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Development of a novel ultra-wideband antenna and prototype scanner for detection and location of voids… Dotto, Kim V. 2004

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DEVELOPMENT OF A NOVEL ULTRA-WIDEBAND ANTENNA AND PROTOTYPE SCANNER FOR DETECTION AND LOCATION OF VOIDS IN WOOD  by  Kim V. Dotto, P.Eng. B.Sc. The University of British Columbia, 1979 B.A.Sc. The University of British Columbia, 1982 M.A.Sc. The University of British Columbia, 1995  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES ELECTRICAL AND COMPUTER ENGINEERING  THE UNIVERSITY OF BRITISH COLUMBIA March 22, 2005 © Kim V. Dotto, P.Eng. 2005  Abstract  The design of a prototype ultra-wideband scanner for the detection of voids in wooden models is presented along with the design of a novel Ultra-Wideband Antenna.  The design and performance of a new type of antipodal tapered slot antenna are described. The three-dimensional structure of the antenna is given as well as the experimental results for gain, radiation pattern, cross polarization, VSWR and Return Loss (S ). The new Fleur-de-Lis u  (FDL) antenna shows a 10 dB bandwidth greater than 20 GHz with an S,, Return Loss curve that is flatter than those for current antipodal tapered slot antenna designs. The effects of varying physical parameters are also investigated, giving some insight into the antenna's wideband operation.  The FDL antenna is used as the basis for an ultra-wideband RF scanning system, which is used to measure ultra-wideband transmission (S ) response profiles. These transmission 21  response profiles show that it is possible to determine the size of a cylindrical object of metal or dielectric material with a set of readings taken over an ultra-wideband frequency range for a single transmission line of sight. It is also shown that, with a simple pattern-matching algorithm, it is possible to detect and locate the position of an air-filled void in a "cylindrical" wooden model with readings taken over an ultra-wideband frequency range for a single transmission line of sight.  ii  Table of Contents  Abstract  ii  List of Tables  vii  List of Figures  viii  List of Abbreviations  xiv  Acknowledgements  1.0  2.0  xv  Introduction  •.  1  1.1  Wood Properties and Composition  2  1.2  Dielectric Properties of Wood  3  1.2.1  Polarization, Relaxation Times and Transmitted Spectrum  5  1.2.2  Polarization Components  6  1.3  Current Non-Destructive Testing Methods  9  1.4  Theoretical Model  11  1.5  Ultra-wideband RF Void Detection  13  Antenna Characteristics  14  2.1  Antenna Measurements and Characterization  14  2.2  Impedance Matching, VSWR and S„  15  2.3  Polarization  18  2.5  Phase Measurements  21  iii  3.0  2.6  Gain Measurement  22  2.7  Frequency Dependence  24  Wideband Antennas  25  3.1  Existing Ultra-Wideband Antenna  25  3.2  Broadband Microstrip Patch Antennas  26  3.2.1  28  3.3  4.0  Air-Core Microstrip Antenna  Tapered Slot Antennas  29  Fleur-de-Lis Antenna  35  4.1  FDL Antenna Design  38  4.2  FDL Antenna Characterization  41  4.2.1  S„ Return Loss  43  4.2.1.1 S Reflection Coefficient Results  44  4.2.1.2 Change in S„ with Angle of Flare  45  4.2.1.3 Change in S with Curvature of Flare  49  n  u  5.0  4.3  Cross and Co-Polarization  50  4.4  Gain Measurements  61  Antenna Modelling  64  5.1  FEKO Model FDL Antenna  65  5.2  FEKO Model S Return Loss Coefficient Results  66  5.2.1  FEKO Design Parameter Sensitivity Study  66  5.2.2  Comparison of FEKO Model Results and S Measurements  5.3  6.0  n  FEKO Model Cross and Co-Polarization  FDL Ultra-Wideband Scanner  n  86 90  97  iv  7.0  6.1  Scanner Design  97  6.2  Scanner Characterization  98  6.2.1  Phase versus Distance Measurements  98  6.2.2  Far Field Considerations  103  6.2.3  Diffraction Effects  104  Void Detection  107  7.1  Detection of Voids  107  7.1.1  108  Model Analysis  7.1.1.1 Position of Removed Elements versus S , Spectral Curve 112 2  7.1.1.2 Spectral Comparison Between Models M, and M  2  7.1.1.3 Curve Matching and the Figure of Merit  112 114  7.1.1.4 Comparison of Magnitude, Cumulative Error and  7.2  8.0  Pattern Matching Algorithms  119  7.1.1.5 Void Detection using Pattern Matching Algorithm  121  Determination of the Outer Dimensions of a Cylindrical Model  124  Conclusions and Future Work  128  8.1  Future Work  129  8.1.1  FDL Antenna  129  8.1.2  Ultra-wideband Scanner  130  8.1.3  Full Tomographic Inversion  131  8.1.4  Other Fields  131  Bibliography  132  v  Appendix A - FDL S Reflection Coefficient versus Flair Angle for Flat Ground Planes . 143 n  Appendix B - Example FEKO Model Creation File For FDL Antenna  147  Appendix C - 1GHz to 13.5 GHz Results for Model Heights 0 to 91 cm  152  Appendix D - Cougar A2CP12029 Wideband Amplifier Specifications  156  Appendix E - Spectral Curve Matching Algorithm Code  158  Appendix F - Transmission Coefficient S versus Frequency For Standard Models  161  21  Appendix G - Table of Model Wins vs. Element Removed for Model Rotated 90 degrees 172  Appendix H - Photos of FDL Antenna and Connector  174  List of Tables  4.1: Gain versus Frequency For Optimal FDL and Guillanton Vivaldi Antennas 7.1: Comparison of Matching Algorithms for M  2 G  vs. reference models M  1 A  62  thru M . . . . 120 1T  7.2: Number of comparison wins for sample models M thru M  2 T  122  Gl: Number of comparison wins for sample models M thru M  2 X  rotated 90 degrees . . . . 172  2  2  vii  List of Figures  1.1: Theoretical Spectral Curves  12  2.1: Transmission Line Circuit  15  2.2: S Parameters for a two port device  17  2.3: Linear, Circular and Elliptical Polarizations  20  2.4: Test Arrangement for Gain Transfer Method  23  3.1: Microstrip Patch Antenna Construction  27  3.2: S Reflection Coefficient Showing lOdB Bandwidth for Air Core Patch Antenna . . . . 29 n  3.3: Examples of Tapered Slot Microstrip Antennas  31  3.4: Antipodal Linear Tapered Slot Antenna Configuration  31  3.5: Side View of Guillanton Balanced Antipodal Vivaldi Antenna  32  3.6: End View of Guillanton Balanced Antipodal Vivaldi Antenna  32  3.7: S Reflection Coefficient for Guillanton Balanced Antipodal TSA  33  4.1: Fleur-de-Lis Antenna  37  4.2: Design Parameters for FDL Active Member  38  4.3: Design Parameters for FDL Ground Planes  39  4.4: Design Parameters for FDL Ground Plane Flare  39  4.5: Possible Ground Plane Curvatures for the FDL Antenna  40  4.6: Cancellation of the Horizontal Component of the E-field  42  4.7: FDL S„ Reflection Coefficient from Agilent 8510C Network Analyser  44  4.8: FDL Flare Angle  45  4.9: S Reflection Coefficient for FDL Antenna with Flare Angle of 0 degrees  46  u  u  4.10: S Reflection Coefficient for FDL Antenna for Flare Angles of 9 to 45 degrees . . . . 46 u  4.11: S Reflection Coefficient for FDL Antenna for Flare Angles of 45 to 53 degrees . . . 48 n  4.13: S Reflection Coefficient for FDL Antenna with Exponential Curve d =3cm  49  4.14: S,, Reflection Coefficient for FDL Antenna with Exponential Curve d =6cm  51  n  2  2  viii  4.15: Sn Reflection Coefficient for FDL Antenna with Exponential Curve d =9cm  51  4.16: S,, Reflection Coefficient for FDL Antenna with Exponential Curve d =12cm  52  4.17: S Reflection Coefficient for FDL Antenna with Exponential Curve d =13cm  52  4.19: E-Plane Cross and Co-Polarization for Guillanton Vivaldi  54  4.20: H-Plane Cross and Co-Polarization for Guillanton Vivaldi  55  4.21: E-Plane Cross and Co-Polarization for FDL Antenna with No Flare  55  4.22: H-Plane Cross and Co-Polarization for FDL Antenna with No Flare  56  4.23: E-Plane Cross and Co-Polarization for FDL Antenna with 3cm Flare  56  4.24: H-Plane Cross and Co-Polarization for FDL Antenna with 3cm Flare  57  4.25: E-Plane Cross and Co-Polarization for FDL Antenna with 6cm Flare  57  4.26: H-Plane Cross and Co-Polarization for FDL Antenna with 6cm Flare  58  4.27: E-Plane Cross and Co-Polarization for FDL Antenna with 9cm Flare  58  4.28: H-Plane Cross and Co-Polarization for FDL Antenna  59  4.29: Absolute Gain versus Frequency for the FDL and Guillanton Vivaldi Antenna  62  5.1: FEKO Model FDL Antenna  65  5.2: FEKO Model FDL S„ for L ^ . O O cm to 9.50 cm (0.25 cm increments)  68  5.3: FEKO Model FDL S„ for L ^ . 7 5 cm to 10.50 cm (0.25 cm increments)  68  5.4: FEKO Model FDL S„ for L^IO.OO cm  69  5.5: FEKO Model FDL S„ for L =2.50 cm to 3.50 cm (0.25 cm increments)  69  5.6: FEKO Model FDL S„ for L =3.75 cm to 5.50 cm (0.25 cm increments)  70  5.7: FEKO Model FDL S„ for L =3.25 cm  70  5.8: FEKO Model FDL S„ for L =2.00 cm to 2.75 cm (0.25 cm increments)  71  5.9: FEKO Model FDL S for L =3.00 cm to 4.00 cm (0.25 cm increments)  71  5.10: FEKO Model FDL S„ for L = 2.5 cm  72  5.11: FEKO Model FDL S„ for L =0.40 cm to 1.65 cm (0.25 cm increments)  72  5.12: FEKO Model FDL S„ for L =1.90 cm to 3.90 cm (0.25 cm increments)  73  5.13: FEKO Model FDL S„ for L =1.65 cm  73  2  2  u  2  2  2  2  3  n  3  3  4  4  4  ix  5.14: FEKO Model FDL S„ for L =0.00 cm to 2.25 cm (0.25 cm increments)  74  5.15: FEKO Model FDL S„ for L =2.55 cm to 3.00 cm (0.25 cm increments)  74  5.16: FEKO Model FDL S„ for L =2.50 cm  75  5.17: FEKO Model FDL S,, for h,=5.00 cm to 7.50 cm (0.50 cm increments)  75  5.18: FEKO Model FDL S„ for h.^8.0 cm to 9.0 cm (0.50 cm increments)  76  5.19: FEKO Model FDL S,, for h^.50 cm to 11.00 cm (0.50 cm increments)  76  5.20: FEKO Model FDL S„ for h,=9.00 cm  77  5.21: FEKO Model FDL S„ for h =0.00 cm to 1.50 cm (0.50 cm increments)  77  5.22: FEKO Model FDL S„ for h =2.00 cm to 6.00 cm (0.50 cm increments)  78  5.23: FEKO Model FDL S„ for h =0.50 cm  78  5  5  5  2  2  2  5.24: FEKO Model FDL S for h =l .00 cm to 4.50 cm (0.50 cm increments)  79  5.25: FEKO Model FDL S„ for h =5.00 cm to 7.00 cm (0.50 cm increments)  79  n  3  3  5.26: FEKO Model FDL S„ for h =5.00 cm 3  80  5.27: FEKO Model FDL S„ for h =0.10 cm to 0.60 cm (0.10 cm increments)  80  5.28: FEKO Model FDL S„ for h =0.70 cm to 1.50 cm (0.10 cm increments)  81  4  4  5.29: FEKO Model FDL S„ for h =0.70 cm 4  5.30: FEKO Model FDL S for d^O.lO cm to 0.30 cm (0.10 cm increments) n  81 82  5.31: FEKO Model FDL S„ for d^O.40 cm to 1.50 cm (0.10 cm increments)  82  5.32: FEKO Model FDL S for d^O.50 cm  83  n  5.33: FEKO Model FDL S„ for d =1.00 cm to 3.50 cm (0.50 cm increments)  83  5.34: FEKO Model FDL S„ for d =4.00 cm to 8.50 cm (0.50 cm increments)  84  2  2  5.35: FEKO Model FDL S for d =9.00 cm to 15.00 cm (0.50 cm increments)  84  5.36: FEKO Model FDL S„ for d =l 1.00 cm  85  5.37: Optimal FEKO Model FDL S„ Reflection Coefficient  86  5.38: FEKO Model FDL S„ Reflection Coefficient Phase  87  5.39: FEKO Model FDL S„ Smith Chart  87  5.40: FEKO Model FDL Antenna Input Impedance  88  n  2  2  x  5.41: E-Plane Cross and Co-Polarization for FEKO Model FDL Antenna  89  5.42: H-Plane Cross and Co-Polarization for FEKO Model FDL Antenna  89  5.43: Radiation Pattern at 3 GHz (a) Total (b) E-plane (c) H-plane  92  5.44: Radiation Pattern at 6 GHz (a) Total (b) E-pane (c) H-plane  93  5.45: Radiation Pattern at 9 GHz (a) Total (b) E-plane (c) H-plane  94  5.46: Radiation Pattern at 12 GHz (a) Total (b) E-plane (c) H-plane  95  5.47: Radiation Pattern at 15 GHz (a) Total (b) E-plane (c) H-plane  96  6.1: Prototype FDL Scanner System  97  6.2: Alignment of Antennas in Prototype FDL Scanner  99  6.3: Phase Angle vs. Offset Distance For Horn to Horn  101  6.4: Phase Angle vs. Offset Distance For Horn to FDL VH2A  101  6.5: Phase Angle vs. Offset Distance For Horn to FDL VH2B  102  6.6: Phase Angle vs. Offset Distance For FDL VH2A to FDL VH2B  102  6.7: Transmission Coefficient S versus Model Height  106  6.8: Transmission Coefficient S versus Model Height (reflective metal sheet)  106  7.1: Diagram of Wooden Model showing Element Designation and Location  108  7.2: FDL Scanner with Model . . .  108  7.3: FDL Scanner with Wiltron Vector Analyser and Wideband Amplifier  109  7.4: Spectral Curve from Intact Model M, .  110  7.5: Spectral CurvefromM  110  21  21  1 G  7.6: Spectral Curve Difference between M, and M 7.7: Spectral Curves for M„ M  1 H  and M  7.9: Spectral Results for models M  1 G  1 G  .111  1 P  and M  Ill  113  2 G  7.10: Two curves with similar shape with constant offset between them  115  7.11: Two curves with similar shape with short span error  115  7.12: Section Length for f  118  Start  showing f ^ , and f  Upper  7.14: S log Magnitude versus Frequency for Metal Cylinders of varying size 21  125  xi  7.15: Plot of Peak Frequency versus Cylinder Size for Metal Cylinders  125  7.16: S log Magnitude versus Frequency for Wood Cylinders of varying size  126  7.17: Plot of Peak Frequency versus Cylinder Size for Wood Cylinders  126  A l : S Reflection Coefficient for FDL Antenna for Flare Angles of 0 degrees  143  A2: S,, Reflection Coefficient for FDL Antenna for Flare Angles of 9 degrees  143  A3: S Reflection Coefficient for FDL Antenna for Flare Angles of 18 degrees  144  A4: S Reflection Coefficient for FDL Antenna for Flare Angles of 26 degrees  144  A5: S Reflection Coefficient for FDL Antenna for Flare Angles of 33 degrees  145  A6: S Reflection Coefficient for FDL Antenna for Flare Angles of 45 degrees  145  A7: S Reflection Coefficient for FDL Antenna for Flare Angles of 49 degrees  146  A8: S Reflection Coefficient for FDL Antenna for Flare Angles of 53 degrees  146  2!  n  n  u  u  u  n  u  CI: Transmission Coefficient S spectrum showing baseline with no model present . . . . 152 21  C2: Transmission Coefficient S spectrum for Model Heights 2 to 13 cm  152  C3: Transmission Coefficient S spectrum for Model Heights 15 to 20 cm  153  C4: Transmission Coefficient S , spectrum for Model Heights 23 to 28 cm  153  C5: Transmission Coefficient S spectrum for Model Heights 30 to 38 cm  154  C6: Transmission Coefficient S , spectrum for Model Heights 41 to 56 cm  154  C7: Transmission Coefficient S spectrum for Model Heights 58 to 76 cm  155  C8: Transmission Coefficient S spectrum for Model Heights 79 to 91 cm  155  D l : Cougar A2CP12029 Specifications  156  D2: Transmission Coefficient S versus Frequency for Cougar A2CP12029  157  F l : Transmission Coefficient S spectrum for model M  x  161  F2: Transmission Coefficient S spectrum for model M  1 A  161  F3: Transmission Coefficient S spectrum for model M  1 B  162  F4: Transmission Coefficient S spectrum for model M  1 C  162  F5: Transmission Coefficient S spectrum for model M  ] D  163  F6: Transmission Coefficient S spectrum for model M  1 E  163  21  2I  2  21  2  21  21  21  21  21  21  21  2]  21  xii  F7: Transmission Coefficient S spectrum for model M  1 F  164  F8: Transmission Coefficient S spectrum for model M  1 G  164  F9: Transmission Coefficient S spectrum for model M  1 H  165  2]  21  21  F10: Transmission Coefficient S spectrum for model M„  165  21  Fl 1: Transmission Coefficient S spectrum for model M 21  F12: Transmission Coefficient S spectrum for model M 21  166  u  166  1 K  F13: Transmission Coefficient S spectrum for model M  1 L  167  F14: Transmission Coefficient S spectrum for model M  1 M  167  F15: Transmission Coefficient S spectrum for model M  1 N  168  21  21  21  F16: Transmission Coefficient S spectrum for model M , 21  0  168  F17: Transmission Coefficient S spectrum for model M  1 P  169  F18: Transmission Coefficient S spectrum for model M  1 Q  169  F19: Transmission Coefficient S spectrum for model M  1 R  170  F20: Transmission Coefficient S spectrum for model M  1 S  170  F21: Transmission Coefficient S spectrum for model M  1 T  171  21  21  21  21  21  HI: Three quarter View of FDL antenna  174  H2: Top View of FDL Antenna Showing Fleur-de-Lis Profile  174  H3: FDL Connector Showing Assembly method  174  xiii  List of Abbreviations  BW  bandwidth  dB  Decibels  DUT  Device Under Test  FDL  Fleur-de-Lis  FEKO  FEldberechnung bei Korpern mit beliebiger Oberflache  GHz  Gigahertz  GPIB  General Purpose Interface Bus  GPS  Global Positioning Satellite  MHz  Megahertz  MoM  Method of Moments  PCB  Printed Circuit Board  PO  Physical Optics  LTSA  Linear Tapered Slot Antenna  TSA  Tapered Slot Antenna  UTD  Uniform Theory of Diffraction  UWB  Ultra Wideband  VSWR  Voltage Standing Wave Ratio  Acknowledgements  I would like to thank my supervisor Dr. M.J. Yedlin for his support, encouragement, enthusiasm and advice during this thesis project. I would also like to thank my wife Patricia for her support and patience, and my children Alex and Laura for their view on the world to help keep everything in perspective.  I would also like to acknowledge Dr. David Michelson and Kim Lam for their help during my thesis project.  xv  Chapter 1  1.0  Introduction  Each year telephone companies, power distribution companies and government departments install or replace a large number of telephone/power poles. The vast maj ority of these poles are made of wood and have a finite service life. In 1999 BC Hydro estimated that it replaces 4000 wooden poles per year [1]. Replacing these poles is very expensive and the longer a pole can be left in service, the lower the operating costs for the utility or government. As well, there is an environmental cost associated with replacing these poles as trees must be cut to produce the replacement poles and the retired poles must be disposed of.  The length of service of a telephone pole is determined mostly by how well it withstands the elements of nature. Rain, ice and snow, temperature, sun and insects all contribute to the eventual breakdown of the pole by introducing cracks and voids that weaken the pole structurally. These voids also allow bacteria and fungi to enter the pole, causing rot, which further weakens the pole. If the structural integrity of a pole deteriorates excessively, the pole will eventually break under stress, most likely during a period of high storm activity. The results of such a catastrophic failure are power and communication outages, which can sometimes last for days.  In addition to pole management and replacement, the management, cutting and harvesting of forests requires knowledge of the internal condition of the trees to be harvested. The presence or absence of cracks, insect damage or rot can determine if a tree is suitable for harvesting or should be left to promote good reforestation practices [2].  1  Chapter 1 - Introduction Currently, the most common method for determining the condition of these items is visual inspection of the outside of the object or coring of the tree, log or pole. Visual inspection means looking at the surface condition of the object and assuming that the degradation of the structural integrity on the inside of the object is proportional to the visual damage on the outside. Coring involves boring a hole in the tree or log with an instrument known as an increment borer and removing a cross-section of material. It is hoped that an examination of the cross-section of material removed from a single sample will determined the condition of the entire object  [3-7].  Neither visual inspection nor core sampling can adequately determine the profile for the entire object. Internal damage to a tree or pole is often done by burrowing insects that leave only small visual traces of their presence on the outside of the tree. Coring can detect internal damage if a core that contains damaged material is removed, but to do a profile of a tall tree or pole would require many core samples, which is both time-consuming and expensive. In addition, coring is a destructive testing method. Once the core sample has been removed, a hole remains, which opens the tree or log to more internal damage from insects and weather. For processing logs into lumber, coring is not an acceptable test mechanism as it introduces holes into the finished product, which would lessen the strength and value of the lumber. Clearly what is needed is a non-invasive and non-destructive method for determining the interior condition of these objects.  1.1  Wood Properties and Composition  Wood is not a homogeneous material. Different types of wood are made from different materials and have differing properties such as density and chemical composition. While chemical composition changes with density, density is related to the way the wood was grown, rather than the chemical composition itself. Wood that grows faster is less dense than slower  2  Chapter 1 - Introduction growing wood, and knots that are denser than trunk wood are formed by growing branches. Nondestructive testing based on density changes has been performed and will be discussed later.  The chemical makeup of the wood depends upon the species of wood and the growth pattern of the tree. Once a tree has been cut, its chemical composition can be ascertained by standard chemical methods. This does not, however, help for non-destructive testing. One feature that depends upon chemical composition, however, and that can be examined nondestructively, is the wood's dielectric property. It has been shown that several factors such as frequency, temperature, moisture content, density, electric field and grain direction all have an effect on the dielectric behaviour of wood [8].  1.2  Dielectric Properties of Wood  The dielectric properties of wood are normally characterized by two parameters: the real part of the relative dielectric constant (e') and the dielectric loss tangent (tgd). The relative dielectric constant tells us by how much the capacity of a capacitor with the insulating material between its conducting surfaces is greater than that of the same capacitor in which the vacuum is dielectric. In principle, the dielectric constant is a measure of how much electric potential energy is stored in the material when it is placed in a given electric field [9]. The dielectric loss tangent is numerically equal to the ratio between the active current and the reactive current in a material [10]. The dielectric loss factor (e'-tgb) is also used to characterize the dielectric properties of wood. The values of e' and tgb are dimensionless.  The total dielectric effect of samples are determined by the bulk dielectric properties of the various materials that make up that piece and, in general, e' can depend on frequency in with significant changes in the microwave region due to different types of polarizations [11]. 3  C h a p t e r 1 - Introduction  Wood (wood cell walls) is a composite material that is made up mostly of the 3 following compounds: cellulose, hemicellulose and lignin. Cellulose and hemicellulose are polysaccharides, which make up 70% -75% of the wood. Lignin is a mixture of polymers based on phenyl propane units and accounts for between 18% - 30%. The remainder is made up of ash and other substances that are soluble in either ether or water. In addition, the dielectric properties of the sample will depend upon the amount of water in the wood sample.  Cellulose, hemicellulose and lignin are polar polymers. These substances are considered to have high molecular weights and have a number of polar groups. As such, they are subject to dipole-radical polarization. This kind of polarization is caused by the movement of the polar group with respect to the main body of the molecule. The polarizability of each of the materials depends on a number of factors: the type of polar group (-OH, -CH OH, etc), the molecule to 2  which the group is attached, and the surrounding environment (presence of other polar groups, including water). The amount of polarization, energy loss and the relaxation or response frequency will change depending on the combination of materials that make up the sample under consideration.  Water is present in any sample of wood. The amount present and its form are determined by the conditions under which the tree was grown and how the wood has been treated since harvesting. Water is present in 3 forms in wood: free, bound and ice. Free water is water found inside the cell cavities. Bound water is water bound in the cell walls themselves. Ice forms when the temperature drops below 0°C . As the temperature drops free water first forms into ice. As the temperature drops further, to between -50°C and -80°C, the bound water freezes. It appears that below -80°C most of the freezing has occurred and a small portion of the water (-5%) remains unconverted to ice. Under the influence of an external electric field both dry and moist wood are considered polar dielectrics. 4  Chapter 1 - Introduction  1.2.1  Polarization, Relaxation Times and Transmitted Spectrum  One of the important properties of wood is its polarization capabilities. With no applied external field, the net sum of charges in a sample adds up to zero, and there is no charge displacement in the sample. Under the influence of an external electric field, the materials that make up a sample of wood undergo a realignment, and the sample acquires a net dipole moment. The sample acquires a total moment P, which is the sum of all individual dipole moments.  Wood is a linear dielectric material [10] up to the point at which an applied electric field causes the wood to break down. For our application, we will be using small applied field strengths well below this limit. Wood is a material for which the dielectric polarization depends linearly on the strength of the applied field E. P is then given by  P = z °E  (1.1)  s  where P and E are both vector quantities X = electric susceptibility e = permittivity of free space= 8.854x 10" F/m. 12  0  Since the electric susceptibility can also be written as X = ( E ' - 1)  (1.2)  P = (s'~ \)soE.  (1.3)  this gives  5  Chapter 1 - Introduction 1.2.2  Polarization Components  The total polarization of a sample of wood can be broken down into a sum of five kinds of polarization that take place in moist wood:  P=P +P +P +P +P e  a  d  v  (1.4)  z  where P = electronic polarization e  P = ionic (atomic) polarization a  P = dipole (orientation) polarization d  P = interfacial (structural) polarization v  P = electrolytic polarization. z  Electronic polarization arises from the shift of the electrons in orbit around the nucleus and occurs in a very short time (10  14  to 10 " seconds) after the application of the electric field. 16  It does not depend on the temperature and is outside of the range of RF frequencies.  Ionic polarization is due to the elastic displacement of atoms in a molecule as well as the displacement of charged ions in molecules with ionic bonds. In this case the polarization occurs because the applied electric field causes the different charge centres in the molecules to move relative to each other and their normal equilibrium locations. This polarization increases with a rise in temperature. As the molecules heat up, the increased thermal energy causes an increase in distance between ions, which tends to weaken the interaction between them. The time to produce this kind of polarization in response to an applied field is about 10" to 10" seconds. 12  13  6  C h a p t e r 1 - Introduction  Dipole polarization is caused by the rotation of dipolar molecules in alignment with an applied electric field. Dipole polarization depends upon temperature because the thermal motion of the molecules tends to randomize the alignment of the molecules. Dipole polarization is present in water as well as in other polar molecules that make up wood. One other type of dipole polarization is dipole-radical polarization. Cellulose, hemicellulose and lignin possess polar groups such as -OH or -CH OH, which will realign in the presence of an electric field relative to 2  the rest of the molecule. Both types of dipole polarization will also show a gradual increase or decrease with the application or removal of an electric field. The realignment of the molecules or radical groups within a molecule are not instantaneous. Forces and interactions between molecules will slow the alignment process. After the molecules have aligned, random thermal motion will cause the alignment to gradually disappear in the absence of the applied field. This effect is called dielectric relaxation. The value of the polarization diminishes in accordance with the exponential law [10]:  P (t) = P (0)exp(-t/t ) d  d  (1.5)  0  where  P (0)  = the polarization level at the time the field is removed  t  = dipole polarization relaxation time  d  t  0  = current time  The relaxation time is the period of time taken for the polarization level to decrease by a factor of e = 2.72 times relative to its initial value. Usually t is in the range of 10" to 10" 6  12  0  seconds and for this reason manifests itself at frequencies below 10 Hz. 12  The value of t^  increases with a decrease in temperature due to the reduction of thermal motion. Dipole 7  C h a p t e r 1 - Introduction  polarization also causes a dissipation of electric energy, which is transformed into thermal energy. The energy used to align the molecules is released as thermal energy through the physical interaction with other molecules.  In nonuniform (heterogeneous) materials, interfacial polarization can take place. Moist wood is composed of substances in the solid, liquid and gaseous phases. The cell walls absorb moisture to form bound water (water that is less free to move). Inside the cell walls, in the interfibril channels and cell wall channels, and inside the cell itself, there is both air and water vapour. If the quantity of moisture exceeds the fibre saturation point, there is free water as well. Under normal conditions the cell wall material and thefreeions in the wall and the cell cavities will align themselves due to different contact potentials. Under the influence of an external electric field, these alignments will be distorted by the electric field. After the imposition of the electric field, the realignment will gradually take place and the polarization will increase. This increase in polarization is also bound by a relaxation time and the time constant for this kind of relaxation is between 10" and 10" seconds [10]. 3  8  Electrolytic polarization can occur since moist wood is made up of a number of chemical substances and usually has a residual electrochemical or electrolytic polarization due to the displacement of dissociated ions. When an external field is applied, there will be an increase in the dissociation of the chemical components and a corresponding increase in the electrolytic polarization. The increase in this type of polarization is much slower and is between 10" and 10 4  2  seconds.  Under the influence of an electric field, all of the different types of polarization will take place. The effect of each of the types of polarization will depend on the chemical composition  8  Chapter 1 - Introduction of the wood, the amount of free and bound water, the size of the cellular structures and the frequency of the applied external field. The variety of polarizations in wood will lead to a varying response to an applied electric field at different frequencies [12].  The responses of these  dielectric materials will also be different than those of the voids in an object which possesses no dielectric or polarizable materials This is the key property that should allow voids in the wooden models to be located by an examination of the spectral response to a range of radio frequency signals.  1.3  Current Non-Destructive Testing Methods  While there are currently many different types of non-destructive testing methods being evaluated by the wood industry, many are not suitable forfieldapplication and others suffer from limitations in their ability to detect certain types of defects. The most important requirements for non-destructive testing are: 1) the ability to make measurements to determine if a tree or log is suitable; 2) the ability to scan the entire sample or at least the critical areas; 3) the ability to produce fast results in thefieldin real time [13].  All non-destructive testing methods rely on the different material properties between clear wood and wood with defects. Current methods include CT Scan using X-rays [14-17], Impulse Radar [14], Radio Frequency Moisture Scanning [18] as well as sound wave transmission [19], NMRrelaxometry [20], thermography [21], Visible Light Spectral Analysis [22] andpolarimetry [23].  The CT X-ray method functions reasonably well on logs in industrial settings such as sawmills but can not be taken into thefielddue to the nature of the equipment. Additionally, CT scans have problems detecting the differences between areas of knots, voids and higher density  Chapter 1 - Introduction wood in materials with high moisture content [14]. Also, the high cost of CT equipment and operation, which is about 100 times more expensive than other methods [14], and the time required to produce a standard tomographic image [24] means that CT imaging is unsuitable for most industrial environments.  Sound wave technology uses travel times based on differing wood densities to provide information about the internal state of a log. Although the equipment is relatively inexpensive, the test is far from non-destructive. To perform the required measurements, two transducers must be placed on opposite sides of the log or tree. This requires removing the bark from the tree or driving pins into the tree before testing begins [19]. This opens the tree to insect and environmental damage along the 2mm- to 20mm-wide gaps opened in the bark and wood. Additionally, since the process requires good mechanical contact, it is difficult to automate this process. Even once good mechanical contact is made, the results can be inconclusive. For very knotty trees, transmission times are highly variable, and the relationship between transmission time and defect position is not clear. Although large voids and severely degraded material can be detected, it is difficult to identify the type of defect or determine if multiple defects are present [14]. Additionally, due to the high noise and vibration environment of mills, noise interference is significant.  Thermography and NMR techniques are based on the bulk properties of the wood being examined and can be used to detect large differences in the wood being tested. However, the measurements are not sensitive enough to localize defects nor to detect small changes [20, 21]. These methods are also subject to errors introduced by ambient conditions such as local temperature and humidity.  10  Chapter 1 - Introduction Impulse radar in the microwave range has also been used for non-destructive testing of wood. Due to their relatively long wavelengths, microwaves can penetrate deeply into the materials. Microwaves are reflected or diffracted from any boundaries between materials of differing properties. Because clear wood, wood with no defects, provides relatively insignificant boundaries, abrupt changes caused by defects will generate more noticeable changes. Current use of impulse radar is limited to a small range of frequencies in the GHz range. The impulse radar is scanned along the length of the log, rather than a cross-section, and this produces a series of wavy lines on a chart, called a pulse-echo chart, that depend upon the internal features of the log. A log with few defects produces a chart that is "relatively smooth"; one with severe degradation produces a chart that is "very wavy." It has been found that the pulse-echo charts do not generate a repeatable set of numerical values that can be used in an automated process, nor do they provide a detailed or easily interpreted image [14].  1.4  Theoretical Model  It is possible to create a theoretical model of a log or tree section by dividing up a large cylinder into the sum of an arbitrary number of smaller dielectric cylinders [25]. This model is constructed from a number of regular cylinders of dielectric material. To simulate a void or defect in the model log, one or more of the smaller cylinders can be removed from the model. If the model is then subjected to an EM plane wave, the resulting field at any point in space can then be calculated. If this is repeated over a number of frequencies, a graph of the response at a chosen point in space vs. frequency can be created.  Figure 1.1 shows the resulting spectral curves generated by a theoretical model that has had a number of single elements removed from the model at different times [26]. Although the curves shown in Figure 1.1 have similar profiles that overlap at some frequencies, there are 11  C h a p t e r 1 - Introduction  Computational Results for Models Base. H and P 2 H  •  •  •  1  0  1  2  3  4  5  6  Frequency [GHz]  Figure 1.1: Theoretical Spectral Curves small differences between them that appear when a larger frequency range is examined. The information from a single frequency is not sufficient to differentiate between the signals generated by the removal of the different elements. To successfully differentiate between the removal of the different elements, the profiles must be recorded over an wider bandwidth. Even over a relatively large bandwidth of a GHz or two, there is not a sufficient difference in the spectral curves to uniquely determine which element was removed from the model. To differentiate between the curves generated by the removal of the different elements, it will be necessary to use an ultra-wide bandwidth of more than a few GHz. 12  Chapter 1 - Introduction  1.5  Ultra-wideband RF Void Detection  The hypothesis for this project is that the dielectric properties of a wood sample will differ due to the contributions made by the different polarization components. These dielectric properties will also differ between clear wood and wood with defects or voids present in the sample due to the absence of the various polarization components. The differing net dielectric properties of the wood and the voids will produce differing responses to radio signals at different frequencies. Transmitting a number of microwave radio frequency signals over an ultra-wide bandwidth through a sample of varying composition should result in a set of spectral curves that are directly related to the composition of the sample. It should be possible, having previously identified these spectral curves for objects with voids in known locations, to identify the location of a void in an unknown sample by comparing newly obtained spectra to those previously collected for known voids. By use of a wide range of frequencies rather than a single frequency or a small range of frequencies, it should be possible to overcome the problems associated with current microwave methods and repeatably and uniquely identify the location of voids in wooden objects.  13  Chapter 2  2.0  Antenna Characteristics  Since one of the goals of this thesis is to measure the properties of wood over a wide range of microwave frequencies, it was necessary to use a wide bandwidth antenna to transmit the test signals. Most antennas radiate with varying efficiency at different frequencies, and this variation can lead to problems with signal degradation [27]. If the input impedance of an antenna varies with thefrequency,the signal entering the antenna will be distorted by the varying impedance match [28,29] and will result in poor measurement results or insufficient uniqueness in the data due to domination by a smaller number of frequencies. Since we expect to see small differences between the spectral curves produced by voids at different locations, this project requires an antenna that is capable of radiating over a multi-gigahertz bandwidth with a flat input impedance response so that the effects of varying power radiation and signal distortion can be minimized. For ultra-wideband antennas, a good impedance match must be designed fromfirstprinciples, "not added as an afterthought" [30].  2.1  Antenna Measurements and Characterization  For this thesis a network analyser was used to measure the frequency response characteristics, and the antenna was treated as if it were a circuit element. As such, the antenna can be thought of as simply another component in the transmission line circuit. For this antenna, as well as for all other transmission line circuits involving antennas, the main purpose was to provide an impedance match between an electromagnetic wave propagating in a waveguide or cable and a wave propagating infreespace [31].  As such, the characterization of an antenna  involves measuring both those parameters. There were, however, additional important antenna characteristics that also needed to be considered when choosing the antenna for this project, such  14  Chapter 2 - Antenna Characteristics as the antenna's radiation pattern and polarization [27]. This chapter will give a brief explanation of those parameters that are important for the antenna, as well as some relationships between them.  2.2  Impedance Matching, VSWR and S  n  There are many parameters characterizing the match or mismatch of one circuit element with another: impedance, reflection coefficient and voltage standing-wave ratio. The main measure of an antenna's input performance that is normally reported is its S, j impedance match over the antenna's bandwidth. For a transmission line circuit (as shown in Figure 2.1)  X Figure 2.1: Transmission Line Circuit  when a signal is injected into the circuit, if there is a mismatch between the line impedance Z and 0  the load impedance Z , some of the energy of the injected signal is reflected back into the circuit. L  For an antenna this means that any mismatch between the antenna's impedance and that of free space will cause less energy to be radiated by the antenna on transmission, or less energy to be absorbed by the antenna on reception.  15  Chapter 2 - Antenna Characteristics This reflection loss is expressed by means of the Voltage Standing-Wave Ratio (VS WR), which is defined as the ratio between the magnitude of E  m a x  and the magnitude of E . min  E max V  S  W  R  =  \E-  <">  where E  m a x  = the maximum voltage in the standing wave pattern  E  m i n  = the minimum voltage in the standing wave pattern.  While low VSWR is not a design necessity as long as the antenna is an efficient radiator, if the VSWR is high, some form of matching network must be placed between the transmitter and antenna to minimize mismatch loss. If there are reflections in the circuit, then E  m a x  is defined as  the maximum voltage of the peak in the standing wave caused by the reflection and E  m i n  is the  minimum voltage of the trough of the standing wave. If there is a perfect match with no reflection, then there is no standing wave generated and E  m a x  equals E . In this case the VSWR min  is equal to 1. As the mismatch between the circuit and load impedance increases, the standing wave grows and the size of the VSWR increases. The mismatch is also often characterized by a reflection coefficient known as T, where T is defined as ZL T  =  Zo  ^VYo  •  (2-2)  The reflection coefficient is related to the VSWR by equation (2.3):  VSWR=j-^  .  (2.3)  16  Chapter 2 - Antenna Characteristics An antenna is a two-port device and as such can be analysed like any other network component. For a general two-port device under test (DUT) as is shown in Figure 2.2 all four S parameters are shown.  S Parameters S  Forward T r a n s m i s s i o n  2 1  Port 1  Port 2  S „ Forward Reflection  S  S  1 2  2 2  R e v e r s e Reflection  Reverse Transmission  Figure 2.2: S Parameters for a two-port device  The S is the forward reflection coefficient and is identical to V. Hence, u  ZL - Zo  Sn=———=Y ZL  + Zo  .  (2.4)  Although the reflection coefficient S is a vector, which has both magnitude and phase, n  it is commonly reported as a scalar value (as is the VSWR) which is the magnitude of S . All u  S and VSWR values presented in this thesis will be given in dB. n  In addition to being a measurement of the mismatch between the circuit and load impedance, the reflection coefficient S is also a measure of the power that is transferred to the u  device under test. In our case, since the device under test is an antenna, S is a measure of the u  power that is radiated by the antenna versus the power that is supplied to the antenna. This 17  Chapter 2 - Antenna Characteristics relationship is given by  Percent of Power Transferred  = (1 —\Sjjf )* 100  (2.5)  For an antenna the bandwidth is determined by the upper and lower frequencies where a VSWR = 2.0 corresponds to an S,,(dB) ~ -10 dB [32]. Although this is a somewhat arbitrary value, for an S,, below -10 dB, 90% of the power supplied to the antenna is transmitted.  2.3  Polarization  , For an electromagnetic wave sinusoidally varying in time, the wave is characterized at any observation point by its frequency, magnitude, phase and polarization. The polarization of an antenna is the polarization of the wave radiated by the antenna when transmitting. At some point in space, at a distance sufficiently far from the antenna, the phase front (surface of constant phase) of the radiated wave becomes nearly planar. At this point the wave is referred to as a plane wave, and its electric field (E-field) and its magnetic field (H-field) lie in the same plane. The polarization of a plane wave is defined as its electricfieldvector orientation as a function of time, at a fixed position in space. Specifying only the electric field is sufficient since the magnetic field is readily found from E using Maxwell's equations.  In general, an electric field traces out an elliptical path over time.  If that ellipse is  collapsed along the x or y axis, the resulting figure is a vertical or horizontal line. In these cases the antenna is said to have vertical or horizontal linear polarization, as shown in Figure 2.3 (a) and (b). In many cases the E-plane is shown to correspond to the x axis. The field can, however, be oriented in any fixed direction in the x-y plane.  18  Chapter 2 - Antenna Characteristics If the two axes of the ellipse are identical the figure traced is a circle. For this to happen the magnitude of the E-field does not change with time; only its orientation in space changes. An antenna that produces a wave front with this property is said to have circular polarization, as shown in Figure 2.3 (c) and (d). For a circularly polarized antenna there are two further possibilities. While the E-field is rotating it can rotate to the right or to the left. If the wave front is travelling towards the observer (i.e., the observer is looking at the antenna) and the E-field rotates clockwise, the polarization is said to be left-hand polarized; if it rotates counter clockwise it is said to be right-hand polarized. If both the magnitude and direction of the E-field vector change in time, the figure produced is an ellipse and the antenna will have elliptical polarization. Elliptical polarization is also either right-handed or left-handed, as shown in Figure 2.3 (e) and  The polarization of an antenna is important because it affects the strength of the signal that ultimately reaches the receiver. If the polarization of the transmitting antenna does not match the polarization of the receiving antenna, there is a resulting drop in the power that is transferred between the transmitter and the receiver. If the two antennas are oriented in such a way that their E-planes align, then the two antennas are said to be co-polarized. If the E-plane of one antenna is aligned with the H-field of the other antenna (in which case the two E-planes are rotated at 90 degrees to each other) then the two antennas are said to be cross-polarized.  2.4  Antenna / Radiation Pattern  A radiation pattern, also known as an antenna pattern, is a graphical representation of an antenna's far-field radiation properties. For any given antenna the radiation pattern will vary in terms of distance and observation angle in three-dimensional space. Typically, radiation pattern  19  Chapter 2 - Antenna Characteristics  (a) Vertical Linear  Polarization  ^  y  (b) Horizontal Linear  E  y  /  / 1  /  \ 1  \  \  \  i \  (c) Left-hand Circular  1  E \  \  i  \  /  \  - -  ^ \  1  OJ  Polarization  \  y  Polarization  / y  (d) Right-hand Circular  Polarization  E y {  \  A <^ /  \  (e) Left-hand Elliptical  y  Polarization  y  ( \  /  y  (f) Right-hand Elliptical  Polarization  Figure 2.3: Linear, Circular and Elliptical Polarizations 20  Chapter 2 - Antenna Characteristics measurements are taken in the two principal planes of the antenna, the E-plane, which is the plane that contains the E-field vector, and the H-Plane, that contains the H-field Vector. These planes are perpendicular to each other and are also perpendicular to the wave front plane for a transverse electromagnetic wave. Since the magnitudes of the E and H-fields in free space are related by  (2.6)  the resulting radiation patterns can be reported in terms of the E-field or the H-field intensity [11].  If the radiation pattern is plotted in terms of the field strength, such as volts per metre, or the power density in watts per square metre, then the pattern is called an absolute radiation pattern. In most cases, however, antenna patterns are plotted in relative terms. In other words, the field strength is plotted in terms of its ratio to some reference value that is generally the peak value of the field strength. This is called a normalized radiation pattern. For this thesis, E-field intensity measurements have been used, which will be shown as a normalized rectangular logarithmic plot of relative intensity versus angle.  2.5  Phase Measurements  The radiation pattern of an antenna is actually a vector field and is described by both the magnitude and the phase of the radiated field. Typically, only the magnitude of the radiation pattern is measured. However, for this thesis, the phase component of thefieldis also important. The variation in the far field of the magnitude and phase will provide information about the nature of the wave that is impinging on objects in the field. The knowledge of the shape of the 21  Chapter 2 - Antenna Characteristics wave is important, since one often needs to know that the wave front is planar and in what direction the wave is propagating, in order to determine the orientation of the wave front. If the wave front is not planar or if the wave front is not oriented perpendicular to the central axis of the scanner, the result will differ from the case in which those two conditions are met. For example, if the radiation fields produced by either the transmitting or receiving antennas are not planar or the phase centre is off axis, then measurements of the fields will not show symmetry around the central axis of the antennas. As for most antenna designs, it is the far field and not the near field measurements that are commonly given [31].  2.6  Gain Measurement  In addition to the measurements discussed in previous sections, the gain of an antenna is also needed for complete antenna characterization. Gain is an absolute quantity and is much more difficult to measure. The gain of an antenna in a particular direction is the ratio of power radiated per steradian in that direction compared to the power that would be radiated per steradian by a lossless isotropic radiator with the same applied power.  Although it is possible to determine the absolute gain of an antenna from first principles, it is more often determined in relation to an antenna of known gain. This method is known as the gain transfer or gain comparison method [31]. It would be best to use an ideal lossless isotropic radiator for the comparison, but since this type of antenna does not exist in practice, the comparison antenna is usually a dipole or standard horn antenna whose gain has been calibrated in a previous measurement.  To perform a gain transfer measurement, a transmitter of fixed peak power P is connected t  to the source antenna that is one of a pair of standard gain antennas. The receiving standard gain 22  Chapter 2 - Antenna Characteristics antenna is then positioned so that the peaks of the radiation patterns for both antennas are aligned. This will ensure the maximum power transfer P between the pair of standard gain antennas, s  which will give a measurement for the maximum gain G between these two antennas. s  Standard Gain Antenna Gs  -< Source Antenna  y—o  PS  y—o  PT  Q  T  Test Antenna  Figure 2.4: Test Arrangement for Gain Transfer Method  Once the power measurement has been taken for the standard gain pair, the receiving antenna is replaced with the test antenna. The power measurement P is then repeated for the test T  antenna. The gain of the test antenna G is then calculated from the known gain of the standard x  gain antenna from the ratio of the received powers.  GT=—GS  () 2J  Ps  The relationship is often more conveniently expressed in terms of decibels as  Gr(dB)  = Pr(dB)  - Ps(dB)+ Gs(dB)  (2.8)  23  C h a p t e r 2 - A n t e n n a Characteristics  2.7  Frequency Dependence  A typical antenna radiates at a number of different frequencies, and the frequency-wave number representation for an electromagnetic wave is given as  E= E pexp(jGX0  jfi-r)  <-) 2  9  where E is the amplitude of the electromagnetic wave, p is the polarization vector, w is the 0  angular frequency, f3 is the wave vector, and f is the position vector. Note that the wave vector can have both a real and negative imaginary part.  All antenna parameters are frequency dependent and values such as the gain of the antenna under test should be written as G (w) rather than just G [33]. For many applications, the T  x  frequency dependence can be ignored since the range of frequencies being used is narrow and the frequency dependencies are small. However, for an application in which a wide range of frequencies is being used, frequency dependencies may vary greatly over the band and can introduce non-linear effects. For example, if an antenna's gain varies greatly over the range of interest, frequencies that have a high gain may overwhelm equipment and prevent the detection of signals where there is lower gain.  24  Chapter 3  3.0  Wideband Antennas  One of the requirements for designing an ultra-wideband system, such as the one that is proposed for this project, is for a suitable pair of antennas that can be used to transmit and receive the ultra-wideband signals. Most conventional antennas radiate efficiently at a single frequency or over a very small frequency range. There are, however, a number of antenna designs that will radiate over a wider range of frequencies, and these types of antennas are known as broadband, wideband and ultra-wideband antennas, depending on the range of frequencies they cover. Whereas there is no single definition for the terms broad or wideband, a broadband antenna will typically cover a frequency range of a few hundred megahertz (MHz). Wideband and ultra wideband antennas, on the other hand, may cover a frequency range of a few gigahertz (GHz) to 10 GHz or more [34-38].  3.1  Existing Ultra-Wideband Antenna  There are a number of different kinds of wideband antennas, each with its advantages and disadvantages [39]. The history of wideband antennas goes back many years. In 1898 Oliver Lodge patented a number of antenna designs, precursors to some of the modern day ultrawideband antennas [40]. The patent showed early versions of bow-tie and biconical antennas, which were later shown to have significant wideband properties. Further types of wideband antennas were designed in the 1930s and 1940s. These included further biconical antenna designs as well as spherical dipole and coaxial, conical and rectangular horn antennas [40].  25  Since the 1960s other classes of wideband antennas have been introduced. These include wideband notch antennas [41], ellipsoid mono and dipole antennas [40], large current radiator antennas [42], magnetic UWB antennas [43], spiral and helical antennas [44-48], bow-tie antennas [49-53], microstrip antennas [54-58] and tapered slot and Vivaldi type antennas [59, 60]. In addition, there are specialty antennas, which do not fall into the classes of antennas previously mentioned, such as printed and stepped fat-dipole [61, 62], fractal [63], dielectric wedge [64,65], disk and half disk [66] and quasi-horn microstrip antennas [67] all of which have also been previously investigated.  The wideband properties of all of the above antennas depend on two key antenna characteristics: 1) their shape and 2) the type of dielectric material present (if any) in their design. The bandwidth of the antenna is affected by the impedance match between the feeding circuit and free space. This in turn is affected by the currents flowing in the antenna. Currents flowing in the antenna are changed by modifying the shape and dielectric properties of the antenna. These modifications will cause the antennas to radiate with varying degrees of efficiency by one of two main mechanisms: 1) a travelling wave mechanism or 2) a resonance mechanism [68].  The bandwidths of these antennas vary greatly within each class of antenna as well as between the different classes and types of antennas, and each have bandwidths from hundreds of MHz to tens of GHz depending on their designs. The one feature that they all share, however, is a greatly varying impedance match over their bandwidth.  3.2  Broadband Microstrip Patch Antennas  Since the early 1970s, a particular class of antennas, know as microstrip patch antennas, has been the subject of a large and on-going series of investigations [69]. Although not all of these types of antenna are broadband, it is instructive to look at this class of antenna in its  26  Chapter 3 - Wideband Antennas simplest form, as it demonstrates the effects that dielectric materials can have on antenna performance. Figure 3.1 shows the construction of a typical microstrip patch antenna.  For antennas of this design, the bandwidth is proportional to the thickness h of the substrate and inversely proportional to 8 the dielectric constant of the substrate material [68], r  Figure 3.1: Microstrip Patch Antenna Construction  BWK  16 I 3)  pc\ V AoJ \LE)\e f j h d  (3.1)  where p is a power ratio dependent on the ratio of patch size to wavelength X  Q  c, is a constant dependent on the index of refraction of the material A is the wavelength of the centre frequency 0  W is the effective width of the conducting patch e  L is the effective length of the conducting patch e  e  hed r  is the radiation efficiency of a horizontal electric dipole on a lossless substrate.  27  Chapter 3 - Wideband Antennas  This means that, as the dielectric constant of the antenna's substrate increases, the bandwidth of the antenna decreases. Although these antennas offer the advantages of a low profile - compatibility with integrated circuit technology and the ability to conform to a shaped surface, which have led to their use in numerous applications such as aircraft, satellite, GPS, mobile communications and remote sensing - the principle disadvantage of these antennas is the limited bandwidth caused by the limited choice of dielectric materials from which a particular design can be fabricated.  3.2.1  A i r Core Microstrip Antenna  As demonstrated in equation 3.1, one of the fundamental properties of a microstrip antenna is the bandwidth dependance upon the dielectric material [69]. It is not possible to obtain materials that possess a dielectric constant outside a narrow range [68]. Typical dielectrics have a dielectric constant value between 2.1 and 5, with some special materials as high as 10 or more, none of which would provide designs for antennas that would be useful for this application. To produce antennas with a wider bandwidth, specialized materials such as microcell foams and air gels have been produced with lower dielectric constants. There are, however, rigidity problems with using these materials. The microcell foams and air gels can be used only in limited thickness ranges and do not stand up well to bonding and manufacturing processes.  To further examine the effects of the dielectric constant on bandwidth, as part of the preliminary investigation for this thesis, a series of microstrip patch antennas with air between the conducting patch and the ground plane, rather than a dielectric material, were designed and constructed. These antennas did indeed show an improved bandwidth over those constructed from printed circuit board material. The standard patch antennas manufactured out of printed circuit board material with 8 of between 2.2 and 3.2 typically have a bandwidth of around 4MHz r  [70]. The air core patch antennas that were designed demonstrated a bandwidth of approximately 28  Chapter 3 - Wideband Antennas 107 MHz, as shown in Figure 3.2, which indicates a failure of equation 3.1 to predict bandwidth behaviour for patches with air rather than a dielectric substrate between the planes.  Although removing the dielectric material did provide a significant improvement for the bandwidth of the patch style antenna, the overall bandwidth for this type of antenna was still only about 100MHz. Reflection Coefficient [SI 1 ] 10.0  0.0 2.0!32 G H z  S  2.199 C3 Hz  -10.0  2.000  2.030  2.060  2.090  2.120  2.150  2.180  2.210  2.240  2.270  2.300  Frequency (GHz)  Figure 3.2: S Reflection Coefficient Showing lOdB Bandwidth for Air Core Patch Antenna n  3.3  Tapered Slot Antennas  The second class of antennas that are useful to examine for this project are the tapered slot antennas (TS A), also known as notch antennas, that belong to a class known as endfire travelling wave antennas. Like patch antennas, they are manufactured on printed circuit board material, but unlike patch antennas, which radiate perpendicular to the conducting surface, they radiate from the edge of the conducting surface [68]. This class of antennas displays one of the widest 29  Chapter 3 - Wideband Antennas bandwidths of any type of antenna and exhibits an S,, curve that is typical of most ultra-wideband antennas - a large bandwidth with many significant dips in the impedance match.  Figure 3.3 shows a number of typical tapered slot antennas and feed arrangements. Those with straight edges on the flare are referred to as linear slot antennas. Those with exponentially curved edges on the flare are referred to as Vivaldi-style antennas due to the V-horn shape of the slot taper. Despite its superior performance, in the past, the TSA antenna was not able to generate broad interest in the research community. This has been due to the fact that the fundamental operation of tapered slot antennas is still not fully understood. As a result, these antennas have been based primarily on empirical designs [68,71]. They do, however, demonstrate one of the largest bandwidths available and are currently being more vigorously investigated due to the availability of electromagnetic analysis software.  The original tapered slot antennas were manufactured on a single-sided printed circuit board with the antenna comprised of a single endfire microstrip. The flare in the microstrip channel was designed to provide an impedance match between the feed andfreespace. Although this did provide an improved impedance match, the bandwidth was still quite small, only a few GHz [68].  To improve the impedance match over a wider range of frequency, the antipodal tapered slot antenna shown in Figure 3.4 was introduced. This consisted of a double-sided circuit board with an active member (light grey) on the top side of the dielectric substrate (white) and a ground plane (dark grey) on the bottom side. This design did improve the impedance match somewhat and provided a larger bandwidth of 10 to 20 GHz, albeit showing the same significant dips in the impedance match. The main problem with this new design, however, was that the antenna showed high levels of cross polarization in the upperfrequencyranges [72].  30  Chapter 3 - Wideband Antennas  (c)  (d)  Figure 3.3: Examples of Tapered Slot Microstrip Antennas: (a) Linear Taper Microstrip Line Fed (b) Linear Taper Coplanar Waveguide Fed (c) Exponential Taper Ground Plane Coplanar Waveguide (d) Exponential Finite Ground Plane Coplanar Waveguide  Figure 3.4: Antipodal Linear Tapered Slot Antenna Configuration  31  Chapter 3 - Wideband Antennas A new type of antipodal TSA was developed by E. Guillanton et. al. [72, 73] in order to address some of the problems with the basic antipodal antenna. This new antenna attempted to overcome the polarization problems by creating a "balanced" three-layered structure with an additional ground plane on the opposite side of the active member. Figure 3.5 shows the substrate  Figure 3.5: Side View of Guillanton Balanced Antipodal Vivaldi Antenna  • Active M e m b e r  Substrate  I 1  II ' — Ground P l a n e s  Figure 3.6: End View of Guillanton Balanced Antipodal Vivaldi Antenna 32  Chapter 3 - Wideband Antennas  material (white) with metalization on the top for one of the two ground planes (dark grey) and the metalization for the active radiating member (light grey) sandwiched in the middle of the substrate. The second ground plane is located directly behind the visible dark grey ground plane shown in the diagram.  Figure 3.6 shows the second ground plane metalization, which is identical to the first, located on the other outer layer.  Reflection Coefficient [B11] 10.00  1.DD  5.00  9.00  13.00  17.00  21.00  Frequency (GHz]  Figure 3.7: S Reflection Coefficient for Guillanton Balanced Antipodal TSA u  The new design did help solve the polarization problem. Although the Guillanton Vivaldi antenna does have a large bandwidth, as can be seen from Figure 3.7 , the S curve does not n  33  Chapter 3 - Wideband Antennas remain below the -10 dB point until after 6 GHz and does not radiate efficiently from 1 to 6 GHz [73]. In addition, the S curve still varies greatly over the bandwidth, with many peaks and n  valleys. As discussed before, this is not the optimal design for an ultra-wide bandwidth antenna.  34  Chapter 4  4.0  Fleur-de-Lis A n t e n n a  As stated earlier, one of the main characteristics that needs to be considered for any ultrawideband antenna used for this project is the S vs. frequency behaviour of the antenna [28]. n  Any short time duration signal, such as a pulse generated by the measurement equipment, will contain a number of frequency components with a specific amplitude and phase relationship. If the antenna's input impedance varied with frequency then the signal applied to the antenna would be modified, causing signal distortion [27].  Since the antennas used in this project acted like a bandpass filter [29], as for any other bandpass filter, the ideal antenna "filter" response should have a flat amplitude and phase response across the bandwidth, as shown in equations 4.1 and 4.2.  C(jco)=R(ja>)  G(jco)  (4.1)  C(jco)  response of the system after transmitted signal has been received  R(jco)  signal applied to system  G(jco)  transfer function of pair of receiving and transmitting antennas  For a matched pair of antennas the ideal transfer function would be  (4.2)  co - co < co < co + co 0  c  Q  c  elsewhere  where co is the desired A bandwidth. l  c  35  Chapter 4 - Fleur-de-Lis Antenna  • For our application, the antennas used were required to provide a flat S response (or n  small variation) over a bandwidth of 13.5 GHz (the available bandwidth of the network analyser that was used for this project) or greater in order to minimize errors introduced by the antenna's frequency dependence.  Although some of the existing UWB antennas described earlier have shown an improved impedance match over their bandwidth, their reflection coefficients still show large variations in magnitude. To improve on this, a new antenna design is required.  As the Vivaldi class of antennas have the largest available bandwidth, the Vivaldi type of antenna was chosen as the basis for the development of a new antenna for this thesis. To provide a standard for comparison, the Vivaldi antenna created and characterized by Guillanton [74] was chosen as the starting point for the new design. It is hoped that, by modifying the Guillanton antenna, a smoother S return loss can be designed into the new antenna. u  The first difference between the new antenna design and the existing Vivaldi antenna design was that, unlike the Vivaldi antenna, the new antenna has no dielectric material between the active and ground plane members. As for the microstrip patch antenna, the dielectric material between the active members and the ground planes has a large effect on the antenna's bandwidth [72]. The bandwidth of the new antenna should increase by removing the dielectric material from between these members and relacing it with air, as it did for the microstrip patch antenna.  The second design difference between the new antenna and the Guillanton antenna is the position and shape of the antenna's ground planes relative to the active member. There have been a number of studies on the effects of changing the shape of the active member and the ground planes on the S ,,Return-Loss response [72-74], but none of these studies has attempted to change  36  Chapter 4 - Fleur-de-Lis Antenna  the distance between the ground plane and the active member other than to change the thickness of the substrate. Since the Vivaldi antenna's active member and ground planes are bound to the dielectric substrate, typically a Printed Circuit Board (PCB), they must be maintained at a fixed distance apart over the entire length of the antenna. Because the new antenna is no longer manufactured on a dielectric substrate, the spacing-between the ground plane and the active members no longer requires to be fixed.  When both of these design considerations were implemented, the general shape of the new antenna was similar to the design shown in Figure 4.1  Figure 4.1: Fleur-de-Lis Antenna  The name Fleur-de-Lis (FDL) was chosen for the new antenna design due to the antenna's resemblance to the French fleur-de-lis when the antenna is viewed from above.  37  Chapter 4 - Fleur-derLis Antenna 4.1  FDL Antenna Design  All of the antennas designed for this thesis were manufactured from 20-oz. (-0.675 mm thickness) copper sheet. Although other metals should work equally well, the 20-oz. copper sheet was chosen because of its ease in machining and bending. To feed the antenna, the active member of the antenna was soldered directly to the coaxial pin of an SMA connector. The two ground planes were connected by bolts to the mounting bracket of the SMA connector, which was in turn connected to signal ground. Photos of the antenna are shown in Appendix H.  Figures 4.2 through 4.4 show the design parameters for the FDL antennas used in this thesis.  *  I*—i-.;  Figure 4.2: Design Parameters for FDL Active Member: ~L - overall length, L - distance from X  2  end of antenna to start of segment S , L +L - distance from segment S to connector end of 2  3  4  2  antenna, L - width of lobe of antenna, h, - height of antenna at flare end, h - separation at end 5  2  between ground and active member, h - height of connector end of active member. 4  38  Chapter 4 - Fleur-de-Lis Antenna  <  >  L*2  Figure 4.3: Design Parameters for FDL Ground Planes: L*, through L* scaled lengths to allow 5  for alignment of curved ground planes, h - height of tail flare of ground planes. 3  L1  Figure 4.4: Design Parameters for FDL Ground Plane Flare: d - separation of ground planes at {  connector end of antenna, d - separation of ground planes at flared end of antenna. 2  39  Chapter 4 - Fleur-de-Lis Antenna  i_i  (d) Elliptical  *  *  i_i  (e) Circular  Figure 4.5: Possible Ground Plane Curvatures for the FDL Antenna Segment S . 6  40  Chapter 4 - Fleur-de-Lis Antenna A number of individual line segments, each with its own geometry, controls the overall shape and size of the antenna by specifying its outline. The curved segments S, and S are 5  elliptical and symmetrical, segments S and S are circular and segment S is exponential in 2  3  4  profile. These segments and profiles were chosen as they best matched the original Guillanton design as well the segmentation used in other studies [72].  As can be seen from Figure 4.1 the ground planes of the antenna are curved while the central active member of the antenna is flat. Due to this curvature, the ground planes of the antenna must be manufactured longer in length than the active member. The ground planes are scaled in length by proportionally scaling each of the linear segments marked L,* through L *. 5  If this scaling is not performed, then the ends of the ground planes would not align with the ends of the active member, which would lead to a change in the direction of the field vectors at the radiating end of the antenna.  The curved segment S shown in Figure 4.4, which lies in the antenna's H-Plane, can 6  take on a variety of profiles. As shown in Figure 4.5(a) through 4.5(e), the S segment can be 6  linear (flat), exponential, irregular, elliptical or circular. It will be shown later in the analysis portion of this paper that the shape and extent of the S curvature has a major impact on the 6  performance of the FDL antenna.  4.2  FDL Antenna Characterization  Since the FDL-style antenna was of a type never before investigated, much of the antenna work in this thesis involved characterizing the basic properties of the antenna. These properties were then compared to those of a Vivaldi antenna of similar dimensions to give a measure of the improvement of the FDL antenna over the Vivaldi antenna, particularly for the S,, parameter.  41  Chapter 4 - Fleur-de-Lis Antenna  Active M e m b e r  Substrate  Ground Plane  Ground Plane  R e s u l t a n t E field  (a) -Active Member  Ground Plane -  1/  —Ground Plane  Resultant E field  (b)  Figure 4.6: (a) Cancellation of the Horizontal Component of the E-field for Balanced Vivaldi Antenna. Looking end on to printed circuit board (b) Cancellation of the Horizontal Component of the E-field for FDL Antenna looking end on at flared ground planes (in the plane of the active member)  42  Chapter 4 - Fleur-de-Lis Antenna In addition, the behaviour of the FDL-style antenna was investigated to determine the effect that changes in parameters such as the separation angle between the ground plane and active members would have on the antenna's performance. This chapter will show the results of these investigations.  4.2.1  S Return Loss n  As described earlier, one of the most important measures of antenna performance is the S,, return loss. Figures 3.5 and 3.6 show the design of a balanced antipodal-type Vivaldi antenna [73, 75] upon which the antennas developed for this thesis were based. For the initial FDL designs, the overall length L, and the heights of the ground plane and active members h,, h and 2  h were taken from the existing antenna developed by Guillanton [73]. This was done 3  intentionally to enable a direct comparison between the FDL antenna and the Guillanton Vivaldi antenna.  The E-field for the Vivaldi antenna is between the active member and ground planes as shown in Figure 4.6 (a). The horizontal components for the E-field cancel each other out leaving only the vertical component of the E-field. The resultant E-field for the FDL antenna will also be determined by the configuration shown in Figure 4.6 (b). In both cases the horizontal components of the E-field from the active member to the individual ground planes cancel each other out, leaving the E-field in the vertical direction. This cancellation of the horizontal components of the E-field is what accounts for the improved cross polarization characteristics of the balanced antipodal antennas versus the non-balanced antennas [75]. Since the FDL antenna also shares the balanced horizontal E-fields one would expect that the cross polarization performance of the FDL antenna, for a moderate flare (small S curvature), should be similar to 6  that of the Guillanton Vivaldi antenna.  43  Chapter 4 - Fleur-de-Lis Antenna 4.2.1.1 S„ Reflection Coefficient Results  For most of the experiments performed in this thesis, a Wiltron 37225A Vector Network Analyser, with a bandwidth limited to a range of 1 GHz to 13.5 GHz, was used to obtain the S,,, S , , cross and co-polarization and gain information.  As a result, most of the information  presented in this paper is limited to this bandwidth.  However, to make a more accurate  2  comparison with the existing Guillanton Vivaldi antenna [73] an Agilent 851OC Vector network analyser, which was not available for most of the void detection measurements, was also used to provide an S curve over a wider bandwidth range of 1 GHz to 21 GHz. n  Reflection Coefficient  10.00  1  -j  1  (S11) 1  1  r-  5.00 0.00 -  n-20.00 o -25.00 -I -30.00 -35.00 -40.00 -I 1.00  1 5.00  i 9.00  1 13.00  1 17.00  21.00  Frequency (GHz)  Figure 4.7: FDL S Reflection Coefficient from Agilent 8510C Network Analyser u  44  Chapter 4 - Fleur-de-Lis Antenna Figure 4.7 shows the S curve for the FDL antenna configuration that produced the n  smallest deviation across the largest bandwidth. When this is compared with the S,, curve shown for the Vivaldi-type antenna in Figure 3.7, it can be seen that the FDL antenna clearly has a flatter profile with no sharp spikes in the S curve. The FDL antenna also shows an S below -10 dB u  n  across the bandwidth from 2.1GHz to beyond the limits of the Analyser at 21 GHz, which is larger than the bandwidth of approximately 6 GHz to 21 GHz, where the curve remains below the -10 dB line.  Both the FDL and Vivaldi antennas show poor impedance matching  characteristics below the 2 GHz limit.  4.2.1.2 Change in S with Angle of Flare n  The design of the best FDL antenna used for this project was produced by experimentation. One of the parameters that determines the behaviour of the antenna is the angle between the ground planes and the active member of the FDL antenna called the Flare angle (shown in Figure 4.8).  Figure 4.8: FDL Flare Angle  45  Chapter 4 - Fleur-de-Lis Antenna Heflection Coefficient (511) i  10.00-  i  i  i  i  i  i  i  i  i  i  i  -  5.000.00-  1  -5.00 -  CD  T3  \\ /I / \  1 -10.00 CD  \J  \  \  \  I1 J  1  \ \  f  \  \  \  I  \  i  g -15.00 1  /  \  \  /  \ l  \  1  -20.00 -  |)  -25.00 -  Ground Plane Angle 0 degrees  [  -30.00 1.00  1  1  1  1  2.00  3.00  4.00  5.00  1  1  1  G.00 7.00  !  8.00  1  1  1  1  9.00 1D.00 11.00 12.00 13.00  Frequency [GHz]  Figure 4.9: S Reflection Coefficient for FDL Antenna with Flare Angle of 0 degrees n  Reflection Coefficient (511) 10.00 -I  1  1  1  1  1  1  1  1  1  '  1  —r-  1  5.00 -  g-mooH 2Q QQ _ --25.00 -30.00 -i 1.00  1 2.00  1 3.00  1 4.00  1 5.00  1 6.00  1 7.00  1 8.00  Ground Plane Angle 9 degrees Ground Plane Angle 18 degrees Ground Plane Angle 2B degrees • Ground Plane Angle 33 degrees Ground Plane Angle 45 degrees 1 1 1 1 r 9.00 10.00 11.00 12.00 13.00  Frequency [GHz]  Figure 4.10: S Reflection Coefficient for FDL Antenna for.Flare Angles of 9 to 45 degrees u  46  Chapter 4 - Fleur-de-Lis Antenna  Figure 4.9 shows the S curve for an FDL antenna with a flare angle of zero degrees. n  This is, in effect, a Vivaldi-style antenna with no dielectric material between the ground planes and the active member. Although the S,, curve for the FDL antenna with a zero flare angle looks similar to that for the Guillanton Vivaldi, the FDL antenna only radiates efficiently at the resonant peaks and not across the bandwidth like the Guillanton Vivaldi.  Figure 4.10 shows the S returns loss of the FDL antenna as the flare angle is changed u  between 9 degrees and 45 degrees (the individual spectral curves are shown in Appendix A). The deep resonances in the spectral curve disappear between 0 degrees and 9 degrees. Between 9 degrees and 45 degrees, the shape of the S,, curve remains relatively constant but the average value of the S reflection coefficient over the bandwidth decreases as the flare angle increases. n  This decrease in'the S reflection coefficient means an increase in the impedance match for the n  antenna as the flare angle is increased, resulting in an increase in the radiated power.  ; !  r v  Figure 4.11 shows the S curve as the angle is increased from 45 degrees to 53 degrees. n  Between 45 degrees and 49 degrees the S, j curve remains relatively constant. The curves for the angles 45 and 49 degrees overlap in the figure shown/Between 49 and 53 degrees the average value of the S  u  reflection coefficient starts to increase, showing a decrease in antenna  performance. This decrease in performance continues as the ground planes are angled further and further away.  The graphs in Figures 4.10 and 4.11 for S versus flare angle show that for an FDL n  antenna with flat (no S curvature) ground planes, the performance of the antenna can clearly be 6  shown to be dependent on the angle of the ground planes with respect to the active member, something that cannot be changed for a Vivaldi-style antenna due to its construction  47  Chapter 4 - Fleur-de-Lis Antenna  Reflection Coefficient [S11) _i  10.00  i  i  i  i_  5. DO  0.00  S  \  -5.0D  1  CD -D  /-O-  „ _  E -10.0D CD §  §•-15.00 Ground Plane A n g l e 45 Degrees Ground Plane A n g l e 49 Degrees -20.00  Ground Plane A n g l e 53 Degrees  -25.00  1 -30.00 1.00  2.00  1 3.00  1 4.00  1 5.00  1 G.00  1 7.00  1 B.00  1 9.00  1 10.00  1 11.00  1 12.00  1 — 13.00  Frequency (GHz)  Figure 4.11: S Reflection Coefficient for FDL Antenna for Flare Angles of 45 to 53 degrees n  on substrates of fixed thicknesses. The graphs also show that there is an optimal angle for which the FDL has its best S performance, and that angle is approximately 45 to 49 degrees. The fact n  that the S; j performance changes with flare angle is due to the change in configuration. As shown in the previous studies mentioned earlier, the shape of the horn of the Vivaldi antenna affects the impedance match much in the same way as the shape of a horn antenna affects its impedance match. The impedance match of the FDL antenna is improved by creating a "horn-like" structure by producing a flare in the 3 dimension,. rd  48  Chapter 4 - Fleur-de-Lis Antenna 4.2.1.3 Change in S with Curvature of Flare n  Although the performance of an FDL antenna improves as a function of flare angle, simply changing the angle between the ground planes and the active member does not produce the optimal design for an FDL antenna. The performance of the FDL antenna can also be improved by changing the shape of the ground planes. The S,, response for the FDL antenna can be improved by bending the ground planes to give them a curved profile (S ) as shown in Figure 6  4.4.  Figures 4.13 through 4.17 show the effects of changing the flare curvature from 3 to 13 cm for an exponential S profile. Figure 4.18 shows all five flare curvatures on a single graph to 6  make a comparison of the S curve versus flare curvature easier. n  Reflection Coefficient (511 ] 5.00 H  1  1  1  1  1  1  1  1  1  1  1 — r  1  0.00 H  -35.00 -  -40.00 -I 1.00  1 2.00  —i 3.00  1  1  1  1  1  1  4.00  5.00  G.OO  7.00  8.00  9.00  1  1  1  1  10.00 11.00 12.00 13.00  Frequency [GHz]  Figure 4.13: S Reflection Coefficient for FDL Antenna with Exponential Curve d =3cm n  2  49  Chapter 4 - Fleur-de-Lis Antenna Figure 4.13 shows the S,, curve for an exponential curve where the separation of the ends of the ground planes , dimension d from Figure 4.4, was set at 3cm. It can be seen that, while 2  there is a change from the S curve for the Vivaldi antenna, the curve still shows at least one n  deep resonance similar to those found in the Guillanton Vivaldi S curve shown in Figure 3.7. u  For a flare with d equal to 6 cm, shown in Figure 4.14, the resonances are gone, but the 2  S,, curve is above the 10 dB point for most of the bandwidth. Although the S profile now u  appears to be more regular, approaching the idealized flat filter profile, in fact, the antenna is not radiating efficiently at this point. This appears to be the transition point between Vivaldi type behaviour and FDL behaviour.  As the flare curvature increases the performance of the antenna improves. Figure 4.15 to Figure 4.17 show the S, curve for flare curvatures of 9 cm, 12 cm and 13 cm respectively. As r  the flare curvature increases, the S curve returns to below the -10 dB level. All three flare u  curvatures between 9 cm and 13 cm show improved S curves. Although the average value of u  the S,, reflection coefficient is lower for the flare curvature of 9cm, the S, j reflection coefficient curves for the 12cm and 13cm flares show a smoother profile. Again, as for change in the flare angle, changing the curve of the ground planes produces a better impedance match by providing a smoother electrical transition between the metal of the antenna and free space. For this thesis the optimal flare for the FDL antenna is between 9 cm to 13 cm for dimension d . 2  4.3  Cross and Co-Polarization  As stated earlier, due to the similar configuration of the E-fields between the FDL and the Guillanton Vivaldi, it was hoped that the FDL antenna would show a similarly good cross-polarization performance. There appeared to be one area, however, where the FDL antenna  50  C h a p t e r 4 - Fleur-de-Lis A n t e n n a  _i  5.00  i  i  Reflection Coefficient (S11)  i  i  i  i  t  i  i  i_  _>-15.00 E  S-20.00 1  Ol  ° -25.00 Exponential Ground Flare d2=Gcm  -3D.00 -35.00 H -40.00 1.00  1  1  2.00  1  3.00 4.00  1  1  5.00  1  1  6.00 7.00 8.00 Frequencii (GHz)  1  1  1  1  r  9.00 10.00 11.00 12.00 13.00  Figure 4.14: S Reflection Coefficient for FDL Antenna with Exponential Curve d =6cm n  2  -j  5.00  Reflection Coefficient (S11)  i  i  i  i  i  i  i_  Exponential Ground Flare d2=9cm  1.00  1  1  1  2.00  3.00  4.00  1—:  5.00  1  1  1  1  1  1  1  r  G.00 7.00 B.00 9.00 10.00 11.00 12.00 13.00 Frequency (GHz)  Figure 4.15: S Reflection Coefficient for FDL Antenna with Exponential Curve d =9cm n  2  51  C h a p t e r 4 - Fleur-de-Lis A n t e n n a Reflection Coefficient [S11)  Exponential Ground Flare d2=12cm  1.00  ~i  2.00  1  3.00  1  4.00  r  5.00  G.00 7.00  8.00  9.00 10.00 11.00 12.00 13.00  Frequency (GHz]  Figure 4.16: S Reflection Coefficient for FDL Antenna with Exponential Curve d =12cm u  2  Reflection Coefficient (S11) _!  I  I  I  I  L  J  I  I  1_  -25.00 -30.00 -35.00 Exponential Ground Flare d2=13cm -40.00 1.00  2.00  3.00  4.00  5.0D G.0Q 7.00  8.00  9.00 10.00 11.00 12.0D 13.00  Frequency [GHz]'  Figure 4.17: S Reflection Coefficient for FDL Antenna with Exponential Curve d =13cm u  2  52  Chapter 4 - Fleur-de-Lis Antenna  Transmission Coefficient (S21) 5.00 -j  '  1  '  —i  1  1  1  1  0.00 -  1 n  1.00  i  i 2.00  3.00  ~i 4.00  1  1  5.00  B.00  1—• 7.00  1  1  1  1  8.00  9.00  10.00  11.00  •—i 12.00  1— 13.00  Frequency (GHz)  Figure 4.18: S Reflection Coefficient for FDL antenna with curvatures of 3cm to 13cm n  did not outperform the Vivaldi antenna at larger flare curvatures. This did not create a problem for this application as the measurements that were taken were performed along the axis of the antenna where the cross-polarization is low at all frequencies and flares.  Figure 4.19 shows the E-Plane cross and co-polarization pattern for the Vivaldi antenna from the Guillanton paper at 9 GHz. Figure 4.20 shows the H-Plane cross and co-polarization pattern for the same antenna. The Vivaldi shows good results for both the E and H-planes, with the cross-polarization down approximately 18 dB along the bore sight for the E-plane and 16 dB  53  Chapter 4 - Fleur-de-Lis Antenna  E Plane Co and Cross Polarization @ 9 GHz  —.  -10.00 -  •U_ m  a)  T3 =>  A  -15.00 •  E O)  -20.00 -  I  i  v  a)  *  \ -25.00 •  I  I i  \ \  \  -30.00 - co-polarization - cross polarization -35.00 -90.00  -60.00  -30.00  0.00  30.00  60.00  90.00  Angle (degrees)  Figure 4.19: E-Plane Cross and Co-Polarization for Guillanton Vivaldi  for the H-plane. The E-plane cross-polarization remains lower than the co-polarization amplitude for the entire range between -90 degrees and 90 degrees. The H-plane cross-polarization becomes comparable to the co-polarization at angles around +/- 45 degrees.  Figures 4.21 and 4.22 show the E and H-plane cross and co-polarization readings for the FDL antenna with no flare (flat ground planes) at 9 GHz as well. As would be expected, the EPlane cross-polarization level is approximately 14 dB lower than the co-polarization level for FDL antenna, versus 16 dB for the Vivaldi antenna. For the E-plane, however, the FDL antenna showed a drop in the co-polarization curve towards the outer edges (corresponding to higher angles) which the Vivaldi antenna does not show. The H-plane performance of the FDL antenna  54  Chapter 4 - Fleur-de-Lis Antenna  H Plane Co and Cross Polarization @ 9 GHz 0.00  •35.00 -J -90.00  , -E0.00  1 -30.00  , 0.00  , 30.00  , 60.00  1 90.00  Angle (degrees)  Figure 4.20: H-Plane Cross and Co-Polarization for Guillanton Vivaldi No Flare (Flat) E Plane Co and Cross Polarization  -90  -60  -30  0  30  E0  90  Angle (degrees)  Figure 4.21: E-Plane Cross and Co-Polarization for FDL Antenna with No Flare  55  C h a p t e r 4 - Fleur-de-Lis A n t e n n a  Figure 4.22: H-Plane Cross and Co-Polarization for FDL Antenna with No Flare  Figure 4.23: E-Plane Cross and Co-Polarization for FDL Antenna with 3cm Flare  56  Chapter 4 - Fleur-de-Lis Antenna  3 cm Flare H Plane Co and Cross Polarization  -  '  ^^  i'  •  Q.  E  XI 01  N  T5  E  \  \  V \  ,'  co-palariiation cross polarization 0  30  Angle (degrees)  Figure 4.24: H-Plane Cross and Co-Polarization for FDL Antenna with 3cm Flare 6 cm Flare E Plane Co and Cross Polarization  - co-polarization - cross polarization  Angle (degrees)  Figure 4.25: E-Plane Cross and Co-Polarization for FDL Antenna with 6cm Flare  57  Chapter 4 - Fleur-de-Lis Antenna 6 cm Flare H Plane Co and Cross Polarization  - co-polarization - cross polarization  Angle (degrees)  Figure 4.26: H-Plane Cross and Co-Polarization for FDL Antenna with 6cm Flare 9 cm Flare E Plane Co and Cross Polarization  m 0)  - co-polarization - cross polarization •20  a— •so Angle (degrees)  Figure 4.27: E-Plane Cross and Co-Polarization for FDL Antenna with 9cm Flare  58  C h a p t e r 4 - Fleur-de-Lis A n t e n n a  9 cm Flare H Plane Co and Cross Polarization  to 0)  Angle (degrees)  Figure 4.28: H-Plane Cross and Co-Polarization for FDL Antenna with 9cm Flare  was slightly improved over that of the Vivaldi antenna. While the polarization curves for the Vivaldi antenna meet at an angle of approximately 45 degrees, the curves for the FDL antenna do not meet until past 60 degrees.  The fact that there are differences between the cross- and co-polarization of the two antennas is due to the mechanical differences between them. Since the Vivaldi antenna's ground and active members are closely spaced, there is only a small current induced in the antenna by a wave polarized perpendicular to the surface of the antenna. This current is less affected by the angle at which the antenna is oriented in this plane due to the endfire nature of the Vivaldi antenna. For the FDL, however, the wide separation between the active and the ground members allows a stronger current to be induced and shows a stronger angle dependency since, unlike the  59  Chapter 4 - Fleur-de-Lis Antenna  Vivaldi antenna, the profile of the FDL antenna that is exposed to the incoming wave changes greatly with the angle.  Figures 4.21 through 4.28 show the change in shape of the cross- and co-polarization curves as the flare is increased from flat through 9 cm. As the flare increases, the E-plane crosspolarization levels remain relatively constant when compared to the co-polarization level along the main axis. The cross-polarization remains around 12 dB to 14 dB lower than the co-polarization level at zero degrees and the cross-polarization curve remains relatively flat. The E-plane co-polarization curve, however, changes in shape as the flare is increased, changing from a relatively flat shape to one with multiple valleys. Once the flare reaches d = 9cm, the cross and 2  co-polarization curves meet briefly at around 50 degrees, at which point, due to geometry, the ;  exposed profiles of the antennas in the E and H-planes lead to similarly induced currents in both • -V  planes.  "•<•:•:..••  The co-polarization curve for the H-plane changes like that of the E-plane co-polarization curve, with multiple peaks and valleys occurring as the flare curvature increases. The H-plane copolarization level does not appear to change as fast as that of the E-plane, with the multiple peaks showing up at a flare curvature with d = 9cm for the H-plane co-polarization curve versus d = 2  2  6cm for the E-plane. The H-plane cross-polarization curve shows the most dramatic change as the flare curvature increases. For the E-plane the cross-polarization level is always below that of the co-polarization level. As the flare curvature increases the cross-polarization curve loses its "flat" profile and starts to develop symmetrical peaks at around the +/- 30 degree angle, again due to the antenna's geometry. These peaks increase in height until the cross-polarization is at the same level as the co-polarization, at an angle of 30 degrees for a flare curvature with d = 6cm. 2  At d = 9 cm the cross-polarization levels at 30 degrees are significantly above those of the co2  60  Chapter 4 - Fleur-de-Lis Antenna polarization. The cross-polarization curve always shows a minimum value at 0 degrees (along the main axis).  As stated earlier, the minimum at zero degrees and the maximum at around 30 degrees can be explained by the geometry of the FDL antenna. In cross-polarization measurements the E-field from the transmitting antenna is oriented in the H-plane of the receiving antenna. At zero degrees the antenna is symmetric to the incoming E-field around the E-plane of the antenna. Therefore, any electric fields induced between the active member and the grounds are cancelled out due to symmetry. As the receiving antenna is rotated in the H-plane, the symmetry is lost, with one of the ground planes being more exposed to the incoming electric field than the other. The electric fields no longer cancel each other, resulting in an increase in power transmitted to the receiving antenna. As the antenna is further rotated, the active member of the antenna becomes shielded by the ground plane and the gap between the active member and the ground planes is no longer in the correct orientation to induce currents in the antenna.  4.4  Gain Measurements  To perform relative gain measurements, an antenna with a known gain calibration must be used for the calculation. Since there are no standard antennas that will cover the entire 1-13.5 GHz bandwidth of the FDL antenna, multiple standard gain antennas would have been needed to cover the entire frequency range. The results for gain versus frequency for this thesis are limited to the range of 8 GHz to 12 GHz because, only one standard gain antenna was available for use. Gain measurements were performed using a Narda model 640 Standard Gain horn, which has a range of 8 GHz to 12.25 GHz.  61  Chapter 4 - Fleur-de-Lis Antenna  Table 4.1 shows the gain results for the FDL Antenna, with exponential S profile d = 6  2  9cm, compared to those for the Guillanton Vivaldi antenna. Upon first examination it appears that the gain for the FDL antenna is significantly lower than that for the Vivaldi antenna. However, an examination of the S curve in Figure 3.7 for the Guillanton antenna shows that the reported n  Frequency (GHz)  2  4  6  8  9  10  11  12  FDL Gain (dB)  N/A  N/A  N/A  3.7  3.6  4.4  4.8  4.7  Vivaldi Gain (dB)  3.2  5.8  4.2  N/A  7.8  8.2  N/A  8  Table 4.1: Gain versus Frequency For Optimal FDL and Guillanton Vivaldi Antennas  FDL Absolute Gain vs Frequency  Frequency GHz  Figure 4.29: Absolute Gain versus Frequency for the FDL and Guillanton Vivaldi Antennas 62  C h a p t e r 4 - Fleur-de-Lis A n t e n n a  gain measurements for the Vivaldi antenna in the range between 8 GHz and 12 GHz were taken from the peak resonance frequencies shown at 9 GHz, 10 GHz and 12 GHz. These measurements give a false impression of the overall gain of the antenna.  Table 4.1 shows that the gain of the Guillanton antenna at 2 GHz and 6 GHz as listed at 3.2 dB and 4.2 dB. These values correspond to points on the S curve in Figure 3.7.where there u  is no sharp peak. At these points the gain of the Vivaldi antenna is similar to the gain of the FDL antenna and is in the range of 3 to 4 dB.  Figure 4.29 shows a graph of the FDL and Guillanton antennas' gain versus frequency. The dotted trend lines, calculated by least squares fit, as shown in Figure 4.29, also show that the FDL and Vivaldi's antenna's gain generally increases as the frequency increases. This is normal for most wideband antennas such as the Vivaldi and the horn antennas [73, 76].  63  Chapter 5  5.0  Antenna Modelling  Since the FDL antenna is a new design that produced results significantly different from any other antenna, it was not possible to check the experimental results against an existing FDL antenna. To determine a design for an FDL antenna that gave the flattest S response, a series of n  computer simulations were run using the FEKO electromagnetic field analysis software.  The name FEKO is an abbreviation derivedfromthe German phrase FEldberechnung bei Korpern mit beliebiger Oberflache (field computations involving bodies of arbitrary surface) [77]. Among its other uses, such as the analysis of electric fields around objects in space, FEKO can be used to calculate the various parameters of a model antenna. FEKO is based on the Method of Moments (MoM) and calculates the electric surface currents on conducting surfaces and equivalent electric and magnetic surface currents for dielectric materials. Once the current distributions are calculated for the model antenna, the near field, the far-field, the input impedance and the S parameters of the antenna can be determined.  For this thesis, the FEKO simulations for the FDL antenna were created by varying each oftheL„L , L , L , L , h,, h , h , h , d and d parameters independently to see how these would 9  3  4  5  2  3  4  (  2  affect the performance of the FDL antenna's S Return-Loss response. Due to limitations in time n  and available computing power, it was not possible to create models and produce results for the complete model space, nor was it possible to run cross and co-polarization and radiation patterns for models for all values of L[ through d . Cross and co-polarization and radiation patterns for a 2  single representative model were also run, corresponding to one of the physical antennas created during this project.  64  Chapter 5 - Antenna Modelling To calculate the S graphs and far field plots, FEKO was run using a single instance of u  this FDL antenna model. To calculate the cross and co-polarization values, two instances of the FDL model were used. The second instance of the FDL model was rotated 180 degrees around the z axis and then translated in the model's space so that the two instances of the FDL model were facing each other at a distance.  5.1  FEKO Model FDL Antenna  Figure 5.1 shows the model antenna divided into 2700 triangular sections. The surfaces are divided up automatically by the FEKO program. The number of sections is dependent upon the target analysis frequencies and is calculated to guarantee a valid solution. An example of an original FEKO design file is shown in Appendix B.  Figure 5.1: FEKO Model FDL Antenna  65  Chapter 5 - Antenna Modelling 5.2  FEKO Model S Return Loss Coefficient Results n  Figures 5.2 to 5.3 7 show the results of the FEKO calculations for the FDL model antenna's S parameter. In addition to comparing the FEKO results to measurements for one of the FDL u  antennas constructed for this project, a sensitivity study was performed using FEKO to determine which of the design parameters were most important in determining S  u  behaviour and to  determine the values that give the best S performance. n  5.2.1  FEKO Design Parameter Sensitivity Study  As shown earlier in Figures 4.3 and 4.4, the FDL antenna design is based on constructing the antenna from a number of segments. The critical parameters for determining the shape of the antenna were the length parameters L, through L , the height parameters h, through h and the 5  4  separation parameters d d , which control the spacing and the curvature of the ground planes l5  2  with respect to the active member.  As can be seen from figures 5.2 through 5.36, varying each of the parameters has an effect on the S parameters for the model antenna. There are, however, four parameters that have a u  greater effect on flattening the S curve below the -10 dB level than the others. These four u  parameters are L h , d, and d . For shorter overall lengths, L, produces an S,, curve that has deep l 5  4  2  valleys, with one significant one at around 6 GHz. The frequency of the centre point of this valley decreases proportionally with the increase in the over all length, L of the antenna. This feature l 5  is similar to other antennas where a single radiation mode dominates and produces a resonance at which most of the antennas energy is radiated.  66  Chapter 5 - Antenna Modelling  As the height, h , of the throat of the active member of the antenna is changed, the S 4  u  curve tends to remain reasonably flat, or at least does not develop any deep resonances. The curve's position does, however, drop below the -10 dB level, to a minimum value at around h =0.7 cm. For h values above or below this value, the curve tends to rise above the -10 dB level 4  4  which would indicate that the match is not as good. The throat of the active member is where the antenna signal is fed into the antenna via the connection to the SMA connector. The FDL and Vivaldi antennas are based on tapered slot antennas, which are often fed with varying stripline arrangements. For the FDL antenna, it is most likely that the poor impedance match with the varying h values is due to similar slotline impedance mismatches between the coaxial feed and 4  the throat.  The d, parameter that controls the spacing between the ground planes and the active member of the antenna near the throat at the SMA connector shows a similar behaviour to that of the h parameter. This is also most likely due to the stripline feed behaviour, which like tapered 4  slot antennas, also depends upon the distance between the ground plane and the active member. For tapered slot antennas the stripline behaviour also depends upon the dielectric material as well as the distance between the planes. For the FDL, however, as stated earlier, there is no dielectric material present between the ground planes and the active member.  The parameter that makes the biggest difference in the flatness of the S curve is the d n  2  parameter, which controls the size and curvature of the flare of the ground planes. This dependence on d is what was found experimentally and is confirmed by the FEKO models. As 2  seen in Figures 5.33 through 5.36, changing the distance d does not affect the frequency of the 2  resonances, only the depth. As the size of d approaches its optimal value at about 11 cm, the 2  valleys in the S curve reach a minimum as the energy radiated by the antenna is more evenly n  67  Chapter 5 - Antenna Modelling Reflection Coefficient (S11 ] 1D.00 ,  5.00 -  0.00  -I  -40.00 -] 1.00  , 2.00  , 3.00  , 4.00  , 5.00  , 6.00  , 7.00  , 8.00  , 9.00  —, 10.00  , 11.00  , 12.00  , 1 13.00  Frequency [GHz)  Figure 5.2: FEKO Model FDL S„ for L,=8.00 cm to 9.50 cm (0.25 cm increments) Reflection Coefficient (S11 j 10.00 -|  :  1  5.00 -  0.00  -I  -25.00 -  -30.00 -  -35.00 -  -40.00 -| 1.00  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  2.00  3.00  4.00  5.00  6.00  7 00  8.00  9.00  10.00  11.00  12.00  ,— 13.00  Frequency [GHz]  Figure 5.3: FEKO Model FDL S for L,=9.75 cm to 10.50 cm (0.25 cm increments) u  Chapter 5 - Antenna Modelling Reflection Coefficient (S11)  1.00  2.00  3.00  4.00  5.00  E.00  7.00  8.00  9.00  10.00  11.00  12.00  13.00  Frequency [GHz]  Figure 5.4: FEKO Model FDL S for L,=10.00 cm n  Reflection Coefficient (S11) 10.00  6.00 -  0.00 -  -25.00 -  -30.00 -  -35.00 -  -40.00 -( 1.00  ,  1  1  ,  ,  ,  ,  2 00  3.00  4.00  5.00  E.00  7.00  8 00  , 9.00  , 10.00  , 11.00  , 12.00  , 13.00  Frequency (GHz)  Figure 5.5: FEKO Model FDL S„ for L =2.50 cm to 3.50 cm (0.25 cm increments) 2  Chapter 5 - Antenna Modelling Reflection Coefficient (S11)  Figure 5.6: FEKO Model FDL S„ for L =3.75 cm to 5.50 cm (0.25 cm increments) 2  R eflection Coefficient [S11)  1.00  2.00  3.00  4.00  5.00  E.00  7.00  8.00  9.00  10.00  11.00  12.00  Frequency (GHz)  Figure 5.7: FEKO Model FDL S„ for L =3.25 cm 2  13.00  Chapter 5 - Antenna Modelling Reflection Coefficient (S11 ]  n  -20.00  t.00  2.00  3.00  4.00  5.00  G.00  7.00  8.00  9.00  10.00  11.00  12.00  13.00  Frequency [GHz]  Figure 5.8: FEKO Model FDL S„ for L =2.00 cm to 2.75 cm (0.25 cm increments) 3  Reflection Coefficient (S11)  1.00  2.00  3.00  4.00  5.00  6.00  7.00  6.00  9.00  10.00  11.00  12.00  13.00  Frequency (GHz)  Figure 5.9: FEKO Model FDL S„ for L =3.00 cm to 4.00 cm (0.25 cm increments) 3  Chapter 5 - Antenna Modelling Reflection Coefficient (S11)  1.00  2.00  3.00  4.00  5.00  6.00  7.00  B.OO  9.00  10.00  11.00  12.00  13.00  Frequency [GHz)  Figure 5.10: FEKO Model FDL S„ for L = 2.5 cm 3  Reflection Coefficient [S11J  120 .0  13.00  Figure 5.11: FEKO Model FDL S„ for L =0.40 cm to 1.65 cm (0.25 cm increments) 4  72  Chapter 5 - Antenna Modelling ReflectionCoefficient(S11]  Figure 5.12: FEKO Model FDL S„ for L =1.90 cm to 3.90 cm (0.25 cm increments) 4  Reflection Coefficient (S11 ]  1.00  2.00  3.00  4.00  5.00  6.00  7.00  6.00  9.00  10.0  11.00  12.00  Frequency (GHz)  Figure 5.13: FEKO Model FDL S„ for L =1.65 cm 4  13.00  Chapter 5 - Antenna Modelling Reflection Coefficient (S11) 10.00 -|  s.oo -  o.oo -I  -25.00 -]  -30.00 -  -35.D0 -  -40.DD O 1.00  1  ,  1  1  1  1  1  1  1  1  1  1  2.00  3.00  4.00  5.00  6.00  7.00  6.00  9.00  10.00  11.00  12.00  13.00  11  Frequency (GHz)  Figure 5.14: FEKO Model FDL S for L =0.00 cm to 2.25 cm (0.25 cm increments) u  5  Reflection Coefficient (S11) 10.00 -|  1  5.00 -{  o.oo J  •25.00 -  -30.00 -  •35.00 -  •40.00 -J 1.00  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  2.00  3.00  4.00  5.00  6.00  7.00  8.00  9.00  10.00  11.00  12.00  ,_ 13.00  Frequency (GHz)  Figure 5.15: FEKO Model FDL S„ for L =2.55 cm to 3.00 cm (0.25 cm increments) 5  74  Chapter 5 - Antenna Modelling Reflection Coefficient [S11 ]  DI -2°-°°  Figure 5.16: FEKO Model FDL S„ for L =2.50 cm 5  Reflection Coefficient (S11 ]  Figure 5.17: FEKO Model FDL S„ for h,=5.00 cm to 7.50 cm (0.50 cm increments)  75  Chapter 5 - Antenna Modelling Reflection Coefficient [S11 ] 1D.00 -|  5 00 -  0.00  i  -25.00 -  -30.00 -  -35.00 -  -•0.00 -I 1.00  ,  ,  ,  1  ,  ,  ,  ,  ,  ,  ,  ,  2.00  3.00  4.00  5.00  E.00  7.00  S.00  9.00  10.00  11.00  12.00  13.00  Frequency [GHz]  Figure 5.18: FEKO Model FDL S for h,=8.0 cm to 9.0 cm (0.50 cm increments) n  Reflection Coefficient [S11 ] 10.00 -|  .  5.00 -  Boa \  -25.00 -I  •30.00 -  -35.00 -  -40.00 \ 1.00  ,  ,  ,  ,  1  ,  ,  ,  ,  ,  ,  ,  2.00  3.00  4.00  5.00  E.00  7.00  8.00  9.00  10.00  11.00  12.00  13.00  Frequency [GHz]  Figure 5.19: FEKO Model FDL S„ for h,=9.50 cm to 11.00 cm (0.50 cm increments)  76  Chapter 5 - Antenna Modelling R eflection Coefficient (S11)  6 00  7.00  8.00  9.00  10.00  11.00  12.00  13.00  Frequency [GHz)  Figure 5.20: FEKO Model FDL S„ for h,=9.00 cm Reflection Coef f icient [S11)  1.00  2.00  3.00  4.00  S.00  9.00  7.00  8.00  9.00  10.00  11.00  12.00  13.00  Frequency (GHz)  Figure 5.21: FEKO Model FDL S„ for h =0.00 cm to 1.50 cm (0.50 cm increments) 2  Chapter 5 - Antenna Modelling Reflection Coefficient (S11)  1.00  2.00  3.00  4.00  5.00  6.00  7.00  0.00  9.00  10.00  11.00  12.00  13.00  Frequency (GHz)  Figure 5.22: FEKO Model FDL S„ for h =2.00 cm to 6.00 cm (0.50 cm increments) 2  Reflection Coefficient (S11 ]  1.00  2.00  3.00  4.00  5.00  6.00  7.00  S.00  9.00  10.00  11.00  12.00  13.00  Frequency (GHz)  Figure 5.23: FEKO Model FDL S„ for h =0.50 cm 2  78  Chapter 5 - Antenna Modelling Reflection Coefficient (S11J  1.00  2.00  3.00  4.00  5.00  7.00  8.00  9.00  10.0  11.00  12.00  13.00  Frequency [GHz]  Figure 5.24: FEKO Model FDL S„ for h =1.00 cm to 4.50 cm (0.50 cm increments) 3  Reflection Coefficient (S11)  1.00  2.00  3.00  4.00  ,  5.00  6.00  7.00  BOO  9.00  10.00  11.00  12.00  13.00  Frequency [GHz]  Figure 5.25: FEKO Model FDL S„ for h =5.00 cm to 7.00 cm (0.50 cm increments) 3  79  Chapter 5 - Antenna Modelling Reflection Coefficient (S11)  4.00  5.00  600  7.00  8.00  9.00  10.00  1100  12.00  19.00  Frequency [GHz]  Figure 5.26: FEKO Model FDL S„ for h =5.00 cm 3  Reflection Coefficient [S11]  1.00  2.00  3.00  4.00  5.00  G.00  7.00  8.00  9.00  10.00  11.00  12.00  13.00  Frequency [GHz)  Figure 5.27: FEKO Model FDL S„ for h =0.10 cm to 0.60 cm (0.10 cm increments) 4  Chapter 5 - Antenna Modelling Reflection Coefficient (511)  Figure 5.28: FEKO Model FDL S„ for h =0.70 cm to 1.50 cm (0.10 cm increments) 4  Reflection Coefficient (S11)  1.00  2.00  3.00  4.00  5.DD  6.00  7.00  8.00  9.00  10.00  11.00  12.00  Frequency (GHz)  Figure 5.29: FEKO Model FDL S for h =0.70 cm n  4  13.00  Chapter 5 - Antenna Modelling Reflection Coefficient [S11 ] 10.00 -|  5.00 -  oo.o -I  -25.00  -30.00 -  •35.00 •  •40.00 •) 1.00  ,  ,  ,  ,  ,  1  ,  ,  ,  ,  ,  ,  2.00  3.00  4.00  5.00  G.OD  7.00  8.00  3.00  10.00  11.00  12.00  13.00  Frequency (GHz)  Figure 5.30: FEKO Model FDL S„ for d,=0.10 cm to 0.30 cm (0.10 cm increments) Reflection Coefficient (511) 10.00 -|  .  5.00 -  0.00  -I  -25.00 J  -30.00 -  -35.00 -  •40.00 -| 1.00  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  2.00  3.00  4.00  5.00  S.00  7.00  3.00  9.00  10.00  11.00  12.00  r13.00  Frequency (GHz)  Figure 5.31: FEKO Model FDL S for d,=0.40 cm to 1.50 cm (0.10 cm increments) n  82  Chapter 5 - Antenna Modelling Refection Coefficient [S113  3  -15.0  1.00  2.00  3.00  4.00  5.00  6.00  7.00  8.00  9.00  10.00  11.00  12.00  13.00  Frequency [GHz)  Figure 5.33: FEKO Model FDL S„ for d =1.00 cm to 3.50 cm (0.50 cm increments) 2  83  Chapter 5 - Antenna Modelling Reflection Coefficient [511) 10.00 -|  :  5.00 •  0.00  -I  -35.00  -•0.00 -|  ,  1.00  r-U  2.00  3.00  ,  ,  ,  ,  1  ,  ,  ,  ,  ,  4.00  5.00  E.00  7.00  8.00  9.00  10.00  11.00  12.00  13.00  1  Frequency [GHz]  Figure 5.34: FEKO Model FDL S„ for d =4.00 cm to 8.50 cm (0.50 cm increments) 2  Reflection Coefficient (S11)  1  10.00 -|  5.00 -  0.00  -25.00 -  -30.00 -  •35.00 -  •40.00 -I 1.00  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  ,  2.00  3.00  4.00  5.00  E.00  7.00  8.00  9.00  10.00  11.00  12.00  13.00  Frequency [GHz]  Figure 5.35: FEKO Model FDL S for d =9.00 cm to 15.00 cm (0.50 cm increments) u  2  84  Chapter 5 - Antenna Modelling Reflection Coefficient [S11) 10.00 i  5.00 -  0.00 •  •25.00 -I  -30.00 .  -35.00 -  -4D.00 -I 1.00  1  ,  1  1  1  1  1  ,  1  1  1  1  2.00  3.00  4.00  5.00  G00  7.00  8.00  9.00  10.00  11.00  12.00  13.00  Frequency [GHz]  Figure 5.36: F E K O Model F D L S„ for d =l 1.00 cm 2  distributed across the bandwidth. This is the behaviour that the F D L antenna design was intended to produce.  The other parameters do not play as large of overall role in flattening the S curve. In n  some cases, L , L , L , h, and h , there is a single large drop in the S at one or two frequencies, 2  3  4  2  n  which would indicate a single resonant mode. In other cases, such as h and L , there appears to 3  5  be little dependence on the parameter, with no resonances appearing. The sensitivity study did show, however, that the overall shape of the antenna is important and that each of the parameters that control the shape of the antenna has a role in flattening the S  u  return loss curve.  The design for the FDL antenna, which was determined by the F E K O sensitivity study, was: L,=10 cm, L =3.25 cm, L =2.50 cm, L =1.65 cm, L =2.5 cm, h]=9.0 cm, h =0.5 cm, h =5.0 2  3  4  5  2  3  85  Chapter 5 - Antenna Modelling cm, h =0.7 cm, d,=0.5 cm, d =l 1.0 cm, with the corresponding S curve shown in Figure 5.37. 4  2  n  This FEKO design corresponds very well to the best FDL design that was constructed and tested in the lab. The design for the best antenna was: L,=10 cm, L =3.3 cm, L =2.50 cm, L =1.7 cm, 2  3  4  L =2.4 cm, h,=8.2 cm, h =l .2 cm, h =5.0 cm, h =0.5 cm, d,=0.5 cm, d =l 1.0 cm. For the antennas 5  2  3  4  2  tested in the lab, there was little difference in the measured S curve for values between d =9 cm n  2  and d =13 cm. 2  5.2.2  Comparison of FEKO Model Results and S Measurements n  Figure 5.37 shows the S curve for the FEKO model FDL antenna configuration that n  corresponds to the actual antenna that produced the maximum bandwidth with the flattest Reflection Coefficient (511) 10.00 5.0D 0.00 -5.00 m s  -10.00 DJ  ^  Ol  -15.00  ro ™ -20.00 -25.00 Agilent Measurements -30.00  FEKO Results  -35.00 -40.00 1.00  5.00  9.00  13.00  17.00  21.00  Frequency [GHz]  Figure 5.37: Optimal FEKO Model FDL S„ Reflection Coefficient  86  Chapter 5 - Antenna Modelling  87  Chapter 5 - Antenna Modelling  T  1.00  1  1  1  1  1  1  1  1  1  1  3.00  5.00  7.00  9.00  11.00  13.00  15.00  17.00  19.00  21.00  Frequency (GHz)  Figure 5.40: FEKO Model FDL Antenna Input Impedance  S,, profile. When the S,, curve from the FEKO model is compared with the S curve shown for u  the actual antenna in Figure 4.7, and also shown in grey on Figure 5.37, it can be seen that FEKO model FDL antenna and the actual antenna both have a flat profile with no sharp spikes in the S,, curve. Although the FEKO model FDL antenna also shows an S below 10 dB across the entire n  bandwidth from 2.1GHz to 21 GHz, the measured S profilefromthe actual antenna is flatter u  than the FEKO model and slightly further below the - 10 dB level.  Figure 5.38 shows the phase of the S,, parameter that oscillates in a narrow range between -10 and -80 degrees. This is also demonstrated in Figure 5.39, which shows the Smith Chart for the antenna and Figure 5.40, which shows the real and imaginary parts of the antenna's  88  Chapter 5 - Antenna Modelling  FEKO H Plane Cioss and Co Polarization  Chapter 5 - Antenna Modelling input impedance over the bandwidth. These graphs show that the antenna does perform with constant impedance over the ultra-wide bandwidthfromabout 2 to 21 GHz.  5.3  FEKO Model Cross and Co-Polarization  Figures 5.41 and 5.42 show the cross- and co-polarization for the E and H-planes for the FEKO model FDL antenna with 9 cm flare. A" comparison of these graphs with those shown in Figures 4.27 and 4.28 show that the relative magnitudes between cross- and co-polarizations for the model are very similar to those for the actual antennas. The model cross- and co-polarization graphs also show the same relative shapes as the actual antenna cross- and co-polarization graphs.  To calculate the cross- and co-polarization values, FEKO uses one model to describe both the transmitting and receiving antennas. As described earlier, the second antenna is created by rotating and repositioning a copy of the first antenna in FEKO's model space. In contrast, the experimental measurements for the actual antennas were performed using two different physical antennas. Although the two physical antennas were fabricated at the same time, differences in their flare profiles, due to the fact that the flares were bent by hand, means that, unlike the model antennas, the physical antennas are not identical to each other. An attempt was made to have the flares machine bent, but there was no equipment available that could perform the required task. In future, for mass production, the antennas could be machined using a tool and die process, but the cost for this was too prohibitive for prototyping.  In addition, as the values for the FEKO antennas are calculated in infinite space, conditions similar to those surrounding the physical test site are not replicated for the FEKO models. The site for the physical antenna measurements was located on the roof of a building, where the antennas under test are located approximately 2 metres above the roofing surface. One  90  Chapter 5 - Antenna Modelling of the antennas is mounted directly on the side of the roofs penthouse; the other is mounted on a movable dolly with a fibreglass mast. Although this arrangement gives reasonable results, the environment is not identical to the infinite space model that is used by FEKO. Also, in addition to the difference in physical surroundings, the FEKO models are not affected by gravity, whereas the spacing between the active member and the ground planes varies somewhat for the actual antennas as they are rotated in the E- and H-planes while performing the measurements.  Some of the resulting differences in the graphs between the models and the actual antenna are likely due to these differences between the model's configuration and the antenna's construction.  5.4  FEKO Model Far Field  Figures 5.43 through 5.47 show the far field lines of constant magnitude for the E- and Hplanes as well as the total field for 3, 6, 9, 12 and 15 GHz. The FEKO software was limited to a maximum of 15GHz (above this frequency the model and analysis data would not fit into the existing program memory and a program error was generated). The graphs show that as the frequency increases the antenna remains roughly endfire with 2 frontal lobes. The number of side lobes tends to increase as the frequency increases, but the overall shape of the field does not change that greatly from 3 to 15 GHz, which suggests that the performance of systems using this type of antenna should remain consistent over this range. These radiation patterns are also similar to those for Vivaldi-type antennas [78].  91  Chapter 5 - Antenna Modelling  (b)  (c)  Figure 5.43: Radiation Pattern at 3 GHz (a) Total (b) E-plane (c) H-plane  Chapter 5 - Antenna Modelling  (b)  (c)  Figure 5.45: Radiation Pattern at 9 GHz (a) Total (b) E-plane (c) H-plane  Chapter 5 - Antenna Modelling  (b)  (c)  Figure 5.46: Radiation Pattern at 12 GHz (a) Total (b) E-plane (c) H-plane  95  Chapter 5 - Antenna Modelling  Chapter 6  6.0  FDL Ultra-Wideband Scanner  6.1  Scanner Design  The proposal for this thesis, is to detect voids in wooden objects, such as trees or telephone poles, by transmitting rf signals through an object and measuring the received signals. These signals are then used to determine if enough information is present in the received signals to determine the location of the voids.  Figure 6.1: Prototype FDL Scanner System  To accomplish this, a prototype scanner, shown in Figure 6.1, was constructed. The scanner consisted of two FDL antennas mounted upon brackets, one for transmitting, the other for receiving at either end of the scanner. The two ends of the scanner were held together by a pair of solid rods that were used to maintain afixeddistance between the antennas and to ensure  97  Chapter 6 - Ultra-Wideband Scanner  that the antennas remain properly aligned. The distance between the antennas can be adjusted by replacing the separating rods with rods of varying length. At each end of the scanner the mounting brackets were affixed to a dot matrix printer carriage. The carriages were removed from a pair of Roland PR-1215 dot matrix printers, which gave the scanner a span of 14.75 inches (which corresponds to 1775 steps for the stepper motor drivers). This arrangement works out to approximately 120 steps/inch or a horizontal resolution of 0.00833 inches.  Although the  resolution is far greater than needed for scanning, the positioning of the antennas between test runs was critical, and the use of the printer mechanisms allowed for the accurate repositioning required.  The driving circuit for the stepper motors was constructed from components taken from the original printer drivers with the addition of a PIC 16C73B microcontroller. The scanner was controlled via the serial port of a standard MS Windows-based laptop. The magnitude and phase readings for the received S signal were recorded using a Wiltron 37225A Vector Network 21  Analyser, which was controlled from the same laptop via a GPIB interface. Once the scanner and the analyser were connected to the laptop, the scanner operation and data recording were completely controlled and fully automated by the laptop.  6.2  Scanner Characterization  Since the scanner employed a pair of FDL antennas, rather than a single FDL antenna, some additional work was required to characterize the antennas within the scanner configuration. The following sections describe the results of this characterization.  98  Chapter 6 - Ultra-Wideband Scanner  6.2.1  Phase versus Distance Measurements  Although, as stated earlier, every attempt was made to manufacture two identical antennas, due to the exponential curvature of the FDL ground planes it was necessary to bend the ground planes by hand. Even for a single FDL antenna, the right side ground plane curve and the angle between the ground plane and the active member were not identical to those of the left side ground plane. Part of the characterization process for the scanner involved determining the shape of the wave front at the receiver and the zero phase alignment in the horizontal direction for the wave [80]. To accomplish this, four sets of measurements were taken. The first set of readings was taken between two known antenna horns to determine if the alignment of the scanner was correct. The second and third sets of readings were taken to determine if there was any phase offset between the alignment for the horn antennas and the alignment of a single horn antenna and a single FDL antenna. The fourth set of readings was used to check the alignment of the two FDL antennas when used as a transmitter/receiver pair.  Figure 6.2: Alignment of Antennas in Prototype FDL Scanner  For each set of measurements, the antennas were first centred in the middle of their  99  Chapter 6 - Ultra-Wideband Scanner horizontal range. The relative phase measurement between the two antennas was adjusted so that the angle was 0 degrees. The receiving antenna was then stepped horizontally along its range, and the phase was measured at a number of positions relative to the zero phase angle alignment. For planar wavefronts, in the far field of the antennas, if the transmitting and receiving antennas were perfectly aligned for the zero phase angle measurement, moving either one of the antennas from this position should have caused the phase angle measurement between the antennas to decrease. If the antennas were not aligned when the zero phase angle measurement was taken, then moving the antennas away from this position in one direction or the other would have resulted in an increase in the phase angle until the antennas were aligned. Once the alignment point had been reached, any further movement would have again resulted in a decrease of the measured phase angle.  The results for the four sets of measurements are shown in Figures 6.3 to 6.6. Figure 6.3 shows the phase versus horizontal offset for the two horn antennas. It shows that the alignment for the two horn antennas was correct. The minimum phase angle between the two antennas occurs at an offset distance of zero. This means that the transmitting and receiving horn antennas at either end of the scanner were correctly aligned for zero offset. This could only have occurred if the overall geometry of the scanner was correct.  Figure 6.4 shows the results of the Phase Angle versus Offset Distance measurements for transmission from a standard Horn to the first of two FDL antennas designated VH2A. The peak of the phase curve was at an offset of 5 mm from the zero phase alignment for the horn to horn transmission. With the 1288 mm separation between the antennas, this offset distance corresponded to an offset angle of approximately 0.22 degrees.  100  Chapter 6 - Ultra-Wideband Scanner  Horn to Horn Phase vs Offset Distance @ 9 GHz  y  /  N s  / /  ,1  /  \  \  /  \ \  /  /  \  / /  1  \  \ \  \  /  /  \\  / /  \  /  \  \  /  Offset Distance (mm)  Figure 6.3: Phase Angle vs. Offset Distance For Horn to Horn Horn to FDL VH2A Phase vs Offset Distance @ 9 GHz  /  N  /  /  /  J  /  J  /  \  A  j  -100  / /  0)  </>  (0  S.  /  /  \ \\  \\ \  /  /  \  \  /  t  -120  \  \  1  5  \  /  \  \  -50  0  50  Offset Distance (mm)  Figure 6.4: Phase Angle vs. Offset Distance For Horn to FDL VH2A  101  C h a p t e r 6 - U l t r a - W i d e b a n d Scanner Horn to FDL VH2B Phase vs Offset Distance t » 9 GHz  s  /  /  /  /  /  /  /  \  \  \  \  \  \  \  S|  \ \\  /  / /  /  \\  /  \  /  .SD  0  50  Offset Distance (mm)  Figure 6.5: Phase Angle vs. Offset Distance For Horn to FDL VH2B  FDL VH2A to FDL VH2B Phase vs Offset Distance @ 9 GHz  /  J  /  /  /  f  /  \  /  \  f  1  J  / 1  /  1  \  \  \\  \V  \,  \  t1  1  \  \  \  J  \  j  -50  0  50  Offset Distance (mm)  Figure 6.6: Phase Angle vs. Offset Distance For FDL VH2A to FDL VH2B  Chapter 6 - Ultra-Wideband Scanner Figure 6.5 shows the results of the Phase Angle vs. Offset Distance measurements for transmission from a standard horn to the second of the two FDL antennas designated VH2B. This antenna showed the peak in the phase curve to be at an 8 mm offset from the horn to horn transmission, with a resulting offset angle of approximately 0.36 degrees.  Figure 6.6 shows the results of the Phase Angle vs. Offset Distance measurements for transmission from FDL antenna VH2A to FDL antenna VH2B.  The phase peak for this pair  occurred at an offset of 13 mm, which corresponds to an offset angle of 0.58 degrees. Since the measured offsets were very small, the total offset distance and angles for the FDL to FDL transmission are, as expected, equal to the sum of the offsets for the individual horn to FDL transmissions. The size of the relative offsets were very small, corresponding to 61 steps for the driving motor and belt, arid could be corrected if required. For this project, an offset of the two antennas was actually desirable. If the antennas were perfectly aligned, if thefieldsbetween the two antennas were perfectly symmetrical and if the wooden model under test was completely homogeneous in its make up, then by reason of symmetry, the received spectra created by two different voids located symmetrically on opposite sides of the wooden model's central axis would be identical. If this were true we would lose the ability to uniquely determine the presence of the void. Ensuring that the antennas were not aligned means that the symmetry was eliminated.  6.2.2  Far Field Considerations  To ensure that the scanner would be free from any near field effects, it was necessary to determine the antenna's separation.  In the far field the angular distribution of power is  independent of the distance (i.e., the wavefront is planar) [32].  Typically, this distance is  determined by the formula [80] 2D  2  r  (6.1)  A 103  Chapter 6 - Ultra-Wideband Scanner where D is the maximum linear dimension of the antenna A is the operating wavelength.  Although the FDL antennas that were used with the scanner were capable of transmitting beyond 13.5 GHz, this was the maximum frequency of interest since this was the maximum frequency of the Wiltron Vector Analyser used for taking measurements. While we did not use all of the bandwidth of the antenna, the performance of the FDL antenna over this smaller range was still an improvement over existing antennas in terms of the flatter S distortion.  n  curve and signal  A frequency of 13.5 GHz corresponds to a A of approximately 2.22 cm. The  maximum dimension of the antenna is 10.2 cm, which gives the far field distance as  r  2  = —  (10.2  2.22  cm)  2  cm  —  * 94 cm  (6-2)  Therefore, to avoid possible near field effects, the transmit and receive antennas for the scanners needed to be located 2 metres apart so that the wooden models were placed in the far fields of both antennas.  6.2.3  Diffraction Effects  As well as determining the alignment and separation of the antennas, the scanner characterization had to take into account the effect of multiple signal paths due to diffraction over the top and bottom ends of a test model and reflection from surrounding objects.  104  C h a p t e r 6 - U l t r a - W i d e b a n d Scanner  To test for diffraction effects, a series of test models ranging in height from 1 inch (2.54 cm) to 36 inches (91 cm) were placed between the scanner antennas. The received spectrum between 1 GHZ and 13.5 GHz was recorded for each model. Figure 6.7 shows the results for models with heights of 69 cm, 76 cm and 84 cm. As the model height increases, the curves get closer and closer in profile. For model heights greater than 69 cm, there is almost no discernable difference between the curves, as is shown in the figure by the overlapping curves. This means that the minimum height of a model must be at least 69 cm to ensure that the height of the model was sufficient to avoid the effects of diffraction around the ends of the model.  To minimize reflections from surrounding objects, the testing and calibration of the scanner and the recording of model data were performed in appropriate locations. The scanner was positioned in an area where the nearest objects were located at a distance of at least 3 or more times the largest dimension of the scanner. The only object close enough to cause reflections was the table upon which the scanner was mounted. To test for a problem with reflections from the table, the scanner was placed on top of a large sheet of aluminum that extended past the outer dimensions of the scanner to provide a reflective surface beneath the scanner. The test with models of varying heights was repeated with the metal sheet in place.  Figure 6.8 shows the results for models with heights of 69 cm, 76 cm and 84 cm with the metal sheet in place. As for the measurements taken without the metal sheet, the measurements taken with the metal sheet showed the same height dependency. The spectral curves merged for model heights greater than 69 cm, again indicating that the minimum height of a model needed to be 69 cm or more to avoid diffraction effects.  The complete results for all models between 0 cm and 91 cm, as well as the calibration spectrum with no model between the antennas, appear in Appendix C.  105  Chapter 6 - Ultra-Wideband Scanner Transmission Coefficient (S21) 10.00  i_  . J  i  _i  i  i  L  5.00  ' 0.00  7.i  •5.00  -10.00  -15.00  i Model Height G9 cm Model Height 7E cm Model Height 84 cm  -20.00  -25.00 -i 1.00  1 1 3.00 4.00  1 2.00  i i  1 /  1 1 1 5.00 B.00 7.00  1 r B.00 9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure 6.7: Transmission Coefficient S versus Model Height 2!  Transmission Coefficient (S21) 10.00  5.00  \A  1  J  i  i  i  i  i  i  i_  0.00  V  .g -5.00  -10.00 1 *  -15.00  i  \i  Model Height G9 cm Model Height 76.cm Model Height B4 cm  -20.00  -25.00 -i 1.00  I  1 2.00  1 1 3.00 4.00  1 5.00  1 1 B.00 7.00  \i  1 8.00  1 1 1 1 r 9.00 10.00 11.00 12.D0 13.00  Frequency (GHz)  Figure 6.8: Transmission Coefficient S versus Model Height (reflective metal sheet) 21  106  Chapter 7  7.0  V o i d Detection  As stated at the beginning of Chapter 6, the objective of building the scanner was to determine the location of voids in wooden objects using ultra-wideband.rf signals. Rather than using a standard tomographic approach, which requires too much time and precision for a cost effective industrial process [14, 17, 24], a pattern-matching algorithm was used to match the spectral curves from unknown samples to those from a set of previously recorded baseline spectra.  7.1  Detection of V o i d s  To determine if it is possible to detect voids inside a wooden cylinder using the FDL scanner, a simplified model was constructed from standard commercial 2x4 graded lumber. The model shown in Figure 7.1 consists of 20 lengths of kiln-dried fir 2x4 (SPF 1 grade) measuring 80 cm in length. This length was chosen to eliminate any diffraction effects, as previously discussed in section 6.2.3.  Each length of 2x4 was stood on end next to the others to form the roughly cylindrical shape shown. Each individual position in the models was labelled A to T to track which piece of the model was currently removed so that the model could be disassembled and reassembled. The figure shows the model in its normal position, but the model could also be rotated around its centre axis if needed. This model is referred to in this chapter as Model M, and element A from model M, is referred to as M , element B M 1 A  1 B  and so on. A second model, called M , was also 2  constructed from similar lengths of kiln-dried fir 2x4 to be used as our unknown sample model.  107  C h a p t e r 7 - V o i d Detection  E  K  A  F  I.  Ii  G  AfrK  Q ft  C  H  N  S  D  T  ,,,/  /  P  Figure 7.1: Diagram of Wooden Model showing Element Designation and Location  7.1.1  M o d e l Analysis  An analysis of the wooden model using the FDL scanner was performed by placing the model between the two FDL scanner antennas, as shown in Figure 7.2 .  Figure 7.2: FDL Scanner with Model 108  C h a p t e r 7 - V o i d Detection  Port 1 of the Wiltron Vector Analyser was then connected to the FDL antenna VH2B to be used as the signal transmitter. The FDL antenna V2HA was then connected to Port 2 of the Wiltron Analyser via a Cougar A2CP12029 wideband amplifier (see specifications in Appendix D) as shown in Figure 7.3. The wooden test model was placed at the midpoint between the scanner antennas, and the resulting S , transmission spectrum was recorded using the Wiltron 2  Analyser in a range from 1 GHz to 13.5 GHz. The S spectrum was first recorded for the basic 21  model with all elements in place and then for the model with each one of its elements individually removed to determine the baseline spectral curves. The model was then rotated by 90 degrees and the measurements were repeated. This allowed the FDL Scanner system to record a large number of spectra, which could be used later for comparisons. In all, a combined total of 389 different spectra from models M, and M were recorded for analysis. The scanning was automated via a 2  Pentium III laptop running Win2K connected to the Analyser via the GPIB input. WIrtron Vector Analyzer  ooo oo ooo oo oo o oo ooo  Wideband Amplifier  o o ooo o o ooo  S 3  » « p  <  >  RS232 Controller FDL Scanner with Model under Test GPIB  \  i. i. V"  .'•  .—n  ' . ^ a c c r r T r ;  .  Figure 7.3: FDL Scanner with Wiltron Vector Analyser and Wideband Amplifier  109  er 7 - V o i d Detection  Transmission Coefficient [S21 ] 10.00  _i  i  i  i  i  i_  6.00  7.0D  8.00  5.00 0.00 -5.00 -10.00 -15.00 -20.00 -25.00 No Missing Elements -30.00 1.00  2.00  3.00  4.00  5.0D  3.0D 10.00 11.00 12.00 13.00  Frequency [GHz)  Figure 7.4: Spectral Curve from Intact Model M , Transmission Coefficient (S21) 10. DO  —J  I  1  I  6.00  7.00  8.00  L  -25.00 Missing Element G -30.00 1.00  2.00  3.00  4.00  5.00  -1 1 1 — r 9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure 7.5: Spectral Curve from M1G  C h a p t e r 7 - V o i d Detection  10.00  Transmission Coefficient [S21]  _i  L.  5.00 0.00 -5.00 -10.00 -15.00 -20.00 H -25.00 -30.00  Model M-| with no elements removed Model M-|G with element G removed  -35.00 -40.00 1.00  n  2.00  1  1  3.00  4.00  r  5.00 B.00 7.00  B.00  9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure 7.6: Spectral Curve Difference between M, and Mi . G  10.00 5.00 0.00  P.  -5.00  Transmission Coefficient [S21)  A\  Ii \  I\  m B  -10.00  CD  T3  1-15.00 H Ol CD  1-20.00 -25.00 Model M-| with no elements removed Model M-|H with element H removed Model M-| p with element P removed  -30.00 -35.00 H -40.00 1.00  i  i  2.D0 3.00  i  4.00  i  i  5.00 6.00  i  7.00  i  8.00  i  i  i  1  1—  9.00 10.00 11.00 12.00 13.D0  Frequency (GHz)  Figure 7.7: Spectral Curves for M„ M  1 H  and M  ] P  Chapter 7 - Void Detection 7.1.1.1 Position of Removed Elements versus S Spectral Curve 21  The first thing that can be seen from the initial scans of model M, with no elements removed versus scans of model Mjwith one or more elements removed is that the spectrum that is produced varies depending upon which element is removed from model M,. Figure 7.4 shows the spectrum produced by irradiating the intact model M,, and figure 7.5 shows the spectrum produced by removing a single element (M ) from the model. Although the two graphs look 1G  identical, if they are overlaid on the same graph, as is shown in Figure 7.6, there are small but measurable differences between the two curves, which is what was expected from the theoretical model.  Figure 7.7 shows three curves, one curve for the model M,, one curve for the model M  ] H  and one curve for model M , each overlapped on the same graph. Again, it can be seen from an 1P  examination of these three curves that there are differences between the spectra produced by the intact model and models that have a single void in them caused by the removal of a single element from the model. This difference shows that the shape of the spectral curves are due, at least in part, to the position of the element removed from the model. The same holds true for the curves produced by the removal of each of the other elements from the model. The graphs for the rest of the elements appear in Appendix F.  7.1.1.2 Spectral Comparison Between Models Mj and M  2  As stated earlier, a second model was constructed from similar 2x4 material from a different set of 2x4s, and in addition to measuring the S responses for model M 2)  l 5  with and  without the elements removed, the S responses were measured for model M . It was hoped that 21  2  112  C h a p t e r 7 - V o i d Detection  j  10. DO  Transmission Coefficient (S21) i i i i_  5.00 0.00  w  -5.00  m B  -10.00  OJ T3  S -15.00 cc ^-20.00 _g -25.00  (II-  -30.00  —  [2]  Model M-|G with element G removed Model M2G with element G removed  -35.00 -40.00 -i 1.00  1  1  1  1  1  1  1  1  2.00  3.00  4.00  5.00  G.00  7.00  8.00  9.00  1  1  r  10.00 11.00 12.0D 13.00  Frequency (GHz]  Figure 7.9: Spectral Results for models M  1 G  and M  :  by comparing the sets of spectral curves from both models the differences in the curves could be attributed to the voids and not simply small differences in the wood that made up the models.  Figure 7.9 shows the results for the removal of element G from models M, (M ) and M 1G  2  (M ) . Note that the two curves are similar but not identical. The question is, are these two 2G  curves similar enough to each other and different enough from all the other spectral curves produced by removing different elements that a unique match can be made? If a match between these two 113  Chapter 7 - Void Detection curves can be determined then the location of an "unknown" void in model M can be found by 2  comparing the spectral curves from model M with a baseline set of curves from model M,. 2  7.1.1.3 Curve Matching and the Figure of Merit  A number of approaches can be used to determine the similarity between curves. Assume that there are two curves on a graph, a reference curve C and a sample curve C . The simplest R  s  matching algorithm is to compare the value of the C to the value of C at each point along the R  s  curve and count the number of matching points. The best match would then be assigned between the two curves with the highest number of matches.  The second method for matching two curves is to find the difference, 6M, between these curves at each point along the curve . If this difference is then taken as the error in the match, a cumulative error can be calculated by summing the individual errors. Alternately, the absolute value of the individual errors can be summed to give a total error for the entire match. The larger the cumulative or absolute error, the worse the match. The best match between two curves would then be the two curves whose differences show the lowest cumulative error. N  (7.1)  ;'=1  These approaches would work well for curves that are identical in magnitude along their entire length. For curves that possess the same relative shape, but are offset by a fixed difference in magnitude, as shown in Figure 7.10, these approaches will produce a large cumulative error (shown in grey) and poor matches by either algorithm. These methods would give a poor matching result even though the curves are very similar in shape. 114  C h a p t e r 7 - V o i d Detection  Figure 7.10: Two curves with similar shape with constant offset between them  C h a p t e r 7 - V o i d Detection  Similarly, curves that are very similar in shape over most of their length but have a short span where there is a major difference between the curves, as shown in figure 7.11, will also have a large cumulative error (shown in grey) and a poor match between the curves.  In practice, these two types of problems are likely to occur on a regular basis in the kinds of environments where an instrument based on the scanner would be used. In the field, or in an industrial environment such as a sawmill, electrical noise from motors and compressors is likely to affect the recording of the spectral data. Differences in relative magnitude are likely to occur due to calibration and power factors, and small "glitches" or spikes in the spectral curves are likely to occur from spurious electromagnetic radiation.  To overcome these problems, a new algorithm was developed for determining a match between two curves. Rather than examining the curves as a whole, the curves are examined in smaller sections to see if these sections match. The total number of matching sections between the two curves is summed to calculate a "figure of merit" for the match. If a large number of reference curves are compared with the sample curve at the same time, then the reference curve that has the highest number of matching sections (highest figure of merit) is deemed to be the match to the sample curve for the analysis.  The algorithm matches sections of curves by determining over what range of frequencies two curves share a similar shape. To accomplish this, a frequency is chosen as a starting frequency f . The difference in magnitude between the sample curve and each of the reference Start  curves at the starting frequency is calculated.  SM/start = c Rfstart- cSfstart  (7.2)  116  C h a p t e r 7 - V o i d Detection  This is the same as the 6M error as discussed earlier in this section. However, rather than summing this value to produce a cumulative error, SM is used as an offset target between the two curves at this frequency.  For this algorithm, the sections of two curves are said to match over the range of frequencies where SM remains constant to within a fixed percentage of the original separation distance. This means that the sections of the two curves that remain separated by a fixed offset (as shown in Figure 7.10) would be considered matching sections. The length of the matching section is determined by  Section Length = where f  Upper  is the lowest frequency greater than f  highest frequency less than f  Start  Start  fupper -  /Lower  (7.3)  where SM no longer matches and f^,. is the  where SM no longer matches (Figure 7.12).  In practice, if the algorithm tries to match the target SM exactly or within too small a percentage of the original separation, the length of a section does not extend more than a few frequencies on either side of the starting frequency. This result leads to many reference curves matching the sample curve over very small ranges of frequencies. This, in turn, makes it harder to distinguish a better match from a poorer one. If, however, the condition for matching SM is relaxed so that SM need only be constant within a 10% deviation, then the lengths of the sections grow to a reasonable size.  Once the length of the matching section for each of the reference curves has been calculated at a particular starting frequency, the best match to the sample curve (for that frequency) is chosen to be the reference curve that has the longest section length. A "win" is then 117  C h a p t e r 7 - V o i d Detection  assigned to that reference curve. If there is a tie with two or more reference curves having the same longest section length for a particular starting frequency, then a win is awarded to each of those reference curves. This means that the total number of wins across all reference curves may not be the same in all instances.  This matching process is then repeated for each frequency across the entire spectral range. The cumulative number of wins is recorded for each of the reference curves and the reference curve that has the highest number of wins is considered the curve that best matches the sample curve. The code for the matching algorithm can be found in Appendix E.  Transmission Coefficient [S21) 10.00 H  1  1.00  1  '  1  1  '  1  A  5.00-  •40.00 -I  1  1 2.00  1—:—i 3.00  4.00  1  1  1  1  1  1  1  1  5.00  G.OD  7.00  8.00  9.00  1D.00  11.00  12.00  1— 13.00  Frequency [GHz]  Figure 7.12: Section Length for f  Start  showing f j ^ , and f  t  118  Chapter 7 - Void Detection  7.1.1.4 Comparison of Magnitude, Cumulative Error and Pattern Matching Algorithms  Table 7.1 shows the results for the comparison of the M model curves Mj through M  1 T  2 G  spectral curves to the set of  using the 4 different algorithms: point by point magnitude,  cumulative error, cumulative absolute error and the new matching algorithm.  For the point by point magnitude comparison, the highest number in the column corresponds to the Model 1 curve that best matches the curve from model M . 2G  For the  cumulative error and the cumulative absolute error, the lowest number in each respective column corresponds to the best match between curves. For the new matching algorithm, it is again the highest number that corresponds to the best match between the reference and sample models. In each column, the number corresponding to the best match is indicated in bold.  For the point by point magmtude comparison method, the reference model that was selected by the algorithm was model M . The correct curve M 1 M  1 G  was tied with two other  reference models as the second best match. However, out of 1601 possible points to match, none of the matches scored greater than 17 points, which does not provide enough differentiation to make a good selection.  For the cumulative error comparison, the reference curve that was selected was model M . u  The correct curve M  1 G  was chosen as the fourth best match. For the cumulative absolute error  comparison, the reference curve that was selected as the best match was again M . For this 1 M  algorithm the correct model M  1 G  was chosen as the second best match.  119  Chapter 7 - Void Detection  Model  Point by Point  Cumulative Error  Absolute Error  Match  M,  13  192  1181.5  53  M  1A  2  -305.3  2306.8  42  M  1 B  3  405.88  2103.2  34  M  I C  4  398.5  1578.6  33  M  1 D  5  -107.4  1606.2  53  M  1 E  1  64.2  2111.9  86  M  1 F  3  670.1  3023.3  6  M  1 G  15  -38.6  576.3  390  M  1 H  15  -66.9  859.5  137  M„  3  -356  2530.8  9  M  u  3  -6.5  2045.1  27  M  1 K  2  -25.5  2110.9  48  M  1 L  15  -137.8  2352.2  60  17  -70.8  499.9  269  6  -168.6  1021.7  146  2  -101.6  2500  78  M,  M  . . .  M  1 N  M  1 0  M  1P  11  -364.4  2081.9  22  M  1Q  6  25.5  2162.5  18  M  1 R  6  84.9  1318.6  40  M  IS  9  -70.5  1374.3  70  M  1 T  4  -434.7  2409.4  25  M  2 G  1601  0  0  1601  Table 7.1: Comparison of Matching Algorithms for M  2 G  vs. reference models M  1 A  thru M  120  Chapter 7 - Void Detection The new algorithm, however, clearly chose M  1 G  as the best match to model M . It is 2G  interesting to note that the three next best matches for the curve M M, , M H  1 M  and M , which are the three locations nearest the M 1 N  1 G  2 G  using the new algorithm were  that share a similar environment  within the model.  Although the results in Table 7.1 are presented only for the comparison between model M  2 G  and the reference models, the different curve-matching algorithms show a similar behaviour  for the other curves as well, with the new algorithm outperforming the others in all cases.  7.1.1.5 Void Detection using Pattern-Matching Algorithm  Tables 7.2(a) and 7.2(b) show the results for the matching algorithm for comparing the spectral curves for sample models M  2 A  through M , with each of the curves for models M, 2T  through M . Each entry in the table is the number of wins that each of the reference curves was 1T  assigned when compared to each of the sample curves. The highest number of wins for each model is shown in bold.  If the shape of the S curves are determined by the location of the voids in the models, 21  then the largest number of wins for the sample model M model M , as should M 1 A  2 B  to M  ] B  2 A  should correspond to the reference  and so on. This should lead to all of the entries on the diagonal  of the table being highlighted in bold. As can be seen from Tables 7.2(a) and 7.2(b) this is indeed the case. The curves from the sample model are correctly matched to the curves from the reference model. This shows that there is information about the location of the voids being transmitted in the S spectrum, and it is possible to determine the location of the voids within the 21  interior of the wooden models.  121  C h a p t e r 7 - V o i d Detection  Model  M  M,  322  n/a  68  102  n/a  n/a  43  101  40  36  n/a  24  n/a  53  106  n/a  n/a  49  43  100  75  n/a  31  n/a  416  235  n/a  n/a  148  164  205  46  n/a  162  n/a  122  277  n/a  n/a  35  66  43  8  n/a  M, M M  A  1 B  1 C  2  M  2 A  M  2 B  M  2 C  M  2 D  M  2 E  M  M  2 F  2 G  M  2 H  M  2I  M  2J  M  1 D  62  n/a  81  91  n/a  n/a  36  37  37  71  n/a  M  1 E  28  n/a  38  36  n/a  n/a  40  35  34  102  n/a  M  1 F  43  n/a  55  38  n/a  n/a  359  18  36  30  n/a  M  1 G  70  n/a  102  47  n/a  n/a  42  239  60  9  n/a  66  n/a  79  31  n/a  n/a  98  215  278  10  n/a  M„  35 ''  n/a  27  35  n/a  n/a  82  30  38  467  n/a  M„  67  n/a  41  50.  n/a  n/a  146  47  20  61  n/a  M  1 K  63  n/a  12  19  n/a  n/a  '53  31  75  32  n/a  M  I L  25  n/a  89  34  n/a  n/a  209  21  33  59  n/a  51  n/a  61  75  n/a  n/a  4  187  109  9  n/a  187  n/a  94  46  n/a  n/a  92  148  129  16  n/a  67  n/a  21  48  n/a  n/a  40  38  27  234  n/a  M  I H  M,  .  M  M  1 N  M  1 0  M  1 P  47  n/a  58  28  n/a  n/a  32  26  76  55  n/a  M  1 Q  82  n/a  85  41  n/a  n/a  27  37  88  70  n/a  M  1 R  126  n/a  104  92  n/a  n/a  29  71  99  97  n/a  M  1 S  87  n/a  57  86  n/a  n/a  17  57  40  40  n/a  M  1 T  48  n/a  11  140  n/a  n/a  19  16  74  27  n/a  Table 7.2: (a) Number of comparison wins for sample models M thru M vs. reference models 2  2J  M, thru M . Note n/a indicates data unavailable. 1X  122  Chapter 7 - Void Detection  Model  M  M,  n/a  33  121  99  30  n/a  n/a  99  139  n/a  M  1 A  n/a  16  53  71  29  n/a  n/a  16  89  n/a  M  1 B  n/a  76  35  99  77  n/a  n/a  53  59  n/a  M  1 C  n/a  23  155  98  34  n/a  n/a  115  73  n/a  M  1 D  n/a  55'  42  27  44  n/a  n/a  93  95  n/a  M  I E  n/a  84  43  51  22  n/a  n/a  13  56  n/a  M  1 F  n/a  161  7  18  43  n/a  n/a  26  43  n/a  M  1 G  n/a  16  83  98  11  n/a  n/a  80  71  n/a  M  1 H  n/a  55  60  200  26  n/a  n/a  159  54  n/a  n/a  40 "'  7  39  158  n/a  n/a  49  44  n/a  n/a  37.  .42  66  29  n/a  , n/a .. ..34  58  n/a  n/a  96  61  62  118  n/a  n/a  28  48  n/a  n/a  495  26  74  27  n/a  n/a  86  58  n/a  n/a  45  390  92  23  n/a  n/a  69  169  n/a  n/a  49  109  290  23  n/a  n/a  194  58  n/a  n/a  33  85  40  574  n/a  n/a  5  102  n/a  M„  M  M  2 L  : ;  2 M  M  2 N  M  2 0  M  2 P  M  2 Q  M  2 R  M  2 S  M  2 T  M  1 K  M  1 L  M  1 M  M  1 N  M  1 0  M  1 P  n/a  139  29  30  109  n/a  n/a  13  91  n/a  M  I Q  n/a  32  60  19  55  n/a  n/a  27  83  n/a  M  1 R  n/a  74  139  113  24  n/a  n/a  441  115  n/a  s  n/a  23  139  43  106  n/a  n/a  36  904  n/a  1 T  n/a  41  25  22  44  n/a  n/a  49  51  n/a  M, M  '  2 K  Table 7.2 (b) Number of comparison wins for sample models M  2 K  thru M  2 T  vs. reference models  M, thru M . Note n/a indicates data unavailable. 1T  123  Chapter 7 - Void Detection The graphs of the S response curves for the reference model M„ with no elements 21  removed, and M  1 A  through M , with single model elements A through T removed, are shown in 1T  Appendix F. Appendix G shows the results for the model rotated 90 degrees.  Data for Models M , M , M , M , M , M , M , M 2 A  2 D  2E  2J  2K  2P  2Q  2 X  are unavailable due to incorrect  data returned by the Wiltron Vector Analyser. For these sample models, the data were returned as zeros. It was not possible to repeat these measurements later as the original test setup was no longer available.  7.2  Determination of the Outer Dimensions of a Cylindrical Model  The void detection algorithms presented in the preceding sections of this thesis depend upon the ability to compare unknown samples with the results from pre-scanned models. In order for an instrument based on this device to be useful, it would be necessary to make some initial selection of which models could be used for the comparisons. In practice, a catalogue of the various voids that would be found in a tree or log would be made from scanning a number of representative samples from trees or poles of various diameters.  When the initial characterizations for the scanner were performed, it was noticed that one of the abilities of the scanner was to easily determine the diameter of a cylinder placed between the antennas. The ability to determine the external size of the object under test could be used to provide the information required to perform the initial model selection from the catalogue described above.  If pre-scanned spectral information is stored according to the external  dimensions of the models tested, a new sample can then be compared to prestored models using size as one of the initial determining criteria.  124  C h a p t e r 7 - E x p e r i m e n t a l Results  Transmission Coefficient [S21 ] 10.00-  i  J  i  i  L  5 cm Metal Cylinder 8 cm Metal Cylinder 12 cm Metal Cylinder 24 cm Metal Cylinder  5.00 0.00 -5.00 01 T3  (D (4) (3) (2)  f  ' E •-10.00  Peakl  03  j?-15.00  V :  \i  J  -2D. 00 H  Peak 3  M  \  I;' \: »  Peak 4  Peak 6  k  p |< 5 ea  -25.00 -30.00 1.00  1  1  i  1  2.00  3.00  4.00  5.00  i  1  1  1  6.00 7.00 8.00 Frequency (GHz)  1  1  1  r  3.00 10.00 11.00 12.00 13.00  Figure 7.14: S log Magnitude versus Frequency for Metal Cylinders of varying size 21  Peak Frequency vs Metal Cylinder Diameter  Peaks Peaks .—  3  X— —  X- -  re a  •—•  X  Peak4  X ~~ -  — - x - ~~ '  Peak 3 Peak 2  x---  Peakl x  Cylinder Diameter (cm)  Figure 7.15: Plot of Peak Frequency versus Cylinder Size for Metal Cylinders 125  C h a p t e r 7 - E x p e r i m e n t a l Results  Transmission Coefficient (S21) i  i  i  i  i  i  i  i_  B cm Wood Cylinder 10 cm Wood Cylinder 12 cm Wood Cylinder  Peak 6  -30. DO 1.D0  1  1  1  2.D0  3.00  4.00  1  1  1  5.00  B.00  7.00  1  1  B.00  9.00  1  1  1  r  10.00 11.00 12.00 13.00  Frequency (GHz)  Figure 7.16: S log Magnitude versus Frequency for Wood Cylinders of varying size 21  Peak Frequency vs Wood Cylinder Diameter  X_  x  5 &  — x  X  x Peak5  x  X  *  x~  PeakE  X Peak 4  - x Peak 3  x  4) X  x  X  x Peak 2  x  x  re X  9  ID  Peakl  11  Cylinder Diameter (cm)  Figure 7.17: Plot of Peak Frequency versus Cylinder Size for Wood Cylinders 126  C h a p t e r 7 - E x p e r i m e n t a l Results  The ability to detect the size of the cylinder between the antennas was characterized by the change in the frequency of six major valleys in the log Magnitude versus Frequency curves shown in Figure 7.14. If the frequency of each of these peaks is plotted versus the size of the cylinder and fitted with a linear interpolation, the result is a family of graphs. Figure 7.15 shows the family for the series of metal cylinders whose spectral curves are shown in Figure 7.14.  From the graph shown in Figure 7.15, it is quite easy to determine the diameter of an unknown cylinder by interpolating the results. Although the family of curves shown in Figure 7.15 is for metal cylinders, Figures 7.16 and 7.17 show the results for a set of wooden cylinders of differing diameters. The slopes of the curves differ from that for the metallic cylinders, but the shift in peak position changes in a similar fashion to that for the metallic cylinders.  127  Chapter 8  8.0  Conclusions and Future Work  The goal of this thesis is to determine if the detection of large scale voids in wooden objects was possible using a simple microwave rf device. The hypothesis for this thesis is that, due to the dielectric nature of the materials that make up wood, there should be a difference between the interaction of radio waves with an object composed of these dielectric materials when compared to the interaction of the radio waves with voids in these objects that contain no dielectric materials. It was also hypothesized that due to the complex nature of the materials and the construction of wood that these interactions would be frequency-dependent and that this frequency dependence could be used to locate voids within a solid wooden object.  This thesis has clearly shown that the transmission of electromagnetic waves through an object are affected by the difference in dielectric properties (presence or absence of a dielectric material) inside the object. It has also been demonstrated that the differences in the dielectric properties inside the object can be detected outside the object via the transmitted S ispectrum. It 2  has also been demonstrated that the effects on the transmitted EM waves are position-dependent and not simply a property of the bulk material, and that the effects are also frequency-dependent over an ultra-wide range of frequencies. It has also been shown that the frequency-dependent effects can be used to locate the position of voids within a dielectric object. It was also shown that the object's outer dimensions could be determined by examining the transmitted spectrum.  The construction of a prototype ultra-wideband scanner has demonstrated that, in addition to meeting the theoretical goals of this project, a practical instrument design is also possible. This prototype design provides the groundwork for an instrument capable of detecting large-scale voids in solid wood objects such as trees or telephone poles that is simple in construction, low in cost and requires only a simple comparison routine rather than a complete tomographic reconstruction. 128  Chapter 8 - Conclusions and Future Work  In addition to meeting the goals of large-scale void detection, this project also developed a new type of ultra-wideband antenna. The FDL antenna has an S reflection coefficient with a n  flatter response over an ultra-wide bandwidth than that of all existing antenna designs. The development of this novel antenna, and the corroboration of the physical design by computer modelling, should allow for further improvements in other areas where an ultra-wideband antenna is required such as impulse and ground penetrating radar and ultra-wideband communications. The FDL antenna is now covered under the World International Property Organization Patent Cooperation Treaty (PCT) Publication Number WO 02/089253 A l [81], US Patent 20040150579, with further patent filings underway with individual applications filed in the US, Canada and Europe.  This thesis also presents a new algorithm for matching curves in 2D space. This algorithm performs better than standard comparison methods by allowing for offset errors and errors caused by short duration noise.  8.1  Future Work  While this thesis has answered a number of fundamental questions about the FDL antenna, it has also raised new areas for further investigation. The work on the FDL antenna and the scanner, while substantial, has just begun.  8.1.1  FDL Antenna  The optimal FDL antenna design described in this thesis is just one of many possible configurations covered in the FDL patent application, as shown in Figure 4.5. The profile for the 129  Chapter 8 - Conclusions and Future Work ground planes for the FDL antenna for this thesis is that of an ellipse. The other profiles, such as circular, parabolic and irregular that were mentioned, still need to be investigated to determine the complete characteristics for those styles of FDL antenna. The effects of these different profiles on the S j j reflection coefficient and the cross- and co-polarization are currently unknown. In addition, the effects of changing the overall size of the antenna as well as the shape of the antenna's active member and ground planes will need to be examined now that a basic model for computer analysis has been created.  8.1.2  Ultra-wideband Scanner  In addition to the FDL antenna itself, there are a number of avenues of further work to be done in the area of the ultra-wideband scanner. The work for this thesis involved the detection of singular regularly shaped voids in solid models of regular composition. In the field, there exists the need to detect multiple irregularly shaped voids in objects under examination and voids in objects of irregular composition. Work also needs to be done to determine the smallest size voids that can be detected for an antenna/scanner system within a given frequency range and the positional resolution of the scanner system.  The sliding window method used for a comparison of the spectral curves worked well for this thesis. This method of analysis, however, depends on having pre-determined models for comparison in order to perform its void detection. This approach works well in the lab and would work well in a controlled environment where a database of previously scanned samples could be used for comparison. Thus this scanner system may be well suited to a lumber mill or pole manufacturing/testing facility where large numbers of objects of similar size and shape are processed.  130  Chapter 8 - Conclusions and Future Work 8.1.3  Full Tomographic Inversion  An alternate solution to the detection problem would be a full tomographic imaging solution in which no predetermined models are required. This approach is currently being investigated by Kim Lam, one of the other students in Dr. Matt Yedlin's research group working on the dielectric scattering approach [26].  8.1.4  Other Fields  While the work in this thesis focusses on the detection of voids in wooden models, the applications for an ultra-wideband antenna are numerous. Currently, there is much research taking place on the development of ultra-wideband systems for Ground Penetrating Radar (GPR), for Radar Imaging and for highspeed/high bandwidth communications. 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DD  -i  1  1  1  1  1  1  •20.00 -\  I  I  i  i  i  _  Ground Plane Angle 0 degrees  -25.00 -30.00 1.00  1  I  !  2.00  3.00  4.00  I  I  ,  5.00 G.00 7.00  1  8.00  1  ,  ,  ,  ,  9.00 10.00 11.00 12.00 13.00  Frequency [GHz]  Figure A l : S Reflection Coefficient for FDL Antenna for Flare Angles of 0 degrees n  Reflection Coefficient (S11 ] 10.00  -J  1  1  1  1  1  1  1  1  1  1  1  1_  5.00 Q.00 -5.00 -10.00 I  '-15.0D -20.00 H  Ground Plane Angle 9 degrees  -25.00 -30.00 1.00  1  2.00  |  |  3.00 4.00  |  |  |  5.00 G.00 7.00  1  1  ,  1  1  1  B.00 9.00 10.00 11.00 12.00 13.00  Frequency (GHz]  Figure A2: S Reflection Coefficient for FDL Antenna for Flare Angles of 9 degrees u  143  Appendix A - FDL S Reflection Coefficient vs. Flair Angle for Flat Ground Planes n  Reflection Coefficient (S11)  —j  1.DD  2.00  !  |  3.00 4.00  I  I  5.00 6.00  I  1  7.00  8.00  I  — [  9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure A3: S Reflection Coefficient for FDL Antenna for Flare Angles of 18 degrees n  Reflection Coefficient [S11 ] 10.00  -i  1  i  i  i  i  i  i  i_  5.00 0.00  I -5.00 CD n  1 -10.00 ro j?-15.00-20.00 -  Ground Plane Angle 2G degrees  -25.00 -30.00 1.00  — i  2.00  1  1  3.00 4.00  1  1  5.00 6.00  1  1  7.00 8.00  1  1  1  1  r  9.00 10.00 11.00 12.00 13.00  Frequency [GHz)  Figure A4: S Reflection Coefficient for FDL Antenna for Flare Angles of 26 degrees n  144  Appendix A - FDL S Reflection Coefficient vs. Flair Angle for Flat Ground Planes n  Reflection Coefficient (S11) 10.00  _i  i  i  i  i  i  i  i  i  i  i  i_  5.00 0.00 -. -5.00 -10.00 •15.00 -20.00  Ground Plane Angle 33 degrees  •25.00 -30.00 1.00  — i  2.00  1  3.00  1  1  1  4.0Q 5.00 6.00  1  1  1  1  1  1  1—  7.00 B.00 9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure A5: S Reflection Coefficient for FDL Antenna for Flare Angles of 33 degrees n  Reflection Coefficient [S11 ] 10.00  1  i  i  i_  Ground Plane Angle 45 degrees  -30.00 1.00  — i  2.00  1  1  3.00 4.00  1  1  5.00 6.00  1  1  7.00 8.00  1  1  1  1  r  9.00 10.00 11.00 12.00 13.00  Frequency [GHz]  Figure A6: S Reflection Coefficient for FDL Antenna for Flare Angles of 45 degrees u  145  Appendix A - FDL S Reflection Coefficient vs. Flair Angle for Flat Ground Planes n  Reflection Coefficient [S11 ] i  i  i  j  -20.00  i_  Ground Plane Angle 43 degrees  -25.00 -30.00 1.00  2.00  3.00  4.00  5.00 B.00 7.00 B.00 3.00 10.00 11.00 12.00 13.D0 Frequency (GHz)  Figure A7: S Reflection Coefficient for FDL Antenna for Flare Angles of 49 degrees n  Reflection Coefficient (511) _i  1.00  -i  2.00  i  i  3.00 4.00  i  i  5.00 6.00  i _  1  7.00  1  1  1  r  1  1  B.00 9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure A8: S Reflection Coefficient for FDL Antenna for Flare Angles of 53 degrees n  146  Appendix B - Example FEKO Model Creation File For FDL Antenna ** Default PRE f i l e f o r r a d i a t i o n problems ** Date created: March 13 2003 ** Variables ** Optional s c a l i n g f a c t o r (e.g. s e t to 0.001 i f a l l geometrical ** coordinates etc. are to be defined i n mm instead of metres) #scaling = 1 ** Frequency and wavelength #freq =1.5el0 ** frequency i n Hertz #lam = #c0/#freq ** wavelength i n metre, #c0 = speed of l i g h t i n vacuum #lam = #lam/#scaling ** scale the wavelength as desired (e.g. to mm) ** Parameters f o r segmentation #seg_rad = #lam/1000 ** radius of the wire segments #seg_len = #lam/10 ** maximum length of wire segments # t r i _ l e n = #lam/12 ** maximum edge length f o r t r i a n g u l a r patches IP #seg_rad # t r i _ l e n #seg_len ** Geometry o f r a d i a t i n g structure ** A FEMAP model may be included with the IN card ** IN 1 3 "filename.ext" ** DP DP  Add feed points GAM1 GAM2  0 0000 0 0000  -0 .0025 -0 .0025  0.00250 -0.00251  DP DP  GBM1 GBM2  0 0000 0 0000  0.0025 0.0025  0.00250 -0.00251  DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP  GA1 GA2 GA3 GA4 GA5 GA6 GA7 GA8 GA9 GA10 GA11 GA12 GA13 GA14 GA15 GA16 GA17 GA18 GA19 GA20 GA21 GA22 GA23 GA24  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  -0 .0025 -0 .0025 -0 .0035 -0 .0035 -0 .0046. -0 .0046 -0 .0058 -0 .0058 -0 .0072 -0 .0072 -0 .0086 -0 .0086 -0 .0102 -0 .0102 -0 .0120 -0 .0120 -0 .0140 -0 .0140 -0 .0161 -0 .0161 -0 .0185 -0 0185 -0 .0211 -0 0211  0.0250 -0.0250 0.0115  0000 0000 0050 0050 0100 0100 0150 0150 0200 0200 0250 0250 0300 0300 0350 0350 0400 0400 0450 0450 0500 0500 0550 0550  T0.0115  0.0070 -0.0070 0.0044 -0.0044 0.0030 -0.0030 0.0025 -0.0025 0.0025 -0.0025 0.0025 -0.0024 0.0025 -0.0022 0.0027 -0.0019 0.0037 -0.0017 0.0058 -0.0014  Appendix B - Example FEKO Model Creation File For FDL Antenna DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP DP  GA25 GA26 GA27 GA28 GA29 GA30 6A31 GA32 6A33 GA34 GA35 GA36 GA37 GA38 GA39 GA40 GA41 GA42 GA43 GA44  LA  1  PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM  GA1 GA3 GA5 GA7 GA9 GA11 GA13 GA15 GA17 GA19 GA21 GA23 GA25 GA27 GA29 GA31 GA33 6A35 GA37 GA39 GA41  DP DP DP DP DP DP DP DP  GB1 GB2 GB3 GB4 GB5 GB6 GB7 GB8  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  GA3 GA5 GA7 GA9 GA11 GA13 GA15 GA17 GA19 GA21 GA23 GA25 GA27 GA29 GA31 GA33 GA35 GA37 GA39 GA41 GA43  GA4 GA6 GA8 GA10 GA12 GA14 GA16 GA18 GA20 GA22 GA24 GA26 GA28 GA30 GA32 GA34 GA36 GA38 GA40 GA42 GA44  GA2 GA4 GA6 GA8 GA10 GA12 GA14 GA16 GA18 GA20 GA22 GA24 GA26 GA28 GA30 GA32 GA34 GA36 GA38 GA40 GA42  0600 0600 0650 0650 0700 0700 0750 0750 0800 0800 0850 0850 0900 0900 0950 0950 1000 1000 1050 1050  -0.0239 -0.0239 -0.0271 -0.0271 -0.0306 -0.0306 -0.0344 -0.0344 -0.0386 -0.0386 -0.0432 -0.0432 -0.0483 -0.0483 -0.0539 -0.0539 -0.0600 -0.0600 -0.0668 -0.0668  GAM2  GAM1  0 0 0 0 0 0 0 0  0.0025 0.0025 0.0035 0.0035 0.0046 0.0046 0.0058 0.0058  0000 0000 0050 0050 0100 0100 0150 0150  0.0094 -0.0012 0.0162 -0.0009 0.0303 -0.0006 0.0392 -0.0004 0.0410 -0.0001 0.0410 0.0002 0.0410 0.0004 0.0410 0.0007 0.0410 0.0010 0.0410 0.0013  0.0250 -0.0250 0.0115 -0.0115 0.0070 -0.0070 0.0044 -0.0044  Appendix B - Example FEKO Model Creation File For FDL Antenna D P  6 B 9  0  0 2 0 0  0  0 0 7 2  0 . 0 0 3 0  D P  G B 1 0  0  0 2 0 0  0  0 0 7 2  - 0 . 0 0 3 0  D P  G B 1 1  0  0 2 5 0  0  0 0 8 6  0 . 0 0 2 5  D P  G B 1 2  0  0 2 5 0  0  0 0 8 6  - 0 . 0 0 2 5  D P  G B 1 3  0  0 3 0 0  0  0 1 0 2  0 . 0 0 2 5  D P  G B 1 4  0  0 3 0 0  0  0 1 0 2  - 0 . 0 0 2 5  D P  G B 1 5  0  0 3 5 0  0  0 1 2 0  0 . 0 0 2 5  D P  G B 1 6  0  0 3 5 0  0  0 1 2 0  - 0 . 0 0 2 4  D P  G B 1 7  0  0 4 0 0  0  0 1 4 0  0 . 0 0 2 5  D P  G B 1 8  0  0 4 0 0  0  0 1 4 0  - 0 . 0 0 2 2  D P  G B 1 9  0  0 4 5 0  0  0 1 6 1  0 . 0 0 2 7  D P  G B 2 0  0  0 4 5 0  0  0 1 6 1  - 0 . 0 0 1 9  D P  G B 2 1  0  0 5 0 0  0  0 1 8 5  0 . 0 0 3 7  D P  G B 2 2  0  0 5 0 0  0  0 1 8 5  - 0 . 0 0 1 7  D P  G B 2 3  0  0 5 5 0  0  0 2 1 1  0 . 0 0 5 8  D P  G B 2 4  0  0 5 5 0  0  0 2 1 1  - 0 . 0 0 1 4  D P  G B 2 5  0  0 6 0 0  0  0 2 3 9  0 . 0 0 9 4  D P  G B 2 6  0  0 6 0 0  0  0 2 3 9  - 0 . 0 0 1 2  D P  G B 2 7  0  0 6 5 0  0  0 2 7 1  0 . 0 1 6 2  D P  G B 2 8  0  0 6 5 0  0  0 2 7 1  - 0 . 0 0 0 9  D P  G B 2 9  0  0 7 0 0  0  0 3 0 6  0 . 0 3 0 3  D P  G B 3 0  0  0 7 0 0  0  0 3 0 6  - 0 . 0 0 0 6  D P  G B 3 1  0  0 7 5 0  0  0 3 4 4  0 . 0 3 9 2  D P  G B 3 2  0  0 7 5 0  0  0 3 4 4  - 0 . 0 0 0 4  D P  G B 3 3  0  0 8 0 0  0  0 3 8 6  0 . 0 4 1 0  D P  G B 3 4  0  0 8 0 0  0  0 3 8 6  - 0 . 0 0 0 1  D P  G B 3 5  0  0 8 5 0  0  0 4 3 2  0 . 0 4 1 0  D P  G B 3 6  0  0 8 5 0  0  0 4 3 2  0 . 0 0 0 2  D P  G B 3 7  0  0 9 0 0  0  0 4 8 3  0 . 0 4 1 0  D P  G B 3 8  0  0 9 0 0  0  0 4 8 3  0 . 0 0 0 4  D P  G B 3 9  0  0 9 5 0  0  0 5 3 9  0 . 0 4 1 0  D P  G B 4 0  0  0 9 5 0  0  0 5 3 9  0 . 0 0 0 7  D P  G B 4 1  0  1 0 0 0  0  0 6 0 0  0 . 0 4 1 0  D P  G B 4 2  0  1 0 0 0  0  0 6 0 0  0 . 0 0 1 0  D P  G B 4 3  0  1 0 5 0  0  0 6 6 8  0 . 0 4 1 0  D P  G B 4 4  0  1 0 5 0  0  0 6 6 8  0 . 0 0 1 3  L A  3  P M  G B 1  G B 3  G B 4  G B 2  P M  G B 3  G B 5  G B 6  G B 4  P M  G B 5  G B 7  G B 8  G B 6  P M  G B 7  G B 9  G B 1 0  G B 8  P M  G B 9  G B 1 1  G B 1 2  G B 1 0  P M  G B 1 1  G B 1 3  G B 1 4  G B 1 2  P M  G B 1 3  G B 1 5  G B 1 6  G B 1 4  P M  G B 1 5  G B 1 7  G B 1 8  G B 1 6  P M  G B 1 7  G B 1 9  G B 2 0  G B 1 8  P M  G B 1 9  G B 2 1  G B 2 2  G B 2 0  P M  G B 2 1  G B 2 3  G B 2 4  G B 2 2  P M  G B 2 3  G B 2 5  G B 2 6  G B 2 4  P M  G B 2 5  G B 2 7  G B 2 8  G B 2 6  P M  G B 2 7  G B 2 9  G B 3 0  G B 2 8  G B M 2  G B M 1  Appendix B - Example FEKO Model Creation File For FDL Antenna P M  6 B 2 9  G B 3 1  G B 3 2  P M  G B 3 1  G B 3 3  G B 3 4  G B 3 0 G B 3 2  P M  G B 3 3  G B 3 5  G B 3 6  G B 3 4  P M  G B 3 5  G B 3 7  G B 3 8  G B 3 6  P M  G B 3 7  G B 3 9  G B 4 0  G B 3 8  P M  G B 3 9  G B 4 1  G B 4 2  G B 4 0  P M  G B 4 1  G B 4 3  G B 4 4  G B 4 2  D P  A M O  0  0 0 0 0  0  0 0 0 0  0 . 0 0 0 0  D P  A M I  0  0 0 0 0  0  0 0 0 0  - 0 . 0 0 2 5  D P  A M 2  0  0 0 0 0  0  0 0 0 0  0 . 0 0 2 5  D P  A M 3  0  0 0 5 0  0  0 0 0 0  - 0 . 0 0 2 5  D P  A M 4  0  0 0 5 0  0  0 0 0 0  0 . 0 0 2 5  D P  A M 5  0  0 1 0 0  0  0 0 0 0  - 0 . 0 0 2 5  D P  A M 6  0  0 1 0 0  0  0 0 0 0  0 . 0 0 2 5  D P  A M 7  0  0 1 5 0  0  0 0 0 0  - 0 . 0 0 2 5  D P  A M 8  0  0 1 5 0  0  0 0 0 0  0 . 0 0 2 5  D P  A M 9  0  0 2 0 0  0  0 0 0 0  - 0 . 0 0 2 5  D P  A M 1 0  0  0 2 0 0  0  0 0 0 0  0 . 0 0 2 5  D P  A M 1 1  0  0 2 5 0  0  0 0 0 0  - 0 . 0 0 2 5  D P  A M 1 2  0  0 2 5 0  0  0 0 0 0  0 . 0 0 2 5  D P  A M I  3  0  0 3 0 0  0  0 0 0 0  - 0 . 0 0 2 5  D P  A M I  4  0  0 3 0 0  0  0 0 0 0  0 . 0 0 2 5  D P  A M 1 5  0  0 3 5 0  0  0 0 0 0  - 0 . 0 0 2 5  D P  A M 1 6  0  0 3 5 0  0  0 0 0 0  0 . 0 0 2 4  D P  A M I  7  0  0 4 0 0  0  0 0 0 0  - 0 . 0 0 2 5  D P  A M I  8  0  0 4 0 0  0  0 0 0 0  0 . 0 0 2 2  D P  A M 1 9  0  0 4 5 0  0  0 0 0 0  - 0 . 0 0 2 7  D P  A M 2 0  0  0 4 5 0  0  0 0 0 0  0 . 0 0 1 9  D P  A M 2 1  0  0 5 0 0  0  0 0 0 0  - 0 . 0 0 3 7  D P  A M 2 2  0  0 5 0 0  0  0 0 0 0  D P  A M 2 3  0  0 5 5 0  0  0 0 0 0  D P  A M 2 4  0  0 5 5 0  0  0 0 0 0  0 . 0 0 1 4  D P  A M 2 5  0  0 6 0 0  0  0 0 0 0  - 0 . 0 0 9 4  D P  A M 2 6  0  0 6 0 0  0  0 0 0 0  0 . 0 0 1 2  D P  A M 2 7  0  0 6 5 0  0  0 0 0 0  - 0 . 0 1 6 2  D P  A M 2 8  0  0 6 5 0  0  0 0 0 0  0 . 0 0 0 9  D P  A M 2 9  0  0 7 0 0  0  0 0 0 0  - 0 . 0 3 0 3  D P  A M 3 0  0  0 7 0 0  0  0 0 0 0  0 . 0 0 0 6  D P  A M 3 1  0  0 7 5 0  0  0 0 0 0  - 0 . 0 3 9 2  D P  A M 3 2  0  0 7 5 0  0  0 0 0 0  0 . 0 0 0 4  D P  A M 3 3  0  0 8 0 0  0  0 0 0 0  - 0 . 0 4 1 0  D P  A M 3 4  0  0 8 0 0  0  0 0 0 0  0 . 0 0 0 1  D P  A M 3 5  0  0 8 5 0  0  0 0 0 0  - 0 . 0 4 1 0  D P  A M 3 6  0  0 8 5 0  0  0 0 0 0  - 0 . 0 0 0 2  D P  A M 3 7  0  0 9 0 0  0  0 0 0 0  - 0 . 0 4 1 0  D P  A M 3 8  0  0 9 0 0  0  0 0 0 0  - 0 . 0 0 0 4  D P  A M 3 9  0  0 9 5 0  0  0 0 0 0  - 0 . 0 4 1 0  D P  A M 4 0  0  0 9 5 0  0  0 0 0 0  - 0 . 0 0 0 7  D P  A M 4 1  0  1 0 0 0  0  0 0 0 0  - 0 . 0 4 1 0  D P  A M 4 2  0  1 0 0 0  0  0 0 0 0  - 0 . 0 0 1 0  D P  A M 4 3  0  1 0 5 0  0  0 0 0 0  - 0 . 0 4 1 0  0 . 0 0 1 7 .  - 0 . 0 0 5 8  Appendix B - Example FEKO Model Creation File For FDL Antenna DP  AM44  LA  2  BT BT BT PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM  AMO AM0 AMO AM3 AM5 AM7 AM9 AM11 AMI 3 AMI 5 AMI 7 AMI 9 AM21 AM23 AM25 AM27 AM29 AM31 AM33 AM35 AM37 AM39 AM41  ** LA PM PM  0.1050  AM4 AM3 AMI AM5 AM7 AM9 AM11 AMI 3 AMI 5 AMI 7 AMI 9 AM21 AM23 AM25 AM27 AM29 AM31 AM33 AM35 AM37 AM39 AM41 AM43  AM2 AM4 AM3 AM6 AM8 AM10 AM12 AMI 4 AMI 6 AMI 8 AM20 AM22 AM24 AM26 AM28 AM30 AM32 AM34 AM36 AM38 AM40 AM42 AM44  -0.0013  AM4 AM6 AM8 AM10 AMI 2 AMI 4 AMI 6 AMI 8 AM20 AM22 AM24 AM26 AM28 AM30 AM32 AM34 AM36 AM38 AM40 AM42  Add connecting strips 0 6BM1 GBM2 AMI AMO GAM1 GAM2 AMI AMO  ** Apply the scaling factor SF 1 ** EG ** GF ** FR ** AE ** FF ** SP EN  0.0000  AM2 AM2  #scaling  End of geometric input 1 0 0 0 0 Greens Functions f o r Homogenous space 0 Set the frequency 1 0 15e9 500e6 Voltage gap excitation at end of active member 0 0 2 0 1 0 Radiation patterns calculated with the FF card 1 360 360 0 0 0 1 SParameters calculated with the SP card 50  Appendix C - 1GHz to 13.5 GHz Results for Model Heights 0 to 91 cm Transmission Coefficient (S21) 10. DO  I  _J  I  I  I  I  I  L_  5.00 0.00 5, -5.00 cu  1= -1Q.0Q H C3I CD  s  §•-15.00 -20.00  No Model Present [Baseline]  -25.00 H -30.00 —i 1 1 1 1 1 1 1 1 1 1 1 — 1.00 2.00 3.00 4.00 5.00 G.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 Frequency (GHz)  gure CI: Transmission Coefficient S spectrum showing baseline with no model present 21  Transmission Coefficient (S21)  1.00  ~i  1  1  1  1  1  1  1  1  1  r-  2.00 3.00 4.00 5.00 G.00 7.00 B.00 9.00 10.00 11.00 12.D0 13.00 Frequency (GHz)  Figure C2: Transmission Coefficient S spectrum for Model Heights 2 to 13 cm 21  152  Appendix C - 1GHz to 13.5 GHz Results for Model Heights 0 to 91 cm Transmission Coefficient [521] 10.00 •  _l  I  I  I  I  I  I  I  I  L_  5.00 H 0.00 |  -5.00 -  CD T3  1 -10.00 as  j?-15.00 -20.00 Model Heights 15 to 20 cm -25.00 -30.00 1.00  —i  1  1  1  1  1  1  1  1  1  1  1—  2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 Frequency (GHz)  Figure C3: Transmission Coefficient S spectrum for Model Heights 15 to 20 cm 21  Transmission Coefficient (S21) 10.00  _i  1  1  1  1  i  i  i  i  i  i  i_  j?-15.00 -20.00 Model Heights 23 to 28 cm  -25. DD -30.00 1.00  — i  1  1  1  1  1  1  1  1  1  1  1—  2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 Frequency (GHz)  Figure C4: Transmission Coefficient S , spectrum for Model Heights 23 to 28 cm 2  153  Appendix C - 1GHz to 13.5 GHz Results for Model Heights 0 to 91 cm Transmission Coefficient (S21) 10.00  _l  L_  _l  L_  2  g -15.00 H 1  -25.00 Model Heights 30 to 38 cm -30.00 -l 1.00  1 1 1 1 1 r 2.00 3.00 4.00 5.00 G.00 7.00 8.00 9.00 10.00 11.00 12.0D 13.00 Frequency (GHz)  Figure C5: Transmission Coefficient S spectrum for Model Heights 30 to 38 cm 21  Transmission Coefficient (S21)  -30.00 -i 1.00  1 1 1 1 1 1 1 1 1 1 i r2.00 3.00 4.00 5.00 G.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 Frequency (GHz]  Figure C6: Transmission Coefficient S spectrum for Model Heights 41 to 56 cm 21  154  Appendix C - 1GHz to 13.5 GHz Results for Model Heights 0 to 91 cm Transmission Coefficient [S21] 10.00  -30.00 -i 1.00  i  _i  i  i  i  i  i  i_  1 1 1 1 1 1 1 r2.00 3.00 4.00 5.00 6.00 7.00 8.00 3.00 10.00 11.00 12.00 13.00 Frequency (GHz)  Figure C7: Transmission Coefficient S spectrum for Model Heights 58 to 76 cm 21  Transmission Coefficient (S21) 10.00  -I  L_  -25.00 H -30.00 1.00  Model Heights 79 to 91 cm r1 1 1 1 1 1 1 1 1 1 r 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.D0 11.00 12.00 13.00 Frequency [GHz]  Figure C8: Transmission Coefficient S spectrum for Model Heights 79 to,91 cm 21  Appendix D - Cougar A2CP12029 Wideband Amplifier Specifications  PRELIMINARY  COMPONENTS  1  |  6.0 T012.0 GHz SMA CASCADED AMPLIFIER an****™  A2CP12029  HigtiGita...  os mm 23.0 03  High Output Level  Mtob1Mitf0«ftrlA  *37dBm *S1 dBm  High Second Orttet UP.  High Reverse Isolation  35  CougarPak"' SUA Package  (tvKyatage)  dB  High Performance Thin Film CougarPak" SMA Package 4  SPECIFICATIONS Parameter  Typical  Guaranteed' 0»SO*C -55 to+85* C te-tMWt  Smtll»gn>l a»ln<Hn.)  2J,0d6  SD.SdB  4.0 dB  45 dB  l«l  2.0:1  WOdB  tUIn l*tKtiM«« <U«&)  IrputOuput  Pwwtf Output (IIIft.) « tdBeomp.  SSJmA  WOM tN ' WHU I  1.0 dB  +a&.$e©« 35 OB  acCunknKMn.)  ^2  *tJ!dB  Mote* Figure SWW (Mux.)  —  +280 dBm  -  -  350 «1A  >-  r ^ . g c  A2CP12029  Second Outer Harmonic Intercept Pol* Second OKlerTwoTone Intercept Point TKIrd OrdefTwo Tone intercept Point  IT  A B S O L U T E M A X I M U M  Stooge Temperature Maximum Case Temperature , t l a x i m u t i DC Voltage Maximum Continuous RF Input Power Maximum Shan Term Input Power (1 Minul* Max.) Maximum Peak Power (3 u*as Max.) O Series Burn-In Temperature Thermal Resistance' (8je) Junction Temperature Rise Above Case (Tic)  +57 dBm +51 dBm +37 d B m  RATINGS -62 to 125* C +B5* C  Volts +16 dBm 100 Milivattt 05 Watt +12  *85'C •IB^'OVfatt  +62.1 * C  ' T h « m i f »«i»t»»tt«l«tMW*dOfi tofrlpowsrdiwfestcrt.  Figure D l : Cougar A2CP12029 Specifications  156  Appendix D - Cougar A2CP12029 Wideband Amplifier Specifications  Transmission Coefficient (S21] 30.00 i  -20.00 -I 1.00  1  '  1  1  '  1  '  1  1  1  1  1  1  1  1  ,  1  1  1  2.00  3.00  4.00  5.00  6.00  7.00  B.00  9.00  10.00  11.00  12.00  ,— 13.00  Frequency (GHz)  Figure D2: Transmission Coefficient S versus Frequency for Cougar A2CP12029 21  157  Appendix E - Spectral Curve Matching Algorithm Code //Match: Two c u r v e s a r e compared f o r " s i m i l a r i t y " i n shape. //based on a t t e m p t i n g t o match two curves by matching  This algorithm i s  s i m i l a r i t y i n the general  //shapes o f t h e curves b u t a l l o w i n g f o r o f f s e t s and minor i n c o n s i s t e n c i e s . procedure Match; var i,j,k:  integer;  //temporary  loop v a r i a b l e s  modell,model2 : i n t e g e r ;  //temporary  i n d e x f o r two models c u r r e n t l y b e i n g compared  pc : i n t e g e r ;  //PlusCount  i n d e x c o u n t e r f o r walk on c u r v e i n i n c r e a s i n g  //direction mc : i n t e g e r ;  //MinusCount index c o u n t e r f o r walk on curve i n / / d e c r e a s i n g direction  ts  //temporary  : string;  s t r i n g conversion variable  done : b o o l e a n  //exit  delta : real;  / / o f f s e t between two c u r v e s a t c u r r e n t +/- f r e q u e n c y  longest:  / / l o n g e s t l e n g t h f o r match  real  condition  dp : r e a l ;  //dynamic plus/minus  cp : r e a l ;  / / c o n s t a n t p l u s minus f o r t e s t i n g d e l t a s  ModelWins  range f o r t e s t i n g d e l t a s  a r r a y [0..MaxModels] o f i n t e g e r ; / / s t o r a g e a r r a y f o r number o f wins  begin dp:=0.1;  / / i n i t i a l i z e dynamic  cp:=0.01;  / / i n i t i a l i z e constant error  for  i:=-5 t o MaxModels do  //for  j:=0 t o numfreq-1 do  //for  a l l f r e q u e n c i e s i n spectrum  //for  a l l v a l u e s (mag, l o g mag, phase)  for for  k:=0 t o 5 do  i:=0 t o LoadedModels.Items.Count-1 do  i f LoadedModels.Checked[i]  then  i:=0 t o NumFreq-1 do  for  a l l models i n memory  / / f i n d o r i g i n a l curve by l o o k i n g f o r //the model checked i n t h e l i s t b o x  m o d e l l : = E x t r a c t M o d e l N u m b e r ( Lo a d e d M o d e l s . I t e m s [ i ] ) ; for  limit  / / z e r o out a l l a r r a y e n t r i e s  MatchData[i,j,k]:=0; for  range  j:=0 t o LoadedModels.Items.Count-1 do  //save model index  / / f o r each f r e q u e n c y a c r o s s  spectrum  / / f o r each s t a n d a r d model i n memory  begin model2:=ExtractModelNumber(LoadedModels.Items[j]);  //get model index from  list  //MatchData[,,5] h o l d s o r i g i n a l d i f f e r e n c e between c u r v e s a t c e n t r e f r e q u e n c y MatchData[model2,i,5]:=ScanData[modell,i,0]-ScanData[model2,i,0]; mc:=i;  / / s e t mc t o p o i n t t o c e n t r e f r e q u e n c y  done:=false;  / / s e t l o o p c o n d i t i o n t o n o t done y e t  158  Appendix E - Spectral Curve Matching Algorithm Code / / T h i s l o o p performs t h e walk a l o n g t h e c u r v e s towards t h e lower f r e q u e n c i e s . / / S t a r t a t t h e g i v e n f r e q u e n c y ( f C e n t e r ) and decrease t h e i n d e x mc by 1 u n t i l //the magnitude d i f f e r e n c e between t h e two c u r v e s a t f r e q u e n c y i n d e x mc i s / / l a r g e r o r s m a l l e r t h a n t h e magnitude d i f f e r e n c e between t h e two c u r v e s a t t h e / / o r i g i n a l frequency fCentre. //is  The d i f f e r e n c e between t h e magnitude d i f f e r e n c e s  a l l o w e d a s m a l l e r r o r cp  w h i l e not(done)  do  / / w h i l e o f f s e t match i s s t i l l  valid  begin dec(mc);  //move t o t h e next l o w e s t f r e q u e n c y  delta:=ScanData[modell,mc,0]-ScanData[model2,mc,0];  / / c a l c u l a t e d e l t a mag  i f delta<MatchData[model2,i,5]-cp  then done:=true;  //if  i f delta>MatchData[model2,i,5]+cp  then done:=true;  //small or too b i g  i f mc<=0 then done:=true;  current delta too  / / o r out o f data then  end;  //we a r e done walk  / / T h i s l o o p performs t h e same walk as above b u t i n t h e d i r e c t i o n o f i n c r e a s i n g //frequency "pc:=I;  ::'  / / s e r pc t o c u r r e n t c e n t r e f r e q u e n c y  done:=false;  //not done y e t  w h i l e not (done) do  / / w h i l e o f f s e t match i s s t ' i l l  valid  begin inc(pc);  //move t o next h i g h e s t f r e q u e n c y  delta:=ScanData[modell,pc,0]-ScanData[model2,pc,0];  / / c a l c u l a t e d e l t a mag  i f delta<MatchData[model2,i,5]-cp  then done:=true;  //if  i f delta>MatchData[model2,i,5)+cp  then done:=true;  //small or too b i g  i f pc>=NumFreq-l then done:=true;  current delta too  / / o r o u t o f d a t a then  end;  //we a r e done walk  / / A f t e r we have performed t h e walk i n b o t h d i r e c t i o n s s t o r e t h e f r e q u e n c y //range over which t h e o f f s e t remained r e l a t i v e l y c o n s t a n t MatchData[model2,i,0]:=pc-mc-2;  / / s t o r e then l e n g t h o f t h e match by s a v i n g / / h i g h and low ends o f t h e walk pc and mc  end; lbMatchData.Clear;  / / c l e a r r e s u l t s window  //Now t h a t a l l o f t h e l e n g t h s o f t h e matching c u r v e s e c t i o n s have been r e c o r d e d //go through a l l //The  o f t h e r e s u l t s and.check t o see which c u r v e s a r e t h e b e s t matches.  s t o r e d match l e n g t h s a r e then compared f o r a l l  / / f r e q u e n c y i n t h e spectrum. //at  o f t h e t e s t c u r v e s a t each  The curve which has t h e l o n g e s t match l e n g t h  t h a t f r e q u e n c y i s s a i d t o have "won" t h a t comparison.  What t h i s means i s  159  Appendix E - Spectral Curve Matching Algorithm Code / / t h a t t h e curve w i t h t h e l o n g e s t match i s t h e curve t h a t i s most s i m i l a r a t t h a t / / f r e q u e n c y . The curve which i s t h e b e s t match i s t h e one which has t h e h i g h e s t //number o f wins i . e . i s t h e most s i m i l a r t o t h e sample curve a t more p o i n t s a l o n g //the  curve than any o f t h e o t h e r c u r v e s .  f o r i:=-5 t o MaxModels do ModelWins[i]:=0;  / / s e t a l l w i n counts t o z e r o  f o r j:=0 t o NumFreq-1 do  / / a t each f r e q u e n c y  '  begin longest:=0;  / / s e t l o n g e s t l e n g t h o f match t o z e r o  f o r i:=0 t o LoadedModels.Items.Count-1  do  / / f o r each model i n memory  begin model2:=ExtractModelNumber(LoadedModels.Items[i]); i f M a t c h D a t a [ m o d e l 2 , j , 0 ] > d e l t a then  //get model number  / / f i n d l e n g t h o f l o n g e s t match  begin  //at the current frequency  longest:=MatchData[model2,j,0];  //and save i t  end; ... end; • •  . 'i  '.  :  f o r 'i:=0 t o LoadedModels.items.Count-1  do  :. :•  / / f o r each model i n memory  begin model2:=ExtractModelNumber(LoadedModels.Items[i]);  //get model number  / / i f t h i s model's match l e n g t h e q u a l s t h e l o n g e s t match then i t s c o r e s a w i n / / i f more t h a n one model matches t h e l o n g e s t l e n g t h t h e n t h e y each s c o r e a w i n if  (MatchData[model2,j,0]=longest) t h e n i n c ( M o d e l W i n s [ M o d e l 2 ] ) ;  end; end; //end o f comparisons f o r each f r e q u e n c y f o r i:=0 t o LoadedModels.Items.Count-1  do  / / f o r model i n memory  begin model2:=ExtractModelNumber(LoadedModels.Items[i]);  //get model number  ts:='Model'+inttostr(model2)+' Wins:'+inttostr(ModelWins[model2]); fmMatch.lbMatchData.Items.Add(ts);  //add wins t o output  end; fmMatch.Show; end;  //show 'wins'  results  -  160  Appendix F - Transmission Coefficient S ] versus Frequency for Standard Models 2  Transmission Coefficient (S21) 10. DO  1.00  -j  2.00 "'  3.00 4.00 '•'  5.00 G.00 7.0D 8.00  ' '•  1  1  i _  9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  - ' ;  '•  ;  Figure F l : Transmission Coefficient S spectrum for model M 21  Transmission Coefficient (S21) 10.00  _1  I  I  L_  1 -10.0D •1 ni 5  S -15.00 -2D.D0 Missing Element A  -25.00 n  1.00 -30.00  2.00  r-  3.00 4.00  5.00 G.00 7.D0 8.00  9.00 10.00 11.00 12.00 13.00  Frequency [GHz]  Figure F2: Transmission Coefficient S spectrum for model M 1 A 21  161  Appendix F - Transmission Coefficient S versus Frequency for Standard Models 2]  Figure F3: Transmission Coefficient S spectrum for model M 2]  IB  Transmission Coefficient (S21] 10.00  _i  i  i  i  i  i  1  1  1  i_  _i  i  i_  1  1 —  . Missing.Element C -30.00 1.00  — r  2.00  1  1  3.00 4.00  1  5.00 G.00 7.00 8.00  1  1  1  9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure F4: Transmission Coefficient S spectrum for model Mi c 21  Appendix F - Transmission Coefficient S versus Frequency for Standard Models 21  Transmission Coefficient [521] _i  1D.00  i  i  i  i  i  i  i  i  i_  Missing Element D -30.00 1.00  2.00  3.00 4.00  5.00 G.DO 7.00 8. DO  9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure F5: Transmission Coefficient S spectrum for model M ID 21  Transmission Coefficient (521) 10.00  _i  1  i  i_  -J  1  I  L_  5.00 H  Missing Element E -30.00 1.00  2.00  3.00 4.00  5.00 G.00 7.00 8.00  9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure F6: Transmission Coefficient S spectrum for model M IE 2]  163  Appendix F - Transmission Coefficient S versus Frequency for Standard Models 21  Transmission Coefficient [521] 10.00  _J  i  i  i  i  i  i  i  i  i  i_  5.00 ^  Missing Element F -30.00 1.00  -i  2.00  r  1  3.00 4.00  r-  5.00 6.00  7.00 8.00  9.00 10.00 11.00 12.00 13.00  Frequency [GHz]  Figure F7: Transmission Coefficient S spectrum for model MIF 2J  Transmission Coefficient [521] l  10.00  l  5.00 H  .00  2.00  3.00 4.00  5.00 6.00  7.00 8.00  9.00 10.00 11.00 12.00 13.00  Frequency [GHz]  Figure F8: Transmission Coefficient S spectrum for model M 21  1G 164  Appendix F - Transmission Coefficient S versus Frequency for Standard Models 21  Figure F9: Transmission Coefficient S spectrum for model M1H 21  Transmission Coefficient (S21)  1.00  2.00  3.00 4.00  5.00 G.00 ,7.00 8.00  9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure F10: Transmission Coefficient S spectrum for model M 21  n  Appendix F - Transmission Coefficient S versus Frequency for Standard Models 21  Transmission Coefficient (S21) 10.00  _J  I  I  I  I  I  L_  I  5.00 0.00 |  -5.00  m X3  I -10.00 CD  s  j? -15.00 -20.00 -25.00 -30.001.00  Missing Element J 2.00  3.00 4.00  5.00 6.00  7.00 8.00  3.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure Fl 1: Transmission Coefficient S spectrum for model M 21  u  Transmission Coefficient (521) 10.00  _i  i  i  i_  -j  i  i  i_  -25.00 Missing Element K -30.00 1.00  2.00  3.00 4.00  5.00 6.00  7.00 8.00  9.00 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure F12: Transmission Coefficient S spectrum for model M IK 21  166  Appendix F - Transmission Coefficient S versus Frequency for Standard Models 21  Transmission Coefficient (S21)  1.00  -i  1  2.C0 3 00  1  4.00  1  1  1  5.00 6.00  1  1  7.00 • B.00  1  1  1-  9.00. 10.00 11.00 12.00 13.00  Frequency (GHz)  Figure F13: Transmission Coefficient S spectrum for model M 2]  1 L  Transmission Coefficient (521)  -i  1.00  2.00  1  3.00 4.00  1  1—;  1  1  1  1  1  1-  5.00 6.00 7.00 B.00 9.00 10.00 11.00 12.00 13.00 Frequency (GHz)  Figure F14: Transmission Coefficient S spectrum for model MIM 2]  167  Appendix F - Transmission Coefficient S versus Frequency for Standard Models 21  Figure F15: Transmission Coefficient S spectrum for model M 21  1 N  Transmission Coefficient (S21)  -10.00 H  .00  2.00  3.00 4.00  5.00 B.00 7.00 8.00  3.00 10.00 11.00 12.00 13.0D  Frequency [GHz]  Figure F16: Transmission Coefficient S spectrum for model M 21  1 0  168  Appendix F - Transmission Coefficient S versus Frequency for Standard Models 21  Figure F17: Transmission Coefficient S spectrum for model M 2]  Figure F18: Transmission Coefficient S spectrum for model M 2]  169  Appendix F - Transmission Coefficient S versus Frequency for Standard Models 21  Figure F19: Transmission Coefficient S spectrum for model M 21  Figure F20: Transmission Coefficient S spectrum for model M 21  Appendix F - Transmission Coefficient S versus Frequency for Standard Models 21  Figure F21: Transmission Coefficient S spectrum for model M 21  171  Appendix G - Table of Model Wins vs. Element Removed for Model Rotated 90 degrees  Model  M  M,  914  15  63  35  28  11  73  20  6  133  49  M  1 A  27  1026  85  28  121  2  11  19  1  40  5  M  1 B  30  7  567  215  35  11  13  18  18  91  11  M  1 C  42  14  227  776  47  5  51  3  18  61  1  M  I D  9  104  82  335  550  0  6  5  7  44  11  M  I E  43  20  70  24  29  1082  206  31  53  158  219  M  1 F  59  24  66  23  9  57  318  51  65  206  67  M  1 0  49  5  61  24  7  38  134  832  130  135  23  M  1 H  34  14  52  5  5  49  61  206  1006  125  46  M„  43  9  77  22  56  49  77  119  96  495  95  M„  24  30  53  78  70  113  142  43  18  120  846  M  1 K  21  17  73  45  20  68  47  29  69  66  23  M  1 L  57  13  56  40  14  24  247  69  15  167  76  M  1 M  47  14  53  35  6  8  91  40  25  144  6  M  1 N  30  4  52  23  13  6  50  70  75  114  26  58  10  70  39  35  61  88  20  16  158  38  M,  0  2  M  2 A  M  2 B  M  2 C  M  M  2 D  2 E  M  M  2 F  2 G  M  2 H  M  2I  M  2J  M  1 P  102  30  54  29  12  55  29  81  19  42  92  M  1 Q  30  21  124  13  32  4  32  8  50  51  3  M  1 R  19  9  60  7  61  3  9  6  4  43  1  M  1 S  73  13  77  20  112  9  2  1  8  44  1  M  1 T  8  61  56  10  49  0  13  2  12  48  13  Table Gl: (a) Number of comparison wins for sample models M thru M vs. reference models 2  M, thru M  1 X  with both models rotated 90 degrees  2J  Appendix G - Table of Model Wins vs. Element Removed for Model Rotated 90 degrees  Model  M  2 K  M  2 L  M  2 M  M  2 N  M  2 G  M  2 P  M  2 Q  M  2 R  M  2 S  M  2 T  M,  48  33  26  41  26  98  56  63  20  52  M  1 A  12  2  8  6  20  17  52  61  54  30  M  I B  32  19  7  17  59  14  115  72  39  13  C  10  0  11  28  25  15  69  54  59  27  1 D  3  0  2  0  0  6  70  68  61  40  E  76  31  32  9  48  13  51  58  78  21  M  1 F  44  137  84  40  31  55  45  63  6  10  M  I O  57  5  78  91  40  32  57  50  36  23  H  29  55  157  62  41  12  50 •  49  17  22  M„  20  50  29  57  35  17  60  58  13  14  M„  107  78  44  39  38  13  53  70  77  27  M  1 K  886  112  75  29  24  95  131  56  15  49  M  1 L  51  785  77  147  140  17  58  59  5  16  87  106  730  290  115  71  56  104  5  11  9  122  104  630  101  90  98  61  12  23  M,o  49  126  105  122  774  42  71  52  8  9  M  1 P  114  40  51  32  113  994  128  59  16  82  M  1 Q  9  18  3  6  43  13  947  100  88  105  M  1 R  2  2  3  3  0  2  62  475  140  194  M  1S  13  0  0  1  0  2  62  214  645  29  M  1 T  0  6  0  4  2  4  105  203  35  394  M  1  M M  M  I  1  M, M  M  1 N  Table G l : (b) Number of comparison wins for sample models M M, thru M  1 X  2 K  thru M  2 T  vs. reference models  with both models rotated 90 degrees  173  Appendix H - Photos of F D L Antenna and Connector  Figure H3: FDL Connector Showing Assembly Method. Note: Copper side strips are for mounting F D L to scanner and do not affect the antenna performance. 174  

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