we are getting thehybrid mode, HE11 mode.

    And smooth walled antennas have higher side lobes in the E-plane than in the H-plane.

    Radiation pattern symmetry Low cross polarization Wide bandwidth response

    Some years ago, corrugated horn antennas were restricted to be used in high

    performance applications, like being on board of satellites, earth station radio telescope

    horns, antenna measurement chambers and very few more applications. They were restricted

    to those applications for two main reasons: difficulties in the design and difficulties in the

    manufacture process of a corrugated feed.

    At present, the communication systems require really high performance antennas;

    sidelobe and crosspolar levels should be reduced in the radiation pattern as well as the size of

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    the antenna. Low crosspolar levels are inherent to the corrugated horn antenna technology

    and this parameter has been conveniently improved during the last decades with the use of

    corrugated feeds. But sidelobe level of corrugated horns has got stuck and no improvements

    have been made till the last five years. Probably, the improvement in sidelobe level has not

    been really necessary up to now. The incredible quantity of new communication systems that

    interact between them has made necessary to reduce the mutual interferences through

    sidelobes. In fact, the major benefits from the extremely low sidelobe interference

    characteristics are to reduce both operational costs and also the susceptibility to jamming or

    eavesdropping in military and secure applications.

    3.3.3 CORRUGATED HORN ANTENNA

    Corrugated horns have become now-a-days the preferred choice of feed antenna for

    use in high restrictive applications. This is because of their superior radiation performance

    and in particular their high copolar pattern symmetry and low crosspolarisation.

    Figure: 3.8 corrugations in antenna

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    Figure: 3.9 corrugated horn antenna

    3.3.4 DESIGN PROCEDURE FOR THE CORRUGATED HORN ANTENNA

    The operation principle of corrugated horns can be physically explained by

    considering the way in which the corrugated wall affects the field distribution inside a

    corrugated waveguide as shown in figure 3.10.

    Figure 3.10 design of corrugated horn antenna

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    (1)Calculation of input Radius or throat radius of horn antenna (Rin) :This is the input radius of the corrugated horn antenna, which is shown in the

    figure 3.10. From this radius the source mouth is generated for the input of the TE 11

    and for the TM11 modes.

    Rin or Rthroat = 0.39 *

    (2)Calculation of aperture radius of horn antenna (Rout):Here is the outer radius of the outer mouth of the corrugated horn antenna,

    which is shown in the figure 3.10. From this outer mouth of the antenna, the

    converted mode generated. So related to other parameters can be measured over here.

    Rout = 4.8 * or 5 *

    (3)Calculation of horn antenna length (L):Length of the corrugated horn antenna can be calculated as the length of the

    flare angle of the antenna from the inner radius to outer radius. The length of the horn

    antenna can be,

    L = 6.5 * to 8.5 *

    (4)Corrugation Depth (d) :The corrugation depth is the depth of the corrugation part of the horn antenna,

    which is important due to it, reduces the sidelobes in the radiation pattern.

    Figure 3.11 design of corrugation

    The corrugation depth is shown as in figure 3.11 and it is further calculated as,

    d = / 2 or / 4

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    (5)Period (P):Period (P) is the distance between two corrugations in the corrugated horn

    antenna. It has a variable distance between the ranges depending upon the

    wavelength. It defines the width of the corrugation depth part and the duty cycle part.

    For the period, which is showing in the above figure 3.11, variable range part is as

    below.

    P = / 3 or / 5

    (6)Duty Cycle (W):Duty cycle is the thickness of the corrugation part in the horn antenna, which

    is shown as (W) in the above figure 3.11. The thickness or width of the corrugation

    can be calculated as,

    W = P / 2 or P / 3

    W, the duty cycle or width of the corrugated horn antenna, is depending upon

    the period (P), because its the part of the period.

    (7)Phase center (Pc):Here, defining the phase center as the point from which it appears that an

    antenna radiates spherical waves. Measurements show that the phase center is

    seldom a unique point in a plane, but depends on the pattern angle. The E- and H-

    plane phase centers will also be unequal in general. The phase center can be

    calculated as,

    Pc = 1.85 * or 3.42 *

    (8)Corrugation thickness (Cth):Corrugation thickness is the thickness of the material, which one is assigned to

    the horn antenna. Here silver material can be assigned. The corrugation thickness can

    be calculated as below.

    Cth = 0.02 *

    The corrugation thickness is important because the less thickly the material

    affects the skin effect problem. So the thickness from the calculation must be applied

    to the antenna.

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    Conductor, which is being used for designing Corrugated Horn antenna, is

    silver. And the medium inside the antenna is air.

    3.3.5 FOR THE MONOMODE CORRUGATED HORN ANTENNA

    For the designing of monomode corrugated horn antenna, there are two hyperbolas.

    From that the slant edge of the corrugated horn antenna can be designed. These two

    hyperbolas can be defined as below,

    3.3.6 FOR THE GAUSSIAN PROFILED HORN ANTENNA

    Now a days, working with a new type of corrugated horn antenna, consists on

    generating the fundamental Gaussian beam directly from the TE11 mode. The equation that

    defines the profile is as below,

    Where Wave number k= 2 * /

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    3.4 HYBRID MODE

    Transverse electric and magnetic modes (TEmn and TMmn) are usually well known in

    waveguide theory. On the other hand, hybrid modes (those modes which dont present pure

    transverse components along the waveguide) are not so well known. It is interesting to aid in

    the knowledge of corrugated horn antennas to deepen in the understanding of hybrid modes

    of a corrugated waveguide.

    A linear electric field for low cross polar level will be desirable but it cannot be

    obtained with smooth waveguides that only support pure transverse electric (TEmn) or a pure

    transversemagnetic (TMmn) modes. These modes have the aperture electric field lines curved.

    Therefore a multimode horn should be designed. In, a special horn design to obtain anappropriate mode mixture by the addition of TE11 and TM11 modes in a particular proportion

    and phase is presented, but its bandwidth is very narrow.

    The TE11 mode is as input power working in a circular mono-mode waveguide. This

    mode does not have a good radiation pattern and for large number of applications it cannot be

    used as radiation source. So, it is necessary to transform it into another mode more adequate

    to radiate. This mode conversion will take place by using the component that we present in

    this paper. This component use corrugated waveguide technology due to its high-

    performance, i.e. the high symmetry, wide bandwidth and robustness. HE11 mode is the

    fundamental mode of the corrugated waveguide. For the generating the HE11 mode there must

    be use of the both the modes which are transverse electric mode (TE 11) and transverse

    magnetic mode (TM11) with the ratio of 85 % of TE11 mode and 15 % of TM11 mode. This is

    because while using only TE11 mode, the generated hybrid mode HE11 is not pure and less

    efficient while using this type of combination the produced or generated hybrid mode is

    99.19 % efficient. For the balanced condition, i.e. supposing hybrid condition can be seen in

    the table 3.3.

    TE Mode TM mode

    Table 3.3 mixture of TEmn and TMmn mode

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    The HE11 mode has highly desired radiation pattern characteristics for applications

    like satellite communications, radar, remote - sensing, etc, nevertheless, when the

    requirements are more stringent this mode is not good enough and we must look for other

    solution. This one corresponds to the fundamental Gaussian beam, which has outstanding

    features, such as being a free space mode, having high matching efficiency with a reflector,

    no side lobes, perfect symmetry. The hybrid modes HE11 present at the aperture of a circular

    waveguide perfectly linear electric field lines.

    Figure 3.12 field pattern of HE11 mode

    If we assume balanced hybrid condition, hybrid modes can be defined with the

    following simplified equations,

    3.4.1 FOR HEmn MODE

    The HEmn modes in a horn antenna are characterized by Hz and the Ez component is

    non zero. Both z components are present in the hybrid modes.

    From the Maxwells and Helmholtz equation,

    The HEmn mode equation are expressed as,

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    3.4.2 FOR EHmn MODE

    Different different modes patterns of HEmn and EHmn are shown in figure.

    Figure 3.13 field pattern of different modes of HE and EH mode

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    CHAPTER 4: DESIGN IN HFSS

    4.1 INTRODUCTION TO HFSS

    HFSS is a high-performance full-wave electromagnetic (EM) field simulator for

    arbitrary 3D volumetric passive device modelling that takes advantage of the familiar

    Microsoft Windows graphical user interface. It integrates simulation, visualization, solid

    modelling, and automation in an easy-to-learn environment where solutions to your 3D EM

    problems are quickly and accurately obtained. Ansoft HFSS employs the Finite Element

    Method (FEM), adaptive meshing, and brilliant graphics to give you unparalleled

    performance and insight to all of your 3D EM problems. Ansoft HFSS can be used to

    calculate parameters such as S Parameters, Resonant Frequency, and Fields.

    The Ansoft HFSS Desktop provides an intuitive, easy-to-use interface for developing

    passive RF device models. Creating designs, involves the following:

    1). Parametric Model Generationcreating the geometry, boundaries and excitations

    2). Analysis Setupdefining solution setup and frequency sweeps

    3). Resultscreating 2D reports and field plots

    4). Solve Loop - the solution process is fully automated

    To understand how these processes co-exist, examine the illustration shown below.

    Figure: 4.1 flow chart of the HFSS software

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    4.2 DESIGNING OF CIRCULAR WAVEGUIDE IN HFSS

    As per the design calculation, the circular waveguide is designed. Its transmitting medium is vacuum The boundary of circular waveguide is perfect E or perfect H field and which is the

    cylinder face.

    Then applying the excitation to the input and output ports.Input port, having a single mode and the output port, having with different number of

    ports.

    This ports indicating the different modes of TE mode. This waveguide design as working with the 10 GHz frequency.

    So dimension must be chosen as its working frequency is above cut off frequency.

    Now analyze the waveguide port power or S-matrix for the all modes at 10 GHzfrequency

    Figure: 4.2 design of circular waveguide in HFSS

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    4.2.1 DESIGN STEPS FOR CIRCULAR WAVEGUIDE

    Step: 1

    As per design calculation, first takes the cylinder of radius 1.17 cm, which is

    calculated as the considered for frequency band X having the centre frequency 10 GHz can

    be passing through the waveguide and generate the transverse electric mode or also

    transverse magnetic mode. The material assigned to this cylinder is vacuum.

    Here the material is assigned vacuum because of the considering and generating the

    ideal waveguide. So no obstacles affects to the radiation in the waveguide by the other

    particles. Dimensions are as shown in figure 4.3.

    Figure: 4.3 designed dimension of circular waveguide

    Step: 2

    Assign the boundary conditions for the waveguide. As per generating the transverseelectric mode, the cylindrical surface of the cylinder, assigned with the perfect E boundary as

    shown in figure 4.4.

    Here the boundary is perfect E, so its conductivity is higher. So maximum power

    transmission can be possible and also getting the E field pattern at the end of the waveguide,

    which is the end circle part of the cylinder.

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    Figure: 4.4 assigning perfect E boundary to the surface

    As per generating the transverse magnetic mode, the cylindrical surface of the

    cylinder, assigned with the perfect H boundary as shown in figure 4.5.

    Figure: 4.5 assigning perfect H boundary to the surface

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    Step: 3

    In HFSS, Assign the Excitation to the waveguide. Here first assign the input

    waveport at the starting circle of the cylinder, which is having an integrated line in the

    positive Z direction. From that the power source can be work.

    Here the input excitation waveport can be seen as in figure 4.6.

    Figure: 4.6 assigning excitation, waveport at the input

    At the output circle of the cylinder, there is also one waveport assigned. In this

    waveport there are number of modes can be added. Higher mode of TE can be generated.

    Like for as an example this number of modes can be 6.

    This output waveport is the output of the waveguide, which is the exit part of the

    radiation. So generated signals from the waveport 1 can be pass through the waveport 2.

    Figure: 4.7 assigning excitation, waveport at the output

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    Step: 4

    In HFSS,Assign the analysis part. In the analysis part set the solution frequency to

    the 10 GHz, centre frequency for the X band.

    Also adding the frequency sweep assign to the waveguide. Which is for x band it is

    for 8 GHz to the 12 GHz. And the frequency sweep increment is assigned. This frequency

    sweep is mainly 3 types.

    1) Discrete type2) Fast type3) Interpolating type

    Figure: 4.8 assigning solution frequency for analysis

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    4.3 RESULTS AND ANALYSIS OF CIRCULAR WAVEGUIDE

    Result: 1 Return Loss

    Figure: 4.9 rectangular plots for return loss

    Here is the return loss of the circular waveguide for the transverse electric mode. The

    return loss is almost below the -50 dB level, which is compared to good result. Because the

    reflected back power is minimum, so that the maximum power can be transmit through the

    output port. Therefore maximum radiation can be done to the end.

    The plot for the return loss which is frequency verses power in dB, here the frequency

    is in the range of 8 GHz to the 12 GHz. The plot is as shown in figure 4.9.

    Result: 2 Dominant mode

    For TE11 modes:

    The dominant mode of the transverse electric mode is TE11 mode. The field pattern is

    shown in figure 4.10. In this field pattern the radiation at the centre is almost linear and at the

    top and bottom side is curved.

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    Figure: 4.10 dominant mode TE11

    After simulating, the circular waveguide through the HFSS software getting the result

    of field pattern of the dominant mode, at the input waveport, of the transverse electric mode

    TE11 mode.

    For TM10 modes:

    Figure: 4.11 dominant mode TM10

    The dominant mode of the transverse magnetic mode is TM10 mode. The field pattern is

    shown in figure 4.11.

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    Result: 3 Different modes at output waveport

    For TEmn modes:

    The generated different modes of the transverse electric mode are shown as below.

    Figure: 4.12 different modes pattern of TE

    For TMmn modes:

    The generated different modes of the transverse magnetic mode are shown as below.

    Figure: 4.13 different modes pattern of TM

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    Result: 4 E field and H field Plot for circular waveguide

    The E field and the H field plot in the waveguide as shown in figure 4.15 to 4.19 for

    both the modes, transverse electric and transverse magnetic mode. This radiation is passing

    from one waveport to the other in positive y direction.

    For TE11 modes:

    For E field:

    Figure: 4.14 cross section E field pattern of circular waveguide for TE

    For H field:

    Figure: 4.15 cross section H field pattern of circular waveguide for TE

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    For TM10 modes:

    For E field:

    Figure: 4.16 cross section E field pattern of circular waveguide for TM

    For H field:

    Figure: 4.17 cross section H field pattern of circular waveguide for TM

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    Result: 4 S Matrixes

    Figure: 4.18 S matrix of circular waveguide

    Here as shown above the S matrix for the given frequency 10 GHz. Here we can see

    that the for the S11 parameter the reflected back power is very low, while in comparing the s

    parameter for S12 is approximately 0.95, which is compared to high.

    The total sum is 1, which can be the sum of all s parameters square. Here is the proof

    as below,

    Sum = (0.00078391)2

    + (0.95141)2

    + (0.30793)2

    + (0.00068413)2

    = 1.0

    So the total sum, reflected and transmitted is getting total 1.

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    4.3 DESIGNING OF CONICAL HORN ANTENNA IN HFSS

    As per the design calculation, conical horn antenna is designed in HFSS. The

    designed horn antenna is shown as below.

    Figure: 4.19 design of conical horn antenna in HFSS

    As shown in figure 4.19, based upon the specifications, the conical horn antenna is

    taken up for study and verifying results related to the antenna.

    The results of the tested conical horn antenna are as follows.

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    Result: 1 Return Loss

    As shown in the figure the return loss of the conical horn antenna, at the center

    frequency 10 GHz, is -31.17dB. Here all over frequency band, X- band, having the return loss

    below -25 dB.

    Figure: 4.20 return loss of conical horn antenna

    Result: 2 Radiation Pattern

    Figure: 4.21 radiation pattern of conical horn antenna

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    Result: 3 Gain Pattern

    Figure: 4.22 gain pattern of conical horn antenna

    Result: 4 VSWR (Voltage Standing Wave Ratio)

    Figure: 4.23 VSWR

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    CHAPTER 5: CONICAL CORRUGATED

    HORN ANTENNA DESIGN

    5.1 DESIGN OF THE CORRUGATED HORN ANTENNA IN MATLAB

    The corrugated horn antenna design for its basic structure is implemented in

    MATLAB and its source code is mentioned here.

    This MATLAB code is for the basic two equations, which are illustrated in chap 3.

    These equations are as below.

    For The Monomode Smooth Circular Waveguide,

    This MATLAB code defines the antenna parameters like antenna inner and

    outer surfaces.

    MATLAB CODE:

    clc;

    clear all;

    close all;

    freq=input('Enter the valyu of the value of fequency in Ghz=');

    c=3*10^10;

    lamda=c/(freq*10^9);

    l=8*lamda;

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    display(l);

    rin=0.39*lamda;

    alpha=1.3;

    k=(2*pi/lamda);

    for z=0:0.5:l; %% for r(t)

    eon=z/(alpha*k*rin*rin);

    r(2*z+1)=rin*sqrt(1+(eon.*eon));

    end

    display(r);

    z2=0:0.5:l;

    subplot(2,1,1)

    plot(z2,r(2*z2+1),'--bs',z2,-r(2*z2+1),'--bs');

    grid on;

    for z=0:0.5:(l/2) %% for f1(t)

    eon1=z/(alpha*k*rin*rin);

    f1(2*z+1)=rin*sqrt(1+(eon1.*eon1));

    end

    display(f1)

    for p=1:25

    c(p)=f1(p)+((lamda/2)-((p-1)*(((lamda/2)-(lamda/4))/48)));

    end

    for p=1:(l/2) %% slop for f1(t)

    m1(p)=f1(p+1)-f1(p);

    m2(p)=c(p+1)-c(p);

    end

    for z=(l/2):0.5:l %% for f2(t)

    eon2=((l)-z)/(alpha*k*rin*rin);

    b2=rin*sqrt(1+(eon2.*eon2));

    eon3=(l/2)/(alpha*k*rin*rin);

    b3=rin*sqrt(1+(eon3.*eon3));f2((2*z+1)-24)=(-b2)+(2*b3);

    end

    display(f2);

    for p=1:25

    d(p)=f2(p)+((lamda/2)-(((p+24)-1)*0.015625));

    end

    for p=1:24 %% slop for f2(t)

    n1(p)=f2(p+1)-f2(p);

    n2(p)=d(p+1)-d(p);

    end

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    z1=1:l;

    z2=1:0.5:((l/2)+0.5);

    z3=((l/2)+0.5):0.5:l;

    z4=0:0.5:(l/2);

    z5=(l/2):0.5:l;z6=1:25;

    subplot(2,1,2);

    plot(0:0.5:(l/2),f1,l/2:0.5:l,f2,0:0.5:(l/2),-f1,l/2:0.5:l,f2,z4,c(z6),z4,-

    c(z6),z5,d(z6),z5,-d(z6));

    grid on;

    The generated plot for the centre frequency 10 GHz is as below.

    Figure: 5.1 basic structure of corrugated horn antenna

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    5.2 DESIGNING OF CORRUGATED HORN ANTENNA IN HFSS

    As per the design calculation, the corrugated horn antenna is designed. Its transmitting medium is air. The material assigned is silver to the antenna so boundary of corrugated horn antenna

    is the conductivity of the silver material.

    Then applying the excitation to the input port. Covering the whole antenna by the medium air. Because antenna practically worked

    in the media air and as using the software tool HFSS it is require to simulate the

    antenna, it must be solved inside the medium.

    Assigning the radiation boundary to the outer cylinder which is air. Because of theradiation pattern absorb the radiation signals which are generated from the antenna so

    that the radiation pattern can be identify.

    This antenna design as working with the 10 GHz frequency.So dimension must be chosen as its working frequency is above cut off frequency.

    Now analyze the field plot and field pattern at the mouth of the horn antenna.

    Figure: 5.2 Design of corrugated horn antenna in HFSS

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    5.2.1 DESIGN CALCULATIONS FOR CORRUGATED HORN ANTENNA

    As per the following design equations the calculations are shown here.

    Parameters Equations Expected Values

    Input Radius of horn antenna (Rin) 0.39 * 1.17 cm

    Horn Antenna length (L) L = 6.5 * to 8.5 * 19.5 to 25.5 cm

    Corrugation Depth (d) / 2 or / 4 1.5 to 0.75 cm

    Period (P) / 3 or / 5 1 to 0.6 cm

    Duty Cycle (w) P / 2 or P / 3 0.5 or 0.334 cm

    Phase centre (Pc) 1.85 * 5.55 cm

    Corrugation thickness (Cth) 0.02 * 0.06 cm

    Table 5.1 general design parameters for corrugated horn antenna

    Now the design parameters are shown in Table 5.2.

    Parameters Value

    Input Radius of horn antenna (Rin) 1.17 cm

    Horn Antenna length (L) 24 Cm

    Corrugation Depth (d) 1.5 Cm

    Period (P) 1 Cm

    Duty Cycle (w) 0.5 Cm

    Phase centre (Pc) 5.55 Cm

    Corrugation thickness (Cth) 0.06 Cm

    Table 5.2 considered design parameters for corrugated horn antenna

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    5.2.2 DESIGN STEPS FOR CORRUGATED HORN ANTENNA

    Step: 1

    As per design calculations first take the polyline and generate the tooth for the

    corrugation antenna. Here considering the period (p) and the duty cycle (w).

    Period (p) = 1.0 cm

    Duty cycle (w) = 0.5 cm

    As per the MATLAB program the every point for the inner and outer surface can be

    implemented through polyline. This generated two hyperbolas, which has having the depth of

    / 2 to /4. At the starting edge the depth of the corrugation is / 2 and linearly detrimentally

    to at the end of the antenna, at the mouth, with depth of / 4. The basic structure designed in

    HFSS is as shown in figure 5.3.

    Figure: 5.3 polyline design for corrugation in HFSS

    This designed basic structure in HFSS, having only outer line. So for assigning the

    material cover the line. For this purpose, the starting and the end edge are connected through

    the polyline.

    Now perform the operation by the modeler tab on the toolbar. Apply coverline from

    the surface option. The generated coverline polyline structure is as shown below.

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    Figure: 5.4 coverline the polyline for generate the conical horn antenna

    Step: 2

    Now from the step 1 the corrugation design is performed. Now for the design

    structure of corrugated horn antenna this polyline sweep around to the y axis for the 360,

    which is as shown in figure 5.5.

    Figure: 5.5 sweep around the axis

    After this sweep operation, the generated structure for the corrugated horn antenna is shown

    in figure 5.6.

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    Figure: 5.6 generated corrugated horn antenna

    Now assign the material, which is silver.

    Step: 3

    In HFSS, Assign the Excitation to the horn antenna. Here first draw one circle at

    origin with radius of outer surface of the input side of horn antenna and another circle at the

    mouth of the antenna having a radius of 9 cm, which is taken as an outer surface dimension.

    Now for assigning the waveport at the first circle, which is at origin having an

    integrated line in the positive z direction. The waveport assignment is shown figure 5.7.

    Figure: 5.7 assigning waveport for the source

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    Step: 4

    In HFSS, this antenna can simulate in any medium, so for that the air medium be

    generated, which has a radiation boundary.

    This boundary is assigned due to reason of generating the radiation pattern of the

    corrugated horn antenna. The radiation boundary has characteristics of absorbing the

    radiation signal which are generating from the antenna. This radiation boundary can be far

    field or near field.

    Figure: 5.8 assigning radiation boundary

    So the designed corrugated horn antenna is inside the cylinder, which is air.

    Step: 5

    Assign the analysis part. In the analysis part set the solution frequency to the 10 GHz,

    centre frequency for the X band.

    Also adding the frequency sweep assign to the corrugated horn antenna. For x- band it

    is 8 GHz to 12 GHz. And the frequency sweep increment is assigned. This frequency sweep

    is mainly of 3 types.

    4) Discrete type5) Fast type6) Interpolating type

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    Here considering the discrete type frequency sweep with the increment of 0.125 GHz.

    Total 33 calculations can be done.

    Figure: 5.9 solution frequency for analysis

    And the frequency sweep is as below

    Figure: 5.10 frequency sweep for the X-band

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    5.3 RESULT AND ANALYSIS OF CORRUGATED HORN ANTENNA

    After designing the corrugated conical horn antenna in HFSS software as per the design

    calculations, the equations and selected specifications, the corrugated conical horn antenna can be

    shown as below.

    Figure: 5.11 calculated and generated corrugated horn antenna in HFSS

    After simulating the corrugated horn antenna in HFSS, the generated results are as follows.

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    Result: 1 Return Loss

    Here is the return loss of the corrugated horn antenna is as above for the frequency

    range of 8 GHz to 12 GHz, x-band. Here this return loss is below -10 dB and at the solution

    frequency at 10 GHz it is -29.7818 dB. In the return loss of the corrugated horn antenna the

    generally loss is below -20 dB and it has a spikes in the band below -30 dB. The reflected

    back power is very low so that the maximum power can be transmit through the output port.

    Therefore maximum radiation can be done to the end.

    Figure: 5.12 rectangular plot for return loss

    The plot for the return loss which is frequency versus power in dB, (Frequency range

    8 GHz - 12 GHz) is shown in figure 5.12.

    Result: 2 Radiation Pattern

    The radiation pattern of the corrugated horn antenna is as shown in figure 5.13. This

    radiation pattern is pencil beam, which is very important because this antenna is used for

    satellite communication and radar system, where sidelobes may cause the problem. Here The

    elevation pattern for =0 and =90 degrees would be important. Therefore the 2D and 3D

    patterns are as shown in figure 5.13 and 5.14.

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    Figure: 5.13 Radiation pattern of the horn antenna

    Radiation Pattern in 3D

    Figure: 5.14 Radiation pattern in 3D

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    Figure: 5.15 Radiation pattern in dB

    Result: 3 Gain Pattern in dB

    Here designed the corrugated horn antenna with calculation is so that the gain would

    be approximately 22 dB. The generated gain pattern as shown in figure 5.16 and its

    maximum value is 20.88 dB.

    Figure: 5.16 Gain pattern in dB

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    Result: 4 VSWR (Voltage Standing Wave Ratio)

    Figure: 5.17 VSWR

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    Result: 5 E field and H field Plot for corrugated horn antenna on mouth

    At the mouth position of the corrugated horn antenna the E field and H field plot at 10

    GHz frequency is shown in figure 5.18 and figure 5.19.

    This generating E and H field plot is as the Gaussian plot. So at the centre part the

    higher power generated and uniformly distributed to the aperture of the horn antenna.

    E field Pattern at 10 GHz:

    Figure: 5.18 Gaussian E field pattern on mouth of the antenna

    H field Pattern at 10 GHz:

    Figure: 5.19 Gaussian H field pattern on mouth of the antenna

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    Result: 6 E field and H field Plot for corrugated horn antenna for the cross

    sectional view

    As the source waveport generate the signals they pass through the antenna in positive

    y direction. Here the cross sectional view for the E field and H field pattern is shown in figure

    5.20 and 5.21.

    Here as we can see, the radiation passes through the corrugation. So that the reflected

    back signals from the corrugation, affects the radiation, which is most important in this

    project. Due to this reflection, the side lobes of the E field and H field may reduced and

    generated pencil beam radiation with high power, which has a higher directivity. And due to

    this reflection back signals; mode conversion also can be done.

    E field Pattern:

    Figure: 5.20 cross sectional view of E field pattern of the antenna

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    H field Pattern:

    Figure: 5.21 cross sectional view of H field pattern of the antenna

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    Result: 7 E field and H field Distribution on mouth of the corrugated horn

    antenna

    E field distribution:

    Vector Plot:

    Figure: 5.22 E field vector plot on mouth of the antenna

    H field distribution:

    Vector Plot:

    Figure: 5.23 H field vector plot on mouth of the antenna

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    CHAPTER 6: CONCLUSION

    6.1 CONCLUSION

    As per the design the circular waveguide and the corrugated conical horn antenna, the

    conclusion arises from that is, the circular waveguide is simulated properly with specific

    dimensions and the simulated results are suitable with the desired results. The circular

    waveguide have the very low return loss and different mode patterns can be studied from that.

    The E and H field pattern can also be studied for both the cross sectional view and at the

    output port. This field pattern can see by the animation command in the HFSS.

    Now, for the corrugated conical horn antenna, the lack of software resources and thelack of availability of desire hybrid mode in HFSS software, the result of the output mode,

    which is Hybrid mode, could not be seen. And in further there is not possible to applying

    both the TE mode and TM mode mixture in the source waveport and not possible any kind of

    mixture of different ratio.

    So for verifying the results I have considered the different parameters for the antenna.

    For that first verifying the return loss and it was below -30 db. So it can be considered. And

    it have good radiation pattern, which is pencil beam pattern with higher directivity and low

    side lobe levels. The most important parameter is verifying the Gaussian beam at the mouth

    of the corrugated horn antenna. Here from the simulated result the maximum power at the

    centre and the uniformly detrimentally to the aperture. So we can say that the desired output

    may be generated through this design of antenna.

    But this type of Gaussian beam radiation is achieved for whole band, for 8 GHZ to the

    10 GHz. But from this design, which I have made, I got the result for 8 GHz, 9 GHz, 10 GHz,but not the proper for the 11 GHz and 12 GHz. So further calculations can make it solve by

    varying the variable values like length, period and duty cycle.

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    6.2 FUTURE WORK

    Now a days, working with a new type of corrugated horn antenna, consists of

    generating the fundamental Gaussian beam directly from the TE11 mode. The equation that

    defines the profile is as follows,

    But, now the difference is in value of, it has to be bigger, in this way; the horn

    antenna aperture velocity is slower, and so it can control the mode conversion between the

    TE11 and the HE11 mode, and also use the impedance adapter. With this type of horn antenna,

    the total Gaussian conversion efficiency will decrease a little bit. For verifying the result first,

    showing the far field radiation pattern and bandwidth studies are varying the corrugation

    period (p), Changing the corrugation duty cycle between 7p/8 and p/2 on an adapter length.

    The new Gaussian profiled horn antenna study is under process.