De-embedding multiplexers by Schur reduction

This paper proposes a method to extract the characteristics of the filters composing a multiplexer. Scattering measurements of the multiplexer are given at some frequencies, together with information regarding the location of the transmission zeros of each filter. From these measurements we first compute a stable rational approximation of the scattering matrix (transfer function). Then we show that the chain matrices of the filters can be recovered, up to a constant matrix, by unchaining suitable components at each port of the multiplexer. The unchaining operation relies on a Schur reduction for an interpolation problem formulated for the structure thereby obtained, with the interpolation points being precisely the transmission zeros of the filter. Since transmission zeros are often located on the imaginary axis, we are dealing with a boundary interpolation problem.