根据Ruehli的PEEC(Partial Element Equivalent Circuit)模型[5],矩形截面互连线(Interconnect)的部分电感定义为一个六重积分解析式,由于使用该式计算自感时,被积函数会存在奇异点,因此需要研究准确简便的自感计算方法。文中首次使用泰勒级数展开法计算得到了矩形互连线自感公式。该方法从自感公式出发,先计算二重解析积分,然后把被积函数中的复杂函数展开成泰勒级数,从而转化为幂级数的逐项积分,推得自感计算公式是以导体尺寸为变量的简单显式函数。计算结果表明,该公式与直接积分方法具有同样的计算精度,并且比其它自感计算公式更加准确有效。
Partial inductance is first introduced in[5].Rectangular across sectional interconnect partial inductance is defined by a 6-level integration.As the integrand is singular for self-term,it is a time consuming calculation.This paper will present a novel closed-form formula for the rectangular interconnect partial self-inductance.Started from the definition of interconnect partial self-inductance,we first do the 2 levels analytical integration,then use Taylor Series Expansions to approximate the integrand and derive the final CAD formula which is a simple explicit function of the interconnect size.Direct integration method is used to validate our formula′s accuracy.Also compare with other formulas,it shows our formula is more robust and efficiency.