Application of the Wheeler Incremental Inductance Rule for Robust Design and Modeling of MMIC Spiral Inductors
Keywords:
Application of the Wheeler Incremental Inductance Rule for Robust Design and Modeling of MMIC Spiral InductorsAbstract
A physics based model using Wheelers incremental inductance rule for calculating the change in inductance due to variations in line width and thickness for planar circular spiral inductors is given. It is shown that the series resistance of an MMIC inductor can be used as a figure of merit for the robustness of the inductor against etching variations in line width during fabrication. Circular inductors are shown to have less inductance variation than rectangular inductors. This model can be evaluated quickly using a circuit simulator without the need for expensive EM analysis. In the electromagnetic modeling of MMIC inductors, a fine grid and several sheets are used to accurately model the current distribution and determine the resistance. SonnetTM is used to accurately model the 3D characteristics of thick conductors such as loss and effects of physically thick metal. A procedure based on the Richardson extrapolation method is used to extract the resistance values without long computation time. Applications include calculating the change in inductance due to overor under-etching of metal lines during fabrication. For 2 to 4 turn inductors with variations in line width of +/-20% of the nominal width, the average variation in modeled inductance is within 8% of the EM simulated variation.
Downloads
References
H. A. Wheeler, “Formulas for the Skin
Effect,” Proc. IRE, vol. 30, no. 9, pp. 412-424,
Sept. 1942.
R. A Pucel, D. J. Masse, and C. P. Hartwig,
“Losses in Microstrip,” IEEE Trans. Microw.
Theory Tech., vol. 16, no. 6, pp.342-350, June
R. K. Hoffmann, Handbook of Microwave
Integrated Circuits, Boston, Artech House,
G. Kompa, Practical Microstrip Design and
Applications, Boston, Artech House, 2005.
L. Dworsky, Modern Transmission Line
Theory and Applications, New York, Wiley,
G. A. Ellis, “Application of Wheeler’s
Incremental Inductance Rule for Simulating
the Effect of Etching Variations in Circular
Inductors in MMICs,” INAS 2009, Dec. 2009.
Sonnet Suites, Release 12, “Users Guide”,
Chapter 18, Syracuse NY, 2009.
K. Chatterjee, “A Stochastic Algorithm for the
Extraction of Partial Inductances in IC
Interconnect Structures,” Applied
Computational Electromagnetic Society
(ACES) Journal, vol. 21, no. 1, pp. 81-89,
March 2006.
H. A. Wheeler, “Transmission-Line Properties
of Parallel Strips Separated by a Dielectric
Sheet,” IEEE Microw. Theory Tech, vol. 13,
no. 3, pp. 172-185, March 1965.
D. L. Sanderson, J. C. Rautio, R. A. Groves,
and S. Raman, “Accurate Modeling of
Monolithic Inductors using Conformal
ELLIS: APPLICATION OF THE WHEELER INCREMENTAL INDUCTANCE RULE FOR MODELING OF MMIC SPIRAL INDUCTORS 492
Meshing for Reduced Computation,” IEEE
Micro. Mag., pp. 87-96, Dec. 2003.
Microwave Offices 2008, AWR, MWO/AO
User’s Guide.
I. J. Bahl, “High Performance Inductors,”
IEEE Trans. Microw. Theory Tech., vol. 49,
no. 4, pp. 654-664, April 2001.
S. Abdelbagi and G. A. Ellis, “Effects of
Variations in Line Width on the Equivalent
Circuit Model of Microstrip Spiral Inductors
Implemented using GaAs Technology,”
SCOReD 2008, pp. 267-1–267-4, Nov. 2008.
G. A. Ellis, “Application of the Wheeler
Incremental Inductance Rule for Robust
Design and Modeling of MMIC Spiral
Inductors,” 26th Annual Review of Progress in
Applied Compuatational Electromagnetics,
Tampere, Finland, April 26-29, 2010.
R. C. Culver, “The Use of Extrapolation
Techniques with Electrical Network Analogue
Solutions,” Brit J. Appl. Phys., vol. 3, pp. 376-
, 1952.
H. E. Green, “The Numerical Solution of
Some Important Transmission Line
Problems,” IEEE Trans. Microw. Theory
Tech, vol. MTT-13, no. 5, pp. 676-692, 1965.
R. Garg, Analytical and Computational
Methods in Electromagnetics, Boston, Artech
House, 2008.
S. Butterworth, “On the Alternating Current
Resistance of Solenoidal Coils”, Proc. Roy.
Soc. vol. 107A, p. 693, 1925.
