1 43 CHAPTER 2 MICROSTRIP REFLECTARRAY ANTENNA AND PERFORMANCE EVALUATION 2.1 INTRODUCTION This work begins with design of reflectarrays with conventional patches as unit cells for operation at Ku Band in view of its application in satellite news gathering. Subsequently, a new crossed dumb-bell shaped unit cell is designed and analyzed for its phase characteristics, on two different substrates viz. RT-duroid and FR4. Reflectarrays with these unit cells were constructed and their performances have been evaluated. Results of these arrays have been compared with the reflectarrays constructed with conventional microstrip patches. 2.2 REFLECTARRAY DESIGN steps: The design and evaluation of a reflectarray involves following Computation of phase requirement at each unit cell using MATLAB. Determination of phase compensation using Waveguide Simulation Method. Construction and Optimization at design frequency Performance evaluation
2 Phase Calculations The phase shift that must be introduced at each element to produce a collimated beam in a given direction is determined in this section. Considering the coordinate system detailed in Figure 2.1, the progressive phase distribution on the reflectarray surface that produces a beam in the direction as known from array theory, is expressed as (, ) cos (2.1) where k o is the propagation constant in free space, b, b are the elevation and azimuth angles respectively of the incident beam and (x i, y i ) the coordinates of element i. On the other hand, the phase of the reflected field at each reflectarray element is equal to the phase of the incident field, as a result of propagation from the feed, plus the phase shift introduced by each cell, as (, ) + (, ) (2.2) where r (x i,y i ) is the phase of the reflection coefficient, or phase shift, for element i, d i is the distance from the phase center of the feed to the cell. From equations 2.1 and 2.2, the phase shift required at each element is obtained as, (, ) = ( ( + ) ) (2.3) The change in path difference leads to phase difference. Figure 2.2 shows the required phase shift on the reflectarray of 11 x 11 elements with the focal point centered that produces a pencil beam in a direction normal to the surface. For the reflectarray design, the phase of the reflection coefficient S 11 of each element must be adjusted to match these phases.
3 45 Figure 2.1 Geometry of the printed reflectarray Figure 2.2 Phase shift distribution for = 0 degree & = 0 degree
4 46 The phase shift given by Equation 2.3 is achieved by varying one of the geometrical parameters of the reflectarray elements which includes the length of the square patch and the radius of the clover patch in the proposed unit cells. The main beam can be tilted to any desired direction by suitably changing the phasing characteristics at each element in the array aperture. Figure 2.3 shows the phase distribution required for a scattered beam tilted 30 degrees along the elevation plane. Figure 2.3 Phase shift distribution for = 30 degrees & = 0 degree Unit Cell Design Figure 2.4 shows the very popular approach of using an H-wall waveguide simulator also known as parallel plate waveguide simulator, where top and bottom surfaces of the waveguide are electric conducting walls(pec), while the left and right walls are magnetic field walls(pmc), for testing the phase characteristics of a given unit cell.
5 47 Figure 2.4 An H-wall waveguide simulator to calibrate the reflectarray element phase-change Vs element-change The design of unit cell and its phase characterization has been implemented using available full wave simulation using CST Microwave Studio. Basic building block for a single layer unit cell of reflectarray is designed at Ku-band frequency of GHz. The periodicity of the unit cell reflectarray is based on the existing standard waveguide dimension. Boundary conditions shown in Figure 2.4 are used in the simulation setup for TEM- Mode propagation (Infinite Array Approach). 2.3 CLOVER (CROSSED DUMB-BELL) SHAPED UNIT CELL DESIGN Each element designed is to be printed on RT6002 substrate with thickness (t = mm), loss tangent of and relative permittivity =2.94.
6 48 The unit cell with clover shaped patch is shown in Figure 2.5 and the dimensions of the clover patch are shown in Figure 2.6. The size of the unit cell L = 4R. Figure 2.5 Dual crossed dumb-bell (clover) unit cell Figure 2.6 Radius variation of the clover structure In the simulation, there is only one unit cell being excited using TEM mode. In this mode, a unit cell is actually illuminated by a linearly polarized plane wave with a normal incidence. In the real world, there is no such way to excite the corresponding unit cell using TEM mode propagation. Therefore, a real metallic waveguide is needed in order to measure the phase variation of the proposed unit cell configuration. In this case, a unit cell will be excited by a coaxial probe of the waveguide adapter in TE 10 mode.
7 Phase Compensation The phase of the reflected wave is controlled by varying the resonant dimensions of the proposed unit cells. Empirical phase curves are obtained by estimating the phase shift against variation of the length of square patch and the radius of the clover patch. For the analysis and design of a reflectarray, it is more practical to obtain the phase shift through electromagnetic simulations. A full wave technique is used to obtain the phase curves as a function of length by considering the incidence of a plane wave on an infinite array of square patches. This approach takes into account the mutual coupling effects between the reflectarray elements, as well as the reflections from the ground plane supporting the unit cell. Further amplitude of reflection coefficient must be nearly equal to one (0 db), provided that there is no grating lobe or surface wave generation, because of the ground plane. A small reduction in amplitude is produced by the dissipative losses in the dielectric material and the conducting ground plane. The radius of the dual crossed dumbbell unit cell is chosen as the phase compensating physical parameter and empirical phase variation curve is obtained as shown in Figure 2.7 (a). A total 414 degrees phase variation is obtained for the radius ranging from mm to mm. The reflection characteristics of the clover shape unit cell are illustrated in Figure 2.7 (b).the reflection coefficient of db is observed at GHz. It can be concluded that the clover unit cell has a good reflection coefficient and therefore they can be considered as a good reflector as the reflection is more than 90%.
8 50 Reflection Phase, degree Radius R, mm Figure 2.7 (a) Phase Variation Vs Radius of the clover unit cell S 11, db Frequency, GHz Figure 2.7 (b) Reflection Coefficient (S 11 ) of the Clover unit cell Construction of Reflectarray with Clover Shaped Patch as Array Element (with RT-Duroid substrate) For constructing a 11 x 11 array, the phase compensations to be introduced by various unit cells of the array based on their location is precalculated using MATLAB code with the following as input data: Frequency Array size
9 51 Substrate material Angle of incidence for both elevation and azimuth The code computes phase compensations based on these input parameters by calculating the path differences. Now based on these data and the data obtained in Figure 2.7(a), radius of the clover for each element location for all the 121 elements is calculated. With these computed radius values, the 11 x 11 reflectarray is constructed Ku- Band Reflectarray Antenna Figure 2.8 shows the structure of the clover shaped patch reflectarray. A wideband horn antenna, operating at Ku Band, is chosen as the illumination feed (Details of the Feed Horn given at Appendix1) as shown in Figure 2.9. Figure 2.8 Reflectarray construction clover patch as unit cell
10 52 Except the four corner elements, remaining 117 elements are placed in the array (11 x 11). The size of the reflector is 14 cm x 14 cm and initially, the feed is kept at a distance of 12.6 cm (f/d =0.9). To overcome the problems of under illumination (f << D) or spill over (f >> D), the f/d ratio is optimized at 0.9. Figure 2.9 Reflectarray antenna horn fed-clover unit cell Results with RT6002 Substrate Figure 2.10(a) depicts the gain pattern at Ku band without ground plane. It is noticed that with the addition of ground plane, the gain of the reflectarray increases since the ground plane minimizes the back radiation. By introducing a ground plane of thickness 0.035mm, the SLL and the back lobe have been reduced and the main lobe level also increased by a considerable value as shown in Figure 2.10(b), which shows the gain pattern with ground plane. By suitably adjusting the phase at each element, the main beam can be tilted to any desired direction. Figure 2.11 illustrates the 3D visualization of the far field characteristics with narrow beam.
11 53 Gain, db Theta, degree XZ plane YZ plane Figure 2.10 (a) Radiation pattern 2D without ground Gain, db Theta, degree XZ plane YZ plane Figure 2.10 (b) Radiation Pattern 2D with ground Figure D Gain Plot of the clover reflectarray
12 Performance of the Clover Array The performance of the clover reflectarray with RT6002 substrate is summarized below. It can be observed that the gain is db and SLL is db. Phase Variations : 414 degrees Gain : db Side lobe level : db 3 db beam width : 5.6 degrees E- field : dbv/m 2.4 CONSTRUCTION OF REFLECTARRAY WITH CLOVER SHAPED PATCH AS ARRAY ELEMENT (WITH FR4 SUBSTRATE) Unit Cell Design The phase and magnitude variations Vs radius variations for a clover patch on FR4 substrate is given in Figures 2.12 and 2.13 respectively. 100 Reflection Phase, degree h=0.8 mm h=1.6 mm Radius R, mm Figure 2.12 Phase variations Vs Radius variations Clover unit cell
13 55 S 11, db Radius R, mm h=0.8 mm h=1.6 mm Figure 2.13 S 11 variations Vs Radius variations Clover unit cell From Figures 2.12 and 2.13, it can be observed that though h=0.8 mm gives marginally higher phase variations than h=1.6 mm, the magnitude of reflection is much better with h=1.6 mm. Hence, substrate thickness is taken as 1.6 mm for all further designs. It can also be observed that, with FR4 substrate, clover patch exhibits phase variations to the extent of 600 degrees Array Design Clover shaped patch is used as element of the array and the 11 x 11 array is constructed on a grounded (thickness mm) FR-4 ( r =4.3,loss tangent = 0.023) substrate of dimension 126 mm x 126 mm with substrate thickness of 1.6 mm. Radius of the clover, which is the control parameter to achieve the desired phase compensations, for various elements varies from a minimum of 0.55 mm to a maximum of mm, depending on the location of the element. Distance between elements is kept at half-a-wavelength (free space) at GHz and the f/d ratio is kept as 0.8. The array designed with clover unit cells is shown in Figure 2.14.
14 56 Figure x 11 array using clover unit cell with FR4 substrate Results with FR4 Substrate The radiation pattern of the 11 x 11 clover reflectarray in Cartesian coordinates is given in Figure It can be observed from the plot that the maximum gain is 22.2 db and the SLL is db, in YZ plane. The 3dB beamwidth is 10 degrees at the design frequency of GHz, in YZ plane Gain, db Theta, degree XZ plane YZ plane Figure 2.15 Radiation pattern of the clover patch reflectarray
15 Effect of Array Size on Performance The effect of array size on the performance of the reflectarray in terms of its gain is investigated with array sizes of 7 x 7, 9 x 9, 11 x 11, 15 x 15 and the graph showing Gain Vs Number of Elements is given in Figure Gain, db No of Elements Figure 2.16 Effect of array size on performance of the array 2.5 COMPARISON OF RESULTS Results obtained from 11 x 11 reflectarrays of clover patch on RT6002 and FR4 substrates are summarized in Table 2.1: Table 2.1 Comparison of results of RT6002 and FR4 reflectarrays Parameter Rogers RT6002 FR4 Frequency(GHz) r Loss tangent Substrate thickness(mm) Phase Variations(degrees) Gain(dB) Side lobe level(db) db beamwidth(degrees)
16 58 Though it can be observed from the above table that with FR4 substrate comparable gain can be obtained, the performance of the reflectarray with RT6002 is better in view of lesser loss. However for applications where cost is a constraint, reflectarray with FR4 substrate can be used. 2.6 CONSTRUCTION OF REFLECTARRAY WITH SQUARE PATCH AS ARRAY ELEMENT Array Design Square patch is used as element of the array and the array is constructed on a grounded (thickness mm) FR-4 ( r =4.3, loss tangent = 0.023) substrate of dimension 126 mm 126 mm with substrate thickness of 1.6 mm. Size of the square patch which is the control parameter to achieve the desired phase compensations, for various elements varies from a minimum of 0.2 mm to a maximum of 11 mm, depending on the location of the element. Distance between elements is kept at half-a-wavelength (free space) at GHz and the f/d ratio is kept as 0.8. The array designed with square unit cells is shown in Figure Figure Reflectarray structure with square patch as unit cell
17 Results with FR4 Substrate The radiation pattern of the square patch reflectarray is given in Figure It can be observed from the plot that the maximum gain is 17.6 db and the SLL is -6.4 db, in YZ plane. The 3 db beamwidth is 8.4 degrees at the design frequency of GHz, in YZ plane Gain, db Theta, degree XZ plane YZ plane Figure 2.18 Radiation pattern of the square patch reflectarray 2.7 CONSTRUCTION OF REFLECTARRAY WITH RECTANGULAR PATCH AS ARRAY ELEMENT Array Design Rectangular patch is used as element of the array and the array is constructed on a grounded (thickness mm) FR-4 ( r =4.3, loss tangent = 0.023) substrate of dimension 126 mm 126 mm with substrate thickness of 1.6 mm. Width of the rectangular patch which is the control parameter to achieve the desired phase compensations, for various elements varies from a minimum of 2 mm to a maximum of 11 mm, depending on the location of the element. Length of the rectangular patch is kept at 6.4 mm.
18 60 Distance between elements is kept at half-a-wavelength (free space) at GHz and the f/d ratio is kept as 0.8. The array designed with rectangular unit cells is shown in Figure Figure Reflectarray structure with rectangular Patch as unit cell Results with FR4 Substrate The radiation pattern of the rectangular patch reflectarray is given in Figure It can be observed from the plot that the maximum gain is 16.2 db and the SLL is -6.8 db, in YZ plane. The 3dB beamwidth is 12.5 degrees at the design frequency of GHz, in YZ plane Gain, db Theta, degree XZ plane YZ plane Figure 2.20 Radiation pattern of the rectangular patch reflectarray
19 CONSTRUCTION OF REFLECTARRAY WITH CIRCULAR PATCH AS ARRAY ELEMENT Array Design Circular patch is used as element of the array and the array is constructed on a grounded (thickness mm) FR-4 ( r =4.3, loss tangent = 0.023) substrate of dimension 126 mm 126 mm with substrate thickness of 1.6 mm. Radius of the circular patch which is the control parameter to achieve the desired phase compensations, for various elements varies from a minimum of 0.3 mm to a maximum of 5.73 mm, depending on the location of the element. Distance between elements is kept at half-a-wavelength (free space) at GHz and the f/d ratio is kept as 0.8. The array designed with circular unit cells is shown in Figure Figure Reflectarray structure with circular patch as unit cell Results with FR4 Substrate The radiation pattern of the circular patch reflectarray is given in Figure It can be observed from the plot that the maximum gain is 18.5 db and the SLL is -7.2 db, in YZ plane. The 3dB beamwidth is 7.2 degrees at the design frequency of GHz, in YZ plane.
20 62 Gain, db Theta, Degree XZ plane YZ plane Figure 2.22 Radiation pattern of the circular patch reflectarray 2.9 COMPARISON OF RESULTS OF REFLECTARRAYS WITH UNIT CELLS OF DIFFERENT SHAPES Performance of the reflectarrays designed with conventional patch shapes in terms of maximum phase variations, Gain, SLL and 3 db beamwidth are summarized in Table 2.2 and are compared with the performance of the reflectarray with clover unit cell. Table 2.2 Comparison of results with various shapes for unit cell on FR4 substrate Parameter Phase Variations (degrees) Clover Patch Rectangular Patch Square Patch Circular Patch Gain(dB) Side lobe level(db) db beam width (degrees) Bandwidth (1 db Gain variation) in GHz
21 63 From Table 2.2 it is evident that Clover patch Reflectarray is much superior in its performance than the others in terms of Phase variations, Gain and SLL, though the angular width is slightly higher than Square and circular patch arrays. It is evident from the literature that elliptical shape provides better performance than conventional square or rectangular shaped reflecting elements. As clover is a modification of crossed ellipses, it results in better bandwidth performance SLL REDUCTION BY USE OF EBG STRUCTURE With an aim to reduce SLL further, a 7 7 reflectarray with clover unit cell is designed. After evaluating the performance of the reflectarray, a square mushroom EBG layer with connecting vias is designed and placed at the middle of the FR4 substrate and the performance of the reflectarray is again evaluated with the EBG layer in place Introduction to EBG Structures Electromagnetic band gap (EBG) structures (Sievenpiper et al 1999) are periodic structures that initially evolved in the optical domain by the name of photonic band gap (PBG) structures in the late 1980 s. EBG structures may be implemented in different ways; either by etching gaps in the metal of the ground plane, or the signal line, or by drilling periodic holes in the dielectric. These periodic structures have very interesting features which make them very promising candidates to a number of applications. EBG structures allow the propagation of electromagnetic waves in certain frequency bands and forbid them in other bands known as band gap. The surface impedance of these structures can be characterized by an equivalent parallel resonant LC circuit. At low frequencies, it is inductive and supports transverse magnetic (TM) waves. At high frequencies it is
22 64 capacitive, and supports transverse electric (TE) waves. Near the LC resonance frequency, the surface impedance is very high. In this region, waves are not bound to the surface; instead, they radiate readily into the surrounding space (Filippo Capolino 2009). following methods: Characterization of EBG structures is performed using one of the Full-wave numerical simulation of the entire structure based on various methods such as the Finite Element Method (FEM), the Finite-Difference Time-Domain Method (FDTD), the Finite Integration Method (FIT), etc., Dispersion diagram extraction using full-wave numerical simulation of a single cell Equivalent circuit modeling based on lumped elements Scattering parameter characterization Numerical Modeling for Analysis of Electromagnetic Band Gap Structures The role of symmetry is important in an electromagnetic band gap structure when analyzing its behavior. EBG studies are typically based on exploiting interesting symmetry properties, including periodicity in dielectrics of the material that are amenable to analysis using Bloch s theory. This theory can be used to derive the dispersion diagrams of the EBG (Yang Hao & Raj Mittra 2009).
23 65 Analysis of EBG structures is based on the Bloch-Floquet theorem, illustrated by Enoch et al (2003) which describes the theory of wave propagation in infinite media consisting of the periodic repetition of the unit cell. The unit cell corresponds to the so-called first Brillouin zone which is the smallest polygon defined by the centre axes of vectors connecting the points of a periodic lattice around the origin. The Brillouin zone is the most fundamental region for defining the propagation vector for a unit-cell and basically if all the propagation vectors are defined in the Brillouin zone, the entire characteristic of the periodic structure can be obtained. The exact position of pass bands and band gaps in the frequency spectrum can be obtained only by the dispersion relation of surface waves along the contour of the so-called irreducible Brillouin zone (Yang Hao & Raj Mittra 2009). The irreducible Brillouin zone for the 2D periodic structure with the square lattice is depicted in Figure Figure 2.23 Irreducible Brillouin zone
24 66 Computing the dispersion diagram means to calculate the resonant frequencies of Eigen modes along the triangle with nodes marked, X, M which represents the high symmetry points in the spectral domain shown in Figure 2.24(a). Dispersion diagram for the square mushroom is shown in Figure 2.24(b). Frequency, GHz Frequency, GHz to : MODE 1 to : MODE 2 to M : MODE 1 to M : MODE 2 M to : MODE 1 M to : MODE *p, rad *p, rad (a) Illustration (b) Square Mushroom Figure 2.24 Dispersion diagram Therefore the dispersion diagram will start at then to then to M and back to as indicated by the path depicted on the Brillouin zone as shown in Figure The high symmetry points are defined as: = (k x p = k y p = 0) ; = (k x p =, k y p = 0); = (k x p = k y p = ) where p is the periodic interval of the unit cell and k x is the wave number in the x-direction, and the k y is the wave number in the y-direction.
25 Performance of the 7 7 Clover Reflectarray without EBG Structure The front view and side view of the 7 7 array without EBG structure is shown in Figure 2.25(a) and 2.25(b), respectively. Figure 2.25(a) Front view of the 7 7 array without EBG structure 7 7 Clover Array (thickness=0.035 mm) FR4 substrate ( r =4.3) (thickness=1.6 mm) Ground Plane (thickness=0.035 mm) Figure 2.25(b) Side view of the 7 7 array without EBG structure The Cartesian gain plot of 7 7 array without EBG structure is shown in Figure 2.26.
26 68 Gain, db Theta, degree XZ plane YZ plane Figure 2.26 Far-field plot of 7 7 array without EBG structure Performance of the 7 7 Clover Reflectarray with EBG Structure An EBG layer with square mushroom structure of array size 7 7 is designed with the dimension of the square EBG being 3.75 mm, with conducting vias of diameter 0.65 mm connecting each square mushroom to the ground. The front view of the EBG layer is shown in Figure 2.27(a). Side view of the EBG layer with vias connected to the ground plane is shown in Figure 2.27(b). This EBG layer is inserted at the middle of the FR4 substrate, as shown in Figure 2.27(c). Figure 2.27(a) Front view of the 7 7 square mushroom EBG structure
27 69 Figure 2.27(b) Side view of the 7 7 square mushroom EBG structure 7 7 Clover Array (thickness=0.035 mm) FR4 substrate ( r =4.3) (thickness=0.8 mm) 7 7 Square mushroom EBG layer (thickness= mm) FR4 substrate ( r =4.3) (thickness=0.8 mm) Ground Plane (thickness=0.035 mm) Figure 2.27(c) Side view of the 7 7 array with EBG structure The performance of the reflectarray with EBG layer is then evaluated and the far-field plot is given in Figure Gain, db Theta, degree XZ plane YZ plane Figure 2.28 Far-field plot of 7 7 array with EBG structure
28 Reduction of SLL by using EBG Structure SLL of the reflectarray is reduced from db to -18 db by the use of the square mushroom EBG structure and the results are compared in Table 2.3. Table 2.3 Comparison of performance of reflectarray without and with EBG Parameters Without EBG With EBG Gain(dB) SLL(dB) dB beam width(degrees) SUMMARY From the results obtained for various designs as discussed above it is evident that the Reflectarray using clover shaped unit cell promises to provide wide phase variation (414 degrees with RT6002 substrate and 600 degrees with FR4 substrate), high gain (24.03 db with RT6002 substrate and 22.2 db with FR4 substrate) as also better SLL (-18.5 db with RT6002 substrate and db with FR4 substrate), for application as Ku-band antenna at GHz. Also, use of EBG structure for reduction of SLL of the reflectarray, from db to -18 db is shown with a 7 7 array.
29 71 Though the design and fabrication of reflectarrays with microstrip patches is less complex as compared to the design and fabrication of reflectarrays with DR, as DR reflectarray offers certain advantages in terms of wider bandwidth, higher efficiency in view of low losses, an attempt is made to first design a basic DRA unit cell, study its phase characterization and identify parameters for reconfiguration of frequency and pattern, and subsequently design a DR reflectarray for Ku-band applications.
Electromagnetic Band Gap Structures in Antenna Engineering FAN YANG University of Mississippi YAHYA RAHMAT-SAMII University of California at Los Angeles Hfl CAMBRIDGE Щ0 UNIVERSITY PRESS Contents Preface
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