Application of the method of least squares to electromagnetic engineering problems

In this paper, a brief review of the application of the Method of Least Squares (MLS) to electromagnetic engineering problems is presented. By describing the analysis, design, synthesis, and optimization of several antenna and microwave components and devices, the capabilities and power of the MLS for tackling such problems are amply illustrated. The MLS may also be used for the computation of some propagation problems. First, as an introduction to the MLS, its application is presented for some common problems in engineering mathematics, such as the solution of equations (transcendental equations, polynomials, systems of linear and nonlinear equations, etc.), curve fitting of some set of functions to known measurement data, and the determination of Fourier-series coefficients. Next, some specific electromagnetic engineering problems are briefly presented, such as electrostatic problems, the solution of linear operator equations, the solution of integral equations, the solution of differential and integro-differential equations under some specified boundary conditions, the description and application of the Least-Square Boundary Residual Method (LSBRM) (for the solution of the junction of cylindrical waveguides; E-plane metallic strips, both free-standing and on a dielectric slab in rectangular waveguides; etc.), the optimum design of impedance transformers, multi-hole directional couplers, coupled-line, branch-line, and microstrip couplers, coupled-line filters, a Wilkinson power divider, the analysis of wire antennas, slot antennas, ring antennas, and the optimum design of a slot antenna profile. The main theme of the paper is to convey the methods of construction of error functions by the MLS for the analysis or optimum design of the devices used as examples.