A closed-form integral model of spiral inductor using the Kramers-Kronig relations

In this letter, a closed-form integral model is presented for the rectangular micromachined spiral inductor. The Kramers-Kronig relations provide an elegant theory to describe the inductor behavior without having complicated geometric analysis. Simulation and measurement results validate that the model can provide satisfactory prediction to the inductance of on-chip freely-suspended spiral inductors. Meanwhile, unlike conventional Greenhouse-based formulations, the self-resonant frequency of inductor can be predicted using the integral model.

[1]  Stephen P. Boyd,et al.  Simple accurate expressions for planar spiral inductances , 1999, IEEE J. Solid State Circuits.

[2]  J. Long,et al.  The modeling, characterization, and design of monolithic inductors for silicon RF IC's , 1997, IEEE J. Solid State Circuits.

[3]  Hongrui Jiang,et al.  On-chip spiral inductors suspended over deep copper-lined cavities , 2000 .

[4]  C. Kittel.  Introduction to solid state physics , 1954 .

[5]  S. Decoutere,et al.  Physics-based closed-form inductance expression for compact modeling of integrated spiral inductors , 2002 .

[6]  Gary K. Fedder,et al.  Micromachined high-Q inductors in a 0.18-/spl mu/m copper interconnect low-k dielectric CMOS process , 2002 .

[7]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[8]  Charles A. Brau,et al.  Modern Problems in Classical Electrodynamics , 2003 .

[9]  L. Richard Carley,et al.  Micromachined high-Q inductors in a 0.18-μm copper interconnect low-k dielectric CMOS process , 2002, IEEE J. Solid State Circuits.

[10]  M. Allen,et al.  High O spiral-type microinductors on silicon substrates , 1999, IEEE International Magnetics Conference.

[11]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[12]  Eisenstein,et al.  Proton Compton effect: A measurement of the electric and magnetic polarizabilities of the proton. , 1991, Physical review letters.

[13]  Ali M. Niknejad,et al.  Analysis, design, and optimization of spiral inductors and transformers for Si RF ICs , 1998, IEEE J. Solid State Circuits.

[14]  Ali M. Niknejad,et al.  Design, Simulation and Applications of Inductors and Transformers for Si RF ICs , 2006 .

[15]  S. Bantas,et al.  A generic CAD model for arbitrarily shaped and multi-layer integrated inductors on silicon substrates , 1997, Proceedings of the 23rd European Solid-State Circuits Conference.

[16]  H. Greenhouse,et al.  Design of Planar Rectangular Microelectronic Inductors , 1974 .

[17]  S. Asgaran.  New accurate physics-based closed-form expressions for compact modeling and design of on-chip spiral inductors , 2002, The 14th International Conference on Microelectronics,.