Coupling matrix extraction for cascaded-triplet (CT) topology

This paper describes two different approaches for designing cascaded-triplet filters, having generalized Chebyshev characteristics. Both approaches use an orthonormalization procedure (which satisfies the required topology) that leads to a set of nonlinear equations. In the first approach, these equations are solved by a Newton-Raphson (NR) method. The second approach uses an algebraic reduction technique to reduce the number of variables to just one or two. These variables are scanned to find solutions. These approaches are complimentary; the NR method gives great accuracy, but needs suitable starting points to find all solutions, and the algebraic approach has limited accuracy, but reveals all solution regions.