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

(1)对本课题的研究现状进行了综述，并对已知的各种分析方法进行了系统的分类。(2)指出分布元件的特征阻抗函数Zeta_0(S)和分布元件的相位特性的双线性函数Rheta(S)都必须用有理正实函数来逼近BC。提出了用正实函数逼近这些量的方法。与传统的Pade近似方法相比，该方法具有更好的收敛特性。(3)提出了一种新的集总常数单元端接多导体传输线的暂态分析方法，并通过数值仿真验证了该方法的有效性。该方法利用Fettweet提出的求解偏微分方程的多维WDF(Wave Digital Filter)方法。提出了一种新的介质开关等效电路，其等效电路由多导体传输线和集总常数元件组成，并根据实验结果确定了集总常数元件及其元件值。研究了仅由集中元件和分布元件两种谐振段组成的无损耗带通梯形网络的特性，给出了实现的充要条件。(6)给出了有理函数最小逼近最大误差与最小第p逼近最大误差之比的理论下界。对各种函数的数值算例验证了上述下界是对实际值的较好估计。

(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.