Tilted-Ellipse Representation of Standing-Wave Patterns

摘要

A recently introduced, new computer-simulation method provides a fast and inexpensive way for obtaining the multi-dimensional scattering matrices of even very large-scale, multiport microwave systems. The new method simulates measurements of multidimensional, complex scattering matrices, that could only be performed using a very large and expensive multiport Vector Network Analyzer (VANA). Calibrated measurements of complex scattering matrices of any arbitrary size may be simulated by using any available frequency-domain 2D or 3D Maxwell-field solver, provided the solver used can compute the complex values of EM fields, within a given bounded domain. Scattering-matrix measurements, that would require an impracticablly-large and expensive multiport Vector Network Analyzer (VANA) , can be simulated by first computing the electromagnetic field-distributions, within both the multiport microwave system under simulated test (the virtual DUT or V-DUT), and within the inner regions of a set of simulated virtual measurement-lines (V-ML), with each line being connected to a different V-DUT port. The simulation of multidimensional, complex scattering-matrix measurements is based on the results of a rigorous mathematical analysis of the simultaneous propagation of forward and backward waves along the virtual measurement lines. This rigorous analysis has shown that the mutual correlation between the imaginary components, and the real components of the standing-wave fields along the length of each measurement- line, can be quantitatively represented by the parametric equations of a tilted- ellipse, centered on the origin of a 2D planar, Cartesian reference e-frame.