Automatic generation of geometrically parameterized reduced order models for integrated spiral RF-inductors

Abstract

In this paper we describe an approach to generating low-order models of spiral inductors that accurately capture the dependence on both frequency and geometry (width and spacing) parameters. The approach is based on adapting a multiparameter Krylov-subspace based moment matching method to reducing an integral equation for the three dimensional electromagnetic behavior of the spiral inductor. The approach is demonstrated on a typical on-chip rectangular inductor.

Parameterized model order reduction of nonlinear dynamical systems

“…(16) Using then, for instance, polynomial fitting, and introducing additional parameterss j as in II-B and [8], [9] one obtains…”

“…Some are based on statistical performance evaluation [1], [2], [3], [4], others are based on moment matching techniques [5], [6], [7], [8], [9], [10], or on Truncated Balance Realization (TBR) techniques [11], and on quasi-convex optimization techniques [12]. However, to our knowledge, almost all existing PMOR techniques apply only to linear systems.…”

Reduced order models of integrated rf spiral inductors with geometrical and technological automatic parameterization

“…Once we have the equations in the form of (6), a parameterization and model order reduction as described in [1,2] is used to obtain the set of equations (7) and (8):…”

“…This approach has been proposed before for interconnect delay estimation [2], [3], [10] and RF parasitics [13]. More recently, automated methods for the generation of reduced order models targeting integrated spiral inductors have been proposed [1]. The core of the approach is Krylov-subspace based moment-matching method that reduces the integral equation describing the 3D EM behavior of the inductor.…”

“…The substrate region underlying the inductor is accurately modeled using integral equation based Boundary Element Method (BEM). We provide a technique for merging the circuit resulting from substrate mesh with the Partial Element Equivalent Circuit (PEEC) of the inductor and show how the resulting circuit can be solved using existing techniques [1] for parameterization and model order reduction.…”