论文标题
高频电路传递函数的正交合理近似
Orthogonal Rational Approximation of Transfer Functions for High-Frequency Circuits
论文作者
论文摘要
理性函数近似在许多领域找到应用，包括高频电路的宏观建模，控制器设计的模型订单降低，系统响应的插值和外推，高能物理学的替代模型以及基本数学功能的近似值。该模型的未知分母多项式导致非线性问题，可以在Sanathanan-Koerner（SK）迭代后用线性化问题的连续解决方案代替。基于Arnoldi可以获得正交的基础，从而导致稳定的SK迭代。我们提出了稳定的SK的扩展，称为正交有理近似（ORA），可确保实际多项式系数和稳定的电线杆，以实现电网的可靠性。我们还基于块QR分解引入了多端口网络的ORA的有效实现。
Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for high-energy physics, and approximation of elementary mathematical functions. The unknown denominator polynomial of the model results in a non-linear problem, which can be replaced with successive solutions of linearized problems following the Sanathanan-Koerner (SK) iteration. An orthogonal basis can be obtained based on Arnoldi resulting in a stabilized SK iteration. We present an extension of the stabilized SK, called Orthogonal Rational Approximation (ORA), which ensures real polynomial coefficients and stable poles for realizability of electrical networks. We also introduce an efficient implementation of ORA for multi-port networks based on a block QR decomposition.
