Analytical asymptotic extraction technique for bend discontinuity

Abstract

The conventional spectral domain method is too time-consuming to fill the impedance matrix elements because the matrix elements are expressed in terms of infinite double integrals and their integrands exhibit slow convergence and highly oscillating behavior. In the previous research of gap discontinuities, park had successfully derived the analytical transformation of the infinite double integral into a finite one-dimensional integral in calculating the asymptotic impedance matrix elements. This showed the dramatic improvement of the computation time for evaluating the overall impedance matrix elements without sacrificing the accuracy. With extension of the previous work, this dissertation presents efficient computational techniques in case of right-angled bend discontinuity. In order to describe the unknown current distribu-tions, two kinds of expansion functions are used. It is used to describe the current density distribution in regions containing and bordering right-angled bend microstrip junction. In such regions, the current is represented by overlapping rooftop functions with the transverse and longitudinal directions. In this problem, the most time consuming part of filling the matrix elements is the field interactions between rooftops and half rooftops basis functions. Also the matrix element evaluations of the interactions between rooftop and half rooftop basis functions requires extensive computation time, but relatively less than the previous case. To overcome this computation time, we developed new analytical formulas for evaluating the asymptotic impedance matrix by using the above integral transform method. We show that the derived analytical techniques significantly reduce the computational time and improve the accuracy over the conventional method to evaluate the asymptotic part of impedance matrix by eliminating the truncation error for solving right-angled bend discontinuity. To validate this new approach, the commercial software data will be...