# Theory of Helix Antenna

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1 Theory of Helix Antenna Tariq Rahim School of Electronic and information, NWPU, Xian china Review on Helix Antenna 1 Introduction The helical antenna is a hybrid of two simple radiating elements, the dipole and loop antennas. A helix becomes a linear antenna when its diameter approaches zero or pitch angle goes to 90º. On the other hand, a helix of fixed diameter can be seen as a loop antenna when the spacing between the turns vanishes (α 0 º ). Helical antennas have been widely used as simple and practical radiators over the last five decades due to their remarkable and unique properties. The rigorous analysis of a helix is extremely complicated. Therefore, radiation properties of the helix, such as gain, far-field pattern, axial ratio, and input impedance have been investigated using experimental methods, approximate analytical techniques, and numerical analyses. Basic radiation properties of helical antennas are reviewed in this report. The geometry of a conventional helix is shown in Figure 1a. The parameters that describe a helix are summarized below. D diameter of helix S spacing between turns N number of turns C circumference of helix πd A total axial length NS α pitch angle If one turn of the helix is unrolled, as shown in Figure 1(b), the relationships between S, C, α and the length of wire per turn, L, are obtained as: S L sin α C tan α L (S 2 C 2 ) 1/2 (S 2 π 2 D 2 ) ½ 1

2 Fig 1. (a) Geometry of helical antenna; (b) Unrolled turn of helical antenna 2 Modes of Operation 2.1 Transmission Modes An infinitely long helix may be modeled as a transmission line or waveguide supporting a finite number of modes. If the length of one turn of the helix is small compared to the wavelength, L, the lowest transmission mode, called the T0 mode, occurs. Figure 2a shows the charge distribution for this mode. When the helix circumference, C, is of the order of about one wavelength (C 1 ), the second-order transmission mode, referred to as the T1 mode, occurs. The charge distribution associated with the T1 mode can be seen in Figure 2b. Higher-order modes can be obtained by increasing of the ratio of circumference to wavelength and varying the pitch angle. 2.2 Radiation Modes When the helix is limited in length, it radiates and can be used as an antenna. There are two radiation modes of important practical applications, the normal mode and the axial mode. Important properties of normal-mode and axial-mode helixes are summarized below. 2

3 Fig 2. Instantaneous charge distribution for transmission modes: (a) The lowest-order mode (T0); (b) The second-order mode (T1) Normal Mode For a helical antenna with dimensions much smaller than wavelength (NL ), the current may be assumed to be of uniform magnitude and with a constant phase along the helix. The maximum radiation occurs in the plane perpendicular to the helix axis, as shown in Figure 3a. This mode of operation is referred to as the normal mode. In general, the radiation field of this mode is elliptically polarized in all directions. But, under particular conditions, the radiation field can be circularly polarized. Because of its small size compared to the wavelength, the normalmode helix has low efficiency and narrow bandwidth Axial Mode When the circumference of a helix is of the order of one wavelength, it radiates with the maximum power density in the direction of its axis, as seen in Figure 3b. This radiation mode is referred to as axial mode. The radiation field of this mode is nearly circularly polarized about the axis. The sense of polarization is related to the sense of the helix winding. In addition to circular polarization, this mode is found to operate over a wide range of frequencies. When the circumference (C ) and pitch angle (α ) are in the ranges of ¾<C/ <¾ and 12º α15º, the radiation characteristics of the axial-mode helix remain relatively constant. The axial-mode helix possesses a number of interesting properties, including wide bandwidth and circularly polarized radiation; it has found many important applications in communication systems. 3

4 (a) (b) 3 Analysis of Helix Fig 3. Radiation patterns of helix: (a) Normal mode; (b) Axial mode Unlike the dipole and loop antennas, the helix has a complicated geometry. There are no exact solutions that describe the behavior of a helix. However, using experimental methods and approximate analytical or numerical techniques, it is possible to study the radiation properties of this antenna with sufficient accuracy. This section briefly discusses the analysis of normal-mode and axial-mode helices. 3.1 Normal-Mode Helix The analysis of a normal-mode helix is based on a uniform current distribution over the length of the helix. Furthermore, the helix may be modeled as a series of small loop and short dipole antennas as shown in Figure 4. The length of the short dipole is the same as the spacing between turns of the helix, while the diameter of the loop is the same as the helix diameter. Since the helix dimensions are much smaller than wavelength, the far-field pattern is independent of the number of turns. It is possible to calculate the total far-field of the normal-mode helix by combining the fields of a small loop and a short dipole connected in series. Doing so, the result for the electric field is expressed as 2 k 2 ID E η e 16r IS E jk e 4r jkr jkr sinˆ sinˆ 4

5 The axial ratio becomes AR E E 2S 2 2 D The normal-mode helix will be circularly polarized if the condition AR 1 is satisfied. This condition is satisfied if the diameter of the helix and the spacing between the turns are related as C 2S It is noted that the polarization of this mode is the same in all directions except along the z-axis where the field is zero. It is also seen from the equation that the maximum radiation occurs at θ 90º ; that is, in a plane normal to the helix axis. 3.2 Axial-Mode Helix Unlike the case of a normal-mode helix, simple analytical solutions for the axial made helix do not exist. Thus, radiation properties and current distributions are obtained using experimental and approximate analytical or numerical methods. The current distribution of a typical axial-mode helix is shown in Figure 5. As noted, the current distribution can be divided into two regions. Near the feed region, the current attenuates smoothly to a minimum, while the current amplitude over the remaining length of the helix is relatively uniform. Since the near-feed region is small compared to the length of the helix, the current can be approximated as a travelling wave of constant amplitude. Using this approximation, the far-field pattern of the axial-mode helix can be analytically determined. There are two methods for the analysis of far-field pattern. In the first method, an N-turn helix is considered as an array of N elements with an element spacing equal to S. The total field pattern is then obtained by multiplying the pattern of one turn of the helix by the array factor. The result is sin( N ) F( ) C 2 0 cos sin( ) 2 Where, C 0 is a constant coefficient and ks cosθ α. Here, α is the phase shift between successive elements and is given as 2 N 5

6 sin( N ) In the above equation cosθ is the element pattern and 2 is the array factor for a uniform sin( ) 2 array of N equally-spaced elements. The Hansen-Woodyard condition is satisfied. This condition is necessary in order to achieve agreement between the measured and calculated patterns. In a second method, the total field is directly calculated by integrating the contributions of the current elements from one end of the helix to another. The current is assumed to be a travelling wave of constant amplitude. The current distribution at an arbitrary point on the helix is written as I l I e Iˆ jg 0 In the above equation l the length of wire from the beginning of the helix to an arbitrary point LT g pc LT the total length of the helix p phase velocity of wave propagation along the helix relative to the velocity of light c. = azimuthal coordinate of an arbitrary point Î unit vector along the wire Î xˆ sin yˆ zˆ sinα m According to Hansen-Woodyard condition 1 p 2N 2N 1 cos sin [ ] N C 6

7 Figure 4. Approximating the geometry of normal-mode helix Figure 5. Measured current distribution on axial-mode helix 7

8 3.3 Empirical Relations for Radiation Properties of Axial-Mode Helix Approximate expressions for radiation properties of an axial-mode helix have also been obtained empirically. A summary of the empirical formulas for radiation characteristics is presented below. These formulas are valid when 12º α 15º, and ¾<C/ <¾ and N>3. The terminal impedance of a helix radiating in the axial mode is nearly resistive with values between 100 and 200 ohms. Smaller values, even near 50 ohms, can be obtained by properly designing the feed. Empirical expressions, based on a large number of measurements, have been derived, and they are used to determine a number of parameters. The input impedance (purely resistive) is obtained by c R 140 Which is accurate to about ±20%, the half-power beam width by 3/ 2 52 HPBW (deg rees) C NS The beam width between nulls by 3/ FNBW (deg rees) C NS The Directivity is given by 2 15NC S D 3 The axial ratio (for the condition of increased directivity) by 2N 1 AR 2N 4 Modified Helices Various modifications of the conventional helical antenna have been proposed for the purpose of improving its radiation characteristics. A summary of these modifications is presented below. 4.1 Helical Antenna with Tapered End Nakano and Yamauchi have proposed a modified helix in which the open end section is tapered as illustrated in Figure 6. This structure provides significant improvement in the axial ratio over a wide bandwidth. According to them, the axial ratio improves as the cone angle θt is increased. 8

10 Figure 6. Tapered helical antenna Figure 7. 1/2 turn half-wavelength printed resonant quadrifilar helix 10

11 Figure 8 Stub-loaded helix configurations Figure 9 Monopole-helix antenna 11

12 Figure 10 Commercial helix with a cupped ground plane. (Courtesy: Seavey Engineering Associates, Inc, Pembroke, MA). Figure 11 Quadrifilar helix Antenna 12

13 4.5 Mono Pulse Helix Antenna: This antenna is used for Search and tracking radar system. 4.6 Dual Band Helix Antenna: This type of antenna is used for dual band application. Fig 12. Monopulse helix antenna 4.7. A Helix Excited Circularly Polarized Hollow Cylindrical Dielectric Resonator Antenna 13

14 Figure 13. Dielectric resonator antenna excited by helix 4.8. Circularly Polarized Patch-Helix Hybrid Antenna with Small Ground 14

15 Fig 14. patch-helix hybrid antenna with different view 15

16 Fig 15. Spiro helix Antenna References 1. J. D. Kraus and R. J. Marhefka, Antennas for all Applications, 3rd ed.boston, MA, USA: McGraw-Hill, Brandan T. Strojny, and Roberto G. Rojas, Bifilar Helix GNSS Antenna for Unmanned Aerial Vehicle Applications, IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 13, J. H. Wang, Antennas for global navigation satellite systems (GNSS), Proc. IEEE, vol. 100, no. 7, pp , Jul Xudong Bai, Jingjing Tang, Xianling Liang, Member, IEEE, Junping Geng, Member, IEEE, and 16

17 5. Ronghong Jin, Senior Member, IEEE Compact Design of Triple-Band Circularly Polarized Quadrifilar Helix Antennas IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 13, J. M. Tranquilla and S. R. Best, A study of the quadrifilar helix antenna for global position system (GPS) applications, IEEE Trans. Antennas Propag., vol. 38, no. 10, pp , Oct W. Y. Qin, J. Qiu, and Q. Wang, A novel multi-frequency quadrifilar helix antenna, in Proc. IEEE Antennas Propag. Soc. Int. Symp., 2005, vol. (1B), pp Sharaiha and Y. Letestu, Quadrifilar helical antennas: Wideband and multiband behavior for GPS applications, in Proc. ICEAA, Sep.2010, pp W. L. Stutzman, and G. A. Thiele, Antenna Theory and Design John Wiley and Sons, Inc., C. A. Balinus, Antenna Theory: Analysis and Design, 2 nd John Wiley and Sons, Inc.,

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