Design Equations for Spiral and Scalable Cross Inductors on 0.35 μm CMOS Technology

J. Fontebasso Neto, L. C. Moreira, F. S. Correra


This paper presents a set of design equations for spiral and new scalable cross inductors in CMOS 0.35 μm technology, relating electrical parameters of the inductor's equivalent circuit as functions of its geometric dimensions. The procedure used to derive the design equations is described and involves electromagnetic simulation of inductors with different geometric dimensions, extraction of values for equivalent circuit model elements for each inductor and the use of multivariate regression analysis applied to generalized linear models (GLM) based on design of experiments (DoE). A p-type nine elements equivalent electrical circuit was used for the inductors, where all elements values are constants, allowing simulation on SPICE-like softwares. Results from the models obtained for both spiral and scalable cross inductors presented close match to the simulated results.


Planar inductor, Design of Experiments, EM simulation, Mathematical model.

Full Text:



F. W. Grover, Inductance Calculations, New York: D. Van Nostrand, 1946.

E. Pettenpaul and e. alli, CAD models of lumped elements on GaAs up to 18 GHz, IEEE Transactions on Microwave Theory and Techniques, vol. 36, no. 2, pp. 294-304, 1988.

A. M. Niknejad, Analysis, Simulation, and Applications of Passive Devices on Conductive Substrates, University of California, Berkeley, 2000.

R. Thüringer, Characterization of integrated Lumped inductors and Transformers, Technischen Universität Wien, Wien, 2002.

J. Brinkhoff, K. S. S. Koh, K. Kang and F. Lin, Scalable Transmission Line and Inductor Models for CMOS Millimeter-Wave Design, EEE Transactions on Microwave Theory and Techniques, vol. 56, no. 12, pp. 2954-2962, 2008.

J. Gil and H. Shin, Simple wide-band on-chip inductor model for silicon-based RFICs, in International Conference on Simulation of Semiconductor Processes and Devices, SISPAD 2003, Boston, Massachusetts, USA, 2003.

Y. Cao and e. alli, Frequency-independent equivalent-circuit model for on-chip spiral inductors, IEEE Journal of Solid-State Circuits, vol. 38, no. 3, pp. 419-426, Mar 2003.

J. W. Jeong and e. alli, Modeling of T-model equivalent circuit for spiral inductors in 90 nm CMOS technology, in Proceedings of the 2015 International Conference on Microelectronic Test Structures, Tempe, Arizona, USA, 2015.

D. G. Kleinbaum, L. L. Kupper, K. E. Muller and A. Nizam, Applied Regression Analysis and Other Multivariable Methods, 3 ed., Pacific Grove, California, USA: Duxbury Press, 1997, p. 798.

R. L. Mason, R. F. Gunst and J. L. Hess, Statistical Design and Analysis of Experiments, with Applications to Engineering and Science, New York: Jonh Wiley & Sons, 1989, p. 720.

L. Moreira, W. Van Noije, A. Farfan-Pelaez and A. dos Anjos, Small area cross type integrated inductor in CMOS Technology, in IMOC 2007 - Microwave and Optoelectronics Conference, 2007.

E. Rios, S. Garcia, L. Moreira, R. Torres and W. Van Noije, Analysis of the effects of coupling through substrate and the calculus of the Q factor, in 2013 IEEE Fourth Latin American Symposium on Circuits and Systems (LASCAS), 2013.

H. H. Chen, H. W. Zhang, S. J. Chung, J. T. Kuo and T. C. Wu, Accurate Systematic Model-Parameter Extraction for On-Chip Spiral Inductors, IEEE Transactions on Electron Devices, vol. 55, no. 11, pp. 3267-3273, Nov 2008.

D. A. Frickey, Conversions between S, Z, Y, H, ABCD, and T parameters which are valid for complex source and load impedances, IEEE Transactions on Microwave Theory and Techniques, vol. 42, no. 2, pp. 205-211, Feb 1994.

N.-J. Oh and S.-G. Lee, A Simple Model Parameter Extraction Methodology for an On-Chip Spiral Inductor, ETRI Journal, vol. 28, p. 115–118, 2006.



  • There are currently no refbacks.

© Copyright 2007-2016 JMOe Brazilian Microwave and Optoelectronics Society (SBMO) and Brazilian Society of Electromagnetism (SBMag)