Investigation of the scanning performance and enhancement of an electrically large array

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(1)UNIVERSITEIT•STELLENBOSCH•UNIVERSITY jou kennisvennoot. •. your knowledge partner. Investigation of the Scanning Performance and Enhancement of an Electrically Large Array by. Martin N Cavanagh. Thesis presented in partial fulfilment of the requirements for the degree of. Master of Science in Electronic Engineering at the. University of Stellenbosch. Department of Electrical and Electronic Engineering, University of Stellenbosch, Private Bag X1, 7602 Matieland, South Africa.. Supervisor: Prof. KD Palmer. March 2008.

(2) Copyright © 2008 University of Stellenbosch All rights reserved..

(3) Declaration I, the undersigned, hereby declare that the work contained in this thesis is my own original work and that I have not previously in its entirety or in part submitted it at any university for a degree.. Signature: . . . . . . . . . . . . . . . . . . . . . . . . . . . MN Cavanagh. Date: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ii.

(4) Abstract An existing antenna used in satellite communications is investigated with the goal of improving low angle radiation performance and reducing manufacturing costs. To understand this antenna it is modelled, simulated and verified against existing measurements. This verified model is the basis for further investigation. The antenna is separated into two parts with are individually examined and enhancements are proposed for each. Simulations of the resulting final models show that little by way of improvement in the performance can be obtained but bring several key issues to light. The scanning impedance is of particular importance in such an investigation and a method of determining this impedance is recommended.. iii.

(5) Opsomming ’n Bestaande antenna wat in satelliet kommunikasie gebruik word is ondersoek. Die doelwit van die studie is om die werkverrigting van lae hoek uitstraling te verbeter en die vervaardigingskoste te verminder. Om hierdie antenna te verstaan is dit gemodelleer, gesimuleer en verifieer teen bestaande metings. Hierdie model vorm die basis vir verdere ondersoeke. Die antenne is in twee dele opgebreek en albei is individueel ondersoek en verbeteringe is voorgestel. Simulasies van die finale modelle toon dat byna geen verbetering in die werkverrigting verkry kan word nie, maar bring verskeie sleutel kwessies aan die lig. Die skanderingsimpedansie is van kardinale belang in sodanige ondersoek en ’n metode om hierdie impedansie te bepaal, is aanbeveel.. iv.

(6) Acknowledgment A special word of thanks to: • Omnipless for providing the project and financing, especially Ian George and his team. • Professor KD Palmer for his guidance and advice. • My family for being dependable. • JG Hoole. • J Badenhorst. • Professor JH Cloete.. v.

(7) Contents Declaration. ii. Abstract. iii. Opsomming. iv. Acknowledgment. v. Contents. vi. List of Figures. viii. List of Tables. x. Nomenclature. xi. 1 Introduction. 1. 2 Verification of CST Model 2.1 Introduction . . . . . . . . . . . . . . . . . . . 2.2 Model Built in CST . . . . . . . . . . . . . . . 2.2.1 Cavity-Backed Crossed Slot Array . . . 2.2.2 Excitation of the Array . . . . . . . . . 2.3 Comparison Between Measured and Simulated 2.3.1 Influence of Input Impedance . . . . . 2.4 Summary . . . . . . . . . . . . . . . . . . . .. . . . . . . .. 3 3 4 4 5 6 8 9. . . . . . .. 10 10 11 12 12 12 13. . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . .. 3 Examination of a Periodic Radiating Surface 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . 3.2 Travelling and Leaky Waves . . . . . . . . . . . . 3.3 Unit Cell . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Structure . . . . . . . . . . . . . . . . . . 3.3.2 Exciting the Unit Cell Array . . . . . . . . 3.4 Propagation Constants Associated with a Periodic. vi. . . . . . . .. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . Surface. . . . . . . .. . . . . . ..

(8) CONTENTS 3.5 3.6. vii. Sweeping the Dimensions of the Unit Cell . . . . . . . . . . . 3.5.1 Optimal Solution . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 Investigation of the Array Excitation 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 4.2 Alternate Excitations Using a Smaller Array Model 4.2.1 Thinning the Feed . . . . . . . . . . . . . . 4.3 Design of a Proposed Cavity . . . . . . . . . . . . . 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . .. 15 16 17. . . . . .. 18 18 19 20 21 23. . . . . . .. 24 24 25 26 28 29 30. 6 Conclusion 6.1 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . .. 31 32. Bibliography. 33. 5 Final Array Simulations and Results 5.1 Introduction . . . . . . . . . . . . . . . . . . . 5.2 Proposed Feed in Original Array . . . . . . . . 5.3 Hexagonal Surface on Original Array . . . . . 5.3.1 Investigation of Trends Using a Smaller 5.4 Results of the Full Array Without Top Hats . 5.5 Summary . . . . . . . . . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . . Array . . . . . . . .. . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . .. . . . . . .. . . . . .. . . . . . ..

(9) List of Figures 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10. Antenna model on infinite ground plane. . . . . . . . . . . . . . Transparent model of single element and top hat. . . . . . . . . Top view of the antenna array layout with dimensions. . . . . . Radiation pattern with intercardinal steering of the main beam. Normalised array amplitude distribution. . . . . . . . . . . . . . Boresight gain along the x axis. . . . . . . . . . . . . . . . . . . Boresight gain along the y axis. . . . . . . . . . . . . . . . . . . Gain when steered along the x axis. . . . . . . . . . . . . . . . . Gain when steered along the y axis. . . . . . . . . . . . . . . . . Power balance. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3.1 3.2 3.3. Representation of a leaky-wave radiator. . . . . . . . . . . . . . The unit cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two adjacent cells providing a flat face for a port (multipin) excitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alternate excitation sources. . . . . . . . . . . . . . . . . . . . . Electric fields between the hexagonal elements and the line along which they are evaluated. . . . . . . . . . . . . . . . . . . . . . Complete structure with two ports used for simulating the surface. Surface E-field evaluated along the centre of the structure. . . . Results of parameter optimization - combinations of parameters which satisfy requirements. . . . . . . . . . . . . . . . . . . . . .. 11 12. Smaller array model with top hats hidden. . . . . . . . . . . . . Two alternate structures used for excitation. . . . . . . . . . . . Simulated boresight results of the unaltered and two alternate structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two arrays with elements which are not fed crossed out in red. . Simulated results of the two arrays with thinned excitation. . . . Dimensions of 50 Ω transmission lines. . . . . . . . . . . . . . . Model of cavity with new feed (Top hats hidden). . . . . . . . . MWO schematic for determining input impedance. . . . . . . . Comparison of input match between the original and new elements.. 19 20. 3.4 3.5 3.6 3.7 3.8 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9. viii. 4 5 5 6 6 7 7 7 7 8. 13 13 13 13 15 16. 20 20 20 22 22 22 23.

(10) LIST OF FIGURES 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15. Model with proposed new cavity elements replacing the original elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boresight gain along the x axis. . . . . . . . . . . . . . . . . . . Boresight gain along the y axis. . . . . . . . . . . . . . . . . . . Gain when steered along the x axis. . . . . . . . . . . . . . . . . Gain when steered along the y axis. . . . . . . . . . . . . . . . . Model with the surface of hexagonal disks on the original array. Boresight gain along the x axis. . . . . . . . . . . . . . . . . . . Boresight gain along the y axis. . . . . . . . . . . . . . . . . . . Gain when steered along the x axis. . . . . . . . . . . . . . . . . Gain when steered along the y axis. . . . . . . . . . . . . . . . . Trend in one parameter sweep. . . . . . . . . . . . . . . . . . . . Boresight gain along the x axis. . . . . . . . . . . . . . . . . . . Boresight gain along the y axis. . . . . . . . . . . . . . . . . . . Gain when steered along the x axis. . . . . . . . . . . . . . . . . Gain when steered along the y axis. . . . . . . . . . . . . . . . .. ix. 25 25 25 26 26 27 27 27 27 27 28 29 29 29 30.

(11) List of Tables 1-I. Inmarsat aeronautical antenna requirements. . . . . . . . . . . .. 1. 3-I 3-II. Swept Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . Optimal Parameter Combination . . . . . . . . . . . . . . . . .. 16 17. x.

(12) Nomenclature Abbreviations CST CEM FDTD RHCP PRS PEC PCB EBG MWO. = = = = = = = = =. Microwave Studio package of Computer Simulation Technology Computational Electromagnetics Finite Difference Time Domain Right Hand Circurlarly Polarized Partially Reflective Surface Perfect Electric Conductor Printed Circuit Board Electromagnetic Band Gap Microwave Office package of Applied Wave Research. Variables r θ0 φ0 βx βy γx k0. = = = = = = =. Relative permittivity Elevation angle Azimuthal angle Phasing between elements in the x direction Phasing between elements in the y direction Complex propagation constant for propagation in the x direction Free-space wavenumber. xi.

(13) Chapter 1 Introduction An antenna designed for the the Inmarsat-Aero network for satellite-aircraft communications is described in [1]. Table 1-I is reproduced from [2] and lists the basic requirements of this antenna. Competitive markets and higher specification demands require constant improvement of current antennas and development of cheaper, smaller antenna systems with improved performance. Aspects of this antenna have been investigated by both [2] and [3], with several recommendations being made in order to fully understand the operation and radiation mechanism. This forms the motivation and starting point of the work presented here. Table 1-I: Inmarsat aeronautical antenna requirements. Receive frequency. 1530.0 − 1559.0 M Hz. Transmit frequency. 1626.5 − 1660.0 M Hz. Gain Sidelobe levels. > 12 dBi RHCP < 13 dB at 45o from pointing direction. Axial Ratio Coverage. < 6 dB Hemispheral, above 5o from the horizon. The ever increasing computational abilities of modern computers and simulation packages allow larger and more complex models to be analysed within a practical time frame. The Microwave Studio package of Computer Simulation Technology Studio Suite (CST) is used extensively not only to model 1.

(14) CHAPTER 1. INTRODUCTION. 2. the existing antenna but also to propose new ideas. One of the more powerful computational electromagnetic (CEM) tools suited to electrically large, broadband problems is the Finite Difference Time Domain (FDTD), full wave solver. This solver is used wherever possible in this work. Improvements and new releases mean that the package is developing in capability continuously. Some more powerful tools which were not available two years ago are now at the disposal of the user. Mastering and manipulating the more advanced tools such and the post processing templates and macros are some of the skills gained here. Results are taken at 1525 M Hz and 1661 M Hz in order to completely cover the frequency band listed in Table 1-I for all simulations unless otherwise stated. All results are limited to the Right Hand Circularly Polarised (RHCP) component of true gain. One of the downfalls of modelling large, complex structures is that the accuracy of the results of the CEM solver are only as accurate as the model it acts upon. The existing antenna is modelled in CST with accuracy being the primary concern in order to validate the results of further modelling. Decreasing computational time is a secondary concern since this can be done by altering the model and adjusting the simulation settings once an accurate solution is obtained. The antenna consists of an array of fed elements with suspended parasitic disks arranged on top. These disks or top hats are studied as a Partially Reflective Surface (PRS) using a leaky wave analysis and a surface with supposedly enhanced performance is proposed and incorporated into the array. Results from this lead to further investigation of the surface in the array and ultimately to the examination of the array without the surface. The excitation of the cavity-backed crossed slots is also investigated and a new feed is designed and proposed for this element. The goal of this work is to improve understanding of the current performance using simulation tools which are made feasible by increased computational power. Enhancement and simplification of the original design and reduction of current manufacturing costs is also investigated..

(15) Chapter 2 Verification of CST Model 2.1. Introduction. During the design and building of the existing antenna discussed in the previous chapter, extensive performance measurements were made using a tapered antenna test chamber [1]. In this chapter the simulated results of a model created in CST are compared to these measurements. By verifying the model and simulation capabilities, further investigation into some of the operating principles of this antenna is facilitated, and ultimately improvements and recommendations can be made. The physical antenna is detailed and large (several wavelengths long) which means an accurate model is time consuming to produce and compute. The model proposed here has in excess of three million mesh cells when meshed with λ/20 and simulated over the frequency range 0 − 5 GHz (Bandwidth of excitation pulse). The comparison of measurements and simulation is extremely important if any simulated results from future models are to be trusted. Provided the measurements and computation electromagnetic code of CST are accurate, an accurate model will closely reflect the measurements and real world performance.. 3.

(16) CHAPTER 2. VERIFICATION OF CST MODEL. 4. 2.2. MODEL BUILT IN CST. 2.2. Model Built in CST. The model created in CST comprises the ground plane, housing and array of elements and top hats shown in Figure 2.1. The physical measurements were taken with the antenna mounted on a curved ground plane to imitate the fuselage of an aeroplane. However, a flat, infinite ground plane is employed in the model by using open boundary conditions on the four sides and top and a PEC (Perfect Electric Conductor) sheet on the bottom. The housing for the electronics (phase shifters and power splitters) is modelled as a solid, PEC block.. Figure 2.1: Antenna model on infinite ground plane.. 2.2.1. Cavity-Backed Crossed Slot Array. On top of the PEC block shown in Figure 2.1 is the array of elements. The individual cavity-backed crossed slot element with the top hat is shown in Figure 2.2. This cavity is modeled as a PEC cylinder with a PCB (Printed Circuit Board), of permittivity r = 4.8, layer on top. The slots are etched on the dielectric and 8 screws surrounded by vias provide electrical contact and keep the PCB in place on the cylinder. The top hats are modelled as suspended PEC discs and the physical layer of supporting foam is ignored in the model. The complete cavity element in the existing antenna has only one feed point and uses a microstrip feed network to provide phasing to the four crossed slots via semi rigid coaxial cable. Feed points are defined in the model across the.

(17) CHAPTER 2. VERIFICATION OF CST MODEL. 5. 2.2. MODEL BUILT IN CST. slots at the points were the coaxial cable meets the slots and discrete ports are placed at these feed points as shown in Figure 2.2. A computational investigation of the performance and excitation has been done in [3] which explains the development and properties of this cavity-backed crossed slot. The complete array is arranged in a triangular grid comprising 34 elements with dimensions and spacing shown in figure 2.3.. Figure 2.2: Transparent model of single element and top hat..

(18) CHAPTER 2. VERIFICATION OF CST MODEL. 6. 2.2. MODEL BUILT IN CST. 68.5 mm. 301 mm. 3 mm 79 mm 787 mm. Figure 2.3: Top view of the antenna array layout with dimensions.. 2.2.2. Excitation of the Array. The discrete ports referred to in Section 2.2.1 allow both the amplitude and phase of each of the four ports in each of the 34 elements to be manually controlled. The manipulation of the excitation of the individual ports is threefold: • The progressive linear phasing between elements is the mechanism for steering the main beam off boresight in both the x and y axes. Since the array is planar, there are two degrees of freedom which allow the beam to be steered to any combination of −90o < θ0 < 90o and 0o < φ0 < 360o [4]. The equations 2.1 and 2.2 [4] are used to determine the progressive phasing βx and βy in the x and y directions respectively. Given these phase progressions, the angles θ and φ can also be obtained using equations 2.3 and 2.4 [4]. Figure 2.4 shows the radiation pattern when the main beam is steered off axis, and how θ and φ are defined with respect to the x and y axes. βx = −kdx sin θ0 cos φ0. (2.1). βy = −kdy sin θ0 sin φ0. (2.2).

(19) CHAPTER 2. VERIFICATION OF CST MODEL. 7. 2.2. MODEL BUILT IN CST. tan φ0 =. 2. sin θ0 =. . βx kdx. βy dx βx dy. 2. +. (2.3). βy kdy. 2 (2.4). Figure 2.4: Radiation pattern with intercardinal steering of the main beam.. • The feed network of the existing element described in Section 2.2.1 provides quadrature phasing to the crossed slots. Each port within each element is fed with either a 0o , 90o , 180o or 270o phase shift at 1.6 GHz to simulate this phase delay. • An amplitude taper is used in the physical antenna [1] in order to reduce sidelobe levels to the required −13 dB at 45o from the peak over the full range of steer angles. This taper is represented in relief in Figure 2.5 and dictates the amplitude for each element in the array. The same taper is reproduced in the model by manually defining the excitation amplitude.

(20) CHAPTER 2. VERIFICATION OF CST MODEL. 8. 2.3. COMPARISON BETWEEN MEASURED AND SIMULATED RESULTS. at each discrete port. The amplitudes of each of the four ports within an element are equal.. Figure 2.5: Normalised array amplitude distribution.. As a result, the phase of each port depends on both the position of the port within the element and the position of the element within the array, whereas the amplitude of each port depends solely on the position of the relevant element within the array.. 2.3. Comparison Between Measured and Simulated Results. Section 2.2.2 mentions that the ports within an element are fed with quadrature phasing, this is to achieve the correct circular polarization. All the extracted data which is presented for comparison is limited to the right-hand circularly polarized (RHCP) component, as are the measurements with which these simulations are compared. The losses in the phase shifters and power splitter electronics have been quoted at 2.5 dB [1], this value is subsequently subtracted from the simulation results since the model does not account for any of these losses. The Figures 2.6-2.9 show both the measured gain and the simulated gain of the farfield radiation pattern. Comparisons and are made at boresight and when the main beam is steered down to θ = 75o along the x and y axes (φ = 0o and 90o respectively). There exists simulated results for intercardinal steering, as shown in Figure 2.4, but these are omitted here along with the results from.

(21) CHAPTER 2. VERIFICATION OF CST MODEL. 9. 2.3. COMPARISON BETWEEN MEASURED AND SIMULATED RESULTS. the centre of the frequency band (1.6 GHz). The data shown here is sufficient to prove the point. 1.525, 90(boresight), 0(major). 1.661, 90(boresight), 0(major). 20. 20 Measurement Simulation. 10. 10. 5. 5. 0. 0. −5. −5. −10. −10. −15. −15. −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. Measurement Simulation. 15. Gain (dB). Gain (dB). 15. −20. 80. −80. −60. (a) 1.525 GHz. −40. −20 0 20 Angle (degrees). 40. 60. 80. (b) 1.661 GHz. Figure 2.6: Boresight gain along the x axis.. 1.661, 90(boresight), 90(minor). 1.525, 90(boresight), 90(minor) 20. 20 Measurement Simulation. 10. 10. 5. 5. 0. 0. −5. −5. −10. −10. −15. −15. −20. −20. −80. −60. −40. −20 0 20 Angle (degrees). (a) 1.525 GHz. 40. 60. 80. Measurement Simulation. 15. Gain (dB). Gain (dB). 15. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (b) 1.661 GHz. Figure 2.7: Boresight gain along the y axis.. The results shown in Figures 2.6 and 2.7 indicate good agreement (main beams within 1 dB) between the simulated and measured data when the main beam is not steered. This agreement is seen on both extremes of the frequency band. The discrepancies in Figures 2.8 and 2.9 are due to two factors: Firstly, the curved ground plane used in the measurements differs from the infinite.

(22) CHAPTER 2. VERIFICATION OF CST MODEL. 10. 2.3. COMPARISON BETWEEN MEASURED AND SIMULATED RESULTS. 1.525, 5(steered), 0(major). 1.661, 5(steered), 0(major). 20. 20 Measurement Simulation. 10. 10. 5. 5. 0. 0. −5. −5. −10. −10. −15. −15. −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. Measurement Simulation. 15. Gain (dB). Gain (dB). 15. −20. 80. −80. −60. (a) 1.525 GHz. −40. −20 0 20 Angle (degrees). 40. 60. 80. (b) 1.661 GHz. Figure 2.8: Gain when steered along the x axis.. 1.525, 5(steered), 90(minor). 1.661, 5(steered), 90(minor). 20. 20 Measurement Simulation. 10. 10. 5. 5. 0. 0. −5. −5. −10. −10. −15. −15. −20. −80. −60. −40. −20 0 20 Angle (degrees). (a) 1.525 GHz. 40. 60. 80. Measurement Simulation. 15. Gain (dB). Gain (dB). 15. −20. −80. −60. −40. −20 0 20 Angle (degrees). (b) 1.661 GHz. Figure 2.9: Gain when steered along the y axis.. 40. 60. 80.

(23) CHAPTER 2. VERIFICATION OF CST MODEL. 11. 2.3. COMPARISON BETWEEN MEASURED AND SIMULATED RESULTS. flat ground plane in the simulation resulting in the greatest disparity at low angles. Secondly, during the development of the physical antenna the phasing between the elements is adjusted individually and differs from the linear phase progression assumed in the simulation. Since there are more elements along the x axis, there is more manual adjustment and hence a greater discrepancy in the x cut (Figure 2.8) than the y cut (Figure 2.9). The radius of curvature of the ground plane also differs between the two axes. The results at the steered angle (in this case 15o above horizontal or θ = 75o ) are within 1 dB at both frequencies .. 2.3.1. Influence of Input Impedance. The power balance diagram in CST indicates frequencies where energy is absorbed by the structure or radiated out through open boundaries. For a model with over 100 ports this is the simplest method of determining the overall input impedance. The large number of simultaneously excited S-Parameters make them difficult to interpret. As the array is steered the change in mutual coupling between elements results in a change in input impedance. The power balance diagram shown in Figure 2.10 shows the how much energy is absorbed/reflected on boresight and when the array is steered as a result of the change in impedance. The gain that the simulations present in Figures 2.6 - 2.9 is true gain which does not account for this input reflection. The realised gain however, would be reduced by approximately 90% (corresponding to the 90% of energy reflected) when it is steered and approximately 20% when it is not steered..

(24) CHAPTER 2. VERIFICATION OF CST MODEL. 12. 2.4. SUMMARY 1.2 Power balance when steered to θ = 85o. 1.1. Power balance with no steering. Normalized absorbed energy. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2. 0. 0.5. 1. 1.5 Frequency (GHz). 2. 2.5. 3. Figure 2.10: Power balance.. 2.4. Summary. The model developed and implemented here is shown to accurately reflect the existing antenna by comparing simulated results to existing measurements. The few disparities between the model and the physical antenna account for the slight discrepancies in the results. It is standard procedure to refine the meshing of a simulation model and re-simulate until the results converge. CST has a built-in adaptive mesh refinement option which does precisely this under standard conditions, when the excitation is manually specified however, this is not an option. Original simulations were done using λ/10 and λ/15 meshing but it was later refined to the λ/20 referred to in Section 2.1. Manual convergence testing is done by observing the changes in data as the mesh is refined it can be said with certainty that λ/20 meshing provides a converged result since there is no observable change when the mesh is refined further. In the CST FDTD code there are two factors which terminate the solver: The first is the number of pulse widths or length of time which the solver runs for and the second is the steady state energy. In these simulations the.

(25) CHAPTER 2. VERIFICATION OF CST MODEL. 13. 2.4. SUMMARY. determining factor was the steady state energy which was set at −40 dB for the verification simulations. It was later set at −30 dB for subsequent simulations after comparisons showed no observable difference between results. This number is the amount of energy which is still retained in the model, so a smaller number would result in greater accuracy but much longer run-time. From these results and comments it is apparent that the model accurately represents the physical antenna and the current simulation parameters suffice. Further simulations of this model or a derivative of it carry with them a similar high level of credibility..

(26) Chapter 3 Examination of a Periodic Radiating Surface 3.1. Introduction. In order to enhance the performance of this antenna, the radiating mechanism must be understood. This chapter examines the arrangement of top hats as a radiating surface independent of the complex excitation provided by the cavity-backed crossed slots. Previous work on this antenna [1] and [3] suggests that the parasitic disks or top hats enhance the low angle radiation performance. This enhanced low angle performance is a result of the top hats forming a guiding structure for a leaky or fast wave [2]. The work in this chapter is an extension of some of the ideas suggested in [2] with the focus on the characteristics of this arrangement of top hats as a radiating surface. If the antenna discussed in [1] does employ a fast wave mechanism for radiation then there is some possible geometrical arrangement of the top hats which will give optimal results. The aim here is to find this optimal geometry so that is can be incorporated into the complete antenna later. Methods for examining the propagation of leaky wave antennas include the transverse resonance method [5], [6] and a periodic cell examination [7]. Knowledge of the extracted propagation parameters then allows an optimal solution to be synthesized. A different approach is taken here which does not explicitly extract the propagation constants but examines the effect of these parameters as the geometric parameters of the surface change. 14.

(27) CHAPTER 3. EXAMINATION OF A PERIODIC RADIATING SURFACE 15 3.2. TRAVELLING AND LEAKY WAVES. 3.2. Travelling and Leaky Waves. A guiding structure which supports a travelling wave may be categorized as either open or closed. A closed structure has a transverse cross-section completely bounded whereas an open structure does not confine energy to the inside of the guide. A field which is radiated by an open structure comprises of a continuous spectrum of modes as well as the discrete modes found in the closed guide [8]. As a result, the propagation constant of travelling waves in an open structure is complex which accounts for the continuous leakage of energy from within the guide and the exponential increase in energy outside the guide in the transverse direction [9]. Waves of this nature are called leaky or fast waves and antennas using leaky waves fall into two categories, uniform or periodic. A uniform antenna launches a wave from a continuous aperture whereas a PRS leaks energy periodically, an example of a PRS leaky wave antenna in shown in Figure 3.1. Previous work [10], [11], [12] on two dimensional PRS structures show that the surface and geometrical parameters are the dominant factors in determining the radiation characteristics rather than the source or excitation.. z z'. θ0. Feed. h x x'. Figure 3.1: Representation of a leaky-wave radiator..

(28) CHAPTER 3. EXAMINATION OF A PERIODIC RADIATING SURFACE 16 3.3. UNIT CELL. The apparent exponential increase in propagation outside the structure is represented in Figure 3.1. If a point x0 is chosen then the leaky wave propagation increases with increasing z up to a point z 0 , where the exponential is defined in equation 3.1 and z 0 is defined in equation 3.2. This is as a result of the non modal or dispersive nature of leaky wave structures [8].. 3.3. Unit Cell. 3.3.1. Structure. f (z) = e(αz −jβz )z. (3.1). z 0 = x0 tan θ0. (3.2). The physical antenna simulated in Section 2.2 comprises an arrangement of top hats but hexagonal hats result in an improved axial ratio of the radiation [2]. Consequently, as can be seen in Figure 3.3, hexagonal hats are used which results in the spacing between PEC boundaries being uniform throughout the array. The unit cell is the smallest, unambiguous rectangular shape which - when multiplied - reproduces the complete structure. A single cell with parameters is shown in Figure 3.2..

(29) CHAPTER 3. EXAMINATION OF A PERIODIC RADIATING SURFACE 17 3.3. UNIT CELL. s. r. r h s. Figure 3.2: The unit cell.. 3.3.2. Exciting the Unit Cell Array. The wave travelling in a leaky wave antenna propagates in two dimensions along the surface as it radiates. To simplify the analysis only propagation in one dimension is considered here. The complex excitation which the cavities (discussed in Section 2.2.2) provide is circularly polarized. In this analysis the simplified feeds do not completely reflect this circular polarized excitation and prove to be a major downfall of this technique. In order to excite the structure a wave or field must be imposed on the surface or between the surface and the ground plane. If two cells are placed side by side as shown in Figure 3.3 then a flat, homogeneous face is created on which a port can be placed. This is because CST requires any fed interface to be homogeneous for the first three mesh cells. This multipin port excites a field shown in Figure 3.5 on the surface between the top hats. Alternate feeding methods which set up different fields in this structure were also attempted, these include a flat port and a suspended dipole shown in Figure 3.4. These different methods were used in an attempt to recreate the complex excitation fields provided by the slots. The final structure is two cells wide and an arbitrary number of cells in length. The source is applied to one end and both sides are bounded by.

(30) CHAPTER 3. EXAMINATION OF A PERIODIC RADIATING SURFACE 18 3.3. UNIT CELL. Figure 3.3: Two adjacent cells providing a flat face for a port (multipin) excitation.. (a) Full-face port.. (b) Suspended Dipole.. Figure 3.4: Alternate excitation sources.. periodic boundary conditions. A farfield monitor is set up to observe the radiation pattern and an E-field monitor is set up along the surface..

(31) CHAPTER 3. EXAMINATION OF A PERIODIC RADIATING SURFACE 19 3.3. UNIT CELL. Figure 3.5: Electric fields between the hexagonal elements and the line along which they are evaluated.. Figure 3.6: Complete structure with two ports used for simulating the surface..

(32) CHAPTER 3. EXAMINATION OF A PERIODIC RADIATING SURFACE 20 3.4. PROPAGATION CONSTANTS ASSOCIATED WITH A PERIODIC SURFACE. 3.4. Propagation Constants Associated with a Periodic Surface. The complex propagation constant for propagation in the x direction is given in general form equation 3.3. kx = −jγx = βx − jαx. (3.3). A dispersion or Brillouin diagram is an example of a technique which uses a periodic cell to extract the phase propagation of a surface by investigating the propagation within an enclosed area (the Brillouin zone). This is typically done in the frequency domain using a unit cell configuration and exciting the surface with Floquet modes [8]. This method is particularly useful for analysing surfaces which exhibit fast wave characteristics or a band of no propagation such as EBG (Electromagnetic Band Gap) structures and left handed structures or metamaterials. Characterizing the propagation using a dispersion diagram has recently been used in the time domain [7] to extract the attenuation constant as well as the phase velocity. Periodic or unit cell boundaries cannot be used in the time domain solver of CST if the model contains an explicitly defined excitation. An examination of this unit cell without excitation using the Eigenmode Solver in CST was unsuccessful in generating a dispersion diagram because of the inability to deal with the radiated energy. The Eigenmode Solver in CST requires unit cell boundaries which cannot absorb energy and account for radiation from the surface. The attenuation constant αx is related to the rate of leakage of energy as the wave propagates along the guiding structure in the x direction. Higher values of αx indicate that more energy is being radiated per unit length whereas lower values of αx indicate that energy is more tightly bound to the surface and less is radiating per unit length. A characteristic of leaky wave antennas is that the phase velocity is greater than the speed of light in free space or β < k0 , where k0 is the free space wave number. The angle θ0 in Figure 3.1 is given in terms of the wavenumber βx in equation 3.4. From this equation it can be seen that as the phase velocity of the wave approaches infinity, the radiated beam is steered further off boresight and when it equals the speed of light in free space the radiation is vertical..

(33) CHAPTER 3. EXAMINATION OF A PERIODIC RADIATING SURFACE 21 3.4. PROPAGATION CONSTANTS ASSOCIATED WITH A PERIODIC SURFACE. As a result, leaky wave antennas offers inherently good performance when low angle radiation performance is required. sin θ0 =. βx k0. (3.4). The wavenumber βx can be derived directly from the angle but solving for αx is not as simple. In order to define the attenuation per unit length the surface E-field is evaluated along a single longitudinal line (shown in Figure 3.5). Figure 3.7 shows the field strength down the length of the structure and it is obvious that there are reflections from the end of the structure which influence the fields. Two solutions were proposed: Firstly, the structure was made very long (Figure 3.7b) which requires more computational time and secondly, another port or absorbent material was placed at the far end as shown in Figure 3.6. Neither removes the reflections from the end which leaves the attenuation constant uncharacterised..

(34) CHAPTER 3. EXAMINATION OF A PERIODIC RADIATING SURFACE 22 3.5. SWEEPING THE DIMENSIONS OF THE UNIT CELL 1 0.9. Normalized field strength. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. 0. 50. 100. 150 200 Distance (mm). 250. 300. 350. (a) 5 cells 1 0.9. Normalized field strength. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. 0. 200. 400. 600 Distance (mm). 800. 1000. (b) 20 cells. Figure 3.7: Surface E-field evaluated along the centre of the structure.. 3.5. Sweeping the Dimensions of the Unit Cell. In Section 3.4 the influences the attenuation constant and wavenumber have on the radiation pattern are discussed. The farfield monitor provides the simulated radiation pattern, allowing the gain and angle of the main beam to be monitored which indirectly characterizes the complex propagation in the longitudinal direction. The complete parameterized structure shown in Figure 3.6 is simulated using the automated parameter sweep feature in CST. The parameters are swept through the values given in Table 3-I. CST also boasts an automatic optimizer but it is not used for reasons explained in Section 3.5.1. By sifting through the 2300 resulting configurations in MATLAB the parameter combinations which.

(35) CHAPTER 3. EXAMINATION OF A PERIODIC RADIATING SURFACE 23 3.5. SWEEPING THE DIMENSIONS OF THE UNIT CELL. satisfy a predetermined gain at a predetermined angle are collected. Table 3-I: Swept Parameters. 3.5.1. Parameter. Minimum [mm]. Maximum [mm]. Increment[mm]. Spacing (s). 1. 5. 1. Height (h). 10. 30. 1. Radius (r). 10. 33. 1. Optimal Solution. All the combinations which have a gain of more than 2 dBi at an angle of 70o or more, are plotted in Figure 3.8, with the three different projections shown for easier visual interpretation. It can be seen from this figure that there is a variety of parameter combinations which satisfy both the gain and angle requirement however it makes sense to choose a combination of parameters which is least sensitive to slight dimension differences. The automatic optimizer found in CST can also reproduce similar results but this data must still be plotted so that parameter sensitivity can be considered. The most insensitive parameter configuration is highlighted by the circle in Figure 3.8. This is the combination of parameters which is most tightly surrounded by other combinations which also satisfy the criteria. Table 3-II gives the values of this configuration. These dimensions result in this optimal surface having a different periodicity to that of the elements in the array. Table 3-II: Optimal Parameter Combination Parameter. Value [mm]. Spacing (s). 2. Height (h). 25. Radius (r). 15.

(36) CHAPTER 3. EXAMINATION OF A PERIODIC RADIATING SURFACE 24 3.6. SUMMARY. 5 4.5 5. 4. Spacing (mm). Spacing (mm). 4. 3. 2. 3.5 3 2.5 2. 1 40 30. 30. 1.5. 25 20. 20 10. Radius (mm). 15. 1 16. 18. 20. Height (mm). (a). 22 24 Height (mm). 26. 28. 30. (b). 35. 5 4.5. 30. Spacing (mm). Radius (mm). 4. 25. 20. 3.5 3 2.5 2. 15 1.5. 10 16. 18. 20. 22 24 Height (mm). (c). 26. 28. 30. 1 10. 15. 20 25 Radius (mm). 30. 35. (d). Figure 3.8: Results of parameter optimization - combinations of parameters which satisfy requirements.. 3.6. Summary. The arrangement of disks mounted on top of the antenna is investigated as a periodic surface supporting a travelling wave. A surface comprising a triangular arrangement of hexagonal top hats is analyzed using the surface propagation properties of a leaky wave radiator and an optimal geometry for low angle performance is extracted. In Chapter 5 this surface will be incorporated into the existing array structure as a replacement for the top hats and the results will be compared..

(37) Chapter 4 Investigation of the Array Excitation 4.1. Introduction. In the previous chapter the surface of the array was examined separately in an attempt to improve the low angle radiation performance. In this chapter the excitation provided by the cavity-backed crossed slots is examined. The cavity and feed arrangement currently in use is not simple to manufacture. The aim of the work presented here is to reduce the complexity of the feed for the cavity designed in [3]. A superficial examination of a thinned array and different feeding structures is also made here. A new cavity feed is designed and proposed for implementation into the array. If this antenna is operating on the principle of a leaky wave antenna then it may be possible to reduce or thin out the number of elements which are excited and still retain the properties of radiation and hence reduce costs. Fewer fed elements will be able to excite the same fields within the structure but obviously the total input power would decrease. The motivation of the work in this chapter is to reduce either manufacturing costs or reduce the excitation power which would result in a reduction of antenna size or improved performance.. 25.

(38) CHAPTER 4. INVESTIGATION OF THE ARRAY EXCITATION. 26. 4.2. ALTERNATE EXCITATIONS USING A SMALLER ARRAY MODEL. 4.2. Alternate Excitations Using a Smaller Array Model. To investigate some of the factors which influence the coupling, scan impedance and therefore low angle radiation, an array of elements is modelled and simulated. The motivation for a smaller, simpler array is primarily to decrease computational time by decreasing the number of mesh cells of the full array in Figure 2.1 by a factor of ten. This new model (shown in Figure 4.1) is simpler than the full model in that there are fewer elements and the thin layer of dielectric substrate is ignored. The modelled PEC ground plane is smaller but the boundary under the structure sets Etangential = 0, effectively forming an infinite ground plane. The elements are fed using the four quadrature phased, discrete ports across the slots but no amplitude taper is enforced. Steering of this smaller array is only done in along the x axis.. y x. Figure 4.1: Smaller array model with top hats hidden.. The complex fields generated in the array are a result of an interaction of the circularly polarized excitation between the elements. If, as the leaky wave analysis suggests, the excited fields form a travelling wave between the elements and the top hats or surface, then it is possible that these fields may be excited by less elements or a simpler structure. Because of the model discrepancies,.

(39) CHAPTER 4. INVESTIGATION OF THE ARRAY EXCITATION. 27. 4.2. ALTERNATE EXCITATIONS USING A SMALLER ARRAY MODEL. the results from these simulations can only be compared with one another to show trends and characteristics. The cavity cylinders or pillboxes were removed from the array producing a structure shown in Figure 4.2a. The fed disks were then joined together to create a second structure shown in Figure 4.2b. The results are shown in Figure 4.3.. (a) First.. (b) Second.. Figure 4.2: Two alternate structures used for excitation.. Not steered. Steered. 20. 20 Unaltered First Second. 10. 10. 5. 5. 0. 0. −5. −5. −10. −10. −15. −15. −20. −80. −60. −40. −20 0 20 Angle (degrees). (a) Not steered.. 40. 60. 80. Unaltered First Second. 15. Gain (dB). Gain (dB). 15. −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (b) Steered.. Figure 4.3: Simulated boresight results of the unaltered and two alternate structures.. Although the results of the two surfaces in Figure 4.3a show good agreement (within 2 dB) with the unaltered array on boresight, the steered performance is of primary interest. Figure 4.3b shows the poor performance of these surfaces when excited with a linear phase progression. This is due to the absence of the periodicity provided by the pillboxes which provide tighter mutual coupling.

(40) CHAPTER 4. INVESTIGATION OF THE ARRAY EXCITATION. 28. 4.2. ALTERNATE EXCITATIONS USING A SMALLER ARRAY MODEL. when steering the array. To steer an array 90o from boresight requires 100% mutual coupling.. 4.2.1. Thinning the Feed. Figure 4.4 shows two different arbitrarily thinned feeds with the simulated results shown in Figure 4.5. This was done by removing the excitation of these elements as opposed to increasing the elements spacing.. (a) Holes.. (b) Strips.. Figure 4.4: Two arrays with elements which are not fed crossed out in red.. Not steered. Steered. 20. 20 All fed Holes Strips. 10. 10. 5. 5. 0. 0. −5. −5. −10. −10. −15. −15. −20. −80. −60. −40. −20 0 20 Angle (degrees). (a) Boresight.. 40. 60. 80. All fed Holes Strips. 15. Gain (dB). Gain (dB). 15. −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (b) Steered.. Figure 4.5: Simulated results of the two arrays with thinned excitation.. Once again the boresight performance is comparable to the array with all elements fed but the steered performance is more than 5 dB down at the angle of interest (θ = 75o ). By only exciting alternate strips, the array in Figure 4.4b effectively increase the spacing between elements and results in the observed.

(41) CHAPTER 4. INVESTIGATION OF THE ARRAY EXCITATION. 29. 4.3. DESIGN OF A PROPOSED CAVITY. grating lobe. Further investigation by exciting this array as an arrangement of sub-arrays was ruled out due to the lack of success achieved by this method.. 4.3. Design of a Proposed Cavity. The active impedance and mutual coupling of these cavity-backed crossed slots in a smaller array is examined in [3]. A method of modelling a cavity-backed slot is given in [13] but the slots above the cavity are operating well below the cutoff frequency of the cavity. The active impedance changes as a function of steering angle because coupling is affected by progressive phase between elements as stated in Section 2.3.1. Here only the passive input impedance of a single element is examined. The cylindrical cavity itself remains unchanged from the original design in [1], but a new feed is designed using simple transmission lines. This is done to reduce construction costs of the antenna. The scan impedance of an infinite array can be determined by using a unit cell similar to the unit cell in Chapter 3. If the unit cell contains one fed element then the phase between successive cells in the array can be scanned and the impedance can be monitored to produce the scan impedance. This is very important information when determining the efficiency and scan blindness of the antenna. This was unfortunately not implemented in this work and is recommended as the way forward. The 50 Ω wire transmission line shown in Figure 4.6b is used to bring the feed through the cavity (the cavity wall acting as the ground plane). The transparent view of the proposed element in Figure 4.7b shows the vertical feed wire. The 50 Ω coplanar waveguide shown in Figure 4.6a is used on top of the PCB as shown in Figure 4.7a. Each of the four vertical feed wires are excited by waveguide ports below the cavity, resulting in the new feed also having four ports which must be feed with quadrature phasing. A feed network could be designed to combine the ports of each element with the correct phasing but the S-Parameters are exported to Microwave Office (MWO) instead and combined using transmission lines of different electrical lengths. From this circuit (shown in Figure 4.8) the combined input impedance can be extracted. The losses and mismatches in the required feed network are therefore not considered but this method allows.

(42) CHAPTER 4. INVESTIGATION OF THE ARRAY EXCITATION. 30. 4.3. DESIGN OF A PROPOSED CAVITY. 2 mm. 2 mm 0.3 mm. 0.3 mm Air. (a) Coplanar waveguide without a ground plane.. 3.3 mm. (b) Wire conductor above ground plane.. Figure 4.6: Dimensions of 50 Ω transmission lines.. (a) Solid view.. (b) Transparent view.. Figure 4.7: Model of cavity with new feed (Top hats hidden).. the positions of the feed to be changed without requiring a new feed network. The positioning of the vertical feed wire and the position that the coplanar waveguide intersects the slot influence the input impedance. Several parameters, including the positions of the feed lines are swept and the input impedance is monitored using the S-Parameters in the MWO circuit. The input impedances of the various configurations are compared and the impedance of the selected cavity feed is shown in Figure 4.9, along with the passive impedance of an isolated element of the original array. It can be seen that the element has a resonant frequency of approximately 2 GHz when isolated. Because the original element has this frequency characteristic, the new element is designed for the same frequency when isolated. Figure 4.7 shows the element which is chosen to be incorporated into the array in Chapter 5..

(43) CHAPTER 4. INVESTIGATION OF THE ARRAY EXCITATION. 31. 4.3. DESIGN OF A PROPOSED CAVITY. COAX2 ID=CX1 EL=180 Deg Fo=1.6 GHz Z=50 PORT P=1 Z=12.5 Ohm. SUBCKT ID=S1 NET="Sparms01" 2. 3 1. COAX2 ID=CX2 EL=270 Deg Fo=1.6 GHz Z=50. 4. COAX2 ID=CX3 EL=90 Deg Fo=1.6 GHz Z=50. Figure 4.8: MWO schematic for determining input impedance.. old vs new cavity 10 Original element Proposed element. 5 0 −5. S11 (dB). −10 −15 −20 −25 −30 −35 −40 0. 0.5. 1. 1.5 Frequency (GHz). 2. 2.5. 3. Figure 4.9: Comparison of input match between the original and new elements..

(44) CHAPTER 4. INVESTIGATION OF THE ARRAY EXCITATION. 32. 4.4. SUMMARY. 4.4. Summary. A brief investigation has shown that thinning the array by not exciting some of the elements does not reproduce the required excitation for low angle radiation. For radiation at such low angles tight coupling is needed to support the travelling wave. The pillbox is also required not only as a cavity behind the slots but as a periodic mechanism for mutual coupling which is required for low steering. A new cavity is proposed with matched passive input impedance which is simpler and would be cheaper to construct. However, when this proposed cavity is incorporated into the existing array in Chapter 5, the mismatched scan impedance determines the performance of the element..

(45) Chapter 5 Final Array Simulations and Results 5.1. Introduction. In the previous chapters the surface and cavity feed were examined and new proposals were made. In this chapter these new designs are incorporated into the original array for analysis. The purpose is to establish whether these propositions do in fact improve the the low angle radiation performance. The new cavity from Chapter 4 is incorporated into the original array and simulated under the same conditions as the verification which was done in Section 2. In a separate study, the circular top hats are replaced with the surface of hexagonal disks from Chapter 3. These results lead to further investigation of the top hats/surface using the smaller array introduced in Section 4.3. From this smaller array a trend in very low angle (θ > 80o ) gain is observed and this is extended to the full array. The final investigation is of the original array without top hats or the hexagonal surface. All these new models are compared to the results of the model which was verified in Chapter 1 in order to draw realistic conclusions.. 33.

(46) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS. 34. 5.2. PROPOSED FEED IN ORIGINAL ARRAY. 5.2. Proposed Feed in Original Array. The proposed cavities are shown in the array in Figure 5.1. The model parameters, solver setup and excitation settings (amplitude taper and progressive phasing) used here are otherwise identical to those used in Section 2.2. The simulation results of the new cavities are compared in Figures 5.2 - 5.5 to the results of the simulations in Section 2.3.. Figure 5.1: Model with proposed new cavity elements replacing the original elements..

(47) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.2. PROPOSED FEED IN ORIGINAL ARRAY 1.525 not steered x 20 New cavity Original. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 not steered x 20 New cavity Original. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.2: Boresight gain along the x axis.. 80. 35.

(48) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.2. PROPOSED FEED IN ORIGINAL ARRAY 1.525 not steered y 20 New cavity Original. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 not steered y 20 New cavity Original. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.3: Boresight gain along the y axis.. 80. 36.

(49) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.2. PROPOSED FEED IN ORIGINAL ARRAY 1.525 steered x 20. New cavity (steered to 75o) Original (steered to 75o). 15. New cavity (steered to 85o) Original (steered to 85o). Gain (dB). 10 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 steered x 20. New cavity (steered to 75o) Original (steered to 75o). 15. New cavity (steered to 85o) Original (steered to 85o). Gain (dB). 10 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.4: Gain when steered along the x axis.. 80. 37.

(50) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.2. PROPOSED FEED IN ORIGINAL ARRAY 1.525 steered y 20. New cavity (steered to 75o) Original (steered to 75o). 15. New cavity (steered to 85o) Original (steered to 85o). Gain (dB). 10 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 steered y 20. New cavity (steered to 75o) Original (steered to 75o). 15. New cavity (steered to 85o) Original (steered to 85o). Gain (dB). 10 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.5: Gain when steered along the y axis.. 80. 38.

(51) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS. 39. 5.3. HEXAGONAL SURFACE ON ORIGINAL ARRAY. From these results it can be seen that the boresight RHCP gain on the peaks of the main beams is down 3 dB lower than the antenna with the original cavities but still above the specification limit of 12 dB. The sidelobes levels have improved slightly to 15 dB down in the x direction and more than 20 dB down in the x direction. When steered to a low angle (θ = 75o ), the RHCP gain on the peaks is up to 15 dB lower than that of the original antenna. In Figure 5.5a the gain of the array with the new cavities is higher. This demonstrates that this new cavity does not perform when steered and further investigation is regarding the scan impedance is required. The mutual coupling effects of this element in the array also need to be investigated and modelling this structure as unit cells in CST is recomended as the way forward.. 5.3. Hexagonal Surface on Original Array. Figure 5.6 shows the model once the optimized surface of hexagonal disks has replaced the standard circular top hats. The model parameters, solver setup and excitation settings (amplitude taper and progressive phasing) used here are otherwise identical to those used in Section 2.2. The simulation results of the hexagonal disks are compared in Figures 5.7 - 5.10 to the results of the simulations in Section 2.3.. Figure 5.6: Model with the surface of hexagonal disks on the original array..

(52) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.3. HEXAGONAL SURFACE ON ORIGINAL ARRAY 1.525 not steered x 20 Hexagonal surface Top hats. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 not steered x 20 Hexagonal surface Top hats. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.7: Boresight gain along the x axis.. 80. 40.

(53) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.3. HEXAGONAL SURFACE ON ORIGINAL ARRAY 1.525 not steered y 20 Hexagonal surface Top hats. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 not steered y 20 Hexagonal surface Top hats. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.8: Boresight gain along the y axis.. 80. 41.

(54) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.3. HEXAGONAL SURFACE ON ORIGINAL ARRAY 1.525 steered x 20 Hexagonal surface (steered to 75o) Top hats (steered to 75o). 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 steered x 20 Hexagonal surface (steered to 75o) Top hats (steered to 75o). 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.9: Gain when steered along the x axis.. 80. 42.

(55) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.3. HEXAGONAL SURFACE ON ORIGINAL ARRAY 1.525 steered y 20 Hexagonal surface (steered to 75o) Top hats (steered to 75o). 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 steered y 20 Hexagonal surface (steered to 75o) Top hats (steered to 75o). 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.10: Gain when steered along the y axis.. 80. 43.

(56) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS. 44. 5.3. HEXAGONAL SURFACE ON ORIGINAL ARRAY. From these results it can be seen that the boresight RHCP gain on the peaks of the main beams is up to 5 dB lower than the original antenna with the circular top hats. The sidelobes have also deteriorated to only 10 dB down in the y direction. When steered to a low angle (θ = 75o ), the RHCP gain on the peaks is also between 2 and 5 dB lower than that of the original antenna. However, when the steering is to a low angle, the gain values at θ = 90o are within 1 dB. In Figure 5.10b the gain of the structure with hexagonal surface is higher at θ = 90o . The expectation from these results is that the new surface would perform better than the standard circular top hats but this is not the case.. 5.3.1. Investigation of Trends Using a Smaller Array. It is now clear that in order to improve the performance this antenna, an array of elements must be considered and so the smaller array discussed in Section 4.2 is used. Once again the model and simulation discrepancies prohibit these results from being compared to those of the verified model in Section 2.3. Using this smaller model several parameter sweeps were made, including the height of the surface and radius of the top hats. Some of the results of particular interest are shown in Figure 5.11. As the radius of the top hats is decreased and the other parameters are held constant, the low angle (θ > 80o ) RHCP gain increases, to the point where no top hats provide the highest RHCP gain. Further investigation is now required to establish whether this is a general trend, contrary to the findings of [1] and [3], or a result peculiar to this model..

(57) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS. 45. 5.4. RESULTS OF THE FULL ARRAY WITHOUT TOP HATS. Figure 5.11: Trend in one parameter sweep.. 5.4. Results of the Full Array Without Top Hats. Results from simulations of the full array without the top hats are compared to the standard in Figures 5.12 - 5.15. Once again the model parameters, solver setup and excitation settings are identical in both the instances..

(58) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.4. RESULTS OF THE FULL ARRAY WITHOUT TOP HATS 1.525 not steered x 20 No hats With top hats. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 not steered x 20 No hats With top hats. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.12: Boresight gain along the x axis.. 80. 46.

(59) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.4. RESULTS OF THE FULL ARRAY WITHOUT TOP HATS 1.525 not steered y 20 No hats With top hats. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 not steered y 20 No hats With top hats. 15 10. Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.13: Boresight gain along the y axis.. 80. 47.

(60) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.4. RESULTS OF THE FULL ARRAY WITHOUT TOP HATS 1.525 steered x 20 No hats (steered to 75o) Top hats (steered to 75o). 15. No hats (steered to 85o) 10. Top hats (steered to 85o). Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 steered x 20 No hats (steered to 75o) Top hats (steered to 75o). 15. No hats (steered to 85o) 10. Top hats (steered to 85o). Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.14: Gain when steered along the x axis.. 80. 48.

(61) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS 5.4. RESULTS OF THE FULL ARRAY WITHOUT TOP HATS 1.525 steered y 20 No hats (steered to 75o) Top hats (steered to 75o). 15. No hats (steered to 85o) 10. Top hats (steered to 85o). Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. 80. (a) 1.525 GHz 1.661 steered y 20 No hats (steered to 75o) Top hats (steered to 75o). 15. No hats (steered to 85o) 10. Top hats (steered to 85o). Gain (dB). 5 0 −5 −10 −15 −20. −80. −60. −40. −20 0 20 Angle (degrees). 40. 60. (b) 1.661 GHz. Figure 5.15: Gain when steered along the y axis.. 80. 49.

(62) CHAPTER 5. FINAL ARRAY SIMULATIONS AND RESULTS. 50. 5.5. SUMMARY. It is evident that the top hats have little influence on the array at boresight, there is a slight decay of sidelobe levels without the top hats but the main beam is unchanged from the original array. Results for steering angles of θ = 75o and 85o are presented in Figure 5.14 and 5.15. It can be seen that the array without top hats is more steerable in that the gain at 90o is higher than the original. However, the top hats show higher gain at angles of θ < 75o .. 5.5. Summary. Designing an isolated array element does not take into account the effects of mutual coupling and scan impedance which are the primary issues in a tightly coupled array. In an instance such as this the cavity must be designed as an active element using a tool such as the infinite array made up of unit cells in CST. The optimised hexagonal surface does not perform as expected since the design of the surface used an over-simplified excitation which does not reflect the excitation in the array. The smaller array is a useful tools for showing trends since the simulation time is greatly reduced and it imitates the characteristics of the complete array. By removing the top hats the array appears to be more steerable but looses gain at higher angles..

(63) Chapter 6 Conclusion A functional model is developed in Chapter 1 which accurately reflects the measurements of an existing antenna. The discrepancies are put down to the ground plane differences and manual adjustment of the phasing in the existing antenna. An examination of the periodic surface using leaky wave antenna theory leads to the design of an arrangement of hexagonal disks with enhanced performance under the development conditions. When this surface is incorporated into the array the results are poor and it is concluded that the method of excitation is crucial when developing such a surface. The excitation is also examined and it is shown that an array which is steered close to 90o off boresight cannot be thinned and relies heavily on the periodicity and coupling. A new feed for the existing cavity is proposed but because it is designed purely from an isolated, passive impedance point of view, the steered array performance is poor. Without the top hats the structure cannot act as a leaky wave antenna, and a leaky wave structure cannot radiate at θ = 90o because the energy is all bound to the surface and the phase velocity is infinite. This means that this antenna is a combination of a leaky wave radiator and array of elements. At close to 90o the elements couple so tightly that the energy travels along the surface and the top hats reduce the gain. At slightly higher angles the top hats act as a PRS and leak energy which improves the gain. At boresight the top hats have no effect because the radiated energy is not bound to the surface and the mutual coupling between the elements is weaker.. 51.

(64) CHAPTER 6. CONCLUSION. 52. 6.1. RECOMMENDATIONS. 6.1. Recommendations. The differences between the simulated model results and the measured data must be resolved or quantified because the discrepancy is at the angle of particular interest. If any suggestions and improvements are to be made from the simulated models shown here then the effect of the curved ground plane needs to be considered as well as the individual phase adjustment. The proposed element needs to be redesigned using the scan impedance. This can be done by utilising the infinite array in CST consisting of unit cells. This feature is modified in the latest release of CST (2008) and now allows the linear phase between cells to be automatically swept while monitoring the scan impedance. The surface of top hats or hexagons can also be examined using this tool and this is suggested as the way forward. It is believed that simplifications can be made to this antenna which would reduce costs but it appears that the existing high performance antenna is close to optimal with regards to the parameters examined here..

(65) Bibliography [1] George, W., Steyn, P. and Basso, V.: Development of Phased Array Antenna for INMARSAT Aeronautical Applications. South African IEEE AP/MMT Conference, 2005. [2] Marais, S.J.: The Quadrifilar Helix Antenna and its Application to Wide Angle Phase-Steered Arrays. Master’s thesis, University of Stellenbosch, 2006. [3] Voigt, D.: Computational Investigation of a Crossed Slot Cavity-Backed Array Antenna. Master’s thesis, University of Stellenbosch, 2006. [4] Balanis, C.A.: Antenna Theory. 3rd edn. Wiley, 2005. [5] Lovat, G., Burghignoli, P. and Jacksons, D.: Fundamental Properties and Optimization of Broadside Radiation from Uniform Leaky Wave Antennas. IEEE Transactions on Antennas and Propagation, vol. 54, no. 5, pp. 1442 – 1452, May 2006. [6] Sureau, J.: Propagation Constant of Leaky-Wave Antenna for Near EndFire Radiation. IEEE Transactions on Antennas and Propagation, 1967. [7] Kokkinos, T., Sarris, C. and Eleftheriades, G.: Periodic FDTD Analysis of Leaky-Wave Structures And Applications to the Analysis of NegativeRefractive-Index Leaky-Wave Antennas. IEEE Transactions on Microwave Theory and Techniques, vol. 54, no. 4, pp. 1619 – 1630, April 2006. [8] Collin, R.E. and Zucker, F.J.: Antenna Theory, Part 2. McGraw-Hill, 1969. [9] Oliner, A. and Goldstone, L.: Leaky-Wave Antennas I: Rectangular Waveguides. IRE Transactions on Antennas and Propagation, pp. 307 – 319, October 1959. [10] Zhao, T., Jackson, D., Williams, J., Yang, H. and Oliner, A.: 2-D Periodic Leaky-Wave Antennas Part I: Metal Patch Design. IEEE Transactions 53.

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