Double-π fully scalable model for on-chip spiral inductors

Abstract

A novel double-π equivalent circuit model for on-chip spiral inductors is presented. A hierarchical structure, similar to that of MOS models is introduced. This enables a strict partition of the geometry scaling in the global model and the model equations in the local model. The major parasitic effects, including the skin effect, the proximity effect, the inductive and capacitive loss in the substrate, and the distributed effect, are analytically calculated with geometric and process parameters in the local-level. As accurate values of the layout and process parameters are difficult to obtain, a set of model parameters is introduced to correct the errors caused by using these given inaccurate layout and process parameters at the local level. Scaling rules are defined to enable the formation of models that describe the behavior of the inductors of a variety of geometric dimensions. A series of asymmetric inductors with different geometries are fabricated on a standard 0.18-m SiGe BiCMOS process with 100 /cm substrate resistivity to verify the proposed model. Excellent agreement has been obtained between the measured results and the proposed model over a wide frequency range.

Analysis of scalable two-π equivalent-circuit model for on-chip spiral inductors

“…According to the Eqs. (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14), the number of independent elements in Figure 1 is reduced form 28 to only seven (L s1 , L p11 , R p11 , C ox1 , R sub1 , C sub1 , C s ). Then, these seven independent model elements will be calculated by the scalable model comprises of the geometry and process parameters.…”

“…The model parameters of one‐π topology can be directly extracted from measured S‐parameters, but one‐π model fails to represent the decrease of effective series resistance at high frequencies. Two‐π model overcomes this drawback , but it doubles the number of model elements and makes the extraction of parameter more complicated.…”

“…In this article, the development of two‐π scalable model with four ladder skin effect structure has been described in detail. Compared to the conventional model , the number of independent elements is reduced to only seven by semiempirical method in the proposed two‐π model. Therefore, this model is much easy to construct scalable model.…”