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为了快速计算全频率范围内随频率变化的互连导体电感、电阻矩阵 ,提出一种二维电路模型法和边界元法结合的算法。该算法利用电路模型法得到低频下若干频率的电感、电阻值 ;利用边界元方法求解 L aplace方程计算出电容矩阵 ,求逆得到电流完全分布在导体表面时的高频电感矩阵 ;利用电阻矩阵与电感矩阵在高频情况下成立的 Wheeler公式 ,得到高频段的电阻矩阵。对上述低频和高频段的电感、电阻值 ,利用三次样条函数插值 ,得到整个频率范围的变化曲线。计算结果与已有文献的结果进行比较 ,表明该算法是准确的 ;该算法避免求解涡流边界耦合积分方程 ,与已有方法相比大大减少了计算量。该算法可应用于绝大多数大规模集成电路寄生参数提取计算
In order to quickly calculate the inductance and resistance matrix of interconnected conductors with frequency variation in the whole frequency range, a two-dimensional circuit model method combined with the boundary element method is proposed. The algorithm obtains the inductance and resistance of several frequencies at low frequencies by using the circuit model method. Calculate the capacitance matrix by solving the L aplace equation by using the boundary element method, and obtain the high-frequency inductance matrix when the current is completely distributed on the conductor surface by using the resistance matrix. The Wheeler formula for the inductance matrix established at high frequencies yields a high frequency matrix of resistances. The above low-frequency and high-band inductance, resistance, the use of cubic spline interpolation, the entire frequency range of the curve. Comparing the results with the existing ones, it shows that the algorithm is accurate. The algorithm avoids solving integral equations of vortex boundary coupling, which greatly reduces the computational cost compared with the existing methods. The algorithm can be applied to most large-scale integrated circuit parasitic extraction calculation