A Lumped Scalable Model for Silicon Integrated Spiral Inductors

Abstract

A lumped scalable model for spiral inductors in silicon bipolar technology has been developed. The effect of three different cross sections on inductor performance was first investigated by comparing experimental measurements. Using both the results of this analysis and three-dimensional electromagnetic simulation guidelines, several circular inductors were integrated on a radial patterned ground shield for model validation purposes. The model employs a novel equation for series resistance with only one fitting parameter extracted from experimental measurements. All other model elements were related to technological and geometrical data by using rigorous analytical equations. The model was validated using one-and two-port measured performance parameters of 45 integrated inductors, and excellent agreement was found for all considered geometries up to frequencies well above self-resonance.

Scalable lumped modeling of single-ended and differential inductors for RF IC design

“…Measurements of these symmetric inductors were used to extend the validation of the model shown in Figure 4, whose accuracy was previously demonstrated only for single-ended coils [13]. Model validation activity took advantage of experimental data from more than 70 single-ended and differentially driven spirals covering 0.…”

“…In this work a lumped scalable model, previously extracted and validated by comparison with measurements of a large number of single-ended coils [13], is here extended to symmetric devices. The validity of this model is demonstrated up to 20 GHz by comparison with experimental data of a wide set of geometrically scaled symmetric inductors in the range of 0.2-8.3 nH.…”

Characterization and modeling of silicon integrated spiral inductors for high-frequency applications

“…The third (top) metal layer of this technology was used for the spiral, the second one for the underpass and the first one for the ground plane. A radial pattern of oxide trench was adopted to break induced current loops within the buried layer shielding the spiral from the underlying substrate [19,25]. Buried layer contacts were placed at the edge of the ground plane at a distance of 50 lm from the spiral.…”

“…To this aim, simple lumped scalable models are largely employed. Their soundness is strictly related to the availability of accurate closed-form expressions for all the lumped elements and especially for the low-frequency inductance, whose estimation affects both the self-resonance frequency and quality factor calculations [17][18][19]. Some analytical approaches for the inductance calculation are based on the Greenhouse method [20], which is accurate enough but not suitable for simple lumped modeling.…”

“…In [21] both a monomial equation, obtained by least square fitting techniques, and a physics-based expression, based on the current sheet approximation, were developed and compared with measured data of 2.5-to 34-nH inductances. Expression coefficients extracted from extensive EM simulations (carried out with ASITIC [22]) in the range 0.5-100 nH provided satisfactory results only for larger inductances, whereas errors up to 19.9% were observed for smaller values and imputed to measurement inaccuracy. Another physics-based closedform inductance expression was proposed in [23].…”