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This paper presents a new and very efficient integral method for the electromagnetic modeling of planar circuits on multilayered semiconducting substrates. Differently from standard integral approaches, the method leads to a state-space model of the circuit. This model directly permits to find the admittance matrix in the form of a reduced-order pole expansion in the S-domain through standard Krylov sub-space techniques. Three examples demonstrate the really good performances of the method in terms of accuracy and rapidity.