QUAD POLARIZATION WIDEBAND SINUOUS ANTENNA ELEMENTS AND ARRAYS

... tasks, has led to a huge demand for wideband, multifunction antennas Sinuous antennas are chosen as the primary focus for this thesis to achieve quad- polarization, wideband performance while attempting... Recommendations and research directions are proposed for consideration in future developments of broadband, multiple polarization antenna elements and arrays Chapter Review of broadband antennas An antenna. .. these antennas Studies on individual sinuous antenna elements are followed by development of arrays of these antennas A uniform linear array is studied and the common grating-lobe issues in wideband

QUAD POLARIZATION WIDEBAND SINUOUS ANTENNA ELEMENTS AND ARRAYS Ramanan Balakrishnan (B.Eng. (Hons.), NUS ) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2014 DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Ramanan Balakrishnan 15th October 2014 Acknowledgment It would be a gross injustice for me to claim credit for this thesis without acknowledging the numerous people who have been instrumental in its development. I would like to use this section to thank the many individuals whose knowledge, guidance and support were central to this work. Associate Professor Koen Mouthaan for taking me on as his research student and for serving in, and going far beyond, his role of supervisor for this thesis. His guidance, through the multiple discussions on both academia and industry, was deeply valuable in shaping my research over the past few years. His sharp and meticulous attitude towards our work has also strongly influenced the formation of my own methodology and work ethic. Professeur Adjoint R´egis Guinvarc’h from Sup´elec, for being my cosupervisor on this thesis. His expertise in designing antennas proved to be a constant supply of numerous ideas. Many of the antennas used in this thesis are the result of valuable discussions with him. Mr Hongzhao Ray Fang, without whom I highly suspect the timely completion of this thesis. Ray’s knowledge of RF circuitry and the many hours he spent developing the electronics that were used in this thesis warrant special mention. Dr Israel Hinostroza, from Sup´elec, for guiding me during my internship at SONDRA. His insight on spiral antennas and arrays provided for stimulating discussions that helped refine multiple ideas in this thesis. The various measurement campaigns in this thesis would not have been iii possible if not for Professeur Assistant Mohammed Serhir, from Sup´elec, and Mr Joseph Ting, Mr Tan Peng Khiang and Mr Dylan Ang, from Temasek Laboratories at NUS. Their expertise in antenna measurements and kind efforts in accommodating the numerous measurement requests are deeply appreciated. Mdm Lee Siew Choo, Mdm Guo Lin and Mr Sing Cheng Hiong for their sustained support in tackling the unavoidable, and often messy, administrative issues. The former and current members of the MMIC lab, including Tang Xinyi, Hu Zijie and Ashraf Adam for providing a great environment at our small NUS group. Special mention also goes to Panagiotis Piteros, Fr´ed´eric Brigui and Anne-H´el`ene Picot from the SONDRA team, for contributing towards my treasured French experience. Finally, I would also like to thank the vast support network from my family and friends. They were a limitless source of encouragement, enabling the completion of this thesis. iv Contents Abstract viii List of Tables ix List of Figures x 1 Introduction 1 1.1 Advances through broadband design . . . . . . . . . . . . . 2 1.2 Potential applications in radar systems . . . . . . . . . . . . 3 1.3 Motivation for phased arrays . . . . . . . . . . . . . . . . . . 6 1.4 Goals and organization of the thesis . . . . . . . . . . . . . . 8 2 Review of broadband antennas 10 2.1 Techniques to increase antenna bandwidth . . . . . . . . . . 11 2.2 Log-periodic structures . . . . . . . . . . . . . . . . . . . . . 14 2.3 Frequency independent antennas . . . . . . . . . . . . . . . . 16 2.4 Spiral antennas . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5 Sinuous antennas . . . . . . . . . . . . . . . . . . . . . . . . 20 2.6 Summary and choice for further study . . . . . . . . . . . . 22 3 Cavity-backed, four-arm sinuous antenna 23 3.1 Construction of sinuous antennas . . . . . . . . . . . . . . . 23 3.2 Sequential modes for sinuous antennas . . . . . . . . . . . . 28 3.3 Non-sequential modes . . . . . . . . . . . . . . . . . . . . . . 31 v 3.4 Cavity-backing for directional radiation . . . . . . . . . . . . 34 3.5 Prototype and measured results . . . . . . . . . . . . . . . . 36 3.6 Summary on designing sinuous elements . . . . . . . . . . . 48 4 Array configurations of sinuous antennas 49 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 Calculation of array radiation patterns . . . . . . . . . . . . 50 4.2.1 Element spacing and its effect on radiation patterns . 51 4.2.2 Mutual coupling and its impact on the array factor . 53 4.3 Feed network configuration for the array . . . . . . . . . . . 54 4.4 Uniform linear array . . . . . . . . . . . . . . . . . . . . . . 56 4.5 Linear array with variable sized elements . . . . . . . . . . . 61 4.5.1 WAVES . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.5.2 Interstitial packing . . . . . . . . . . . . . . . . . . . 65 4.6 Comparison of the array configurations . . . . . . . . . . . . 69 4.7 Verification with a phased array system simulator . . . . . . 72 4.8 Conclusions and recommendations . . . . . . . . . . . . . . . 75 5 Comparison of spiral and sinuous antennas 78 5.1 Antenna elements . . . . . . . . . . . . . . . . . . . . . . . . 78 5.2 Antenna arrays . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.3 Concluding remarks on spiral and sinuous comparisons . . . 88 6 Connections in planar arrays of sinuous antennas 6.1 90 Frequency limitations due to element sizes and inter-element spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6.2 Planar array of sinuous antennas . . . . . . . . . . . . . . . 92 6.3 Connections between adjacent sinuous elements . . . . . . . 95 6.4 Concluding remarks on use of connections in arrays . . . . . 98 7 Conclusions and recommendations vi 100 Bibliography 106 Appendix A MATLAB code to generate a sinuous arm 113 Appendix B Complete beam steering performance 116 vii Abstract Modern antennas are increasingly being expected to perform multiple functions. The push to having fewer antenna elements, while also covering a larger number of tasks, has led to a huge demand for wideband, multifunction antennas. Sinuous antennas are chosen as the primary focus for this thesis to achieve quad-polarization, wideband performance while attempting to maintain a compact, low-profile shape. Traditional circular-polarization modes are presented together with new techniques for obtaining linear polarization from sinuous antennas. A lowprofile, hollow, metallic cavity is used to replace conventional absorberloaded cavities to obtain compactness in these antennas. Studies on individual sinuous antenna elements are followed by development of arrays of these antennas. A uniform linear array is studied and the common grating-lobe issues in wideband arrays are documented. Arrays with variable sized elements are then developed with the aim of improving such shortcomings. Also, the use of connections between array elements is presented as a technique to optimize the performance of large, planar arrays of sinuous antennas. Finally, a detailed comparison of the performance of sinuous and spiral antennas is presented. The advantages and disadvantages of each of these designs are compared to serve as a reference for future designs of such wideband arrays. viii List of Tables 3.1 Role of design parameters in sinuous antennas. . . . . . . . . 27 3.2 Sequential modes in four-arm sinuous antennas. . . . . . . . 29 3.3 Non-sequential modes in four-arm sinuous antennas. . . . . . 31 3.4 Design parameters chosen for four-arm sinuous element. . . . 37 3.5 Feed network configurations and corresponding polarization modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.1 Design parameters of uniform sinuous array. . . . . . . . . . 92 ix List of Figures 1.1 Typical attenuation across frequency for propagation through foliage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Single channel and composite aerial SAR images. . . . . . . 5 1.3 The USS Klakring, with its mast and top-deck crowded by multiple antennas. . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Phased array system architecture. . . . . . . . . . . . . . . . 7 2.1 Dipoles configurations and bandwidths. . . . . . . . . . . . . 12 2.2 Fundamental Q limits against antenna size. . . . . . . . . . . 13 2.3 Log-periodic dipole array. . . . . . . . . . . . . . . . . . . . 14 2.4 Equi-angular and Archimedean spiral curves. . . . . . . . . . 18 2.5 Band theory of radiation modes in two-arm spirals. . . . . . 19 2.6 Structure of a four-arm sinuous antenna. . . . . . . . . . . . 20 3.1 Sinuous curve with associated design parameters. . . . . . . 24 3.2 One arm of a self-complementary four-arm sinuous antenna. 3.3 Four-arm self-complementary sinuous antenna. . . . . . . . . 25 3.4 Four-arm sinuous antenna modeled in CST Microwave Studio. 27 3.5 Fundamental and higher-order mode radiation patterns in 25 four-arm sinuous antennas. . . . . . . . . . . . . . . . . . . . 30 3.6 Total and polarized radiation patterns for operation in circular mode M+1 . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.7 Radiation patterns for non-sequential modes M2A and M2B . x 31 3.8 Polarization ellipse. . . . . . . . . . . . . . . . . . . . . . . . 32 3.9 Tilt angle and axial ratio in spiral and sinuous antennas. . . 34 3.10 Sinuous antennas with and without absorber-loaded cavities. 35 3.11 Realized boresight gain with reflecting and absorbing cavities. 36 3.12 Prototype of four-arm sinuous antenna with cavity backing. 37 3.13 Input reflection coefficient and input impedance at a single port of the sinuous antenna. . . . . . . . . . . . . . . . . . . 38 3.14 Feed network for the four-port sinuous antenna. . . . . . . . 39 3.15 Anechoic chamber measurement setup in Sup´elec. . . . . . . 40 3.16 Realized boresight gain for circular modes in cavity-backed sinuous antennas. . . . . . . . . . . . . . . . . . . . . . . . . 41 3.17 Boresight axial ratio for circular modes in cavity-backed sinuous antennas. . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.18 Normalized radiation patterns of sinuous antennas in two circular modes. . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.19 Realized boresight gain for linear modes of cavity-backed sinuous antennas. . . . . . . . . . . . . . . . . . . . . . . . . 44 3.20 Co-polarization and cross-polarization gain (measurement) for linear mode of cavity-backed sinuous antennas. . . . . . . 44 3.21 Normalized radiation patterns of sinuous antennas in two linear modes. . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.22 Sinuous antennas with (a) tapered and (b) truncated terminations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.23 Boresight co-polarized gain for the two sinuous terminations when the antennas are operated in a linear mode M2A . . . . 47 4.1 Array factor plots at different element spacings. . . . . . . . 51 4.2 Feed network used for excitation of the arrays. . . . . . . . . 55 4.3 Uniform linear array of sinuous antennas over a ground plane. 56 xi 4.4 Uniform linear array of sinuous antennas in the anechoic chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.5 Input reflections in a uniform linear array of sinuous antennas. 57 4.6 Realized boresight gain of the ULA. . . . . . . . . . . . . . . 58 4.7 Polarization performance of uniform linear array. . . . . . . 59 4.8 Beam steering performance of the ULA of sinuous antennas. 4.9 WAVES configuration of sinuous antennas over a ground plane. 62 60 4.10 Input reflections in a WAVES configuration of sinuous antennas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.11 Realized boresight gain of the WAVES. . . . . . . . . . . . . 63 4.12 Polarization performance of WAVES. . . . . . . . . . . . . . 63 4.13 Beam steering performance of the WAVES of sinuous antennas. 64 4.14 Comparison of sizes of large and small sinuous elements used in arrays with variable sized elements. . . . . . . . . . . . . . 65 4.15 WIPA configuration of sinuous antennas over a ground plane. 66 4.16 Input reflections in a WIPA configuration of sinuous antennas. 66 4.17 Realized boresight gain of the WIPA. . . . . . . . . . . . . . 67 4.18 Polarization performance of WIPA . . . . . . . . . . . . . . 67 4.19 Beam steering performance of the WIPA of sinuous antennas. 68 4.20 Realized gain of the three array configurations. . . . . . . . . 69 4.21 Polarization performance of the three array configurations. . 70 4.22 Beam steering performance of the three array configurations. 70 4.23 Simulation setup in PASS. . . . . . . . . . . . . . . . . . . . 73 4.24 ULA performance using array factor, PASS and measurement. 74 4.25 WAVES and WIPA performance in PASS and measurement. 75 5.1 Sinuous and spiral prototypes. . . . . . . . . . . . . . . . . . 79 5.2 |S11 | of spiral and sinuous antennas with different cavity depths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 xii 5.3 Boresight gain of spiral and sinuous antennas with different cavity depths. . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.4 Boresight axial ratio of spiral and sinuous antennas with different cavity depths. . . . . . . . . . . . . . . . . . . . . . 81 5.5 Radiation pattern of spiral and sinuous antennas with different cavity depths. . . . . . . . . . . . . . . . . . . . . . . 82 5.6 ULA, WAVES and WIPA configurations of sinuous and spiral antenna elements. . . . . . . . . . . . . . . . . . . . . . . 83 5.7 Boresight gain of sinuous and spiral antennas in different array configurations. . . . . . . . . . . . . . . . . . . . . . . 84 5.8 Boresight axial ratio of sinuous and spiral antennas in different array configurations. . . . . . . . . . . . . . . . . . . . 85 5.9 Normalized radiation patterns (boresight and steered) of sinuous and spiral antennas in different array configurations. . . 87 6.1 Planar sinuous array. . . . . . . . . . . . . . . . . . . . . . . 92 6.2 Feed network used for exciting center element of the planar array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.3 Active reflection coefficient of planar array of sinuous antennas. 94 6.4 Boresight gain when center element of the planar array is excited in mode M+1 configuration. . . . . . . . . . . . . . . 94 6.5 Adjacent sinuous elements in unconnected and connected planar arrays. . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.6 Planar array of sinuous antennas with connections across arms of adjacent elements. . . . . . . . . . . . . . . . . . . . 96 6.7 ARC and boresight gain performance (CST simulation) of elements with and without connections. . . . . . . . . . . . . 96 6.8 ARC and boresight gain performance (measured) of elements with and without connections. . . . . . . . . . . . . . . . . . 97 xiii 6.9 Axial ratio performance (measured) of the unconnected and connected arrays. . . . . . . . . . . . . . . . . . . . . . . . . 98 A.1 One arm of a self-complementary four-arm sinuous antenna. 115 B.1 Array feed network (left) and the ULA, WAVES and WIPA configurations of sinuous arrays (right). . . . . . . . . . . . . 116 B.2 Beam steering performance of the ULA of sinuous antennas in circular modes. . . . . . . . . . . . . . . . . . . . . . . . . 117 B.3 Beam steering performance of the ULA of sinuous antennas in linear modes. . . . . . . . . . . . . . . . . . . . . . . . . . 118 B.4 Beam steering performance of the WAVES of sinuous antennas in circular modes. . . . . . . . . . . . . . . . . . . . . . . 119 B.5 Beam steering performance of the WAVES of sinuous antennas in linear modes. . . . . . . . . . . . . . . . . . . . . . . . 120 B.6 Beam steering performance of the WIPA of sinuous antennas in circular modes. . . . . . . . . . . . . . . . . . . . . . . . . 121 B.7 Beam steering performance of the WIPA of sinuous antennas in linear modes. . . . . . . . . . . . . . . . . . . . . . . . . . 122 xiv List of Symbols λ r wavelength relative dielectric constant k wave number, defined as 2π/λ (r, φ) polar coordinates Sij scattering parameters R radius of antenna element τ scaling factor (in log-periodic designs) α angular span parameter (for sinuous antennas) δ spacing parameter (for sinuous antennas) d element spacing (in antenna arrays) Ee (θ) element radiation pattern (in array pattern calculations) ψn wave phase of n-th element (in array pattern calculations) xv List of Abbreviations ARC active reflection coefficient BFN beam former network FOPEN foliage penetrating LHCP left hand circular polarization LPDA log-periodic dipole array PASS phased array system simulator RADAR radio detection and ranging RF radio frequency RHCP right hand circular polarization SAR synthetic aperture radar UHF ultra-high frequency ULA uniform linear array WAVES wideband array with variable element size WIPA wideband interstitially packed array xvi Chapter 1 Introduction Modern wireless systems have grown tremendously over the past few decades. Antennas are among the key components in these systems, enabling the ‘wireless’ aspect by serving as an interface to transmit and receive electromagnetic waves. A few of the modern wireless systems in which antennas play a crucial role include mobile phones, radio receivers, TV broadcasting stations, radar and satellite communications systems. In recent years, there has been a huge growth in wireless communications, microwave imaging, sensors and radars. This has resulted in increased demand for antennas suited for each of these applications. In addition, various application requirements such as conformity, wide operational bandwidth and multi-functionality now need to be satisfied by modern antenna designs. Careful deliberation is required before antennas are chosen for each system. There are different aspects, such as gain, input impedance, bandwidth and pattern beamwidth, which need to be prioritized when designing antennas (the definition of each of these terms can be found in [1]). The development of broadband designs is one of these aspects through which the improvement of antenna technology can be carried out. 1 1.1 Advances through broadband design The electromagnetic spectrum has become highly fragmented in its use across various wireless systems. Each system occupies a different portion of the frequency spectrum suited to its own operational requirement. For example, the various communication standards such as GSM, wireless LAN (WiFi), Bluetooth, WiMAX and LTE operate in different frequency bands. Due to this distribution of systems across multiple frequencies, it becomes difficult to design a single antenna for all systems. Thus, numerous antenna designs have cropped up, each covering specific applications and frequency bands. However, it would be ideal to obtain a single antenna design which can operate across all these bands (i.e. a broadband antenna) and thus simplify the realization of these electronics systems. Broadband antennas can be described as those antennas which satisfy given performance requirements across multiple frequencies. The requirements may specify multiple performance goals in terms of parameters such as input impedance matching, gain, beamwidth and sidelobe levels. Broadband antennas would also allow for realization of frequency diversity in systems. By operating at multiple frequencies, the degrading effects of frequency selective fading can be mitigated. Also, spread spectrum techniques, such as frequency hopping, would be possible and allow for more robust and secure channels [2]. Another means of improving the diversity of systems is through the utilization of multiple polarizations. Also referred to as polarization-diversity, the technique of splitting information across multiple polarizations allows for benefits similar to frequency-diversity. Since many phenomena, such as scattering and reflection, are anisotropic in nature, the use of different polarizations could provide vastly different information about the systems being studied [3]. Thus, the use of signals across a large frequency range together with polarization diversity, can help to realize effective broadband 2 antenna systems. Due to the numerous scenarios in which antennas are used, it is difficult to describe the benefits of broadband operation exhaustively. A particular application needs to be chosen for the purpose of discussion and for maintaining conciseness. 1.2 Potential applications in radar systems Among many applications, radar stands out as particularly well-suited for the application of wideband antennas since electromagnetic waves from different frequencies interact differently with the environment. Low-frequency radars, such as those in VHF/UHF bands, can be used for long distance sensing, while higher frequency radars, such as those in X/Ku bands, are used for high-resolution imaging. Even though high frequency radars are constantly being developed for improved resolution and faster tracking, low frequency systems still remain essential due to their low loss in propagation environments [4]. The expected level of attenuation as signals of different frequencies travel through foliage can be seen in Fig. 1.1. Thus, long distance and foliage penetrating (FOPEN) systems require the low frequency region to optimize performance. A single antenna system which can cover the FOPEN bands as well as the high-resolution bands would help simplify numerous aspects of a radar system. Such systems would result in reduced costs, easier integration, lighter weight and better utilization of space constraints. The additional degree of freedom obtained through the use of multiple polarizations can also be incorporated into radar systems. Advanced signal processing algorithms utilizing independent sources of data can provide additional information previously unavailable. The use of such polarimetric 3 Specific Attenuation (dB/m) 10 1 10-1 V 10-2 H 10 GHz 1 GHz 100 GHz Frequency V: vertical polarization, H: horizontal polarization 10 MHz 100 MHz Fig. 1.1. Typical attenuation across frequency for propagation through foliage. Source: ITU-R, Attenuation in vegetation, Recommendation series on radiowave propagation, 2013 [5]. data has been demonstrated to be useful specifically for synthetic aperture radar (SAR) applications [6]. The additional polarization data would be useful in characterizing the foliage models and obtaining accurate estimates of the target being imaged while ignoring the high-clutter in these environments. Systems making use of such polarimetric data have been implemented by various studies [7],[8], and their results indicate improved edge detection, texture characterization and change detection. Without the ability to record polarimetric data, the images would be similar to the individual images seen in Fig. 1.2a. However, by having a system which can simultaneously acquire multiple sources of data and combine them, it is possible to bring out additional details as seen in Fig. 1.2b. However, radar systems have been historically implemented with small bandwidths, operating in specific frequency bands. This has led to numerous systems being developed, each optimized only for specific frequency bands and polarization states. For example, UHF/VHF band radars (used for long range and ground 4 * E(sB , B⊥ ) = ⎡⎣U ( A, A⊥ ) a ( B , B⊥ ) ⎤⎦ E(sA, A⊥ ) (31) * E(sA, A⊥ ) = ⎡⎣U ( B , B⊥ ) a ( A, A⊥ ) ⎤⎦ E(sB , B⊥ ) Single vs. Multi polarization sar data (32) Now, introducing the results of (30) and (32) into (27) we get The main property of the span is that it is polarimetrically invariable, that is, it does not depend on the polarization basis employed to describe the polarization of the electromagnetic waves. Now, if we consider the definition (11) into (19) we get ( ) |Shh| |Shv| |Svv| (dB) -15dB -30dB (dB) 0dB (a) (a) |Shh+ Svv| |Shh- Svv| |Shv| (b) Fig. 1.2. Aerial SAR images obtained using (a) separate channels and (b) a composite of individual channels. Source: European Space Agency, Polarimetric SAR Data Processing and Education Tool (PolSarPro), 2006 [7]. 14 Span penetrating systems) and S/X band radars (used for short range and higher Figure 5 Intensities of the elements of the scattering matrix measured in the basis (h,v) and the resulting span. resolution) are implemented as completely distinct systems. The use of difTherefore, the span presents the same limitations as the radar cross section in order to represent the polarimetric information contained in the scattering matrix, that is, the important ferent systems to achieve broadband and multiple polarization information 9 often leads to crowding and operational difficulties in tactical environments. Fig. 1.3 shows the top-deck of a typical frigate. Multiple HF whip antennas, a VHF parabolic dish and numerous radomes for K/Ku-band radar and satellite communications can be seen. The numerous systems clustered together could also lead to degradation of each other’s performance. If complete functionality of systems can be Fig. 1.3. The USS Klakring, with its mast and top-deck crowded by multiple antennas. Source: P. Farley, USS Klakring, United States Navy release, 2012 [9]. 5 (33) −1 * E(sB , B⊥ ) = ⎜⎛ ⎣⎡U ( B , B⊥ ) a ( A, A⊥ ) ⎦⎤ ⎟⎞ ⎣⎡ S( A, A⊥ ) ⎦⎤ ⎣⎡U ( B , B⊥ ) a ( A, A⊥ ) ⎦⎤ E(iB , B⊥ ) ⎝ ⎠ −1 *T Since the transformation matrix ⎡⎣U ( A, A⊥ ) a ( B , B⊥ ) ⎤⎦ is unitary, i.e., [U ] = [U ] , we get (20) SPAN ⎡⎣ S( ⊥ ,// ) ⎤⎦ = 4π (σ ⊥⊥ + 2σ ⊥ // + σ //// ) (dB) * ⎡U ( B , B ) a ( A, A ) ⎤ E(sB , B ) = ⎡ S( A, A ) ⎤ ⎡U ( B , B ) a ( A, A ) ⎤ E(iB , B ) ⊥ ⊥ ⎦ ⊥ ⊥ ⎦⎣ ⊥ ⊥ ⎦ ⊥ ⎣ ⎣ (34) maintained while only requiring a single antenna system operating across multiple bands, large savings can be realized. Ideally, it would be best if these systems are also developed with a low-profile to allow for conformal integration. 1.3 Motivation for phased arrays To further extend the capabilities of antenna systems, a logical step would be to investigate array configurations of antennas. An obvious advantage in developing arrays is the increase in overall system gain. Another, perhaps more significant advantage, which is not possible without using arrays, is the capability of beam steering. Expensive and failure-prone mechanical systems for orienting antennas are no longer needed if the pointing of antenna beams can be controlled electronically. Phased arrays are the typical means of achieving such control in antenna systems [10]. A phased array of antennas comprises of multiple radiating elements, distributed over multiple locations, which can work together in a coordinated manner. The amplitude and phase of inputs to each element in a phased array can be controlled to modify the radiation characteristics as required. The additional flexibility introduced by such a system includes not only the capability to obtain beams of different sizes (from broad, fanbeams to narrow, pencil-beams), but also the ability to electronically steer these beams to a particular direction. Fig. 1.4 shows the basic structure of a phased array system. A signal which is incident at an angle (θ) to the plane of the array, would impinge on the distributed elements with differing phase fronts. The difference in path lengths between adjacent elements can be geometrically calculated (equal to d sin θ) and a phase difference (∆φ = d sin θ/λ) applied across adjacent elements to point the beam to this angle. This electroni- 6 θ Antennas d … Phase shifters Power divider Fig. 1.4. Phased array system architecture. cally steerable functionality in phased array systems allows for automated scanning through various angles without the complications of mechanically rotated systems. Development of phased arrays with broadband functionality require significant engineering effort in multiple areas. Starting with the antennas, requirements would dictate that the broadband antenna elements have wide or, optimally, an omni-directional radiation pattern to allow for large steering angles. Also, the entire RF front-end architecture should be broadband in order to effectively collect and combine the energy received by the antennas. Broadband phase-shifters, amplifiers and power-combiners are some of the minimum components required. A broadband, multiple polarization, steerable phased array would allow for robust capabilities in radar systems by integrating FOPEN and high-resolution capability, while also having advanced features such as frequency-hopping (to avoid detection and jamming) and beam steering (to track multiple/moving targets). 7 1.4 Goals and organization of the thesis With the motivations established by the previous section, the goals of this thesis are identified as developing an antenna operating over a frequency range of two octaves (from 0.6 to 2.4 GHz) which also has quad-polarization (dual-circular and dual-linear) operation. The antenna will also be integrated into a phased array demonstrator for confirming beam steering capability across the wide operating range. A number of challenges will be identified and tackled in the process of building the final system. Apart from designing a broadband antenna which provides complete polarization control over the entire frequency range, such a system also requires significant effort in designing the electronics of the RF front-end. Thus, it needs to be noted that this thesis focuses only on the development of specific antenna elements. Details about the design, realization and performance of the RF components used in this work can be found in the doctoral thesis of Fang Hangzhao [11]. Starting with a review of existing work, Chapter 2 discusses the options for broadband antenna elements and also general techniques for increasing bandwidth in antennas. A short comparison of the popular options is made before sinuous elements are chosen for further investigation. Chapter 3 explores the construction, theory of operation and measurement of sinuous antennas. These antennas are built with practical constraints, such as low-profile and uni-directional radiation, in consideration and recommendations on adapting the design to other use cases are provided. Array configurations of these antennas are detailed in Chapter 4. After analyzing common problems in building wideband arrays, linear configurations of sinuous antennas are realized. New layout options for obtaining compact arrays are also presented in this chapter. As this work was developed in parallel with the study of spiral antennas 8 by Fang Hangzhao [11], a detailed comparison is made between the sinuous and spiral designs in Chapter 5. That chapter provides detailed information on how the two designs operate given fixed specifications. An introduction into uniform planar arrays of sinuous antennas is presented in Chapter 6. A preliminary investigation into connected planar arrays of such antennas is conducted with the aim of improving low-frequency performance. Finally, Chapter 7 provides a summary of the complete thesis. Recommendations and research directions are proposed for consideration in future developments of broadband, multiple polarization antenna elements and arrays. 9 Chapter 2 Review of broadband antennas An antenna is defined as the “part of a transmitting or receiving system that is designed to radiate or to receive electromagnetic waves” by the IEEE Standard Definitions of Terms for Antennas [1]. At a fundamental level, they can be seen as structures which facilitate the coupling of energy between a guiding medium and a propagation channel (usually free-space). In practical realizations, antennas utilize time-varying electric currents flowing across their surface to generate time-varying electric and magnetic fields (following Maxwell’s equations). These fields are then propagated as electromagnetic waves. Thus, it is not surprising that the performance of an antenna is highly dependent on its physical characteristics i.e. its shape, size, and material composition. The bandwidth of an antenna can be defined as the frequency range within which the operation of the antenna in terms of a particular characteristics satisfies specified standards. The characteristics commonly considered include input impedance, gain, and polarization. Also, since these characteristics may not vary in the same manner, the definition of bandwidth in each situation becomes non-obvious. This chapter will mainly use the definition of bandwidth with respect to the impedance and pattern performance (gain, axial ratio and side-lobe level) of a given antenna. 10 2.1 Techniques to increase antenna bandwidth As explained earlier, the different dimensions of an antenna play crucial roles in its performance. The example of a dipole, which is one of the simplest types of antennas that has been exhaustively studied in existing literature, can be used to explain this effect. Consider a dipole of length l. This dipole will efficiently radiate electromagnetic signals at a wavelength λ, according to the relation l = λ/2. Thus, given fixed values for l, only a narrow range of frequencies around a wavelength of λ = 2l are radiated. The typical values of the bandwidth around this center frequency are between 5 to 10% [12]. Having understood such bandwidth constraints, we will look at techniques to increase the bandwidth while maintaining the overall size of the antenna. Thus, the main motivation of this section is to understand techniques to increase an antenna’s bandwidth while maintaining fixed size constraints. In the case of the classical dipoles, the bandwidth can be increased by ‘fattening’ the dipoles i.e. increasing the cylindrical radius of typical wire dipoles. This allows for a larger variation in the physical extents of the antenna, resulting in reduced resonant effects. This translates to an increased bandwidth of operation for the dipole. The ratio between the length (l) and the diameter (d) of the dipole’s cylinder can be used as an estimate for the bandwidth: antennas with a l/d ratio of bandwidth of about 5%, while those with a larger l/d ratio of 5000 have a 250 show a bandwidth of 30% [13]. This technique has often been implemented to develop variations on dipole antennas, such as biconical, discone and bow-tie antennas [14]. Due to their extended size and tapering structure, these antennas are can be used as effective broadband radiators. This process can be summarized as seen in Fig. 2.1. Note that the maximum dimension of each of the four 11 antennas shown in Fig. 2.1 is the same, i.e. the bounding sphere for each of the four cases has the same radius. (a) (b) (c) (d) Fig. 2.1. Dipoles configurations, arranged in increasing order of bandwidths given fixed sizes. This approach of associating the volume occupied by the antenna with its bandwidth has been extensively studied in literature [15],[16],[17]. The approach of modeling the volume occupied by the antenna as a sphere of radius r was first proposed by Chu [18] and later expanded by Harrington [19]. The explanations used in this section closely follow the methods developed in the mentioned works. The fractional bandwidth (FBW) of an antenna can be related to the quality factor Q of a system through (2.1), where f0 is the center frequency and bandwidth is denoted by ∆f . F BW = 1 ∆f = f0 Q (2.1) The Q of an antenna was derived using equivalent electrical circuits for the electromagnetic modes contained within the antenna sphere. It was shown that for the lowest order TM mode, the Q is proportional to the radius of the antenna sphere and also the wave number k (= 2π/λ) as shown in (2.2) [18]. Q 1 (kr)3 (2.2) This equation is considered as the fundamental limit on the size of an antenna: a low value of Q, i.e. a large bandwidth, would dictate the use of 12 a large r. This variation of Q with sphere size is shown in Fig. 2.2, where the different curves denote different radiation efficiencies (ecd = 100, 50, 10 and 5). The figure is adapted from [15] in which the bandwidth of different antennas was compared. For a given sphere size (kr), it is seen that a Goubau antenna has a better bandwidth performance (lower Q) than a dipole. A spiral antenna in turn has a bandwidth larger than both. Though the initial derivations were for electrically small antennas, the principles are seen to remain valid for other designs as well [20]. Fig. 2.2. Fundamental Q limits against antenna size. Adapted from source: R. C. Hansen, “Fundamental limitations in antennas,” Proc. IEEE, Vol. 69, No. 2, February 1981[15]. Thus, it can be said that “the bandwidth of an antenna can be improved only if the antenna utilizes efficiently, with its geometrical configuration, the available volume within the sphere” [13] (the sphere denoting the bounding volume occupied by the antenna). 13 2.2 Log-periodic structures The previous section focused on increasing the bandwidth given an initial ‘narrow band’ antenna design. However, there are also means to combine multiple resonant elements to achieve broadband operation. Logarithmically periodic structures are such a class of antennas which can be used as effective radiators over large bandwidths [21]. As the name suggests, these antennas have structures which are repeated at intervals periodic with the logarithm of frequency. As a result, the performance characteristics of these antennas are also periodic when considered against frequency in the log-scale. The most common of these antennas is the log-periodic array of dipole antenna (LPDA) developed by Isbell [22]. Despite appearing very similar to Yagi-Uda antennas [23], the LPDA operates under different principles. While the Yagi consists of a single excited element with a reflector and multiple directors, the LPDA instead consists of a series of dipoles, the length of subsequent sections varying by a fixed geometric ratio (τ , (2.3)). This factor can be called the log-periodic growth factor of the array and determines the repetition rate of the performance in log-frequency scales. τ= ln Rn = Rn+1 ln+1 𝑙𝑛 (2.3) 𝑙𝑛+1 𝑅𝑛 𝑅𝑛+1 Fig. 2.3. Log-periodic dipole array with different dimensions indicated. 14 The performance of these antennas has been extensively investigated and numerous sources provide reference design values to obtain different levels of performance from LPDAs [24],[25]. Such design equations can be used to build LPDAs operating over very wide bandwidths, while satisfying given specifications for gain and input impedance. The end-fire beam from these antennas is focused in the direction of the shorter elements. Also, the beam is linearly polarized with the axis of polarization aligned with the orientation of the dipoles. It is possible to obtain a polarization orthogonal to the initial polarization by either mechanically rotating the array, or by adding another array oriented perpendicular to the first. The second approach of adding a ‘crossed’ array is preferable over the first, since it adds the ability to electronically control the polarization. This can be seen as a trade-off decision between choosing mechanically rotating parts or increased size footprints. If both elements of the crossed array are simultaneously excited with a 90◦ phase shift between them, then circular polarization can also be obtained. Due to the three-dimensional structure, and ‘crossed array’ requirement for dual polarization, the log-periodic dipole array is not a viable solution for applications requiring conformal antennas. Antennas which are meant to be integrated on platforms, such as airborne systems, require ease of integration with planar surfaces and LPDAs present considerable difficulty in this aspect. Also, these antennas have unequal beamwidths in different planes of their radiation patterns [26], which is undesirable when planning for beam steering in 2-D scanning arrays. 15 2.3 Frequency independent antennas As noted in the earlier discussions, the characterization of an antenna structure by its physical dimensions, i.e. its length, width, and height, were seen as limiting factors. To overcome these limitations, a breakthrough in the development of ‘frequency-independent’ antennas was made based on the realization of structures which could be completely specified using only angles. This theory of frequency-independent antennas was developed by Rumsey [27], close to the time when log-periodic structures were also developed. These frequency-independent antennas demonstrated far greater achievable bandwidths than previous records at that time. While previous broadband antennas were working over a frequency ratio of 2 : 1, the frequencyindependent designs were capable of frequency ratio of more than 20 : 1. In theory, the size of an antenna is typically calculated in terms of the electrical length. Thus scaling down all physical dimensions by a factor of 2 should leave all performance characteristics (such as gain, impedance and polarization) unaffected if the frequency of interest is doubled. This is because the structure continues to appear the same in electrical-length terms. This scaling idea was extended to imply that a model which remains invariant to scaling in any dimension would be a frequency-independent structure. The invariance with length is achieved by specifying a structure using only angles. The formulation of these types of antennas was first proposed in [27] and later expanded in [28]. The material presented below closely follows the explanations in the works cited above. Consider a curve represented in polar coordinates by the equation: r = F (θ, φ) (2.4) When scaling this curve by a factor k, the frequency of interest is scaled by a factor 1/k. In order for the curve to be invariant at both these scales, 16 the condition imposed is that the curve remains a rotated version of itself as in: kF (θ, φ) = F (θ, φ + φo ) (2.5) This equation can now be solved to yield the solutions allowed for F (θ, φ) and is shown in (2.6). r = F (θ, φ) = eaφ f (θ) (2.6) where a = 1 dk and f (θ) is any function. k dφo Depending on the choice of f (θ), a number of different curves can be generated and each of these would lead to different types of frequencyindependent antennas. For an antenna to be completely frequency independent, it should extend to an infinitely large size, while also having an extremely precise center region. However, this is not achievable in real life, and truncation at both the ends of the structure is necessary. These practical considerations result in limitations for the bandwidths of these antennas. Consider a frequency-independent antenna being fed from the center region. As the signals propagate through the structure, the different frequency components are radiated in decreasing order of frequency. Starting with the highest frequency components, as the currents continue to travel along the antenna, lower-frequency parts would be radiated. However the truncation of the antenna into a finite structure, results in a limit on how far the currents can travel. If there are any low frequency components which are not radiated by the time the end is reached, then they get reflected and are not radiated. Thus, the limit on the extents of the antenna establishes the low frequency cutoff. The size of the antenna is once again seen as the crucial factor in achieving broadband designs. 17 2.4 Spiral antennas One of the earliest frequency-independent antenna to be developed was the equiangular spiral [29]. These spirals can simply be seen as those curves in which the function f (θ) is set to obtain the overall curve equation as r = Ceaφ . A similar spiral curve obtained by having a fixed increase in the radius with each turn is called an Archimedean spiral [30]. Both curves are shown in Fig. 2.4. The first documented spirals were in slot-form [31], however, subsequent versions have focused on printed strip methods due to their ease in manufacturing [30],[32],[33]. By duplicating and rotating the curve, multiple copies can be obtained, resulting in multi-arm spirals. 90 90 120 120 60 150 150 30 180 0 210 30 180 330 240 60 0 210 300 330 240 300 270 270 (a) (b) Fig. 2.4. Polar representations of common spiral curves (a) equi-angular and (b) Archimedean. The radiation from spiral antennas is modeled by a ‘radiating ring’ theory (or ‘band theory’) developed in [30] (Fig. 2.5). Consider a twoarm spiral in which the center of each arm (A and A ) is excited with a phase difference of 180◦ . As the currents travel along each arm, the phase difference between the two arms continues to progressively change. Consider a point B along the first arm and B along the second arm, where the circumference of the spiral corresponds to one wavelength (λ) at a particular frequency. At this region, the phases between adjacent arms would be exactly aligned. This results in strong radiation occurring from 18 C’ C A’- A + B B’ Fig. 2.5. Band theory of radiation modes in two-arm spirals. this region, called the mode 1 region of the antenna. This is known as the traveling wave mode of the spiral and is the most common mode used to make spirals exhibit broadband behavior. Due the periodic nature of signal phase, other in-phase regions are also present at regions where the circumference corresponds to larger integer multiples of the wavelength. These subsequent regions are referred to as the higher order modes of the spiral (modes 2, 3, ...). The radiating mode of the spiral can be controlled by the amplitude and phase of the inputs to each of these arms. A N -arm spiral is considered to be able to radiate in N − 1 modes. Each of these modes has a fixed phase-shift between adjacent arms and the magnitude of this phase-shift determines the mode number [32]. As suggested by the circular winding, spiral antennas radiate circular polarization, with the sense of winding (clockwise or counter-clockwise) differentiating between right-circular and left-circular polarization. It is important to note here that spiral antennas have bi-directional radiation patterns with opposite senses of polarization in the upper and lower hemispheres. Conical versions of spiral antennas are also possible. These designs 19 involve projecting the shape of a spiral onto a cone and thereby obtaining uni-directional radiation from the antenna [34],[35]. Apart from their broadband behavior and circular polarization ability, spiral antennas also have wide beamwidths and due to their different modes are capable of sum and difference operation. Due to such features, spiral antennas are extensively used in many systems including those for communications, electronic counter measures, remote sensing and satellite communications [32]. 2.5 Sinuous antennas In the previous two sections, log-periodicity and frequency-independece were introduced as two distinct methods to achieve broadband performance. A type of antenna which combines both of these techniques, to harness the benefits of both design ideologies, is the sinuous antenna. First developed by DuHamel in his patent [36], sinuous antennas are pedagogically treated as ‘folded’ equiangular spiral antennas. This can be easily seen from the picture of a four-arm sinuous antenna shown in Fig. 2.6. Starting from an equiangular spiral, applying periodic ‘fold-backs’ on each arm, would result in a sinuous structure. Fig. 2.6. Structure of a four-arm sinuous antenna. 20 The frequency independence in this structure is inherited from the spiral antenna: a scaling of the antenna results in a structure which is identical to the original, except for rotation through an angle. Due to this strong similarity with spirals, sinuous antennas also exhibit many of the same properties. Like spirals, sinuous antennas are broadband and have large beamwidths [37]. They are also planar and their manufacturing follows the same principles as in spiral antennas. However, there are also a few clear differences between spiral and sinuous antennas. Unlike spirals, sinuous antennas do not have a fixed sense of winding. As a result, there is no polarization selectivity in the structure of sinuous antennas. It can be said that sinuous antennas contain an interleaving-type structure of left and right-handed spirals, resulting in the lack of a polarization filtering capability [38]. However, as will be seen in later chapters, the polarization in a sinuous antennas can still be controlled through electronic means, without any changes to the structure. This is achieved by varying the mode in which the antenna operates (i.e. the phase relationships between the multiple arms of the antenna). The periodic intervals at which the sinuous ‘fold-backs’ occur follow a geometric progression, i.e. the ratio between adjacent sections is fixed. These adjacent sections of differing radii are called cells and the size ratio between adjacent cells is called the growth factor. This parameter plays a role similar to the scaling technique used for elements in LPDAs. This results in a log-periodic variation (against frequency) in the performance of a sinuous antenna. Due to their quad-polarization capability, while retaining broadband behaviour, sinuous antennas appear as promising candidates for the goals initially outlined in this thesis. These antennas can also satisfy conformal requirements for integration, by being realized in planar form. 21 2.6 Summary and choice for further study Each of the antennas described so far comes with its own advantages and disadvantages. Due to the differences in requirements across various applications, there cannot be a single ‘best’ antenna. While the broadband dipole-based designs and LPDAs provide simple modes of operations, they fail at supporting dual-polarization. Whereas, the spiral and sinuous antennas support dual-polarization but require complex feed networks. Also the differing requirements for gain, bandwidth, conformal integration and size further complicate the selection of an antenna. However, a decision still needs to be made for further progress to be made and in view of the requirements as stated in Chapter 1, sinuous antennas are chosen as the primary focus for this thesis. The decision is based on the broadband, multiple polarization capability of these antennas, even in planar versions. Also, due to their limited adoption in modern systems, sinuous antennas also warrant further inspection to obtain a clearer understanding of the principles behind their operation. 22 Chapter 3 Cavity-backed, four-arm sinuous antenna Sinuous antennas, as described in the previous chapter, are broadband antennas capable of radiating multiple-polarizations. In this chapter, they will be investigated in more detail, covering all aspects from construction and operating modes to practical realizations and measured results. Sinuous antennas are typically designed with an even number of arms in order to maintain a balanced configuration. Two-arm sinuous antennas are capable of providing a single circular polarization. However, there are no methods to control the sense of polarization obtained from them. In order to successfully obtain multiple modes of operation, a minimum of four arms is required. Thus, a four-arm sinuous antenna will be studied here, with the consideration that it is to be later used in array configurations. 3.1 Construction of sinuous antennas A sinuous curve can be considered as an equiangular spiral curve of increasing radius which has periodic fold-backs in its structure. Geometrically, it is described as consisting of P cells, with the pth cell located at a distance Rp from the centre. The distance between adjacent cells is determined by 23 Y 𝛼 O 𝑟 ϕ X 𝑅𝑝+1 𝑅𝑝+1 = 𝜏𝑝 𝑅𝑝 𝑅𝑝 Fig. 3.1. Sinuous curve with associated design parameters. the growth factor τp . Equation (3.1) can be used to describe the closed form equation (in polar (r, φ) coordinates) of a single sinuous curve [36]. φ = (−1)p αp sin 180◦ log (r/Rp ) , log τp Rp+1 ≤ r ≤ Rp (3.1) The parameter αp in these equations is used to control the angular span of the sinuous curve. In most log-periodic designs of sinuous antennas, the parameters αp and τp are kept constant, i.e. αp = α and τp = τ for all p. A sinuous curve and the associated parameters are shown in Fig. 3.1. This curve is then duplicated and the two copies are rotated by an angle +δ/2 and −δ/2. The two curves form the outer covers for a single arm of the antenna. At the inner and outer ends created, circular arcs of radii equal to R1 and RP are used to achieve tapered terminations. The angle parameters α and δ together determine the width and gap of the arms and thus, the overall metal to non-metal ratio in the antenna. One arm of a four-arm sinuous antenna, generated by using α = 45◦ and δ = 22.5◦ is shown in Fig. 3.2. Appendix A provides a complete MATLAB program to generate such sinuous structures. This single arm is then copied and rotated through an angle of 90◦ , 180◦ and 270◦ , to obtain a four-arm antenna as seen in Fig. 3.3. 24 60 40 Y (mm) 20 0 −20 −40 −60 −80 0 20 40 X (mm) 60 80 100 Fig. 3.2. One arm of a self-complementary four-arm sinuous antenna. 100 80 60 Y (mm) 40 20 0 −20 −40 −60 −80 −100 −100 −50 0 X (mm) 50 100 Fig. 3.3. Four-arm self-complementary sinuous antenna. In general, to obtain a N -arm antenna, the values of α = 180◦ /N and δ = α/2 are used in generating the arm. Following this, N copies of the arm are made and the n-th arm is rotated through an angle of (360◦ × n)/N . This procedure would result in a N -arm sinuous antenna with a self-complementary design, i.e. containing equal metal and nonmetal parts. The values of the outer radius R1 and the log-periodic scaling ratio τ are left as design variables to be optimized for each use case. Sinuous antennas are often considered as folded variations of the equiangular spiral antenna. The sinuous antenna can be visualized by considering 25 an equiangular spiral antenna and periodically folding each arm back on itself as the distance from the center increases. However, differences arise when considering the location of radiating regions in sinuous antennas. Spiral antennas radiate from regions where the circumference of the spiral is equal to an integer multiple of the wavelength. The radiating region for sinuous antennas, however, is determined by the location of half-wavelength sections along the arms. Specifically, the relation between the antenna parameters and the location of the radiation region for a wavelength λ is given by (3.2). This can be generalized to obtain the low-frequency cutoff (denoted by λL ) obtainable from a sinuous antenna of outer radius R1 (3.3). r(α + δ) λ/4 λL = 4R1 (α + δ) (3.2) (3.3) The number of arms, N , in a sinuous antenna determines the modes that can be supported by the antenna. In a sinuous antenna of N arms (considering even values for N ), the radiation modes are numbered from M−n to Mn , where n ∈ {1, 2, ..., N/2}. However, due to the rotational and reflectional symmetry present in sinuous structures, modes M−n and Mn (being mirror images of each other), have identical radiation characteristics, except for the sense of polarization. Table 3.1 summarizes all the design parameters discussed so far and their role in the performance of the antenna. Typical values for each of the parameters are also shown to provide a starting point for common sinuous designs. This thesis will focus on four-arm sinuous antennas, which correspond to the minimum number of arms needed to support both dual-circular and dual-linear polarization. 26 Table 3.1 Role of design parameters in sinuous antennas. Parameter Denotes Typical values Role Determines the number of modes obtainable. N Number of arms 4, 6, 8 R1 Outer radius λL 2π to λL 3π/4 Sets the lower frequency limit. Controls the ratio between adjacent cells and number of cells given a fixed size. τ Growth factor 0.6 to 0.9 α Angular span 22.5◦ to 90◦ δ Angular spacing 11.25◦ to 45◦ These two parameters together control the angular span, interleaving and input impedance of the antenna. The sinuous structure is drawn using a custom MATLAB script and then imported into a full-wave electromagnetic simulator. The transient time-domain solver of CST Microwave Studio is used to simulate the operation of the sinuous antenna (Fig. 3.4). Fig. 3.4. Four-arm sinuous antenna modeled in CST Microwave Studio. 27 3.2 Sequential modes for sinuous antennas Because sinuous antennas are multi-port antennas, they require special attention when considering excitation configurations. Typically, a N -arm sinuous antenna is center-fed with N -ports (one port per arm). However, as in spiral antennas, other configurations such as feed-points at the external ends [39], or along the arms are also possible [40]. Since the fundamental operation is unchanged as long as an effective feeding solution is used, only the center-fed, four-arm, four-port configuration will be considered here. The first restriction imposed on the excitation configuration is that the overall feed has to be balanced, i.e. for every port with an input power of pa = pejθ , there should be another port with input power pb = pe−jθ (p denoting the magnitude, and θ the phase). This restriction is similar to that for differentially-fed antennas. However, note that the sinuous antenna may also contain other arm-pairs which do not obey this rule. Traditionally, the other restriction has been to maintain a fixed phasedifference between adjacent ports, also referred to as sequential excitation of the ports. Such a sequential excitation of the ports, together with evenly spaced positioning of the N -arms helps sinuous antennas to achieve rotationally symmetric radiation patterns. Combining the two restrictions together, the minimal phase-difference between adjacent ports of a N -arm sinuous antenna is 360◦ /N . This minimal phase-difference corresponds to the first radiation mode (M1 ). An integer multiple (m) of this value can also be used and would result in the antenna radiating in a higher mode (Mm ). This allows for the definition of the modes of a sinuous antenna to be based on port configurations. The periodic nature of the phase of a signal (with a period of 360◦ ), results in limits for the values that m can take, i.e. |m| ≤ N/2 . Larger values of m would simply wrap-around and become identical to lower modes. To provide a clear example, the sequential-modes of a four-arm sinuous antenna 28 are provided in Table 3.2. Note that modes M−2 and M+2 are completely identical, while modes M−1 and M+1 have the order of ports reversed. Table 3.2 Sequential modes in four-arm sinuous antennas. Mode number Port 1 Port 2 Port 3 Port 4 M−2 0◦ −180◦ 0◦ −180◦ M−1 0◦ −90◦ −180◦ −270◦ M+1 0◦ 90◦ 180◦ 270◦ M+2 0◦ 180◦ 0◦ 180◦ Inspecting modes M+1 and M−1 in Table 3.2 more carefully, it can be seen that the four ports can be divided into two pairs of differentiallyfed ports, with quadrature phase difference between the pairs. The pair of ports 2 and 4 are exactly 90◦ apart from ports 1 and 3. This excitation is strongly reminiscent of crossed-dipoles and dual-fed patch antennas, which are used for generating circular polarization. Like in these antennas, this excitation configuration in sinuous antennas also results in circularly polarized radiation. However, sinuous antennas maintain the circularly polarized radiation over a much larger bandwidth due to their broadband characteristics. Modes M−1 and M+1 are called the fundamental modes, while modes with greater phase increments are called the higher order modes of the antenna. The differences between these modes are primarily observed in their radiation patterns. The fundamental modes have strong radiation along the normal to the plane of the antenna, while the higher order modes have a null at boresight. The difference in the radiation patterns between the fundamental modes and the higher order modes can be seen in Fig. 3.5. The antennas used to generate these patterns do not have any cavity backing, and thus there is strong radiation in both upper and lower hemispheres. As mentioned earlier, modes M−1 and M+1 can be distinguished based 29 M -1 M + 1 M ± 2 0 1 0 3 3 0 3 0 5 0 3 0 0 R e a liz e d g a in (d B i) -5 6 0 -1 0 -1 5 -2 0 2 7 0 9 0 -1 5 -1 0 -5 2 4 0 1 2 0 0 5 2 1 0 1 0 1 5 0 1 8 0 Fig. 3.5. Fundamental and higher-order mode radiation patterns in fourarm sinuous antennas. on the sense of circular polarization radiated. In mode M+1 , the radiation in the upper and lower hemispheres are of two opposite polarizations: the lower hemisphere is right-circularly polarized, while the upper is leftcircular. The polarization in the hemispheres is switched for mode M+1 in the same antenna. To demonstrate this, the total, left-circular (LHCP) and right-circular (RHCP) polarized patterns of the antenna in mode M+1 can be seen in Fig. 3.6. L H C P R H C P T o ta l 0 1 0 3 3 0 3 0 5 0 R e a liz e d g a in (d B i) -5 3 0 0 6 0 -1 0 -1 5 -2 0 2 7 0 9 0 -1 5 -1 0 -5 2 4 0 1 2 0 0 5 1 0 2 1 0 1 5 0 1 8 0 Fig. 3.6. Total and polarized radiation patterns for operation in circular mode M+1 . 30 3.3 Non-sequential modes Even though most implementations of sinuous antennas use sequentially phased inputs at the antenna ports, it is not a compulsory requirement. In this thesis, non-sequential excitations of the ports are proposed and analyzed. This is done with the aim of solving the problem of the boresight null observed for higher order modes. The feed configurations developed in this thesis are called modes M2A and M2B . The subscripts A and B denoting that they are variations on the sequential mode M2 . By rearranging the port excitation into a nonsequential configuration, the destructive interference effect at boresight can be prevented. The new non-sequential feed configurations proposed are shown in Table 3.3. Table 3.3 Non-sequential modes in four-arm sinuous antennas. Mode number Port 1 Port 2 Port 3 Port 4 M2A 0◦ 180◦ 180◦ 0◦ M2B 0◦ 0◦ 180◦ 180◦ M 2 A M 2 B 0 1 0 3 3 0 3 0 5 0 3 0 0 R e a liz e d g a in (d B ) -5 6 0 -1 0 -1 5 -2 0 2 7 0 9 0 -1 5 -1 0 -5 2 4 0 1 2 0 0 5 1 0 2 1 0 1 5 0 1 8 0 Fig. 3.7. Radiation patterns for non-sequential modes M2A and M2B . 31 The radiation patterns obtained when exciting a four-arm sinuous antenna with these non-sequential configurations are shown in Fig. 3.7. Unlike the higher-order modes shown in Fig. 3.5, these non-sequential modes do not have any null in boresight direction. Note that the new configurations still maintain the requirement of having balanced pairs of port excitations, which helps maintain effective radiation from the antenna. Also, despite having patterns similar to the fundamental modes, these non-sequential modes do not exhibit circular polarization, but rather linear polarization. Thus, it can be said that by utilizing non-sequential modes, the previously dual-circular sinuous antennas can now be made dual-linear radiators, achieving quad-polarization. Since sinuous antennas are designed usually for circularly-polarized radiation, the quality of the linear-polarization obtained needs to be carefully analyzed before being accepted. Fig. 3.8 shows the common description of polarization using an ellipse to describe the different components of radiation. Any two mutually perpendicular axes can be chosen to decompose the components of the polarization ellipse. 𝑦 𝐸𝑦 Tilt angle 𝐸𝑥 𝑥 Fig. 3.8. Polarization ellipse showing the terms used to define axial ratio and tilt angle. ˆ x = Ex x ˆ y = Ey ejδ y Considering the two measured fields as E ˆ and E ˆ, the axial ratio and tilt angle can be calculated as shown in (3.4) and (3.5) [3]. 32 Major Axis = Axial Ratio = Minor Axis Ex 2 + Ey 2 + Ex 4 + Ey 4 + 2Ex 2 Ey 2 cos(2δ) Ex 2 + Ey 2 − Ex 4 + Ey 4 + 2Ex 2 Ey 2 cos(2δ) (3.4) Tilt angle = 1 tan−1 2 2Ex Ey cos δ Ex 2 − Ey 2 (3.5) Ideally, for linearly-polarized antennas, the axial ratio should be as large as possible, while the tilt angle is constant. One of the common concerns when generating linear modes in spiral antennas is the stability of the linear polarization obtained. For example, in a broadband, Archimedean spiral antenna, the tilt angle of the polarization ellipse keeps varying with frequency. In drastic cases, this would result in the antenna being verticallypolarized at one frequency, while being the opposite polarization at a different frequency. This is not desirable in broadband antennas which are required to work consistently over the entire bandwidth of operation. This problem does not arise in sinuous antennas due to the constrained angular span of each arm of the antenna and interleaving design. In spiral antennas, each arm wraps around the entire circumference of the antenna, and this translates to a complete rotation of the axis of the linear polarization. However, each arm of the sinuous antenna, as seen in Fig. 3.1 is constrained within a limited sector. This proves to be important in restricting the rotation of the linear polarization. The effects of this polarization wobble in Archimedean spiral antennas and in sinuous antennas are shown in Fig. 3.9. Note that for good linear polarization, the tilt angle should be constant, while the axial ratio is as high as possbile. For a four-arm Archimedean spiral antenna, the tilt angle shows large variations of ±45◦ across frequency with a relatively low axial ratio (< 10 dB) at certain points. A four-arm sinuous antenna of the same size shows considerably less variation in tilt angle (±10◦ , for f > 1.2 GHz), 33 4 5 3 0 3 0 T ilt a n g le (d e g re e ) T ilt a n g le (d e g re e ) 4 5 1 5 0 -1 5 -3 0 -4 5 1 5 0 -1 5 -3 0 -4 5 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 2 .5 3 .0 F re q u e n c y (G H z ) 7 5 7 5 6 0 6 0 A x ia l ra tio (d B ) A x ia l ra tio (d B ) F re q u e n c y (G H z ) 4 5 3 0 1 5 4 5 3 0 0 1 5 0 .5 1 .0 1 .5 2 .0 2 .5 0 3 .0 F re q u e n c y (G H z ) 0 .5 1 .0 1 .5 2 .0 F re q u e n c y (G H z ) (a) (b) Fig. 3.9. Tilt angle and axial ratio in (a) Archimedean spiral and (b) sinuous antennas. while maintaining high axial ratio. These variations are comparable with values reported for two-arm sinuous antennas, which only possess linear polarizations [41]. Thus it can be said that the linear polarization obtained from the nonsequential modes of the sinuous antenna are still usable. The wobble in the axis of the linear polarization is constrained within a sector and the crosspolarization rejection is maintained over a large bandwidth across multiple octaves. 3.4 Cavity-backing for directional radiation The bi-directional radiation patterns observed in planar sinuous antennas will result in complications when integrating these antennas into practical systems. For applications requiring conformal or low-profile integration 34 with metallic surfaces, the backward radiation would severely interact with the surfaces and degrade the performance of the antenna. Thus, it would be ideal if the antenna could be modified to provide uni-directional radiation. The traditional solution to prevent backward radiation has been to support the antenna with a metallic-cavity backing loaded with absorbers. Most designs utilize a cavity with a depth of λ/4 (at the lowest frequency), and with absorbers located between the antenna surface and the metallic cavity [42]. The cross-section of such a design is shown in Fig. 3.10a. The absorbers have the benefit of reducing the interaction between the backward radiation and the metallic surface of the cavity. However, this simply results in completely losing the energy radiated into the lower hemisphere. Other lower height, absorbing designs have also been proposed which involve stepped cavities [43] or metamaterial structures [44],[45]. (a) (b) Fig. 3.10. Cross-sectional view of sinuous antennas with (a) an absorber loaded cavity and (b) a low-profile, hollow cavity. If it were possible to instead reflect the backward radiation into the forward direction, the gain could theoretically be doubled. This would come at the cost of increased interaction between the metallic cavity and the antenna. Low-profile, hollow cavities with a depth in the order of λ/20 are investigated in this thesis (Fig. 3.10b). The hollow cavities reflect backward radiation into the upper hemisphere with a inversion of the polarization. For example, consider a sinuous antenna excited in mode M+1 , with left-circular polarization in the upper hemisphere and right-circular 35 1 2 R e a liz e d G a in (d B i) 9 6 3 0 -3 B a c k w a rd ra d ia tio n re fle c te d B a c k w a rd ra d ia tio n a b s o rb e d 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 F re q u e n c y (G H z ) Fig. 3.11. Realized boresight gain with reflecting and absorbing cavities. in the lower. Due to the inverting reflection from the cavity, the rightcircular is converted to left-circular polarization when it is reflected to the upper-hemisphere. This results in constructive addition, and the overall gain in the upper hemisphere is significantly improved (Fig. 3.11). The tradeoff associated is the increased reflection observed at the input ports of the antenna. The hollow-cavity demonstrates much stronger radiation at boresight compared to the loaded-cavity. It is observed that the gain is more than doubled at certain points, which may appear impossible. However, note that the plot shows the realized gain which takes into account input matching as well. Due to the interaction with a reflecting cavity, the input matching is different from the case with an absorbing cavity. Thus, the improvement in realized gain is not only due to the reflection of backward radiation, but also due to changes in input matching at certain points. 3.5 Prototype and measured results Following extensive simulations using multiple numerical methods, including CST Microwave Studio (time-domain solver) and HFSS (frequencydomain solver), a final design was chosen. The design parameters of the 36 Table 3.4 Design parameters chosen for four-arm sinuous element. Parameter Value Outer diameter of element (D) 85 mm Log-periodic growth factor (τ ) 0.74 Trace width (α) 45◦ Trace spacing factor (δ) Substrate 22.5◦ Rogers RO4003 Relative dielectric constant ( r ) Thickness (h) 3.35 1.524 mm sinuous antenna can be found in Table 3.4. The overall size of the prototype was set to match that of the Archimedean spiral antenna developed by Fang Hangzhao, discussed in detail in his thesis [11]. This choice was made to enable a reasonable analysis when comparing the two different types of antennas Chapter 5. Also, two cavities with different depths were used in the measurements, to judge the effect of cavity depth on performance. A completely assembled prototype can be seen in Fig. 3.12. The impedance observed at the input ports of the antenna is characterized by the input reflection coefficient. To obtain this value, the S- Fig. 3.12. Prototype of four-arm sinuous antenna with cavity backing. Inset: SMA connectors on reverse for access to input ports. 37 0 -5 -5 -1 0 -1 0 |S 1 1 | ( d B ) |S 1 1 | ( d B ) 0 -1 5 -2 0 -2 5 1 5 m m 1 5 m m -3 0 0 .0 0 .5 1 .5 2 .0 2 .5 -2 0 -2 5 (C S T S im u la tio n ) (M e a s u re m e n t) 1 .0 -1 5 -3 0 3 .0 3 .5 4 .0 0 .0 3 0 m m 3 0 m m 0 .5 1 .0 2 0 0 2 0 0 1 5 0 1 5 0 1 0 0 1 0 0 5 0 0 -5 0 -1 0 0 R e (Z R e (Z Im (Z Im (Z -1 5 0 -2 0 0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .5 4 .0 F re q u e n c y (G H z ) I n p u t i m p e d a n c e ( Ω) I n p u t i m p e d a n c e ( Ω) F re q u e n c y (G H z ) (C S T S im u la tio n ) (M e a s u re m e n t) 1 .5 2 .0 2 .5 3 .0 ), C ), M ), C ), M S T e a s u re m e n t S T e a s u re m e n t 3 .0 3 .5 5 0 0 -5 0 -1 0 0 R e (Z R e (Z Im (Z Im (Z -1 5 0 -2 0 0 4 .0 0 .5 F re q u e n c y (G H z ) 1 .0 1 .5 2 .0 2 .5 ), ), ), ), C S M e C S M e 3 .0 T a s u re m e n t T a s u re m e n t 3 .5 4 .0 F re q u e n c y (G H z ) (a) (b) Fig. 3.13. Input reflection coefficient and input impedance at a single port of the sinuous antenna with a cavity depth of (a) 15 mm and (b) 30 mm. parameters of the antenna were measured at each port while all other ports were terminated with 50 Ω loads. The ports numbered 1 to 4 can be seen in the inset of Fig. 3.12. |S11 | as a function of frequency is shown in Fig. 3.13. The curve shows a cyclic variation with frequency and on further inspection, it was observed that these resonances were log-periodically distributed across frequency. The measured data also shows good agreement with predictions from CST simulations. The frequencies of the deep dips correspond to the wavelengths where the length of a sinuous cell equals one half of the wavelength. This provides an idea on how the antenna can be reconfigured to obtain different passbands: by controlling the lengths of the sinuous cells. The large input reflection in certain regions is due to the presence of 38 0∘ /90∘ /180∘ /270∘ Two-bit Phase shifters Port 3 Port 4 0∘ /90∘ /180∘ /270∘ Port 2 0∘ /90∘ /180∘ /270∘ Port 1 0∘ /90∘ /180∘ /270∘ Four-port Sinuous antenna Power divider Fig. 3.14. Feed network for the four-port sinuous antenna. Table 3.5 Feed network configurations and corresponding polarization modes. Mode number Port 1 Port 2 Port 3 Port 4 Polarization M−1 0◦ 270◦ 180◦ 90◦ Circular : RHCP M+1 0◦ 90◦ 180◦ 270◦ Circular : LHCP M2A 0◦ 180◦ 180◦ 0◦ Linear : Slant −45◦ M2B 0◦ 0◦ 180◦ 180◦ Linear : Slant +45◦ the low-profile cavity. At low frequencies, the cavity is very close to the antenna in wavelength-terms and thus the matching is severely affected. As expected, this cavity effect decreases with increasing frequency. This is seen as a trade-off against the increased gain and directional radiation requirements. Once the antenna has been characterized in terms of its input reflection, the next step is to measure the radiation performance. This process however, is complicated due to the fact that the antenna contains multiple-ports which need to be excited in a consistent, simultaneous manner. A specific feed-network needs to be designed to obtain the required phase-shifts be- 39 Fig. 3.15. Setup for measurement of the sinuous antenna in the anechoic chamber in Sup´elec. tween the ports over the entire bandwidth of operation. Fig. 3.14 shows the schematic of the feed network that was used for this measurement. More details about the implementation and performance of the power divider and phase-shifters can be found in [11]. The feed-network settings and the expected polarization of the antenna at boresight direction are shown in Table 3.5. The complete system consisting of the four-port antenna together with the feed-network was measured in the anechoic chamber of Sup´elec. Fig. 3.15 shows the system (mounted on top of a styrofoam mast) functioning as a transmitter, while a probe is used to measure the electric field in the near-field region of the antenna. The signal from the probe is carried out of the chamber using optical cables to avoid any interference with the measurements. Finally, the far-field data is obtained using a mathematical transformation of the measured near-field data. The realized gain at boresight for the two circular polarization modes M±1 of the antenna are shown in Fig. 3.16. At low frequencies, the 30 mm cavity performs better than the 15 mm cavity, indicating that the performance of the antenna is improved by increasing the depth of the cavity. 40 9 9 R e a liz e d G a in (d B i) 1 2 R e a liz e d G a in (d B i) 1 2 6 3 0 -3 M + 1 M -6 0 .5 1 .0 1 .5 -1 6 3 0 -3 (L H C P , 1 5 m m ) M 2 .0 + 1 M (R H C P , 1 5 m m ) -6 2 .5 3 .0 0 .5 F re q u e n c y (G H z ) 1 .0 1 .5 -1 2 .0 (L H C P , 3 0 m m ) (R H C P , 3 0 m m ) 2 .5 3 .0 F re q u e n c y (G H z ) (a) (b) Fig. 3.16. Realized boresight gain (measurement) for circular modes in sinuous antennas with cavity depth of (a) 15 mm and (b) 30 mm. However, large cavity-depths are not desirable as they cause nulls at boresight due to destructive interference between the original and reflected waves. Such nulls are observed at frequencies where the cavity depth is equal to one-quarter of the wavelength. For a cavity depth of 30 mm, this interference null was observed to appear at around 5 GHz, well outside the frequency band of interest. As discussed earlier, the axial ratio is used to assess the quality of circular polarization obtained. Fig. 3.17 shows the variation of the axial ratio with frequency, when the sinuous antenna is operated in either of the two circularly-polarized modes. The effect of changing the cavity depth from 15 mm to 30 mm, seems minimal as the axial ratio variation remains quite similar in both cases. The increasing trend of axial ratio at high frequencies (> 2.5 GHz) is due to large phase errors in the phase-shifters of the feed network (which were designed to only work within the frequency range of 0.6 to 2.4 GHz). To understand the radiation characteristics at directions off-boresight, the elevation cuts of the normalized radiation pattern are obtained. These plots help estimate the 3-dB beamwidth of the circular modes and also to verify the front-to-back ratio. For use in phased-array systems, the beam 41 6 M M 5 -1 6 (L H C P , 1 5 m m ) + 1 2 -1 (R H C P , 3 0 m m ) 4 A x ia l R a tio (d B ) 3 (L H C P , 3 0 m m ) + 1 M 5 4 A x ia l R a tio (d B ) M (R H C P , 1 5 m m ) 3 1 2 1 0 0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 0 .5 F re q u e n c y (G H z ) 1 .0 1 .5 2 .0 2 .5 3 .0 F re q u e n c y (G H z ) (a) (b) Fig. 3.17. Boresight axial ratio (measurement) for circular modes in sinuous antennas with cavity depth of (a) 15 mm and (b) 30 mm. should be as wide as possible, while the back radiation should be minimal for ease of integration on metallic surfaces. The radiation patterns shown in Fig. 3.18 indicate that the prototype has a wide beamwidths from 45◦ to 60◦ , while having a front-to-back ratio larger than 30 dB. The beam characteristics are also maintained as the frequency is varied from 0.6 to 2.4 GHz. Next, the linearly-polarized modes obtainable from sinuous antennas are analyzed. The linear-polarization is obtained through the technique of non-sequential feeding that was developed in the previous sections. The feed-network configuration for the two linear modes are as listed in Table 3.5. Instead of conventional horizontal and vertical linear polarization, this antenna radiates linear polarization aligned along the ±45◦ tilt angles. The two ‘slant’ orientations still form a complete, orthogonal pair of linear polarizations. The ±45◦ angles are a consequence of the reference coordinate system used to align the measurement system with the walls of the square cavity. The total realized gain at boresight in the linear modes of the antenna are shown in Fig. 3.19. Similar to the circular modes, the gain of the antenna with a 30 mm cavity is higher than that with a 15 mm cavity. 42 0 .6 G H z ( C S T ) , M o d e + 1 0 .6 G H z ( C S T ) , M o d e - 1 0 .6 G H z ( M e a s ) , M o d e + 1 0 .6 G H z ( M e a s ) , M o d e - 1 0 0 3 3 0 0 0 3 0 -5 3 0 0 6 0 -1 5 -2 0 -2 5 2 7 0 -2 5 9 0 -2 0 -1 5 2 4 0 -1 0 N o rm a liz e d g a in (d B ) -1 0 N o rm a liz e d g a in (d B ) 3 3 0 3 0 -5 1 2 0 3 0 0 -1 0 6 0 -1 5 -2 0 2 7 0 9 0 -2 0 -1 5 -1 0 2 4 0 1 2 0 -5 -5 0 2 1 0 0 2 1 0 1 5 0 1 .2 G H z ( C S T ) , M o d e + 1 1 5 0 1 8 0 1 8 0 1 .2 G H z ( C S T ) , M o d e - 1 1 .2 G H z ( M e a s ) , M o d e + 1 1 .2 G H z ( M e a s ) , M o d e - 1 0 0 3 3 0 0 3 0 0 3 0 -1 0 -1 0 3 0 0 -2 0 6 0 -3 0 -4 0 2 7 0 9 0 -4 0 -3 0 -2 0 2 4 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) 3 3 0 1 2 0 3 0 0 -2 0 6 0 -3 0 -4 0 2 7 0 9 0 -4 0 -3 0 -2 0 2 4 0 1 2 0 -1 0 -1 0 0 2 1 0 0 2 1 0 1 5 0 1 .8 G H z ( C S T ) , M o d e + 1 1 5 0 1 8 0 1 8 0 1 .8 G H z ( C S T ) , M o d e - 1 1 .8 G H z ( M e a s ) , M o d e + 1 1 .8 G H z ( M e a s ) , M o d e - 1 0 0 3 3 0 0 0 6 0 -4 0 2 7 0 -5 0 9 0 -4 0 -3 0 -2 0 2 4 0 3 0 0 -2 0 -3 0 N o rm a liz e d g a in (d B ) 3 0 0 -2 0 6 0 -3 0 -4 0 2 7 0 -5 0 9 0 -4 0 -3 0 -2 0 1 2 0 2 4 0 1 2 0 -1 0 -1 0 0 2 1 0 0 2 1 0 1 5 0 2 .4 G H z ( C S T ) , M o d e + 1 2 .4 G H z ( C S T ) , M o d e - 1 2 .4 G H z ( M e a s ) , M o d e + 1 3 3 0 2 .4 G H z ( M e a s ) , M o d e - 1 0 0 0 1 5 0 1 8 0 1 8 0 3 3 0 3 0 0 3 0 -1 0 -1 0 3 0 0 -2 0 6 0 -3 0 -4 0 2 7 0 9 0 -4 0 -3 0 -2 0 2 4 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) 3 0 -1 0 -1 0 N o rm a liz e d g a in (d B ) 3 3 0 3 0 1 2 0 3 0 0 -2 0 6 0 -3 0 -4 0 2 7 0 9 0 -4 0 -3 0 -2 0 2 4 0 1 2 0 -1 0 -1 0 0 2 1 0 0 1 5 0 2 1 0 1 5 0 1 8 0 1 8 0 Fig. 3.18. Normalized radiation patterns of sinuous antennas in the two circular modes with a 30 mm cavity. 43 Also, the total gain of the antenna in these linear modes is within ±1 dB of the values observed in circular modes (M±1 ). Thus, the performance of the antenna is consistent across its operation in both dual-circular and dual-linear modes. Similar to the use of the axial ratio as a measure of the quality of circular polarization, the gain in the cross-polarization direction is used to assess the quality of the linear polarization obtained. Fig. 3.20 compares the gain values obtained along the co-polarization and cross-polarization directions. The higher the difference between co-pol and cross-pol gain, the better the performance of the antenna in linear polarization mode. 1 2 1 2 R e a liz e d G a in (d B i) 9 R e a liz e d G a in (d B i) 9 6 3 0 -3 M M 2 A -6 0 .5 1 .0 1 .5 2 .0 2 B 2 .5 6 3 0 -3 (1 5 m m ) (1 5 m m ) M 2 A M -6 3 .0 0 .5 1 .0 F re q u e n c y (G H z ) 1 .5 2 .0 2 B 2 .5 (3 0 m m ) (3 0 m m ) 3 .0 F re q u e n c y (G H z ) (a) (b) Fig. 3.19. Realized boresight gain (measurement) for linear modes of sinuous antennas with a cavity depth of (a) 15 mm and (b) 30 mm. 8 R e a liz e d G a in (d B i) 4 0 -4 1 2 6 6 0 0 R e a liz e d G a in (d B i) R e a liz e d G a in (d B i) 1 2 1 2 -6 -1 2 -1 8 -8 -2 4 -1 2 -3 0 -1 2 -1 8 -2 4 -3 0 0 .5 -1 6 -6 1 .0 1 .5 2 .0 2 .5 3 .0 0 .5 F re q u e n c y (G H z ) -2 0 (a) -2 4 -2 8 0 .5 1 .0 1 .0 1 .5 2 .0 2 .5 3 .0 F re q u e n c y (G H z ) C o -p o l C ro ss-p o l (b) Fig. 3.20. Linear mode co-pol and cross-pol gain (measurement) of sinuous 1 .5 2 .0 2 .5 3 .0 antennas with cavity depth of (a) 15 mm and (b) 30 mm. F re q u e n c y (G H z ) 44 The sinuous antenna in linear modes shows a cross-polarization rejection larger than 12 dB at frequencies above 1.2 GHz. Thus, the operation of the antenna in linear mode is considered to be effective above this frequency. The low frequency limit is a consequence of the size constraints imposed on the antenna. It would be trivial to design a sinuous antenna with a larger diameter to have good linear polarization performance at frequencies lower than shown. Fig. 3.21 shows the normalized radiation patterns at various frequencies for linear modes M2A and M2B . These measured patterns confirm that the 3-dB beamwidth and front-to-back ratio of the antenna’s radiation remain consistent across frequency. It is also noted that these values are close to those obtained in the circular modes Fig. 3.18. This further validates that the operation in dual-linear mode is similar to those in dual-circular mode. Note that due to the non-sequential feed configuration, there are no boresight nulls, despite a mode M2 -like configuration. The deep null in the measured co-polarization gain near 1.1 GHz in Fig. 3.20 was unexpected. On further investigation, it was found that this null was the result of the circular taper used for the termination of the sinuous arms. The length of the tapered stub used in this design corresponds to exactly a quarter-wavelength at the frequency of 1.1 GHz. This results in the stub being in a resonant mode at this frequency, which dominates over the conventional traveling-wave mode. The solution to remove this null is to not use tapered ends, but rather right-angled truncations at the outer-edges of the sinuous arms. This goes against the traditional convention for traveling-wave antennas (such as spiral antennas) in which tapered or resistively loaded terminations are preferred [46],[47]. Fig. 3.22 illustrates the difference between tapered and truncated designs in four-arm sinuous antennas. Even though the abrupt edges result in greater reflection of signals 45 0 .6 G H z ( C S T ) , M o d e 2 A 0 .6 G H z ( M e a s ) , M o d e 2 A 0 .6 G H z ( C S T ) , M o d e 2 B 0 3 3 0 0 6 0 -2 0 2 7 0 -2 5 9 0 -2 0 -1 5 2 4 0 3 0 0 -1 0 N o rm a liz e d g a in (d B ) 3 0 0 -1 5 -1 0 6 0 -1 5 -2 0 2 7 0 -2 5 9 0 -2 0 -1 5 -1 0 1 2 0 -5 2 4 0 1 2 0 -5 0 2 1 0 0 1 5 0 2 1 0 1 8 0 1 .2 G H z ( C S T ) , M o d e 2 A 1 .2 G H z ( M e a s ) , M o d e 2 A 1 .2 G H z ( C S T ) , M o d e 2 B 3 0 3 3 0 0 -1 0 3 0 -1 0 3 0 0 -2 0 6 0 -3 0 -4 0 2 7 0 9 0 -4 0 -3 0 -2 0 2 4 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) 1 .2 G H z ( M e a s ) , M o d e 2 B 0 3 3 0 0 1 5 0 1 8 0 0 1 2 0 -1 0 3 0 0 -2 0 6 0 -3 0 -4 0 2 7 0 9 0 -4 0 -3 0 -2 0 2 4 0 1 2 0 -1 0 0 2 1 0 0 1 5 0 2 1 0 1 8 0 1 .8 G H z ( C S T ) , M o d e 2 A 1 .8 G H z ( M e a s ) , M o d e 2 A 1 .8 G H z ( C S T ) , M o d e 2 B 1 .8 G H z ( M e a s ) , M o d e 2 B 0 3 3 0 0 1 5 0 1 8 0 0 3 0 3 3 0 0 -1 0 3 0 -1 0 3 0 0 -2 0 6 0 -3 0 -4 0 -5 0 -5 0 2 7 0 9 0 -4 0 -3 0 2 4 0 -2 0 N o rm a liz e d g a in (d B ) -2 0 N o rm a liz e d g a in (d B ) 3 0 -5 -1 0 N o rm a liz e d g a in (d B ) 3 3 0 0 -5 1 2 0 3 0 0 6 0 -3 0 -4 0 -5 0 2 7 0 -5 0 9 0 -4 0 -3 0 2 4 0 -2 0 -1 0 1 2 0 -1 0 0 2 1 0 0 1 5 0 2 1 0 1 8 0 2 .4 G H z ( C S T ) , M o d e 2 A 2 .4 G H z ( M e a s ) , M o d e 2 A 3 3 0 0 2 .4 G H z ( C S T ) , M o d e 2 B 3 3 0 0 3 0 0 -3 0 -4 0 2 7 0 9 0 -4 0 -3 0 2 4 0 3 0 -1 0 6 0 N o rm a liz e d g a in (d B ) 3 0 0 -2 0 2 .4 G H z ( M e a s ) , M o d e 2 B 0 3 0 -1 0 -2 0 1 5 0 1 8 0 0 N o rm a liz e d g a in (d B ) 0 .6 G H z ( M e a s ) , M o d e 2 B 0 3 0 6 0 -2 0 -3 0 2 7 0 -4 0 9 0 -3 0 -2 0 1 2 0 2 4 0 1 2 0 -1 0 -1 0 0 2 1 0 0 1 5 0 1 8 0 2 1 0 1 5 0 1 8 0 Fig. 3.21. Normalized radiation patterns of sinuous antennas in the two linear modes with a 30 mm cavity. 46 (a) (b) Fig. 3.22. Sinuous antennas with (a) tapered and (b) truncated terminations. from the ends of the antenna, they are still seen as a necessity to avoid the resonant null in linearly-polarized modes. Fig. 3.23 shows the boresight realized gain for the two designs, when they are operated in a linear mode M2A . The expected polarization at boresight is linear polarization ‘slanted’ at an angle of −45◦ with the x-axis. The tapered design shows the gain null around 1.1 GHz, while the truncated design does not. In order to avoid this linear mode resonant null, later designs of the sinuous antennas in this thesis will contain right-angled truncations rather than tapered sections. 1 2 R e a liz e d G a in (d B i) 6 0 -6 -1 2 T a p e re d te rm in a tio n T ru n c a te d te rm in a tio n -1 8 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 F re q u e n c y (G H z ) Fig. 3.23. Boresight co-polarized gain for the two sinuous terminations when the antennas are operated in a linear mode M2A . 47 3.6 Summary on designing sinuous elements The design, realization and measurement of sinuous antennas has been exhaustively detailed in this chapter. By taking the example of a four-arm sinuous antenna element, both broadband and quad-polarization capabilities have been demonstrated. A few suggestions, to aid future designers of sinuous antennas, are made as below. • Four arms are sufficient for sinuous antennas to achieve complete quad-polarization capability. • Apart from traditional sequential modes, non-sequential (yet balanced) modes may also be explored when using sinuous antennas. Due to the ‘fold-back’ nature of the sinuous curves, the linear polarization obtained from these non-sequential modes has minimal rotation of the tilt angle. • If uni-directional radiation and low-profile integration are required, then hollow metallic cavity backings can be used. The choice of the cavity depth should be as large as possible, while avoiding the occurrence of any interference nulls within the operating bandwidth. • The termination of sinuous antennas needs to be approached with caution as any protruding stubs might be resonant at low frequencies of the operating bandwidth. Sharply truncated terminations might have be used to prevent such resonances. 48 Chapter 4 Array configurations of sinuous antennas 4.1 Introduction Antenna arrays are the next logical step to further exploit capabilities discovered during the antenna element design process. However, developing array configurations introduces many issues which need to be solved to realize practical systems. This chapter will be focused on developing array configurations of sinuous antennas, with the goal of identifying and tackling challenges in constructing broadband phased arrays. Linear array configurations will be studied to perform beam steering constrained within a single plane. In order to standardize comparisons in this chapter, the array will always be oriented with boresight along the positive z-axis and elements distributed along the x-axis. In the spherical coordinate system, this means that the radiation direction is towards the θ = 0◦ direction. Also, due to the array being linearly distributed along the x-axis, beam steering capability is only demonstrated in the xz plane (φ = 0◦ ). All references to steering angles are taken to represent elevation angles (θ) within this fixed plane. 49 4.2 Calculation of array radiation patterns The radiation pattern of an array of antennas is traditionally calculated using the principle of pattern multiplication. This approach calculates the overall radiation pattern as the product of the individual element pattern (Ee (θ)) and the array factor (AF (θ)). The principle can be summarized by (4.1), where Et (θ) denotes the total field at a particular direction. Et (θ) = AF (θ) · Ee (θ) (4.1) In this approach, the element pattern Ee (θ) depends only on the antenna element, while the array factor AF (θ) only depends on the position, orientation and phasing of the elements. In principle, this approach allows for separately consider the choice of antenna elements, distinct from the question of element placement in the array. The array factor term, dependent only on the input and location of elements can be written in the form of (4.2) [13]. N an ej(ψn +kdn sin θ) AF (θ) = (4.2) n=1 The equation describes the case of a linear array of N elements placed along the x-axis, with the n-th element located at a distance of dn from the origin and excited with a signal of amplitude an and phase ψn . For the case of a uniformly spaced linear array (dn = nd), in order to obtain a maximum at a direction θ0 , the input phase at the n-th element should be ψn = −nkd sin θ0 . This would translate to having constant phase increments (= kd sin θ0 ) over adjacent elements in the array. Thus, the array factor term for a uniform linear array with N elements and a spacing of d, when steered to an angle of θ0 , can written as shown in (4.3). Note this equation has been simplified by applying equal magnitudes to each element (an = 1). 50 ejnkd(sin θ−sin θ0 ) |AF (θ)| = kd(sin θ − sin θ0 ) 1 2 = kd(sin θ − sin θ0 ) N sin 2 sin N N n=1 (4.3) Thus, the consequences of element placements and excitations in an array can be theoretically formulated independent of the element pattern. However, as will be seen in Section 4.2.2, the assumptions involved in this approach might lead to differences between predicted and actual performance of the array. 4.2.1 Element spacing and its effect on radiation patterns It follows from (4.3), that the array factor is primarily dependent on the number of elements (N ), the element spacing (d) and the desired steering angle (θ0 ). Due to the periodic nature of the sine function, the array factor term, AF (θ), becomes periodic in θ. Fig. 4.1 shows the variation of the array factor with angle (θ) for fixed values of N and θ0 , while d is parametrically varied. The array factor periodically contains positions where the response is at its maximum. It 1 .0 1 .0 0 .8 0 .8 0 .8 0 .6 0 .6 0 .6 0 .4 0 .2 0 .0 -1 8 0 | A F ( θ)| 1 .0 | A F ( θ)| | A F ( θ)| is also seen that with increasing d, these maxima begin aggregating closer 0 .4 0 .2 -9 0 0 θ (a) 9 0 1 8 0 0 .0 -1 8 0 0 .4 0 .2 -9 0 0 θ (b) 9 0 1 8 0 0 .0 -1 8 0 -9 0 0 9 0 1 8 0 θ (c) Fig. 4.1. AF (θ) at different element spacings d. (a) 0.5λ (b) 1λ (c) 2λ for N = 6 and θ0 = 0◦ 51 to each other. The main lobe refers to the maximum obtained at θ = 0◦ , while the other maxima are referred to as grating lobes. In most cases, it is not desirable to have these grating lobes as they lead to ambiguity in the direction of the signal received by the array. From Fig. 4.1, we see that grating lobes begin to appear within the viewing angles (i.e. −180◦ ≤ θ ≤ 180◦ ) when the element spacing d is greater than or equal to the operating wavelength λ. Also note that this is for the situation when the beam is at boresight, i.e. θ0 = 0◦ . When steering the beam to angles off boresight, the issue of grating lobes is further exacerbated and the tighter limits on the spacing between antenna elements can be written in terms of the steering angle (θ0 ) as seen in (4.4) [48]. The equality condition of this equation, specifies the distance at which the grating lobe appears just within the viewing region, i.e. the grating lobe at endfire direction. d≤ λ 1 + sin |θ0 | (4.4) Due to the large size of broadband antenna elements, the minimum distance possible between adjacent elements becomes large. Also, with increasing frequency, this distance becomes significantly larger in wavelength terms and it is often seen to exceed the limit set by (4.4). This can be better explained using a uniform linear array of four-arm sinuous antennas as an example. Consider a sinuous antenna, operating from a lower frequency at wavelength λL to an upper frequency at wavelength of λU = (1/4)λL . The outer diameter of this antenna, as determined from (3.2) and (3.3), is dependent on λL and can be written as D = (4π/3)λL . The center-to-center distance between adjacent elements is fixed by this diameter and thus the tightest inter-element spacing possible in a uniform linear array of these antennas is d = (4π/3)λL . Now, consider this array operating at its highest frequency. The radi52 ating regions are close to the center of the antenna and thus the separation distance between radiating regions, in terms of the high-frequency wavelength (λU ), can be written as d = (16π/3)λU . This is significantly greater than the derived limit (4.4) on d, even in unsteered (θ0 = 0◦ ) conditions, and multiple grating lobes within the viewing region become unavoidable. The large size of the antenna has forced a large element spacing which causes grating lobes. Section 4.5 approaches to reduce the spacing between elements, and therefore the grating lobes, will be discussed. 4.2.2 Mutual coupling and its impact on the array factor One of the key assumptions when using the principle of pattern multiplication is regarding the interaction between adjacent elements of the array. This is commonly referred to as the mutual coupling between elements. The principle of pattern multiplication assumes that there is no mutual coupling between elements and that the pattern of each element is completely uninfluenced by surrounding elements. This approximation is valid in cases where the element patterns are directional and point away from other elements. They also serve as good estimates in the limit of large inter-element spacings. However, both approximations are not valid in the typical configurations of elements in broadband phased arrays. To obtain beam steering capability over large angles, antenna elements with broad beams are desired. Also closely-spaced elements are needed to avoid the issue of grating lobes. Thus, completely ignoring mutual coupling might lead to inaccurate results in broadband phased arrays systems. The effects of mutual coupling between antenna elements has been well documented with many reports detailing its effects on the performance of the antenna array [49],[50]. 53 In the specific case of sinuous antennas, due to the winding and interleaving nature of the arms, significant mutual coupling is to be expected. Thus, caution needs to be exercised when using array factor techniques to predict performance of these arrays. However, the pattern multiplication approach can still be useful to provide a quick, albeit approximate, understanding of the overall performance before diving into the details. 4.3 Feed network configuration for the array In order to successfully measure a complete antenna array, a feed network is required for simultaneously exciting all the input ports. However, to decide on the feed network specifications, the number of elements in the array needs to be decided. This determines the number of power dividers and phase shifters required. A two element antenna array would be limited in its ability to perform beam steering, while a three element antenna array introduces unnecessary complexity by requiring the design of 3 × 1 power dividers. Thus, two and three element designs were skipped and the choice was made to begin with four-element configurations. This decision was based on a cost-benefit analysis to choose the minimum number of antenna elements while still demonstrating phased array capability. Also, since the sinuous elements are multi-port antennas themselves, the array would finally consist of a greater number of individual ports. A four element antenna array comprising of four-port sinuous elements results in a total of 16 input ports. Having decided on the number of elements, the feed network can now be designed for the antenna array. The array feed network used in this thesis is as described in Fig. 4.2. For discussion purposes, it can be separated into two functional blocks. The first block, hereafter called the beam former network (BFN), comprises of a 4 × 1 power divider with four 5-bit 54 phase shifters. This block provides control over the input phase of each antenna element. This beam former network is used to control the steering angle of the array when performing beam steering. Since the phase shifters have 5-bits, the minimum phase shift achievable between antenna inputs is 11.25◦ . The second functional block is the polarization controller. There are four of these polarization controllers, each comprising of a 4 × 1 power divider followed by four 2-bit phase shifters. Each polarization controller is paired with one four-port sinuous antenna element. The phase shifters of the polarization controller are programmable to provide the required phases to excite each sinuous antenna in any of its circular or linear modes (Table 3.5). Thus, the polarization controllers are used to provide quadpolarization capability to the array. Each of these polarization controllers are functionally identical to the antenna feed network used in Chapter 3 (Fig. 3.14). The design, functionality and performance of each of these components are detailed in the doctoral thesis of Fang Hangzhao [11]. … Beam former network Polarization controller (a) (b) Fig. 4.2. Feed network used for excitation of the arrays. (a) Representation of BFN and polarization controllers (b) Built prototype assembled on a mount. 55 4.4 Uniform linear array A uniform linear array (ULA) consisting of four identical sinuous antenna elements is chosen as a baseline array configuration in this thesis. The antenna element developed in Chapter 3 is chosen as the unit cell in this array. The elements are placed as close to each other as possible, and thus the inter-element spacing is very close to the diameter of the element. Based on the results obtained in the previous chapter, a sharply truncated termination is used for all the arms of the antennas. Also, since an element with a cavity depth of 30 mm performed better than the cavity with 15 mm depth, a ground plane located at a distance of 30 mm is used for the arrays. The decision to replace the cavity with a continuous, planar ground plane was made to reduce the overall weight of the array structure. Nylon screws with spacers are used to keep the antenna at a fixed height above the ground plane (Fig. 4.3). The complete phased array system consisting of the beam former network, polarization controllers and the antennas above the ground plane were assembled and tested in the anechoic chamber facilities at Temasek Laboratories (NUS). The experimental setup can be seen in Fig. 4.4. Fig. 4.5a shows |S11 | against frequency at one input port of the sinuous antenna array. This measurement is performed with all other ports terminated with 50 Ω loads. The two curves in the figure indicate the value for a (a) (b) Fig. 4.3. Uniform linear array of sinuous antennas over a ground plane (a) top-view and (b) perspective view. 56 Fig. 4.4. Uniform linear array of sinuous antennas over a ground plane in the anechoic chamber. The beam former network and polarization controllers are located behind the ground plane. single element before and after neighboring elements are placed around it. The difference between the two curves can be seen as the parasitic effect of the neighboring elements on the element impedance. While measuring the S-parameters, only a single port of the array is excited, while all other ports are terminated with 50 Ω loads. This is different from the actual use scenario, in which all ports of the array are excited simultaneously. In order to obtain the overall reflected signal when all ports of the array are excited, the ‘active reflection coefficient’ (ARC) 0 0 -5 -1 0 |A R C | ( d B ) -1 5 |S 1 1 | (d B ) -1 0 -2 0 -2 0 -3 0 -2 5 B e fo re A fte r -3 0 0 .0 0 .5 8 5 m m e le m e n t B F N in p u t -4 0 1 .0 1 .5 2 .0 2 .5 3 .0 0 .0 F re q u e n c y (G H z ) 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 F re q u e n c y (G H z ) (a) (b) Fig. 4.5. (a) |S11 | of single port before and after embedding in an array. (b) Active reflection coefficient (ARC) at one element and at BFN. 57 is used. This parameter can be defined in terms of S-parameters through (4.5). N Smn ejφmn ARCm = (4.5) n=1 φmn denotes the phase difference between the input signals at port m and port n. The active reflection coefficient at port m can be qualitatively seen as proportional to the total power reflected from port m when all ports (including port m) are excited. In (4.5), the Smn term provides information about the coupling between ports of the array, while the ejφmn term specifies the phase relation between them. The ARC at input port 1 of the uniform linear array can be seen in Fig. 4.5b. Note that this is different from the total power reflected at the input of the beam former (which is also shown in the same figure). The realized gain of the array when the beam is aimed at boresight in different modes is shown in Fig. 4.6. From the figure it is clear that the gain of the array across the various modes at each frequency varies within a limit of ±0.5 dB. This confirms that the array is able to function as an effective quad-polarization antenna. 1 8 1 8 1 5 1 5 R e a liz e d g a in (d B i) R e a liz e d g a in (d B i) A divergence of up to 3 dB is observed in the gain of the different modes 1 2 9 M (M e a s u re m e n t) M -1 (M e a s u re m e n t) M + 1 (C S T s im u la tio n ) -1 (C S T s im u la tio n ) 6 + 1 M 3 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 1 2 9 M 0 .6 F re q u e n c y (G H z ) 2 B M 2 A (C S T s im u la tio n ) 2 B (C S T s im u la tio n ) M 3 2 .4 (M e a s u re m e n t) (M e a s u re m e n t) 6 2 A M 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 F re q u e n c y (G H z ) (a) (b) Fig. 4.6. Realized boresight gain of the ULA in (a) circular and (b) linear modes. 58 1 5 2 0 1 5 R e a liz e d g a in (d B i) A x ia l ra tio (d B ) 1 2 9 6 3 M + 1 (L H C P ) M -1 (R H C P ) 1 0 5 0 -5 T o ta l C o -p o l X -p o l -1 0 0 -1 5 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 0 .6 0 .8 1 .0 F re q u e n c y (G H z ) 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 F re q u e n c y (G H z ) (a) (b) Fig. 4.7. Polarization performance of the ULA evaluated using (a) axial ratio in circular modes and (b) cross-pol comparison in linear mode (M2A ). around the frequency of 1.8 GHz. This discrepancy is also noticed in the polarization performance of the array (Fig. 4.7), with the axial ratio and cross-polarization rejection being severely degraded at around 1.8 GHz. A small study was conducted to determine the reason for this anomalous behavior and the following observations were made. • The divergence is not predicted by the principle of pattern multiplication which uses the element pattern together with an array factor. • The 3-dB variations are correctly shown in CST simulations when a full-wave simulation of the entire array is carried out. • When the planar ground plane is replaced with cavities (complete with walls separating adjacent elements), the divergences are no longer present. Based on these observations, it was concluded that the observed deviations around 1.8 GHz were a result of the mutual coupling between the antenna elements. This can be seen as an effect of a resonance mode arising among the elements and with the ground plane. The presence of this mode in the space between the elements and the ground plane is confirmed by 59 the fact that cavities with walls separating adjacent elements can be used to prevent the anomalous behavior. The beam former network which has 5-bit phase shifting capability (or 32 phase states) can produce a large number of different beam steering angles with the given array. Also, at every frequency point and beam angle, the polarization of the array can be independently varied across the four polarization (dual-circular and dual-circular) options. 0 -5 -5 -1 0 -1 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) 0 -1 5 -2 0 -2 5 o 0 -3 0 1 1 .2 5 9 0 o 1 5 7 .5 o -3 5 -4 0 -9 0 -6 0 -3 0 -1 5 -2 0 -2 5 -3 5 o -4 0 0 3 0 6 0 o 1 1 .2 5 9 0 o 1 5 7 .5 9 0 -9 0 -6 0 T h e ta (d e g re e ) -3 0 0 o 3 0 6 0 9 0 6 0 9 0 T h e ta (d e g re e ) (a) M+1 , 0.6 GHz (b) M−1 , 1.2 GHz 0 0 -5 -5 -1 0 -1 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) o 0 -3 0 -1 5 -2 0 -2 5 o 0 -3 0 1 1 .2 5 9 0 o 1 5 7 .5 -3 5 -4 0 -9 0 -6 0 -3 0 0 o -1 5 -2 0 -2 5 1 1 .2 5 9 0 o 1 5 7 .5 -3 5 o -4 0 3 0 6 0 9 0 -9 0 T h e ta (d e g re e ) o 0 -3 0 -6 0 -3 0 0 o o 3 0 T h e ta (d e g re e ) (c) M2A , 1.8 GHz (d) M2B , 2.4 GHz Fig. 4.8. Beam steering performance of the ULA of sinuous antennas across different polarization modes and frequencies. Fig. 4.8 shows the different scanned beams when equal phase shifts of 11.25◦ , 90◦ and 157.5◦ are applied across the elements. The phase shifts are chosen based on the theoretical minimum and maximum steering angles achievable, together with an intermediate point. All four polarization modes of the array are also represented within this figure. The sub-figures 60 cover equally spaced frequency intervals, while including the upper and lower frequency extremes. In order to concisely assess the performance of the array, only select results are presented within this chapter. More extensive measurements results can be found in Appendix B. 4.5 Linear array with variable sized elements Due to each antenna element being electrically large, the inter-element spacing in a linear array of uniform elements is also large. This leads to the problem of grating lobes for these uniform linear arrays. This was clearly seen in the previous section with large grating lobes appearing at the higher frequencies or when steering to wide angles. The sinuous antennas used so far have an outer radius of 85 mm. At the high end of the frequency bandwidth under consideration, the radiation is confined to the center of the antenna and much of the outer region is left unused.This outer region also prevents the radiation centers from being located any closer to each other. So, using smaller sized antenna elements can allow for closer spacing in the antenna array and still provide effective radiation at the high frequencies. In this section, the arrays used will consist of sinuous elements of two sizes, the original size with an outer radius R = 85 mm and a smaller element with an outer radius r = 35 mm. The reasoning behind the size of the smaller element corresponds to the circle of largest radius which can be fitted in a planar array of the original elements. This will be explained in more detail in Section 4.5.2. 4.5.1 WAVES WAVES is an acronym for ‘Wideband Array with Variable Element Sizes’ and, as the name suggests, denotes arrays with elements of different sizes 61 Fig. 4.9. WAVES configuration of sinuous antennas over a ground plane. [51]. The rationale is to build multi-octave antenna arrays using different sized elements to cover different sections of bandwidth. In reported implementations of WAVES configurations, the sizes of the elements are chosen so that (elements at) each size would correspond to a different octave of the desired operating bandwidth [52]. A linear configuration of the variable sized array built is shown in Fig. 4.9. The distance between adjacent elements in the array has been reduced from 2R (in the ULA) to (R + r). Thus, this should enable the radiation centers at high frequencies to be closer to each other and result in lower grating lobes. The magnitude of the reflection coefficient (|S11 |), is shown in Fig. 4.10a. The plot compares the reflection at the input ports of the small and big elements. As expected the small element has a poorer performance at the low frequency region. As in the earlier section, the active reflection coefficient is also studied and compared against the total input reflection at the input port of the beam former (Fig. 4.10b). The radiation characteristics of the WAVES array were also measured using the same feed network at the anechoic chamber in Temasek Laboratories (NUS). The realized boresight gain in circular and linear modes can be seen in Fig. 4.11. The measured gain values show good agreement with predictions from CST simulations. 62 0 0 -5 -1 0 |A R C | ( d B ) -1 5 |S 1 1 | (d B ) -1 0 -2 0 -3 0 -2 0 8 5 m m 3 5 m m -2 5 0 .0 0 .5 1 .0 1 .5 2 .0 e le m e n t e le m e n t 2 .5 E le m e n t in p u t p o rt B F N in p u t p o rt -4 0 3 .0 0 .0 0 .5 1 .0 F re q u e n c y (G H z ) 1 .5 2 .0 2 .5 3 .0 F re q u e n c y (G H z ) (a) (b) Fig. 4.10. (a) |S11 | of a single port of the large and small elements in the array. (b) Active reflection coefficient (ARC) at one element and at BFN. 1 2 1 5 9 1 2 R e a liz e d g a in (d B i) 1 8 R e a liz e d g a in (d B i) 1 5 6 3 + 1 (M e a s u re m e n t) M -1 (M e a s u re m e n t) M + 1 (C S T s im u la tio n ) -1 (C S T s im u la tio n ) 0 M -3 M -6 0 .6 0 .8 1 .0 1 .2 1 .4 9 6 3 -3 1 .6 1 .8 2 .0 2 .2 M 2 B (M e a s u re m e n t) M 2 B (C S T s im u la tio n ) 0 2 .4 0 .6 0 .8 1 .0 1 .2 F re q u e n c y (G H z ) 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 F re q u e n c y (G H z ) (a) (b) Fig. 4.11. Realized boresight gain of the WAVES in (a) circular and (b) linear modes. 1 2 2 0 1 0 1 5 A x ia l ra tio (d B ) R e a liz e d g a in (d B i) 8 6 4 2 0 0 .6 0 .8 M + 1 (L H C P ) M -1 (R H C P ) 1 .0 1 .2 1 0 T o ta l C o -p o l X -p o l 5 0 -5 -1 0 -1 5 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 0 .6 F re q u e n c y (G H z ) 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 F re q u e n c y (G H z ) (a) (b) Fig. 4.12. Polarization performance of the WAVES evaluated using (a) axial ratio in circular modes and (b) cross-pol comparison in a linear mode (M2B ). 63 The polarization performance is evaluated using the axial ratio and the cross-polarization rejection values. From Fig. 4.12a, it is clear that the small elements are not effective radiators at low frequencies, seen by the high axial ratio at low frequencies, which gradually decreases as the frequency increases. Similarly in Fig. 4.12b, the cross-polarization rejection increases from 10 dB at low frequencies to over 20 dB at high frequencies. Due to fewer effective elements at low frequencies, the WAVES array has broad beams and reduced steering capability at low frequencies. This is seen in Fig. 4.13, where the beam steering capability is seen to consistently improve as the frequency is increased. Only a subset of the measured radiation patterns are shown in this figure, with the complete collection being available at Appendix A. 0 0 -5 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) -5 -1 0 -1 5 o 0 1 1 .2 5 9 0 o 1 5 7 .5 o -2 0 -2 5 -9 0 -6 0 -3 0 0 -1 0 -1 5 0 -2 5 1 1 .2 5 9 0 o 1 5 7 .5 o o o 3 0 -3 0 6 0 9 0 -9 0 -6 0 -3 0 T h e ta (d e g re e ) 0 3 0 6 0 9 0 6 0 9 0 T h e ta (d e g re e ) (a) M+1 , 0.6 GHz (b) M−1 , 1.2 GHz 0 0 -5 -5 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) o -2 0 -1 0 -1 5 o -2 0 0 -2 5 1 1 .2 5 9 0 o 1 5 7 .5 o o 0 1 1 .2 5 9 0 o 1 5 7 .5 -1 0 o o -1 5 -2 0 -2 5 o -3 0 -3 0 -9 0 -6 0 -3 0 0 3 0 6 0 9 0 -9 0 T h e ta (d e g re e ) -6 0 -3 0 0 3 0 T h e ta (d e g re e ) (c) M2A , 1.8 GHz (d) M2B , 2.4 GHz Fig. 4.13. Beam steering performance of the WAVES of sinuous antennas across different polarization modes and frequencies. 64 4.5.2 Interstitial packing In all planar configurations of equal-sized circles, interstices, i.e. gaps between the filled structures, are created. By utilizing progressively smaller sized circles, these interstices can filled up in a recursive manner. Fig. 4.14 illustrates the interstices created in a planar rectangular array. At each intersection of four circles, the gap left empty can be filled with a smaller sized circle. The ratio of the radii of the two circles is geometrically given √ as r/R = 2 − 1. 𝑅 𝑅 Fig. 4.14. Comparison of sizes of large and small sinuous elements used in arrays with variable sized elements. This process can be extended in a recursive manner, filling all interstices that arise after each iteration, but is restricted to one step for this thesis. This packing ratio is also the primary reason for using 85 mm and 35 mm sinuous elements in the WAVES. The choice was made in anticipation of maintaining element sizes when comparing an interstitial array against the WAVES. Motivated by this idea of interstitial filling, the ULA from previous sections can be modified to further reduce the gap between adjacent radiating elements. Consider an array of four sinuous antennas placed as shown in Fig. 4.15: it consists of two 85 mm sinuous elements placed in a linear configuration, with the interstices at the top and bottom filled with smaller 35 mm sinuous elements. This array will be named as the ‘Wideband Interstitially Packed Array’ (WIPA). 65 Fig. 4.15. WIPA configuration of sinuous antennas over a ground plane. 0 0 -5 -1 0 |A R C | ( d B ) -1 5 |S 1 1 | (d B ) -1 0 -2 0 -3 0 -2 0 8 5 m m 3 5 m m -2 5 0 .0 0 .5 1 .0 1 .5 2 .0 e le m e n t e le m e n t 2 .5 E le m e n t in p u t p o rt B F N in p u t p o rt -4 0 3 .0 0 .0 0 .5 F re q u e n c y (G H z ) 1 .0 1 .5 2 .0 2 .5 3 .0 F re q u e n c y (G H z ) (a) (b) Fig. 4.16. (a) |S11 | of a single port of the big and small elements in the array. (b) Active reflection coefficient (ARC) at one element and at BFN. As in the earlier sections, the first few plots for this array indicate the input reflection and active reflection coefficient of the elements. These can be seen in Fig. 4.16. The changes in the input reflection coefficient are very minimal, when compared to those from the earlier WAVES section (Fig. 4.10). This is expected as the number and sizes of elements has been kept the same. The active reflection coefficient and input reflection at the BFN also retain the same characteristics as seen in the other arrays. The radiation performance for the WIPA was also measured in the anechoic chamber. The realized gain at boresight is seen in Fig. 4.17 and 66 the axial ratio and co- and cross-polarization in Fig. 4.18. Only minor variations (≤ 0.5 dB) are observed as the polarization is cycled through circular and linear configurations. The array also maintains a low axial ratio in circular modes and high cross-polarization rejection in linear modes throughout the bandwidth of operation. This confirms that the boresight performance of the WIPA is unaffected by the close spacing of elements. Also, the quality of polarization (axial ratio and cross-pol rejection) in WIPA is better than in WAVES, despite both having the same number of elements in each size. 1 8 1 8 1 5 1 5 1 2 1 2 R e a liz e d g a in (d B i) R e a liz e d g a in (d B i) The beam steering performance of the WIPA is shown in Fig. 4.19. 9 6 + 1 (M e a s u re m e n t) M -1 (M e a s u re m e n t) M + 1 (C S T s im u la tio n ) -1 (C S T s im u la tio n ) 3 M 0 M -3 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 9 6 M 2 A (M e a s u re m e n t) M 2 B (M e a s u re m e n t) M 2 A (C S T s im u la tio n ) M 2 B (C S T s im u la tio n ) 3 0 -3 2 .4 0 .6 0 .8 1 .0 F re q u e n c y (G H z ) 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 F re q u e n c y (G H z ) (a) (b) Fig. 4.17. Realized boresight gain of the WIPA in (a) circular and (b) linear modes. 6 5 M + 1 (L H C P ) 1 5 M -1 (R H C P ) 1 0 5 A x ia l ra tio (d B ) R e a liz e d g a in (d B i) 4 3 2 1 0 -5 -1 0 -1 5 -2 0 T o ta l C o -p o l X -p o l -2 5 0 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 -3 0 2 .4 0 .6 F re q u e n c y (G H z ) 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 F re q u e n c y (G H z ) (a) (b) Fig. 4.18. Polarization performance of the WIPA evaluated using (a) axial ratio in circular modes and (b) cross-pol comparison in linear mode (M2A ). 67 As in the WAVES array, the WIPA also has a reduced number of effective radiators at low frequencies, resulting in wider beamwidths at the low frequency region. The separation distance between adjacent elements, when measured along the X-axis, has been reduced from 2R in the baseline case of ULAs to R in the WIPA. As the elements are now closer to each other, this results in a reduction of the grating lobe levels at high frequencies, allowing for improved operation at high frequencies and through larger steering angles. 0 0 -5 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) -5 -1 0 -1 5 -2 0 o 0 1 1 .2 5 4 5 o 7 8 .7 5 o -2 5 -3 0 -9 0 -6 0 -3 0 -1 0 -1 5 -2 0 -2 5 -3 5 o -4 0 0 3 0 6 0 o 1 1 .2 5 4 5 o 7 8 .7 5 9 0 -9 0 -6 0 T h e ta (d e g re e ) -3 0 0 o 3 0 6 0 9 0 6 0 9 0 T h e ta (d e g re e ) (a) M+1 , 0.6 GHz (b) M−1 , 1.2 GHz 0 0 -5 -5 -1 0 -1 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) o 0 -3 0 -1 5 -2 0 -2 5 o 0 -3 0 1 1 .2 5 4 5 o 7 8 .7 5 -3 5 -4 0 -9 0 -6 0 -3 0 0 o -1 5 -2 0 -2 5 1 1 .2 5 4 5 o 7 8 .7 5 -3 5 o -4 0 3 0 6 0 9 0 -9 0 T h e ta (d e g re e ) o 0 -3 0 -6 0 -3 0 0 o o 3 0 T h e ta (d e g re e ) (c) M2A , 1.8 GHz (d) M2B , 2.4 GHz Fig. 4.19. Beam steering performance of the WIPA of sinuous antennas across different polarization modes and frequencies. 68 4.6 Comparison of the array configurations The three configurations of ULA, WAVES and WIPA were each introduced and discussed separately in the previous sections. In this section, the arrays are compared against each other to objectively compare the benefits and disadvantages of each system. Fig. 4.20 shows the realized gain at boresight for the three arrays in one circular mode and one linear mode. The WAVES and WIPA are both observed to have lower gain at low frequencies compared to the ULA. However, the three cases begin to converge as frequency increases. This is a natural consequence of using smaller sized elements (in WAVES and WIPA), which are ineffective at low frequencies. This effect of the small antennas is less pronounced when evaluating the polarization performance of the three arrays. When comparing the axial ratio (Fig. 4.21a) in a circular mode, the ULA has a resonant (mutual coupling) peak at 1.8 GHz, while WAVES generally has a poorer performance at low frequency. Compared to them, the WIPA shows a consistent axial ratio across the entire bandwidth. The cross-polarization rejection is very similar for all three arrays (Fig. 4.21b), with values varying between 5 to 1 8 1 8 1 5 1 5 1 2 1 2 R e a liz e d g a in (d B i) R e a liz e d g a in (d B i) 25 dB. 9 6 3 U L A W A V E S W IP A 0 -3 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 9 6 3 U L A W A V E S W IP A 0 -3 2 .4 0 .6 F re q u e n c y (G H z ) 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 F re q u e n c y (G H z ) (a) (b) Fig. 4.20. Realized boresight gain of the three arrays compared in (a) a circular mode (M+1 ) and (b) a linear mode (M2B ). 69 1 5 4 0 U L A W A V E S W IP A 3 0 A x ia l ra tio (d B ) X -p o l re je c tio n (d B ) 1 2 U L A W A V E S W IP A 9 6 3 0 2 0 1 0 0 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 0 .6 0 .8 1 .0 F re q u e n c y (G H z ) 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 F re q u e n c y (G H z ) (a) (b) Fig. 4.21. Polarization performance of the three arrays evaluated using (a) axial ratio in a circular mode (M+1 ) and (b) cross-pol rejection in a linear mode (M2B ). 0 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) -1 0 -1 0 -2 0 U L A W A V E S W IP A -3 0 -9 0 -6 0 -3 0 0 -2 0 -3 0 U L A W A V E S W IP A -4 0 3 0 6 0 9 0 -9 0 -6 0 T h e ta (d e g re e ) 0 3 0 6 0 9 0 6 0 9 0 T h e ta (d e g re e ) (a) Boresight, 0.6 GHz (b) Boresight, 2.4 GHz 0 0 -1 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) -3 0 -2 0 U L A W A V E S W IP A -3 0 -9 0 -6 0 -3 0 0 3 0 6 0 9 0 -1 0 -2 0 U L A W A V E S W IP A -3 0 -9 0 T h e ta (d e g re e ) -6 0 -3 0 0 3 0 T h e ta (d e g re e ) (c) Max steered, 1.2 GHz (d) Max steered, 1.8 GHz Fig. 4.22. Beam steering performance of the three arrays in a circular mode (M+1 ) at different frequencies and steering angles. Large differences are observed when comparing the radiation patterns at different frequencies and scanning angles for the three arrays. When 70 the beams are directed at boresight direction, the WAVES and WIPA have wider beamwidths at low frequencies (Fig. 4.22a) and lower grating lobes (at high frequencies) than the ULA. When maintaining the beam direction to boresight and increasing the frequency, large grating lobes are observed in the ULA (Fig. 4.22b), which are not present in the WAVES and WIPA. Comparing among the three cases, the level of grating lobes is reduced by 12 dB for WAVES and by 18 dB for the WIPA. In order to confirm the benefit of reduced grating lobes in WAVES and WIPA configurations, two more additional states are studied. By applying a phased input to the elements, the arrays are steered to their respective maximum angles off boresight and the radiation patterns are evaluated. Due to the different spacing and element sizes between the three arrays, the maximum steering angle in each configuration is different. However, the grating lobes in each case are expected to be at their maximum values as the beams have been completely steered. The three arrays are compared under this condition in Fig. 4.22c and Fig. 4.22d. In both the frequency points shown, the WIPA has a lower grating lobe level than the ULA and WAVES. However, the WIPA has a wider beamwidth because it has fewer and more closely spaced elements. Grating lobes now begin to appear in the WAVES configuration in addition to those in the ULA. However, in the WIPA, the grating lobes appear to still be lower (by 8 dB) than the WAVES and ULA cases. Thus, the WIPA is shown to have significant benefits over the array configurations in terms of reduced grating lobes, while maintaining comparable performance in terms of realized gain, axial ratio in circular modes and cross-polarization rejection in linear modes. 71 4.7 Verification with a phased array system simulator The ‘Phased Array System Simulator’ (PASS), a tool developed in-house at the university, has the capability to simulate system-level performance in phased array systems. By taking the individual active element patterns of a phased array, together with detailed parameters of the RF front-end architecture as inputs, PASS is able to simulate the performance of the array when everything is assembled together. PASS is implemented using ADS Ptolemy and MATLAB and has been validated through multiple tests in the past [53],[54]. The motivation to use PASS is to bridge the gap between antenna designers and RF front-end designers. Since antenna patterns and RF performance data can be collected independently and virtually combined in PASS, designers can predict the entire system performance by sharing the data between RF and antenna teams, even before any integrated system test is carried out. An overview of the PASS system can be seen in Fig. 4.23. A few preparatory steps need to be carried out prior to starting this system simulator. These involve preparing either measured or simulated data for the antenna performance as well as for the RF front-end. For this thesis, the BFN and polarization controllers used in the previous sections were first measured and stored as part of the RF front-end circuitry in PASS. Next, the individual S-parameters of the sinuous elements were measured, which are used to determine the active input impedance of the array. Finally, each port of the array was separately excited and the radiation pattern measured in an anechoic chamber. This last set of data served as the active element pattern inputs. Once these sets of data are imported into PASS, no further system 72 Fig. 4.23. (a) Preprocessed data from measured antenna array (b) Simulation setup of PASS. Source: X. Tang and K. Mouthaan, “Phased array system simulator (PASS) - A simulation tool for active phased array design,” in Phased Array Systems Technology, 2013 IEEE International Symposium on, 2013 [53]. measurements are needed to simulate the various beam steering angles and polarization states of the array. By simply selecting the appropriate RF front-end setting and using it with the active element patterns, PASS can directly predict overall system performance. Fig. 4.24 compares the ULA measurements with data obtained from PASS and also predicted patterns based on the principle of pattern multiplication (array factor). The patterns predicted by the array factor method overestimate the quality of nulls obtained in the array radiation pattern, due to their lack of accounting for mutual coupling information. However, since this information is incorporated through the S-parameters and active element patterns, PASS does a better fit with measurement at most points. The different sub-figures are chosen to present a sampling of the various 73 0 -1 0 -1 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) 0 -2 0 -3 0 -4 0 -5 0 -2 0 -3 0 -4 0 -5 0 -9 0 -6 0 -3 0 0 3 0 6 0 9 0 -9 0 -6 0 -3 0 T h e ta (d e g re e ) (a) ULA, 0◦ phasing, 0.6 GHz 3 0 6 0 9 0 (b) ULA, 11.25◦ phasing, 1.2 GHz 0 0 -1 0 N o rm a liz e d g a in (d B ) -1 0 -2 0 -3 0 0 -4 0 -5 0 -9 0 -6 0 -3 0 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) 0 T h e ta (d e g re e ) -1 0 -2 0 -3 0 -4 0 -2 0 -5 0 3 0 -3 0 6 0 9 0 -9 0 T h e ta (d e g re e ) 4 0 (c) ULA, 90◦ phasing, - 1.8 - 9 GHz 0 -6 0 -6 0 -3 0 0 3 0 6 0 9 0 T h e ta (d e g re e ) -3 0 0 3 0 (d) ULA, 157.5◦ phasing, 2.4 GHz 6 0 9 0 T h e ta (d e g re e ) M e a su re m e n t P A S S A rra y F a c to r Fig. 4.24. ULA performance predicted through PASS and array factor method against measurement. frequencies and beam steering angles possible with the ULA. Since the array factor method relies on elements being uniform, it can only be applied to the ULA. For subsequent comparisons, the PASS data is compared directly to the measurements, as array factor techniques are not possible for the unequal-sized or interstitially packed arrays such as the WAVES and WIPA. This further validates the utility of PASS in performing system simulations of unconventional arrays. Fig. 4.25 contains the predictions made by PASS and measured data information for the WAVES and WIPA. Good agreement is seen between the information from PASS and the measured data across the various frequencies, polarizations and beam steering angles represented in the sub-figures. 74 0 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) -1 0 -1 0 -2 0 -2 0 -3 0 -4 0 -9 0 -6 0 -3 0 0 3 0 6 0 9 0 -9 0 -6 0 -3 0 T h e ta (d e g re e ) -1 0 -1 0 N o rm a liz e d g a in (d B ) 0 -2 0 0 -3 0 -6 0 -3 0 0 3 0 6 0 9 0 (b) WAVES, M2B , 157.5◦ phasing, 2.4 GHz 0 3 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) (a) WAVES, M+1 , 0◦ phasing, 0.6 GHz -9 0 0 T h e ta (d e g re e ) 6 0 -1 0 -2 0 -3 0 -2 0 -3 0 9 0 -9 0 T h e ta (d e g re e ) -6 0 -3 0 0 3 0 6 0 9 0 T h e ta (d e g re e ) 4 0 (c) WIPA, M−1 , 45◦ phasing, 0.6 - GHz -9 0 -6 0 ◦ (d) WIPA, phasing, 2.4 GHz 2A -3 0 0 3 0 6M 0 9 0 , 78.75 T h e ta (d e g re e ) M e a su re m e n t P A S S A rra y F a c to r Fig. 4.25. WAVES and WIPA performance predicted through PASS against measurement. Note that PASS supports the system simulation of the phased array system at all of the frequency, polarization and beam steering settings discussed in the previous sections. However, simply due to the large number of configurations possible, it would become unwieldy if all of the results are presented here. So, only a representative selection of the results were presented in this section. 4.8 Conclusions and recommendations This chapter is meant to provide a detailed study of linear arrays of sinuous antennas. Four antennas in a uniform linear array (ULA) configuration 75 were taken as the base configuration to provide a starting basis. The ULA is seen as a reliable method to guarantee low-frequency performance in the arrays, but however, does suffer from large inter-element spacings resulting in grating lobes at high frequencies. Arrays with variable sized elements, placed in a linear (WAVES) and interstitially packed (WIPA) configurations are investigated to overcome these high frequency shortcomings of ULAs. The following points summarize the results presented in this chapter and make recommendations on designing arrays of wideband antennas. • The ULA provides a higher gain than the WAVES and WIPA due to it having more elements covering the low frequency bands. However, this is a trade-off with the grating lobe performance at high frequencies. This trend is expected to continue when designing larger arrays as well. • However, it needs to be noted that the WIPA technique involves only filling the gaps within a given array. Thus, by starting with a large ULA and adding smaller elements in the interstices, the high frequency grating lobe issue can be solved while maintaining the low frequency performance of the original ULA. The increased number of elements in a filled WIPA, when compared to the original ULA, can be considered as the complications introduced by this approach. • The WIPA technique in its current form, is only presented in linear wideband arrays. However, it is noted that it can easily extended to planar arrays as well. The reduction of inter-element spacing can be carried out across the entire plane of planar arrays, leading to better reductions of grating lobes, when compared against uniform planar arrays. • The limiting factor when verifying the operation of wideband arrays with a large number of elements is the number of feed components re76 quired. Since each sinuous antenna has four ports, the total number of ports in a N -element array is 4N , leading to a very large feed network. Introducing smaller sized elements through the WIPA technique can further complicate the feed design task due to the different bands of operations for larger and smaller sized elements. Smart feed architectures which can intelligently partition RF energy between small and large elements, depending on the frequency of operation, would be highly useful components in such arrays. • Wideband elements such as sinuous elements are known to be dispersive across frequency due to their traveling-mode type radiation. This behavior is expected to continue in phased arrays of these antennas as well, resulting in beam distortions (squints) across frequencies when steering the beam. True time delay units when used at the subarray level could help to mitigate these issues. Such extensions to the feed architecture is expected to further complicate the realization of practical, wideband phased array systems. • When designing phased arrays with a large number of components, constraints on measurement capabilities necessitate the need for more advanced simulation capabilities. The use of traditional array factor theory and more advanced system simulators (such as PASS) are seen as essential in the design process. The different prediction techniques still have their disadvantages, for example, array factor estimates ignore mutual coupling interactions between elements. Also, for system simulators such as PASS, it is seen that the combined radiation pattern is very sensitive to inaccuracies in measurements of element patterns. Despite being a few steps away from testing the entire system, it is seen from the results in this chapter that such tools can still used to quickly arrive at initial estimates for array performance. 77 Chapter 5 Comparison of spiral and sinuous antennas At various points in the previous chapters, spiral antennas were repeatedly mentioned and compared against the sinuous antenna. This chapter is used to extend this discussion between spiral and sinuous antennas, and provide performance comparisons between them when both are given the same size constraints. The data about the spiral antennas obtained in this section was obtained through the work of Fang Hangzhao and a more detailed report on his work can be found in his doctoral thesis [11]. 5.1 Antenna elements In order to compare against the sinuous antenna in Chapter 3, a four-arm Archimedean spiral antenna of the same diameter is used. Each arm of the spiral antenna has a width of 3 mm and the spacing between adjacent arms is also 3 mm. A side-by-side picture of the two antennas, both supported by a metallic cavity, can be seen in Fig. 5.1. The excitation modes of spiral antennas are similar to those of the sinuous antenna. However, due to the strict sense of winding, a spiral 78 20 cm (a) (b) Fig. 5.1. Four-arm antennas (a) sinuous (b) spiral. antenna inherently supports one circular polarization better than the other. For the spiral antenna considered here, the preferred circular mode is righthand circular polarization (RHCP). Also, as discussed in Section 3.3 on polarization ellipses, linear polarizations from spiral antennas are not very effective due to large variations in tilt angles. Thus, for this chapter, only the circular modes of both antennas will be compared. Following the convention of previous sections, the input reflection (|S11 |) of the two antennas is first compared in Fig. 5.2. The low-profile, hollow cavities demonstrate strong effects on spiral antenna, leading to multiple ripples in the plot. Also, the spiral antenna is seen to be much more sensitive to cavity depths, showing significant differences when a cavity of -5 -5 -1 0 -1 0 -1 5 |S 1 1 -1 5 |S 1 1 | (d B ) 0 | (d B ) 0 -2 0 -2 0 S p ira l S in u o u s -2 5 0 .0 0 .5 S p ira l S in u o u s -2 5 1 .0 1 .5 2 .0 2 .5 3 .0 0 .0 F re q u e n c y (G H z ) 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 F re q u e n c y (G H z ) (a) 15 mm cavity (b) 30 mm cavity Fig. 5.2. |S11 | of spiral and sinuous antennas with different cavity depths. 79 15 mm depth is substituted with one of 30 mm depth. Next, the realized gain at boresight for the circular modes of both antennas are compared (Fig. 5.3). The ripple effects seen in the input reflection coefficient are also observed in the realized gain plots. At the low-frequency region, it is observed that the spiral antennas have between 2 to 6 dB more gain than the sinuous antennas. Since the size of the two antennas is the same, this data can also be interpreted to mean that spiral antennas can be designed to be more compact than sinuous antennas given the same low frequency limits. However, large periodic ripples are seen in the spiral antennas while the sinuous antenna demonstrates a smooth increase in gain. Also, if equal gain is desired in the different polarization modes, sinuous antennas are recommended since the spiral antenna in inherently right-circularly polarized. 1 2 1 2 R e a liz e d G a in (d B i) 9 R e a liz e d G a in (d B i) 9 6 3 0 -3 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 3 0 -3 S p ira l S in u o u s -6 6 S p ira l S in u o u s -6 2 .4 0 .6 0 .8 1 .0 F re q u e n c y (G H z ) 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 2 .0 2 .2 2 .4 F re q u e n c y (G H z ) (a) RHCP, 15 mm (b) RHCP, 30 mm 1 2 1 2 R e a liz e d G a in (d B i) 9 R e a liz e d G a in (d B i) 9 6 3 0 -3 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 3 0 -3 S p ira l S in u o u s -6 6 S p ira l S in u o u s -6 2 .4 0 .6 F re q u e n c y (G H z ) 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 F re q u e n c y (G H z ) (c) LHCP, 15 mm (d) LHCP, 30 mm Fig. 5.3. Boresight gain of spiral and sinuous antennas with different cavity depths. 80 5 .0 5 .0 S p ira l S in u o u s S p ira l S in u o u s 4 .5 4 .0 4 .0 3 .5 3 .5 A x ia l R a tio (d B ) A x ia l R a tio (d B ) 4 .5 3 .0 2 .5 2 .0 1 .5 3 .0 2 .5 2 .0 1 .5 1 .0 1 .0 0 .5 0 .5 0 .0 0 .0 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 0 .6 2 .4 0 .8 1 .0 (a) RHCP, 15 mm 5 .0 5 .0 1 .6 1 .8 2 .0 2 .2 2 .4 2 .0 2 .2 2 .4 S p ira l S in u o u s 4 .5 4 .0 4 .0 3 .5 3 .5 A x ia l R a tio (d B ) A x ia l R a tio (d B ) 1 .4 (b) RHCP, 30 mm S p ira l S in u o u s 4 .5 1 .2 F re q u e n c y (G H z ) F re q u e n c y (G H z ) 3 .0 2 .5 2 .0 1 .5 3 .0 2 .5 2 .0 1 .5 1 .0 1 .0 0 .5 0 .5 0 .0 0 .0 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 0 .6 F re q u e n c y (G H z ) 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 F re q u e n c y (G H z ) (c) LHCP, 15 mm (d) LHCP, 30 mm Fig. 5.4. Boresight axial ratio of spiral and sinuous antennas with different cavity depths. The axial ratio is used as the metric to compare the quality of polarizations in Fig. 5.4. In RHCP mode, the spiral antenna’s axial ratio is less than 2.5 dB, which is better than the axial ratio of the sinuous antenna which is less than 4.5 dB. However, in LHCP mode, the sinuous antenna maintains its axial ratio performance, while the spiral antenna’s performance is degraded. This is seen as a consequence of spiral antennas being inherently singly-polarized, while sinuous antennas are not. Finally, the normalized radiation patterns are also compared between the two antennas in Fig. 5.5. The spiral antenna demonstrates a larger beamwidth in the RHCP modes at both the high and low frequency limits. However, in the LHCP modes, the pattern of the sinuous remains uniform, while the spiral patterns get distorted at high frequencies due to the creeping in of the M2 boresight null radiation modes. 81 0 .6 G H z , R H C P 0 .6 G H z , R H C P 0 0 3 3 0 3 0 3 3 0 0 0 3 0 -1 0 3 0 0 -2 0 6 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) -1 0 -2 0 2 7 0 -3 0 9 0 -2 0 2 4 0 -1 0 1 2 0 3 0 0 6 0 -3 0 -4 0 -5 0 2 7 0 -5 0 9 0 -4 0 -3 0 2 4 0 -2 0 1 2 0 -1 0 0 2 1 0 0 1 5 0 2 1 0 1 5 0 1 8 0 1 8 0 2 .4 G H z , R H C P 2 .4 G H z , R H C P 0 0 3 3 0 0 3 0 3 0 -1 0 -1 0 -2 0 6 0 N o rm a liz e d g a in (d B ) 3 0 0 -2 0 N o rm a liz e d g a in (d B ) 3 3 0 0 -3 0 -4 0 2 7 0 -5 0 9 0 -4 0 -3 0 -2 0 2 4 0 1 2 0 3 0 0 -4 0 -5 0 2 7 0 -5 0 9 0 -4 0 -3 0 2 4 0 -2 0 -1 0 6 0 -3 0 1 2 0 -1 0 0 2 1 0 0 1 5 0 2 1 0 1 5 0 1 8 0 1 8 0 0 .6 G H z , L H C P 0 .6 G H z , L H C P 0 0 3 3 0 3 0 3 3 0 0 0 3 0 -1 0 3 0 0 -2 0 6 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) -1 0 -2 0 2 7 0 -3 0 9 0 -2 0 2 4 0 -1 0 1 2 0 3 0 0 6 0 -3 0 -4 0 -5 0 2 7 0 -5 0 9 0 -4 0 -3 0 2 4 0 -2 0 1 2 0 -1 0 0 2 1 0 (a ) 1 5 m m c a v ity 1 5 0 1 8 0 2 .4 G H z , L H C P 2 .4 G H z , L H C P ( b 0) 3 0 m m S p ira l S in u o u s 3 0 3 3 0 0 c a v ity 3 0 -1 0 -1 0 -2 0 6 0 -3 0 N o rm a liz e d g a in (d B ) 3 0 0 -2 0 0 .6 G H z , L H C P 0 -4 0 3 3 0 2 7 0 -5 0 9 0 -1 0 -4 0 -3 0 -2 0 2 4 0 -1 0 0 3 0 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) 2 1 0 0 3 3 0 0 0 1 5 0 1 8 0 3 0 0 -2 0 -3 0 2 7 0 -4 0 -5 0 2 7 0 -5 0 9 0 -4 0 -3 0 2 4 0 -2 0 1 2 0 -1 0 2 4 0 1 2 0 0 1 5 0 0 1 8 0 (a ) 1 5 m m 9 0 1 2 0 6 0 -2 0 -1 0 2 1 0 6 0 3 0 0 -3 0 2 1 0 2 1 0 1 8 0 (b ) 3 0 m m c a v ity S p ira l 1 5 0 1 8 0 1 5 0 c a v ity S in u o u s Fig. 5.5. Radiation pattern of spiral and sinuous antennas with different cavity depths. 82 5.2 Antenna arrays After comparing the individual elements, we proceed with a comparison of array configurations of both antennas. The ULA, WAVES and WIPA of sinuous antennas described in Chapter 4 are benchmarked against spiral antenna arrays. The comparison is made by replacing each sinuous element with a spiral element, while maintaining the same element sizes, spacing and feed network. A difference in the cavity depth between the two cases needs to be noted. From Section 5.1, it can be seen that a spiral antenna with a shallow cavity of 15 mm depth performs better than a cavity of 30 mm depth. Thus, the spiral arrays are tested with a ground plane located at a 15 mm depth, whereas the sinuous arrays have a ground plane at 30 mm. The prototypes of the different arrays are shown in Fig. 5.6. Fig. 5.6. ULA, WAVES and WIPA configurations of sinuous and spiral antenna elements. 83 Fig. 5.7 presents the total realized gain, in each of the three array configurations, measured at Temasek Laboratories (NUS). Also, the axial ratio is used in Fig. 5.8 to check the quality of circular polarization. Both LHCP and RHCP data was collected in all configurations. 1 8 1 8 U L A , R H C P 1 5 R e a liz e d g a in (d B i) R e a liz e d g a in (d B i) 1 5 U L A , L H C P 1 2 9 6 1 2 9 6 3 3 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 0 .6 0 .8 1 .0 F re q u e n c y (G H z ) 1 .6 1 .8 2 .0 2 .2 2 .4 2 .0 2 .2 2 .4 2 .0 2 .2 2 .4 1 8 W A V E S , R H C P 1 5 W A V E S , L H C P 1 5 1 2 1 2 9 9 R e a liz e d g a in (d B i) R e a liz e d g a in (d B i) 1 .4 F re q u e n c y (G H z ) 1 8 6 3 0 -3 -6 6 3 0 -3 -6 -9 -9 -1 2 -1 2 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 0 .6 0 .8 1 .0 F re q u e n c y (G H z ) 1 8 1 .2 1 .4 1 .6 1 .8 F re q u e n c y (G H z ) 1 8 W IP A , R H C P 1 5 W IP A , L H C P 1 5 1 2 R e a liz e d g a in (d B i) 1 2 R e a liz e d g a in (d B i) 1 .2 9 6 3 0 -3 -6 9 6 3 0 -3 -6 -9 -9 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 0 .6 F re q u e n c y (G H z ) 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 F re q u e n c y (G H z ) S in u o u s (R H C P ) S in u o u s (L H C P ) S p ira l (R H C P ) S p ira l (L H C P ) Fig. 5.7. Boresight gain of sinuous and spiral antennas in different array configurations. 84 1 5 1 5 U L A , R H C P A x ia l ra tio (d B ) 1 2 A x ia l ra tio (d B ) 1 2 U L A , L H C P 9 6 9 6 3 3 0 0 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 0 .6 0 .8 1 .0 F re q u e n c y (G H z ) 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 2 .0 2 .2 2 .4 2 .0 2 .2 2 .4 F re q u e n c y (G H z ) 1 8 W A V E S , R H C P 1 5 1 2 1 2 W A V E S , L H C P 1 5 A x ia l ra tio (d B ) A x ia l ra tio (d B ) 1 8 1 .2 9 6 9 6 3 3 0 0 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 0 .6 0 .8 1 .0 F re q u e n c y (G H z ) 4 2 1 .4 1 .6 1 .8 F re q u e n c y (G H z ) 4 2 W IP A , R H C P 3 0 3 0 A x ia l ra tio (d B ) 3 6 W IP A , L H C P 3 6 A x ia l ra tio (d B ) 1 .2 9 6 9 3 6 3 0 0 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 0 .6 F re q u e n c y (G H z ) 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 F re q u e n c y (G H z ) S in u o u s (R H C P ) S in u o u s (L H C P ) S p ira l (R H C P ) S p ira l (L H C P ) Fig. 5.8. Boresight axial ratio of sinuous and spiral antennas in different array configurations. In the ULA configuration, the sinuous array demonstrates higher gain than the spiral array, especially at the low frequency region. This difference can be explained by the fact that the sinuous array has better input matching due to the larger cavity depth. The axial ratio performance is similar for the two ULA arrays and both arrays demonstrate a peak at 85 around 1.8 GHz, due to a mutual coupling mode with the ground plane. The WAVES configuration in Fig. 5.7 shows that the sinuous array continues to demonstrate almost equal gain (±1 dB) in RHCP and LHCP modes, while the spiral shows preference to the RHCP mode. The gain in the LHCP mode of the spiral arrays are between 3 to 15 dB lower than the gain in the RHCP mode. However, the axial ratio of the sinuous WAVES is poorer than that obtained in the spiral WAVES, especially at low frequencies. The preference of the spiral arrays towards RHCP mode are clearly seen in the plots, with both the WAVES and WIPA configurations showing between 3 to 15 dB lower gain in the LHCP mode, when compared to RHCP. In the WIPA configuration, this also translates to a significantly poorer axial ratio when the spiral array is operated in LHCP mode. Finally, the normalized radiation patterns of the arrays are compared in Fig. 5.5. Each plot compares the spiral and sinuous arrays in two settings: pointed to boresight and steered to an angle. Also, the patterns for the low and high frequency limits are shown to assess the beamwidth and grating lobes variations. The ULA and WIPA configurations of the sinuous and spiral arrays are very similar to each other. For both boresight and steered settings, the arrays demonstrate comparable beamwidths and steering angles. One point to note in these configurations is that the nulls obtained in spiral arrays are deeper, by about 4 to 12 dB, than those obtained in the sinuous array. The WAVES configurations in Fig. 5.5 are relatively more difficult to analyse. The spiral and sinuous arrays demonstrate varying steering angles and boresight locations despite having identical phase settings in the feed network. This is interpreted as a result of the fewer number of elements and asymmetric positions in the WAVES configurations. 86 0 -6 -6 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) 0 -1 2 -1 8 -2 4 -3 0 U L A , 0 .6 G H z -3 6 -9 0 -6 0 -3 0 0 -1 2 -1 8 -2 4 -3 0 U L A , 2 .4 G H z -3 6 3 0 6 0 9 0 -9 0 -6 0 0 0 -6 -6 -1 2 -1 8 -2 4 W A V E S , 0 .6 G H z -3 0 -9 0 -6 0 -3 0 0 3 0 9 0 -9 0 -6 0 N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) -1 2 -1 8 -2 4 W I P A , 0 .6 G H z 3 0 -3 0 0 3 0 9 0 6 0 9 0 T h e ta (d e g re e ) -6 0 6 0 W A V E S , 2 .4 G H z -3 0 6 0 -6 -3 0 9 0 -2 4 0 -6 0 6 0 -1 8 0 -9 0 3 0 -1 2 T h e ta (d e g re e ) -3 0 0 T h e ta (d e g re e ) N o rm a liz e d g a in (d B ) N o rm a liz e d g a in (d B ) T h e ta (d e g re e ) -3 0 -1 2 -1 8 -2 4 W I P A , 2 .4 G H z -3 0 6 0 9 0 -9 0 T h e ta (d e g re e ) -6 0 -3 0 0 3 0 T h e ta (d e g re e ) S in u o u s (b o re s ig h t) S in u o u s (s te e re d ) S p ira l (b o re s ig h t) S p ira l (s te e re d ) Fig. 5.9. Normalized radiation patterns (boresight and steered) of sinuous and spiral antennas in different array configurations. 87 5.3 Concluding remarks on spiral and sinuous comparisons The performance of spiral and sinuous designs in both element and array configurations were comprehensively explored in this chapter. The benchmarked comparison between these elements is expected to be useful when choices for broadband, dual-circular elements are evaluated. As frequency-independent antennas, radiating in traveling-mode type configurations, spiral and sinuous antennas share many properties. Though the antennas can typically be viewed as equivalent to each other in many applications, there are certain crucial differences between them. These include aspects such as the minimum size requirements and polarization selectivity. Based on the results presented in this chapter, the following summarizes these differences between them. • Given a fixed low frequency limit, spiral designs are expected to be smaller than sinuous designs given identical gain and axial ratio requirements. The size of the sinuous designs may be up to 25% larger to obtain the same gain at low frequencies as those from spiral designs. However, larger cavity depths can be used in sinuous elements to offset this gain deficit, see Fig. 5.3. • Sinuous antennas are better suited for dual-circular polarized applications than spiral antennas. Even though dual-circular operation is possible from spirals, it is strongly dependent on the presence of a hollow, low-profile cavity. As a result, the quality of the opposite circular polarization, say LHCP in a RHCP spiral, degrades strongly with increasing frequency. • The low-profile cavities affect the spiral and sinuous antenna elements in different ways. The cavity in the spiral cases, results in large 88 variations of input impedance, as visible in Fig. 5.2, but the cavity is essential for dual-mode operation. For the sinuous elements, the cavity causes far less input impedance variations. Also, the cavity is not needed for dual-mode operation in sinuous elements, it is only added to achieve uni-directional radiation. • The radiation patterns for both the spiral and sinuous designs are similar, with the spiral elements offering slightly larger 3 dB beamwidths, as shown in Fig. 5.5. Also, spiral arrays demonstrate better roll-off and nulling at directions outside the main beam (Fig. 5.9), which can be advantageous in certain applications. 89 Chapter 6 Connections in planar arrays of sinuous antennas The previous chapters have focused on linear arrays of sinuous and spiral antennas: their design, operational principles and performance characteristics. In this chapter, a technique to optimize the performance of elements in large arrays of sinuous antennas is presented. When large element sizes are used in a planar array of sinuous antennas, the grating lobe problems experienced in linear array continue to be present at high frequencies. Thus, having large elements to operate at lowfrequencies becomes undesirable. This effect of element size resulting in grating lobes will be studied in more detail in this chapter to derive the resulting frequency limits in wideband phased arrays. Following this, a preliminary investigation into connections between neighboring antenna elements will be studied. The use of connections is motivated by their previous use in arrays of spiral antennas to extend the low-frequency limits [55],[56]. The results obtained are presented as a starting point for incorporating inter-element connections into wideband planar arrays of sinuous antennas. 90 6.1 Frequency limitations due to element sizes and inter-element spacing The design of a wideband phased array comprising of sinuous antennas can be seen a tradeoff between the element size and the element spacing. The size of the sinuous antenna determines the low-frequency cutoff, while the element spacing will influence the appearance of grating lobes in the radiation pattern. To understand this tradeoff, consider the following example. We are required to design an array of sinuous antennas operating from a low-frequency wavelength of λL to a high-frequency cut-off wavelength of λU , with beam steering capability (free of grating lobes) up to an angle of ±30◦ . The size of the each element is denoted by D, while the inter-element spacing is represented by d. The sinuous design is kept self-complementary by setting the parameters α = π/4 and δ = π/8. The external diameter for each sinuous element is calculated based on (3.3), to be: D= 4λL λL =⇒ D = 2(α + δ) 3π (6.1) In a tightly-packed planar array of these antennas, the smallest value possible for the inter-element spacing corresponds to the diameter of each element, i.e. d = D. As discussed in Section 4.2.1, this inter-element spacing will now determine the appearance of grating lobes in the radiation pattern of the array. Equation (4.4) can re-written to determine the upper cut-off frequency for grating-lobe-free performance. Combining our calculated value of inter-element spacing with imposed requirement for steering angles, the limit on the high-frequency cut-off wavelength is written as: λ ≥ d(1 + sin |θ0 |) =⇒ λU = D 91 3 2 (6.2) Combining (6.1) and (6.2), the relationship between the upper and lower wavelengths of the array is: λU = 4λL 3π 3 λU 2 =⇒ = ≈ 0.637 2 λL π (6.3) Thus, the lowest frequency achievable in the array is limited to approximately 0.64 times the upper frequency of operation. This restriction on the operating bandwidth is a consequence of avoiding too large an element size. Otherwise, multiple grating lobes would occur at high-frequencies. In this chapter, we will focus on lowering this low-frequency limit seen in these antennas. 6.2 Planar array of sinuous antennas In order to establish a base configuration, we will begin with a simple planar of sinuous antennas as shown in Fig. 6.1. The different parameters of the design are listed in Table 6.1. The elements used in this array are a 0.5x scaled version of the sinuous elements used in earlier chapters. The scaling is done in consideration of practical size constraints and to ensure that the prototype can still be measured in existing facilities. Table 6.1 Array design parameters. Parameter Element diameter (D) Fig. 6.1. Planar sinuous array. 92 Value 85 mm Element growth factor (τ ) 0.74 Trace width (α) 45◦ Trace spacing factor (δ) 22.5◦ Number of elements (N ) 9 Inter-element spacing (d) 90 mm The entire array was fabricated on a Rogers RO4003C substrate of thickness 1.524 mm and dimensions 150 mm x 150 mm. The center element of the array is fed using commercial couplers and baluns in a sequential mode M+1 feed configuration (0◦ , 90◦ , 180◦ , 270◦ ), as shown in Fig. 6.2. Fig. 6.2. Feed network used for exciting center element of the planar array. The feed configuration corresponds to a circular mode of the sinuous antenna and results in LHCP radiation at boresight. Also, note that metallic cavities are not used for the arrays in this chapter. This is done to simplify construction of the prototypes, and also as the focus of this chapter is on improving low-frequency performance and not eliminating backward radiation. The active reflection coefficient at a single port of the center element is shown in Fig. 6.3. The data indicates that the lowest frequency where the reflection coefficient is less than −10 dB is around 1.2 GHz. The observed differences between the simulated and measured data were found to be the result of the simulation mesh constraints and variations in the relative dielectric constant ( r ) between simulation and measurement. Next, the boresight radiation performance of the center element is mea93 0 -5 A R C (d B ) -1 0 -1 5 -2 0 -2 5 -3 0 C S T S im u la tio n M e a su re m e n t 0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 F re q u e n c y (G H z ) Fig. 6.3. Active reflection coefficient of planar array of sinuous antennas. sured in an anechoic chamber. The antenna shows positive realized gain at frequencies above 1.5 GHz, with a steady-state value of 5 dB from 2 GHz. Note that these are the measured gain values when only the center element of the array is excited. This is done to reduce the number of feed components needed for the measurements and to individually characterize the performance of the center element. Due to scaling factor and the lack of a cavity backing, this center element’s gain values are lower than those seen in Chapter 3. The measured values in Fig. 6.4 show good agreement with CST predictions. 1 0 R e a liz e d g a in (d B i) 5 0 -5 -1 0 -1 5 -2 0 -2 5 C S T S im u la tio n M e a su re m e n t 0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 F re q u e n c y (G H z ) Fig. 6.4. Boresight gain when center element of the planar array is excited in mode M+1 configuration. 94 6.3 Connections between adjacent sinuous elements Following the work done in [55] and [56], it was observed that connections between adjacent elements of spiral antenna arrays result in improvements to the low-frequency performance of these arrays. A similar treatment is now applied to sinuous arrays as well. Also, since sinuous antennas do not have a fixed sense of rotation, the same sinuous element can be used in a connected planar array, instead of using alternating cross-polarized spirals as in [55]. The connections which are made across adjacent arms of a sinuous array can be seen in Fig. 6.5. Fig. 6.5. Adjacent sinuous elements in (a) unconnected array (b) connected array. The complete planar array of sinuous element from the previous section, with connections between adjacent elements is shown in Fig. 6.6. Note that it is possible to connect all arms of the sinuous elements with the surrounding neighboring elements. Due to the limited number of antennas used in this example, this is only seen for the center element, which is connected to its four immediate neighbors. The principle behind making the connections is to allow for currents reaching the ends of a sinuous arm to flow into the adjacent element instead of being reflected back. As studied in Chapter 3, it is at the low-frequencies that the currents reach the ends of the antenna. Thus, the connections are expected to improve the low-frequency performance of the antenna, while 95 Fig. 6.6. Planar array of sinuous antennas with connections across arms of adjacent elements. the high-frequency region (which radiates from regions closer to the center) should remain unaffected. Initial simulations of the performance of elements with connections, as shown in Fig. 6.6, were done using CST Microwave Studio. Apart from the connecting structures, the array was kept identical to the previous planar array introduced as the base configuration. The performance of the center element in the unconnected and connected arrays is compared in Fig. 6.7. The active reflection coefficient (ARC) in the connected array suggests that a new low-frequency bandwidth centered around 0.5 GHz is now avail- 1 0 -5 5 R e a liz e d g a in (d B i) 0 A R C (d B ) -1 0 -1 5 -2 0 -2 5 -3 0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 -5 -1 0 -1 5 -2 0 U n c o n n e c te d C o n n e c te d 0 .0 0 -2 5 4 .0 F re q u e n c y (G H z ) U n c o n n e c te d C o n n e c te d 0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 F re q u e n c y (G H z ) Fig. 6.7. ARC and boresight gain performance (CST simulation) of elements with and without connections. 96 able. The starting frequency at which the ARC is less than −10 dB for the connected array is approximately 3x smaller than that of the unconnected array. The realized gain at boresight direction is also shown in Fig. 6.7. This is done to confirm that the benefits obtained in input matching are also translated into improved radiation performance. The connected case shows between 3 to 8 dB more gain at boresight direction than the unconnected case. Also, note that the radiation from the high-frequency region, due to its originating from the center region, is left unaffected by the connections. The boresight realized gain of the two cases at frequencies above 1.5 GHz are almost identical. Following the positive results obtained from CST simulations, measurements were also carried out using prototypes realized on a Rogers RO4003C substrate of thickness 1.524 mm. Both the base-configuration unconnected array and the connected array were measured in the anechoic chamber at Sup´elec. The performance of the measured arrays is shown in Fig. 6.8. The ARC and the realized gain plots show similar performance as predicted through the CST simulations. The new low-frequency band predicted at around 0.5 GHz is confirmed through these measurements. Both the ARC and the realized gain information suggest that the connected array 1 0 -5 5 R e a liz e d g a in (d B i) 0 A R C (d B ) -1 0 -1 5 -2 0 -2 5 -3 0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 -5 -1 0 -1 5 -2 0 U n c o n n e c te d C o n n e c te d 0 .0 0 -2 5 4 .0 F re q u e n c y (G H z ) U n c o n n e c te d C o n n e c te d 0 .5 1 .0 1 .5 2 .0 2 .5 F re q u e n c y (G H z ) Fig. 6.8. ARC and boresight gain performance (measured) of elements with and without connections. 97 has better performance than the unconnected array at lower frequencies. Also, the high-frequencies of both arrays continue to remain identical in the measured data. In order to compare the quality of circular polarization obtained in the two cases, the axial ratio at boresight for the unconnected and connected elements is compared in Fig. 6.9. The axial ratio of the connected case follows a similar profile to the base configuration with exceptions at around 0.7 GHz and 1.35 GHz. However, it needs to be noted that these points of relatively high axial ratio are outside the new low-frequency band obtained at around 0.5 GHz. 1 0 U n c o n n e c te d C o n n e c te d A x ia l ra tio (d B ) 8 6 4 2 0 0 .4 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 F re q u e n c y (G H z ) Fig. 6.9. Axial ratio performance (measured) of the unconnected and connected arrays. 6.4 Concluding remarks on use of connections in arrays This chapter provides a preliminary investigation into the effects of interelement connections in arrays of sinuous antennas. The fundamental highfrequency limitations, due to grating lobes, in wideband arrays motivated this study to divert attention to other regions and focus on the low-frequency performance. Connections, which are already documented to improve lowfrequency performance in spiral arrays, are seen to improve the operation 98 of sinuous arrays as well. Through the use of connections, a low-frequency band at around 3x lower than the traditional low-frequency limit is obtained. The element with connections shows not just improved input matching, but also better gain than an element with no connections. However, there is much more that can be done to exhaustively explore the consequences of connections in sinuous arrays. It is expected that the connections could result in increased mutual coupling between the elements of the array. This could affect the scanning performance of these arrays and warrants further study. Also, the operation of the center element of a connected array in certain regions (such as around 1.25 GHz in Fig. 6.7 and Fig. 6.8) shows strong deviations from its performance in unconnected arrays. Further investigations to explore possibly resonant behavior of the connections could lead to interesting results. Finally, optimization of the shape of the connections, together with resistive loading techniques, could help to control the flow of current across elements. This could result in a finer degree of control over the polarization obtained in the sinuous array. 99 Chapter 7 Conclusions and recommendations Antennas play crucial roles in all the systems they are used in, whether communications, radar imaging or remote sensing. Antennas which can provide consistent performance across large bandwidths with electronically reconfigurable modes are desired for each of these applications. The aim of this thesis, as initially outlined, is to analyze and tackle the challenges in designing broadband multi-polarization antenna elements and arrays. The thesis is directed towards mainly achieving the following objectives: • Broadband operation over at least two octaves, • Being able to switch across any choice of quad-polarization (viz. dualcircular and dual-linear), while maintaining performance irrespective of the choice of polarization, • Electronic beam steering capability over the entire bandwidth of operation, • Reduction of high side-lobes which are known to degrade performance at large steering angles and high frequencies, 100 • Realization of compact, conformal profile with unidirectional radiation. As the first step, a brief, yet focused review of broadband antennas was conducted to assess existing antenna options. The crucial relationship between antenna size and operational bandwidth was explored together with the fundamental limits in antenna design. These techniques proved to be valuable in understanding broadband behavior in antennas. Log-periodic and frequency-independent structures were compared as two classes of broadband designs popular in modern antenna systems. Sinuous antennas, which can be seen as exhibiting both log-periodic and frequencyindependent behavior were chosen as the primary antenna in this thesis. To realize practical implementations, cavity-backed versions of sinuous antennas were designed. The study conducted on the impact of the cavity indicated that the sinuous antenna still demonstrates consistent radiation performance over the entire bandwidth of operation despite increased input reflection. It was also shown that the hollow cavities with low-profiles ( λ/20) can be used without the need for any absorbing material. New non-sequential modes for achieving stable linear polarization were proposed and demonstrated conclusively. The variation of the tilt angle in linear polarization modes was shown to be minimal. These non-sequential modes were shown to be equivalent to higher-order sequential modes. However, the non-sequential modes due to their non-rotationally-symmetric feed configurations were shown to prevent the boresight null of higher-order sequential modes. Also, through the use of a reconfigurable feed network, electronic control over all four polarizations is obtained. Subsequently, broadband phased array concepts and the common issues in realizing such systems were introduced. The large sizes, necessitated by broadband requirements, of antenna elements were seen to frequently result in high side-lobes. 101 To identify additional issues and set a baseline configuration, a uniform linear array (ULA) of sinuous antennas was developed. The performance of this antenna in all four polarizations and various beam steering angles was recorded. Following this, arrays with variable sized elements were explored with the aim to reduce inter-element spacing. Apart from the existing configuration of ‘Wideband Arrays with Variable Element Sizes’ (WAVES), a new configuration based on efficiently packing broadband elements was developed. This new technique is called ‘Wideband Interstitially Packed Arrays’ (WIPA). The performance of these WAVES and WIPA configurations were also extensively evaluated. It was seen that these arrays show improved performance over ULA configurations. The crucial benefit obtained in the closely packed array is the reduced presence of grating lobes in radiation patterns. The operation of the various arrays were also confirmed through the use of a phased array system simulator (PASS). The use of this simulator is motivated by the aim to bring RF and antenna design together. By combining individual active element patterns and RF front-end performance in the software, a realistic estimate of overall system performance is obtained in PASS. The utility of PASS also exists in its ability to perform RF front-end design together with element radiation pattern data, to optimize overall system performance. Spiral antenna designs are benchmarked against the sinuous antennas. The purpose of this exploration was the establish clearly the similarities and differences between these two classes of antennas. The benefits and problems in using either antenna were listed with the aim of simplifying decisions for future designs. Based on the data obtained through this work, spiral antennas are suggested for single polarized, broadband operation with strict size requirements. However, for efficient quad-polarization operation, sinuous antennas are still preferred due to their polarization-independent 102 behavior. Finally, the effect of connections in arrays of sinuous antennas is explored. As in spiral antennas, these connections are seen to improve the low-frequency operation of existing sinuous arrays. Preliminary observations are made documenting the effects of connections, together with suggestions on future research directions. A summary of all the explorations made in this thesis and recommendations arising from them are presented below. • The recurring theme throughout the thesis was the relationship between size constraints and antenna performance. Understanding the fundamental relationships among size, utilization of space and bandwidth are crucial as the theoretical limits of bandwidth are approached. Development of design methodologies based on looking at an antenna as the distribution of metal across a volume could provide unnoticed clues on optimizing antenna designs. Existing techniques to derive limits, such as the Wheeler-Chu limit [17],[18], seem to primarily focus on the impedance bandwidths while not much attention has been given to radiation pattern performance. • In applications where narrow bands are required instead of a continuous stretch of bandwidth, it might be better to carefully evaluate the need for broadband antennas. For cases ranging from dual to quad-band operation, techniques such as matching stubs and slotradiators applied to narrow band antennas might offer good results. If broadband antennas are really required, then sinuous or related logperiodicity based antennas are recommended as their growth factor (τ ) provides a tunable degree of freedom in the design process. • Despite being functionally similar over wide bandwidths, ground planes are not completely equivalent to cavities. Resonance effects within 103 antenna elements or between elements and ground planes are often completely missed in array calculations using the ‘principle of pattern multiplication’. Even, arrays with a relatively small number of elements, such as that in Section 4.4, demonstrate significant deviations from predictions to large resonance/coupling effects. • The appearance of grating lobes are an unavoidable consequence of having physically separated antennas. They may however be mitigated through careful reduction in separation distances by techniques such as interstitial packing (Section 4.5.2). These ‘variable element size’ techniques are useful when applied to traveling wave antennas as such antennas still radiate effectively at high frequencies, despite reductions in size. • As discussed in Chapter 6, connections between elements in broadband arrays can be further investigated. The connections between elements helps in extending the bandwidth of broadband arrays at low-frequencies, but a complete picture regarding the trade-offs of such a design is still missing. Much work remains to be done to verify the operation of a connected array, with its high mutual coupling between elements. Another goal in this area would the optimization of connection shapes to control the flow of currents across the sinuous elements. • Apart from sinuous and spiral antennas, there are also other antennas which may be used to achieve similar goals. For example, Goubau antennas [57] are electrically small antennas which are also wideband. Through the incorporation of wire loops and matching slots into the antenna structure,Goubau antennas could simplify feed configurations. • The use of circuit techniques to enable effective matching of electri104 cally small antennas, as introduced by Friedman in [58], needs to be further investigated . 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Friedman, “Wide-band matching of a small disk-loaded monopole,” Antennas and Propagation, IEEE Transactions on, vol. 33, no. 10, pp. 1142–1148, Oct 1985. 112 Appendix A MATLAB code to generate a sinuous arm The closed-form equation, for a sinuous curve, in polar (r, φ) coordinates can be written as in (A.1). The various design parameters, α, δ and τ can be modified as per the requirements for each design. Rp denotes the radius of the p-th cell in a sinuous curve consisting of P cells. φ = (−1)P αp sin 180◦ log (r/Rp ) , log τp Rp+1 ≤ r ≤ Rp (A.1) MATLAB code to generate a single sinuous arm is given below. This arm can subsequently be copied and rotated to obtain a complete N -arm sinuous antenna. %% Parameters of sinuous antenna N = 4; alpha = pi/4; delta = pi/8; R_outer = 85; tau = 0.74; P = 10; 113 %% Generate the radius of each log-periodic cell R = R_outer.*tau.^[0:P-1]; %% Generate the points in each cell r_total = zeros(0,0); phi_total = zeros(0,0); for p=1:length(R)-1 r = linspace(R(p),R(p+1)+eps,10000); phi = ((-1)^p) * alpha *(sin(pi*log(r/R(p))/log(tau))); r_total = horzcat(r_total,r); phi_total = horzcat(phi_total,phi); end %% Create inner and outer covers to the arm phi_cover = linspace(delta,-delta,50); inner_cover = repmat(R(end), 1, 50); outer_cover = repmat(R(1), 1, 50); %% Plot data in polar form hold on; phi_plot = [phi_total+delta, phi_cover, ... phi_total-delta, fliplr(phi_cover)]; r_plot = [r_total, inner_cover, ... fliplr(r_total), outer_cover]; polar(phi_plot, r_plot); The above code was executed in MATLAB R2010b and the resulting graph is shown in Fig. A.1. 114 60 40 Y (mm) 20 0 −20 −40 −60 −80 0 20 40 X (mm) 60 80 100 Fig. A.1. One arm of a self-complementary four-arm sinuous antenna generated in MATLAB. 115 Appendix B Complete beam steering performance The ULA, WAVES and WIPA arrays of sinuous antennas were extensively characterized, recording their performance across multiple frequencies, polarizations and steering angles. The beamformer network controls the steering angle, while polarization controllers determine the polarization. … Beam former network Polarization controller Fig. B.1. Array feed network (left) and the ULA, WAVES and WIPA configurations of sinuous arrays (right). 116 LHCP at 0.6 GHz RHCP at 0.6 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −35 −90 −60 −30 0 30 60 −30 −90 90 −60 LHCP at 1.2 GHz −30 0 30 60 90 60 90 60 90 60 90 RHCP at 1.2 GHz 0 0 −5 −10 −10 −15 −20 −20 −30 −25 −40 −30 −35 −90 −60 −30 0 30 60 −50 −90 90 −60 LHCP at 1.8 GHz 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −35 −60 −30 0 30 60 −40 −90 90 −60 LHCP at 2.4 GHz 0 −10 −10 −20 −20 −30 −30 −40 −40 −60 −30 30 −30 0 30 RHCP at 2.4 GHz 0 −50 −90 0 RHCP at 1.8 GHz 0 −40 −90 −30 0 30 60 Linear V at 2.4 GHz −50 −90 90 0 −60 −30 0 30 0 11.25 90 157.5 −5 −10 Fig. B.2. −15 Beam steering performance of the ULA of sinuous antennas in circular modes. −20 −25 −30 −100 −50 0 50 100 117 Linear V at 0.6 GHz Linear H at 0.6 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −90 −60 −30 0 30 60 −35 −90 90 −60 Linear V at 1.2 GHz −30 0 30 60 90 60 90 60 90 60 90 Linear H at 1.2 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −90 −35 −60 −30 0 30 60 −40 −90 90 −60 Linear V at 1.8 GHz −30 0 30 Linear H at 1.8 GHz 0 0 −5 −10 −10 −15 −20 −20 −30 −25 −30 −40 −35 −50 −90 −60 −30 0 30 60 −40 −90 90 −60 Linear V at 2.4 GHz −30 0 30 Linear H at 2.4 GHz 0 0 −5 −10 −10 −15 −20 −20 −30 −25 −30 −40 −35 −40 −90 −60 −30 0 30 60 Linear V at 2.4 GHz −50 −90 90 0 −60 −30 0 30 0 11.25 90 157.5 −5 −10 Fig. B.3. −15 Beam steering performance of the ULA of sinuous antennas in linear modes. −20 −25 −30 −100 −50 0 50 100 118 LHCP at 0.6 GHz RHCP at 0.6 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −100 −50 0 50 −25 −100 100 −50 LHCP at 1.2 GHz 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −50 0 50 100 50 100 50 100 50 100 RHCP at 1.2 GHz 0 −35 −100 0 50 −35 −100 100 −50 LHCP at 1.8 GHz 0 RHCP at 1.8 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −25 −20 −30 −25 −30 −100 −35 −50 0 50 −40 −100 100 −50 LHCP at 2.4 GHz 0 RHCP at 2.4 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −100 −35 −50 0 50 Linear V at 2.4 GHz −40 −100 100 0 −50 0 0 11.25 90 157.5 −5 −10 Fig. B.4. −15 Beam steering performance of the WAVES of sinuous antennas in circular modes. −20 −25 −30 −100 −50 0 50 100 119 Linear V at 0.6 GHz Linear H at 0.6 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −25 −20 −30 −25 −100 −50 0 50 −35 −100 100 −50 Linear V at 1.2 GHz 0 50 100 50 100 50 100 50 100 Linear H at 1.2 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −25 −20 −30 −25 −100 −50 0 50 −35 −100 100 −50 Linear V at 1.8 GHz 0 Linear H at 1.8 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −100 −30 −50 0 50 −35 −100 100 −50 Linear V at 2.4 GHz 0 Linear H at 2.4 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −100 −35 −50 0 50 Linear V at 2.4 GHz −40 −100 100 0 −50 0 0 11.25 90 157.5 −5 −10 Fig. B.5. −15 Beam steering performance of the WAVES of sinuous antennas in linear modes. −20 −25 −30 −100 −50 0 50 100 120 LHCP at 0.6 GHz RHCP at 0.6 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −100 −50 0 50 −30 −100 100 −50 LHCP at 1.2 GHz 0 50 100 50 100 50 100 50 100 RHCP at 1.2 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −100 −30 −50 0 50 −35 −100 100 −50 LHCP at 1.8 GHz 0 RHCP at 1.8 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −100 −30 −50 0 50 −35 −100 100 −50 LHCP at 2.4 GHz 0 RHCP at 2.4 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −35 −100 −50 0 50 Linear V at 2.4 GHz −30 −100 100 0 −50 0 0 11.25 45 78.75 −5 −10 Fig. B.6. Beam steering performance of the WIPA of sinuous antennas in −15 circular modes. −20 −25 −30 −100 −50 0 50 100 121 Linear V at 0.6 GHz Linear H at 0.6 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −100 −25 −50 0 50 −30 −100 100 −50 Linear V at 1.2 GHz 0 50 100 50 100 50 100 50 100 Linear H at 1.2 GHz 0 0 −5 −5 −10 −15 −10 −20 −15 −25 −20 −30 −35 −100 −50 0 50 −25 −100 100 −50 Linear V at 1.8 GHz 0 Linear H at 1.8 GHz 0 0 −5 −5 −10 −10 −15 −20 −15 −25 −20 −30 −25 −35 −40 −100 −50 0 50 −30 −100 100 −50 Linear V at 2.4 GHz 0 Linear H at 2.4 GHz 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −100 −30 −50 0 50 Linear V at 2.4 GHz −35 −100 100 0 −50 0 0 11.25 45 78.75 −5 −10 Fig. B.7. Beam steering performance of the WIPA of sinuous antennas in −15 linear modes. −20 −25 −30 −100 −50 0 50 100 122 123 [...]... PASS and measurement 74 4.25 WAVES and WIPA performance in PASS and measurement 75 5.1 Sinuous and spiral prototypes 79 5.2 |S11 | of spiral and sinuous antennas with different cavity depths 79 xii 5.3 Boresight gain of spiral and sinuous antennas with different cavity depths 80 5.4 Boresight axial ratio of spiral and sinuous antennas... 81 5.5 Radiation pattern of spiral and sinuous antennas with different cavity depths 82 5.6 ULA, WAVES and WIPA configurations of sinuous and spiral antenna elements 83 5.7 Boresight gain of sinuous and spiral antennas in different array configurations 84 5.8 Boresight axial ratio of sinuous and spiral antennas in different array configurations...3.8 Polarization ellipse 32 3.9 Tilt angle and axial ratio in spiral and sinuous antennas 34 3.10 Sinuous antennas with and without absorber-loaded cavities 35 3.11 Realized boresight gain with reflecting and absorbing cavities 36 3.12 Prototype of four-arm sinuous antenna with cavity backing 37 3.13 Input reflection coefficient and input impedance at a single port of the sinuous. .. 6.5 Adjacent sinuous elements in unconnected and connected planar arrays 95 6.6 Planar array of sinuous antennas with connections across arms of adjacent elements 96 6.7 ARC and boresight gain performance (CST simulation) of elements with and without connections 96 6.8 ARC and boresight gain performance (measured) of elements with and without... configuration of sinuous antennas 63 4.11 Realized boresight gain of the WAVES 63 4.12 Polarization performance of WAVES 63 4.13 Beam steering performance of the WAVES of sinuous antennas 64 4.14 Comparison of sizes of large and small sinuous elements used in arrays with variable sized elements 65 4.15 WIPA configuration of sinuous antennas... unconnected and connected arrays 98 A.1 One arm of a self-complementary four-arm sinuous antenna 115 B.1 Array feed network (left) and the ULA, WAVES and WIPA configurations of sinuous arrays (right) 116 B.2 Beam steering performance of the ULA of sinuous antennas in circular modes 117 B.3 Beam steering performance of the ULA of sinuous antennas... operation and measurement of sinuous antennas These antennas are built with practical constraints, such as low-profile and uni-directional radiation, in consideration and recommendations on adapting the design to other use cases are provided Array configurations of these antennas are detailed in Chapter 4 After analyzing common problems in building wideband arrays, linear configurations of sinuous antennas... investigation into connected planar arrays of such antennas is conducted with the aim of improving low-frequency performance Finally, Chapter 7 provides a summary of the complete thesis Recommendations and research directions are proposed for consideration in future developments of broadband, multiple polarization antenna elements and arrays 9 Chapter 2 Review of broadband antennas An antenna is defined as the... Normalized radiation patterns of sinuous antennas in two circular modes 43 3.19 Realized boresight gain for linear modes of cavity-backed sinuous antennas 44 3.20 Co -polarization and cross -polarization gain (measurement) for linear mode of cavity-backed sinuous antennas 44 3.21 Normalized radiation patterns of sinuous antennas in two linear modes ... all these bands (i.e a broadband antenna) and thus simplify the realization of these electronics systems Broadband antennas can be described as those antennas which satisfy given performance requirements across multiple frequencies The requirements may specify multiple performance goals in terms of parameters such as input impedance matching, gain, beamwidth and sidelobe levels Broadband antennas would