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Interpolation in the complex plane is employed to handle microwave network functions. This yields an approximating rational function over a specified bandwidth, and leads to a lumped-circuit approximation for the microwave structure, which is used as a basis for the synthesis of matching networks. In various problems involving dissipative devices, the poles of the rational approximating function may satisfy special conditions. In such cases the ideal lumped matching network has a simple realizable form, and may be transformed into a suitable microwave structure. Applications of this method and experimental results are given for the synthesis of a new type broad-band coaxial "chimney" attenuator.