The Modelling of Conformal Antennas and Scatterers using the Method of Moments with B-Splines

Bruce Piper (2011). The Modelling of Conformal Antennas and Scatterers using the Method of Moments with B-Splines PhD Thesis, School of Information Technol and Elec Engineering, The University of Queensland.

       
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Author Bruce Piper
Thesis Title The Modelling of Conformal Antennas and Scatterers using the Method of Moments with B-Splines
School, Centre or Institute School of Information Technol and Elec Engineering
Institution The University of Queensland
Publication date 2011-09
Thesis type PhD Thesis
Supervisor Assoc Prof Nick Shuley
Total pages 279
Total colour pages 74
Total black and white pages 205
Subjects 09 Engineering
Abstract/Summary This thesis is broken up into two major sections. In both sections, the mathematical tools of splines are used in different ways in the theoretical electromagnetic modelling of antennas and scatterers. Splines are well known for their data interpolation and smoothing qualities. In the first section of this thesis, the mathematics of Basis Splines (B-Splines) are “embedded” into the Method of Moments technique. Using the same B-Splines in the geometry as well as in the Method of Moments theory offers some distinct advantages that are highlighted in this thesis. Methods to increase the speed of the computations are addressed and the results are compared with those published in the literature. One conclusion from this research was that fewer wire segments were required to obtain excellent results when compared to traditional methods. The second section uses the mathematics of B-Splines to create the sophisticated geometry of conformal antennas. These antennas can now be imported into many of the modern commercial electromagnetic software packages available to produce very accurate results. From Maxwell's equations in the frequency domain, the Mixed Potential Integral Equation (MPIE) is derived. It is used with the Method of Moments technique to calculate the surface currents on a straight thin-wire. Quadratic B-Splines were used as the basis and testing functions excited from a plane wave incident electric field at different angles. A technique was introduced that entirely uses B-Spline theory to numerically solve the MPIE. This eliminated the traditional method of using conventional numerical Gauss-Quadrature integration. The difficulty with this approach was in developing an accurate analytical method from spline theory to treat the singularity in the thin-wire approximation of the Green's free-space function. When a curved wire is modelled, it is traditionally represented as a large number of straight wire segments. In this thesis, an arbitrary shaped curved wire was modelled using individually curved wire segments of unequal lengths. The same B-Splines used to represent the geometry of the curve are also used in the developed theory improving the efficiency of the code. Elliptical integrals are required to treat the singularity in the Green's free-space function and are represented as a closed form solution. Commercial electromagnetic software using straight thin-wire segments is used to model the same curved wire and the results are compared. The MPIE is then transformed into the time domain where the Time Domain Integral Equation (TDIE) is derived using the Method of Moments and spatial B-Spline basis functions. The currents on a straight thin-wire excited from an incident Gaussian pulse are calculated directly in the time domain and compared with those in the literature using pulse basis functions. Over a large bandwidth in the frequency domain, the currents are also calculated by a commercial electromagnetic software package and converted to the time domain using traditional techniques. The results from all the different methods are analysed by calculating their signature using Complex Natural Resonances (CNRs). Extracting these theoretical natural resonances showed that the inclusion of B-Splines as the basis functions to the TDIE gives a very accurate representation of the natural damped response of the induced current without additional spurious frequencies. It has been known for some time that even with the modern electromagnetic software tools available to the RF Design Engineer, it is often the inaccurate representation of the antenna/scatterer that lets them down. A modern commercial electromagnetic modelling software package has the limitation of only being able to draw shapes which are basic using the graphical front-end available to the user. The second part of this thesis concentrates exclusively on using B-Splines to produce antennas with complex geometry. The B-Splines discussed in this section are enhanced to represent the more powerful Non-Uniform Rational B-Splines (NURBS). A set of NURBS-based geometric software design tools are developed with a design procedure to present a unique set of results for different types of cylindrical and spherical conformal antennas.
Keyword moment methods
b-splines
conformal antennas
microstrip antennas
spherical antennas
software tools
time domain analysis
numerical analysis
Additional Notes Colour pages 27-29, 47, 69-71, 73, 76, 79, 81-83, 86, 90, 91, 94, 101, 109, 112, 113, 115, 125-127, 130-132, 136, 139, 141, 148, 155, 159-161, 164-170, 173, 178-181, 190, 192, 195,196, 198, 200-202, 204, 206, 207, 209, 211, 216, 217, 219, 222, 236, 238, 242, 246, 250, 253, 254, 259, 260. All pages are A4. Print straight from the PDF as a book (Double sided pages). All chapters should start on right hand page.

 
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Created: Sun, 18 Sep 2011, 21:01:27 EST by Bruce Piper on behalf of Library - Information Access Service