Combing Multilevel Green's Function Interpolation Method With Volume Loop Bases for Inductance Extraction Problems

Abstract

Abstract-In this paper, a fast integral equation method is developed for extracting the inductances in RF ICs, RF MEMs, IC packages, and deep submicron ICs etc. This method combines a recently developed Multilevel Green's Function Interpolation Method (MLGFIM) [1,2] with the volume integral equation discretized using Volume Loop (VL) basis functions. In it, instead of using the filaments model to simulate the currents flowing in the inductors, we use the conventional SWG basis functions for this kind of basis functions is flexible for problems with complex geometries. The shortest path finding algorithm is also used to find the source loop basis functions. The inductance extractions from the straight line, the spiral inductors, the bump, and the parallel buses in this paper demonstrate the validity and efficiency of this hybrid method.

Resistances and Inductances Extraction Using Surface Integral Equation With the Acceleration of Multilevel Green Function Interpolation Method

“…In triangle q of a loop basis function support, the loop basis function can be expressed as I q = tq 2∆q , where ∆ q is the area of triangle in RWG bases and t q is defined in Figure 2. Similarly as [6], after some operation in (11), we can obtain that (7) becomes zero if the support of the loop basis function is closed and otherwise it equals the unclosed loop voltage.…”

“…R is defined as |r − r |. This equation is used in [6] for inductance extractions. However, when the frequency is very high and thus the skin depth becomes very shallow, the currents are almost restricted in a very thin shell of the metal.…”

“…However, when the frequency is very high and thus the skin depth becomes very shallow, the currents are almost restricted in a very thin shell of the metal. Consequently, the tetrahedron mesh used in [6] can no longer efficiently model the skin effects. Suppose a plane wave impinges on the surface of a relatively thick metal (Figure 1), where d(r ) is the depth from the surface point r and it is greatly larger than the skin depth, J s is the surface currents.…”

“…However, it is restricted for solving rectangular wire strip problems, because when the upper and lower surfaces of the conductor are not parallel, the internal E fields can not be simply expressed as (2) of [5], viz., E = E + e −γz + E − e +γz , where γ is the propagation constant defined in [5]. Recently, we have developed the volume loop integral equation (VLIE) method [6]. This method is accurate for calculating the inductance and resistance of the metal when its size of cross section is comparable to the skin depth.…”

Inductance Comparison of the Solenoidal Coil of Modular Toroidal Coils Using the Analytical and Finite Element Method

“…These contributions have been based on the application of Maxwell's formula, Neumann's formula, and the Biot-Savart law. The mutual inductance of circular rings can be obtained in analytical or semi-analytical forms expressed over elliptical integrals of the first, second, and third kind, Heuman's Lambda function, Bessel functions, and Legendre functions [12,13]. However, the calculation of the mutual inductance of non-coaxial circular rings is of fundamental practical interest to electrical engineers and physicists.…”