Research of Analysis Method for Very High Speed Integrated Circuits Composed of Distributed and Lumped Elements

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(1) We summarized the state of the art of this research subject and classified systematically various analysis methods so far known.(2) We pointed out that both the characteristics impedance function ZETA_0(s) and a bilinear, functionof the phase characteristics rheta(s) of distributed elements have to bc approximated by rational positive real functions. We proposed the method for approximating these quantities by positive real functions. This resulted in better property of convergence than the conventional Pade approximation method.(3) A new transient analysis method for multi-conductor transmission line terminated with lumped-constant elements was proposed and the validity by numerical simulation was shown. The method utilizes multi-dimensional WDF (Wave Digital Filter), which Fettweis proposed for partial differential equation. Our method solved the difficulty arising from the treatment of mixed lumped- and distributed systems.(4) fi new equivalent circuit for a dielectric Alter was proposed, where the equivalent circuit consists.i multiconductor transmission line and lumped constant elements and its element values are determined from experimental results. The total characteristics of the circuit are much coincident with physical results over wide frequency than usual model.(5) The properties of lossless bandpass ladder network composed of only two kinds of resonant sections consisting of lumped- and distributed-elements were investigated and the necessary and sufficient conditions for realization were given.(6) A theoretical lower bound for the ratio of the maximum error of the minimal approximation to that of the the least pth approximation by a rational function is given. Numerical examples on various kind of functions verified that the above lower bound is a good estimation for the actual values.