尺度变换在互连线高阶模型仿真中的应用

Wang氏RC互连线模型的状态方程避免了矩阵求逆，传递函数采用巧妙的递归算法，使互连线的高阶仿真得以可行。但是在用MalLab做高阶仿真中，当在传递函数向状态方程转换以及用传递函数作阶跃响应和波特图时还是会发生困难。研究表明，困难来自互连线电容C值太小以及仿真阶数过高。对于高阶仿真，增大电容C值是解决发生困难的唯一途径。经过证明，增大电容C值等同于对频率进行尺度变换。电容C值扩大后，对阶跃响应图的时间轴进行同比例缩小或波特图的频率轴进行同比例扩大，即可得到原图。

Application of Scaling in Simulation of High Order Interconnect Model

In Wang's RC interconnect model, the state space avoids matrix inverse and the transfer function uses a nice recursive algorithm, so a very high order interconnect simulation could be executed. But in the higher order interconnect simulation, troubles still exist in transforming the transfer function to the state space function and in making step and bode figures. The results found indicate that the troubles exist because the capacitance is too small or the order of simulation is too high. In very high order simulations the only way out is to augment the capacitance. It is proved that augmenting the capacitance is corresponding to the scaling transform of frequency. Thus the original step and bode figures can be got by scaling.