1Andrew PavacicFriday 24 June 2005 Three Dimensional Ray Tracing to Model Internal Reflections in Off-Axis Lens Antennas Andrew P. Pavacic Prof. G. V. Eleftheriades The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto

2Andrew PavacicFriday 24 June 2005 Introduction Application is a European Space Agency (ESA) 650 GHz radiometric satellite limb sounding instrument for detecting ozone in the upper atmosphereApplication is a European Space Agency (ESA) 650 GHz radiometric satellite limb sounding instrument for detecting ozone in the upper atmosphere Cassegrain reflectors are coupled to a lens antenna feedCassegrain reflectors are coupled to a lens antenna feed Project involves design and radiation pattern testing of a scale model of the feed antenna for the Cassegrain reflector systemProject involves design and radiation pattern testing of a scale model of the feed antenna for the Cassegrain reflector system

3Andrew PavacicFriday 24 June 2005 Dielectric Lens Antenna With Printed Feed Printed feed is modeled in simulation as a set of magnetic current elements computed by Method of Moments (MoM) softwarePrinted feed is modeled in simulation as a set of magnetic current elements computed by Method of Moments (MoM) software Gaussian coupling efficiency is improved by an elliptical substrate lensGaussian coupling efficiency is improved by an elliptical substrate lens 1.For efficient radiation pattern analysis, the printed feed is treated as a source of rays. 2.Ray tracing is used to compute fields at the lens surface, then 3.Schelkunoff equivalent lens surface currents are used to compute radiation patterns. 4.High lens permittivity reduces back-radiation, but increases internal reflections. 5.For ease of fabrication, the elliptical surface is approximated by hemisphere with cylindrical extension.

4Andrew PavacicFriday 24 June 2005 Constant Cross-Sectional Power “Beams” Defined by New 3D Beam Tracing New UofT ray “3D” ray tracing software designed to accommodate distributed feed currents and generalized lens dimensions and curvatureNew UofT ray “3D” ray tracing software designed to accommodate distributed feed currents and generalized lens dimensions and curvature Reflection paths do not remain within a single planeReflection paths do not remain within a single plane Each current element treated as its own coordinate origin and source of beamsEach current element treated as its own coordinate origin and source of beams Each beam obeys laws of energy conservation with constant cross-sectional power despite varying cross-sectional areaEach beam obeys laws of energy conservation with constant cross-sectional power despite varying cross-sectional area Reflection paths are computed on the fly - the same code can be applied to a variety of lens designReflection paths are computed on the fly - the same code can be applied to a variety of lens design Ground Plane y Total Internal Reflection (T.I.R.) First Order Beam x y z Second Order Beam First Order Beam Total Internal Reflection (T.I.R.)

5Andrew PavacicFriday 24 June 2005 Causes of Discrepancies Between Simulation and Measurement Lens curved surface fabrication tolerancesLens curved surface fabrication tolerances Simulation modeling of internally reflected raysSimulation modeling of internally reflected rays Lens permittivity and size in wavelengths (operating frequency)Lens permittivity and size in wavelengths (operating frequency) Near-critical-angle “transition fields” and choice of elliptical vs. extended hemispherical lensNear-critical-angle “transition fields” and choice of elliptical vs. extended hemispherical lens “Filling-in-the-nulls” contribution of discretization noise“Filling-in-the-nulls” contribution of discretization noise “Ground plane currents” and lateral wave radiation“Ground plane currents” and lateral wave radiation Parasitic radiation from CPW transmission linesParasitic radiation from CPW transmission lines Fringing fields in high-frequency patch and rectangular waveguide aperture feedFringing fields in high-frequency patch and rectangular waveguide aperture feed

6Andrew PavacicFriday 24 June 2005 Off-Axis Comparison of Simulation vs. Measurement With Frequency Sweep Displacing the feed off-axis allows the strongest pattern contribution of internal reflections to appear in a direction opposite to that of the steered main beam, thus more easily observedDisplacing the feed off-axis allows the strongest pattern contribution of internal reflections to appear in a direction opposite to that of the steered main beam, thus more easily observed Comparison between simulation and measurement at the operating frequency (a) shows better agreement for some sidelobe levels than for othersComparison between simulation and measurement at the operating frequency (a) shows better agreement for some sidelobe levels than for others Superposition of measured pattern on a 5% frequency-swept simulation (b) identifies upper and lower “bounds” for sidelobe levels, within which the measured pattern may be expected to fallSuperposition of measured pattern on a 5% frequency-swept simulation (b) identifies upper and lower “bounds” for sidelobe levels, within which the measured pattern may be expected to fall Utility of the 3D ray tracing software is to efficiently generate frequency-swept patterns for identifying more general pattern characteristics for design purposesUtility of the 3D ray tracing software is to efficiently generate frequency-swept patterns for identifying more general pattern characteristics for design purposes