Efficient spectral evaluation of mutual coupling between planar antennas

Abstract

Abstract. This work deals with the evaluation of mutual coupling in arrays of apertures or printed radiators and other similar problems. Two analytical-based numerical integration techniques will be described, for the efficient evaluation of the spectral reaction integrals between two arbitrary functions on separated domains in a general stratified medium. These techniques employ novel schemes of contour deformation. The spectral domain formulation is used, and integration is carried out in Cartesian coordinates, taking the x axis along the direction adjoining the centers of the two basis functions involved. In both techniques the kx contour is deformed along the negative imaginary axis in order to turn the oscillating shift exponential into a decaying term. A robust scheme is obtained, with yet additional advantages in the case where many coupling terms at different distances are to be evaluated (as in alignments within arrays). Validation against published data and an application example are presented, along with a discussion of the numerical performances.

Radiation efficiency analysis of submillimeter‐wave receivers based on a modified spectral domain integration technique

“…To overcome all these problems we apply an integration path deformation for both the k x and k y wavenumbers (Figure 2a), e.g., for k x with typical parameters). Similar ideas are suggested by Yang et al [1990] and Garino et al [2000].…”

“…For the detailed analysis of all radiation effects, we have improved the spectral domain integration technique of our surface/volume integral equation approach in Vaupel and Hansen [2000a, 2000b]. Since the parallel plate poles of the corresponding Green's function cause large variations of the integrands, we have consequently used an integration path deformation for both the k x and k y wavenumbers similar as in Yang et al [1990] and Garino et al [2000] together with an integration area reduction to the first quadrant of the k x ‐ k y plane. Due to the smooth integrand behavior achieved by these measures, we apply a piecewise uniform integrand sampling by an appropriate subdivision of the k x ‐ k y plane.…”

Spectral domain analysis of large (M)MIC‐structures using novel quadrature methods

“…Since the highest power occuring in p NÀ1 is t NÀ1 ; the function f ðk x Þ in Equation (3) is integrated exactly up to polynomials of order N À 1: This means, that 3-4 sampling points provide in general higher accuracy than with the procedures in References [12][13][14]. Furthermore, the integration scheme is typically much more robust than comparable Newton-Cotes schemes that often suffer from cancellation effects in case of formulas of higher order [15].…”

“…The simplest kind of a Filon integration scheme is based on a combination of the tapezoidal integration rule with an analytical integration of the shift factors e jk x D x;ynm over each sample interval [13]. More efficient formulas are based on analytical integrations with Lagrange polynomials or cubic splines [14]. Nevertheless, the formulas become quite complicated and it is more cumbersome to extend them to integration schemes of arbitrary order [15].…”