Radiation Analysis and Design of Pyramidal Horn Antenna

Radiation Analysis and Design of Pyramidal Horn Antenna

Radiation Analysis and Design of Pyramidal Horn Antenna

1. Kiran Chand1, Lecturer, Adama Science & Technology University,

   Dr. M V Raghavendra2, Professor, Adama Science & Technology University, K.Sathyavathi3 Lecturer, Mallareddy Group of Institutions,

   In Modern times need for wideband applications has increased. In recent years there have been many research works are going on in the design of antenna system as it is the main source for any communication system. The horn is nothing more than a hollow pipe of different cross sections, which has been tapered (flared) to a larger opening. The type, direction, and amount of taper (flare) can have a profound effect on the overall performance of the element as a radiator. The Horn Antenna is widely used in the EMC measurement, radar and communication system. Especially for wireless broadband applications horn antennas are the best choice. Horn is one of the simplest and probably the most widely used microwave antenna. In this paper we present the design and radiation pattern analysis of a specific horn antenna i.e. Pyramidal Horn. The paper contains introduction to horn antennas, the pyramidal horn, design of Pyramidal horn and conclusion.

   Key words: Horn Antenna, Pyramidal horn, Radiation pattern, Directivity.

   1. The horn is widely used as a feed element for large radio astronomy, satellite tracking, and communication dishes found installed throughout the world [1]. Advantages of horn antenna over other types of antennas are: (a) Less Complexity involve in the design of horn antenna as compared to phased array antennas & corrugated cousins [3]. (b) High data rate systems needs to be operated at a higher frequency range in order to achieve higher bandwidth. This can be easily achieved using a horn antenna (c) complex feeding techniques are required to feed an antenna, rather feeding a horn antenna is less complex (d) If horn antenna is properly designed & optimized than side lobes can be suppressed to very low levels. (e) As the horn is waveguide fed antenna, its Power handling capability is superior to other antennas, especially in the use of TWTs used in satellites, radars and many other applications making it an ideal choice for space applications. Horns have conventionally been used in terrestrial microwave communications. They can also be found on many Line-Of-Site (LOS) microwave relay towers [1]. Among all the horns pyramidal horn has been attracting the designers because of its light weight, simplicity in its design, low VSWR and for its good results. The pyramidal horns are the antennas in which the walls of the rectangular wave guide are flared out in both e-plane and h-plane directions. The applications of pyramidal horn antennas are a) they have been widely used for space applications from the very beginning due to their capability of being best operation from Megahertz to Terra hertz range, b) Used in remote sensing satellites, communication satellites, geographic information & weather satellite, c) Various space programs in which horn antennas are used by NASA, ESA, d) It is used when there is a high gain requirement and e) it is used when there is a high directionality requirement.

   2. The pyramidal horns are popular for their well known attractive features like light weight, low VSWR, low profile and compatibility. As it is being flared in both directions its radiations characteristics are essentially a combination of the e- and h-plane sectoral horns and its geometry coordinate system[7] is shown in Fig.1. The horn can be treated as an aperture antenna. To find its radiation characteristics the equivalent principle techniques can be utilized. To develop an exact equivalent of it, it is necessary that the tangential electric and magnetic field components over a closed surface are known. The closed surface that is usually selected is an infinite plane that coincides with the aperture of the horn. When the horn is not mounted on an infinite ground plane, the fields outside the aperture are not known and an exact equivalent cannot be formed [6]. However, the usual approximation is to assume that the fields outside the aperture are zero. The fields at the aperture of the can be found by treating the horn as a radial wave guide. The fields within the horn can be expressed in terms of cylindrical TE and TM wave functions which include Henkel functions. This method finds the fields not only at the aperture of the horn but also within the horn. To find the fields radiated by the horn, only the tangential components of the e- and/or h-fields over a closed surface must be known. The closed surface is chosen to coincide with an infinite plane passing through the mouth of the horn. The directivity is one of the parameters that is often used as a figure of merit to describe the performance of an antenna. To find directivity, the maximum radiation is formed.

      So, the need to develop a Wideband horn antenna for communication and calibration purposes[6]. With the development of measurement, communication system, radar techniques and electromagnetic, the horn antenna has been widely used which made it one of the most practical antennas. This horn antenna can effectively extend the working bandwidth of the antenna and improve the impedance matching between waveguide and free space [2].

      1. Aperture Fields, Equivalent, and Radiated Fields

         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 [1].

         The tangential components of the e- and h-fields over the aperture of the horn are approximated

         2 2

         2 + 1

         by (x',y') = 0 cos (

         1

         x') [ 2 ] — (1)

         2 2

         2 + 1

         (x', y) = (0 /) cos (

         1

         x') [ 2 ] — (2)

         and the equivalent current densities are approximated by

         2 2

         2 + 1

         , = (0 /) cos (

         1

         x') [ 2 ] — (3)

         2 2

         2 + 1

         , = 0 cos (

         1

         x') [ 2 ] — (4)

         Now after formulating the normalized factors and they are given by

         N = – (E0/) cos sin Ø I1 I2	—	(5)
         NØ = – (E0/) cos Ø I1 I2	—	(6)
         L = E0cos cos Ø I1 I2	—	(7)
         LØ = -E0 sin Ø I1 I2	—	(8)

         The horn can be treated as an aperture antenna.By combining equations (5),(6),(7) and (8) its far- zone (In the far field zone only the Ø components of e-field and h-field are dominant and the radial components (Er = 0) are negligible compared to Ø components) e-field and h- field components are given by

         =

         4

         (or)

         [LØ

         + N] — (9)

         = 0

         4

         [sin Ø 1 + cos I1

         I2] — (10)

         = + [L – N ] — (11)

         Ø 4 Ø

         (or)

         = 0

         4

         [cos Ø cos + 1 I1

         I2] — (12)

         The above equations (9-12) represents the fields radiated by a pyramidal horn which are valied for all angles of observation and they shows that the princpal E-plane pattern (Ø = ) of

         2

         a pyramidal horn is identical to the E-plane pattern of an E-plane sectoral horn on neglecting a

         normalization factor.Similarly the H-plane pattern (Ø = 0) is identical to the H-plane sectoral horn.Therefore the radiation pattern of a pyramidal horn is very narrow in both E and H principal planes and, infact in all planes.Fig.2. illustrates the three-dimentional field pattern of a pyramidal horn(1 = 2 = 6, 1 = 5.5, 1 = 2.75, = 0.5, = 0.25).

         The maximum radiation for a pyramidal horn is not necessarily directed along its axis because,the phase error taper at the aperture is such that the rays emanating from the different parts of the aperture toward the axis are not in phase and do not add constructively.

         To physically construct a pyramidal horn, the dimentions pe of Fig.1(b) and ph of Fig.1(c) should be equal and are given by[1]

         2

         2

         p = (b -b) [ 1]1 2

         — (13)

         e 1 1 4

         2

         2

         p = (a -a) [ 1 ]1 2

         — (14)

         h 1 1 4

         Fig.1 Pyramidal horn and coordinate system

      2. Directivity

      The directivity is one of the parameters that is often used as a figure of merit to describe the performance of an antenna [1]. To find the directivity, the maximum radiation is formed. That is, the maximum radiation of the pyramidal horn is directed nearly along the z-axis ( = 0). Using equations (9) and (12), |E |max, |E|max, and in turn Umax can be written as

      |E

      |max

      = |E0

      sin ø | 1 2 {[C(u) C(v)]2 + [S(u) S(v)]2}1/2

      . {C2 ( 1

      2 1

      ) + S2 ( 1

      2 1

      )}1/2 — (15)

      |Eø

      |max

      = |E0

      cos ø | 1 2 {[C(u) C(v)]2 + [S(u) S(v)]2}1/2

      . {C2 ( 1

      2 1

      ) + S2 ( 1

      2 1

      )}1/2 — (16)

      Umax

      = 2 |E |2

      2

      max

      = |E0

      |2 1 2 {[C(u) C(v)]2 + [S(u) S(v)]2}

      2

      . {C2 ( 1

      2 1

      ) + S2 ( 1

      2 1

      )} — (17)

      Where u and v are defined by

      u = 1

      2

      v = 1

      2

      ( 2

      1

      ( 2

      1

      + 1

      2

      – 1

      2

      ) — (18)

      ) — (19)

      Since P

      rad

      = |E |2( 11) — (20)

      4

      The directivity of the pyramidal horn can be written as

      Dp = 4 Umax = 8 1 2 {[C (u) C (v)] 2 + [S (u) S (v)] 2}

      Prad

      11

      which reduces to

      . {C2 ( 1

      2 1

      ) + S2 ( 1

      2 1

      )} — (21)

      p

      p

      D = 2

      32

      DE DH

      — (22)

      Where DE and DH are directivities of the E- and H- plane sectoral horn and are given by

      DE = 4 Umax

      Prad

      = 64 a 1

      () 2 = 64 a 1

      1

      [C2 ( 1

      2 1

      ) + S2 ( 1

      2 1

      )] — (23)

      DE = 4 Umax

      Prad

      = 4 b 2

      1

      .{[C (u) C (v)]2 + [S(u) S(v)]2} — (24)

      Equation (22) is a well known relationship and has been used extensively in the design of pyramidal horns. The directivity (in dB) of a pyramidal horn, over isotropic, can also be approximated by

      D (dB) = 10[1.008 + log

      ( 1 1)] (L +L ) — (25)

      p 10 2 e h

      Where Le and Lh represent, the losses (in dB) due to phase errors in the E- and H- planes of the horn respectively.

   3. DESIGN OF PYRAMIDAL HORN ANTENNA

      The Horn Antenna can be used as a transmit antenna, receive antenna or as a gain standard with gains from 9.5 to 22.0 dBi [5].It's wide bandwidth and predictability is ideal for many broadband applications. Horns covering different frequency bands with various beam width and gain options are needed. The pyramidal horn is widely used as a standard to make gain measurements of other antennas. To design a pyramidal horn, one usually knows the desired gain G0 and the dimensions a, b of the rectangular feed waveguide. The objective of the design is to determine the remaining dimensions (a1, b1, , , pe, and ph) that will lead to an optimum gain. Optimum

      directivities for the E- and H- plane sectoral horns can be obtained by selecting values of b1 and a1. Since the overall efficiency (including both the antenna and aperture efficiencies) of a horn antenna is about 50%, the gain of the antenna can be related to its physical area. Thus

      G0 = 4 1 1 = 2 3 2 21 = 2 3 2 — (26)

      22

      2

      2

      Since for long horns 2 = and 1 = .For pyramidal horn to be physically realizable, pe, and ph must be equal.using this equality, it can be shown that equation(39) reduces to

      ( 2 – )2 (2 – 1) =( G0 3 1 – )2 ( G02 1 1) — (27)

      Where

      2 2

      63

      = and

      = G02 (1) — (28)

      83

      Fig.2 Three-dimensional field pattern of a Pyramidal horn for 1 = 2 = 6, 1 = 5.5, 1 = 2.75, = 0.5, = 0.25 and = = 5.4544 .

   4. RESULT & CONCLUSION

In this paper we have presented the design and radiation pattern analysis of Pyramidal Horn Antenna. It was designed using advanced PCAAD 5.0 [8] with the following dimensions : E- plane aperture dimension a1=16.370cm and H-plane aperture dimension b1=12.859 cm, E-plane axial horn length pe= ph =27.286 cm . Low aperture diameter is used to have high aperture efficiency low phase factor resulting in compact size. The design was performed to accomplish

an ultra-wide bandwidth (more than 50%), with low side-lobe and cross polar levels. The selected frequency bands were X and Ku. Higher order modes are excited at junction between aperture and waveguide due to large flare angles. The simulation results directivity as 20.8 dB, the horn E-plane 3 dB beam width is 12.600 , the horn H-plane 3 dB beam width is 15.360 maximum E-plane phase error is 1620 and maximum H-plane phase error is 1000.The results of rectangular radiation pattern, polar pattern and 3D patterns are shown in Fig.3,Fig.4 and Fig.5 respectively.

Fig.3. Rectangular field pattern

Fig.4. Polar field pattern

Fig.5. 3D field pattern

REFERENCES

1. Constantine. A. Balanis, "Antenna Theory Analysis & Design",John Wiley, & Sons INC, Third Edition.

2. Brian Kidney,Horn antennasEngineering, 98 16 Antennas 2001 .

3. Kirpal singh,Ajay Siwach,Loveline Kaur Advancement in designingwide band Horn Antenna,IJETT,2013.

4. G.S.N.Raju,Antennas and Wave Propagation,Pearson

5. Lei Yang, Weihua Tan, Zhongxiang Shen, and Wen Wu Wide-Band Wide-Coverage Linear Array of Four Semi- Circular Sector Horns IEEE transactions on antennas and propagation, vol. 60, no. 8, August 2012

6. Ramesh Chandra gupta,Shasank saxena ,Milind B.Maharajan,Rajeev jyoti,Design of Dual- Band Multimode Profiled Smooth-Walled Horn Antennas for Satellite Communication IEEE Antennas and wireless propagation letters,vol9,2010

7. Thomas A Milligan, "Modem Antenna Design", John Wiley & Sons INC, Second Edition.

8. PCAAD 5.0 Help/ Instruction Manual

BIOGRAPHY

R. Kiran Chand received M.Tech. Degree from L.B.R.C.E, Mylavaram, Krishna district. He has more than 5 years of teaching experience. His research area interests are Antenna design and optical Communication. Currently he is working as a lecturer in the department of Electrical and computing engineering at ADAMA Science and Technology University, Adama, Ethiopia.

Dr. M.V.Raghavendra is currently working as Professor, Electrical Engineering Dept, Adama Science & Technology University, Ethiopia. He received his PhD from Singhania University, Rajasthan, India in the field of Optical Communication and he is a Research scholar, Department of Instrument Technology, College of Engineering, Andhra University, Andhra Pradesh, India. He has received his M.Tech Degree from ECE Dep, Vishakhapatnam College of Engineering, Andhra University. His main research includes signal estimation & evaluation of optical communication,

Satellite communication & Microwaves. He has published papers in reputed national & international Journals. He has participated in different national & international conferences. He is a life member of ISTE & ISOI, MIAENG, MIACSIT, and MAIRCC.

K. Sathyavathi received M.Tech. Degree from J.N.T.U, Hyderabad. She has more than 8 years of teaching experience. Her research area interests are Antenna design and Analysis and Image Processing. Currently she is working as a Assistant Professor in the department of Electronics and Communication Engineering at MALLAREDDY Group of Institutions, Hyderabad, India.