Abstract
In this letter, the homotopy continuation (HC) approach for a problem of coupling matrix (CM) extraction is presented. HC method is used to solve the system of polynomial equations that are formulated by comparing polynomial coefficients of given filter scattering parameters S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> and those being described based on well-known relations between scattering parameters and CM. HC requires an initial ( t=0) system of equations with a known solution. During the HC algorithm run, the system and solution are transformed to the final ( t=1) system and solution that is our goal. In our approach, the initial system ( t=0) and its solution are formulated by comparing polynomial coefficients of S-parameters obtained for CM including entries of any, even random, values. To validate the method a numerical experiment has been presented, i.e., CM extraction for measured sixth-order (two regular and two parasitic cross-couplings) filter. The experiment demonstrated excellent results obtained with the proposed method.
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