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2015-08-27
Broadband Green's Function with Low Wavenumber Extraction for Arbitrary Shaped Waveguide and Applications to Modeling of Vias in Finite Power/Ground Plane
By
, Vol. 152, 105-125, 2015
Abstract
In this paper we developed the method of broadband Green's function with low wavenumber extraction (BBGFL) for arbitrary shaped waveguide. The case of Neumann boundary condition is treated. The BBGFL has the advantage that when using it to solve boundary value problems in a waveguide, the boundary conditions have been satisfied already. The broadband Green's function is expressed in modal expansion of modes that are frequency independent. To accelerate the convergence of the Green's function, a low wavenumber extraction is performed. The singularity of the Green's function is also extracted by such low wavenumber extraction. Numerical results show that BBGLF and direct MoM are in good agreement. We next illustrate the application of BBGFL for broadband simulations of vias in printed circuit boards (PCB) by combining with the method of Foldy-Lax multiple scattering equation. The results show that BBGFL are in good agreement with MoM and HFSS. It is also shown that BBGFL is many times faster than direct MoM and HFSS. The computational efficiency in broadband simulations makes this technique useful for fast computer-aided design (CAD).
Citation
Leung Tsang, and Shaowu Huang, "Broadband Green's Function with Low Wavenumber Extraction for Arbitrary Shaped Waveguide and Applications to Modeling of Vias in Finite Power/Ground Plane," , Vol. 152, 105-125, 2015.
doi:10.2528/PIER15072605
References

1. Swaminathan, M., D. Chung, S. Grivet-Talocia, K. Bharath, V. Laddha, and J. Xie, "Designing and modeling for power integrity," IEEE Trans. Electromagn. Compat., Vol. 52, No. 2, 288-310, May 2010.
doi:10.1109/TEMC.2010.2045382

2. Li, E.-P., X.-C. Wei, A. C. Cangellaris, E.-X. Liu, Y.-J. Zhang, M. D’Amore, J. Kim, and T. Sudo, "Progress review of electromagnetic compatibility analysis technologies for packages, printed circuit boards, and novel interconnects," IEEE Trans. Electromagn. Compat., Vol. 52, No. 2, 248-265, May 2010.
doi:10.1109/TEMC.2010.2048755

3. Leone, M., "The radiation of a rectangular power-bus structure at multiple cavity-mode resonances," IEEE Trans. on Microw. Theory and Tech., Vol. 45, No. 3, 486-492, Aug. 2003.

4. Shim, H.-W. and T. H. Hubing, "A closed-form expression for estimating radiated emissions from the power planes in a populated printed circuit board," IEEE Trans. Electromagn. Compat., Vol. 48, No. 1, 74-81, Feb. 2006.
doi:10.1109/TEMC.2005.861377

5. Kim, J.-H. and M. Swaminathan, "Modeling of irregular shaped power distribution planes using transmission matrix method," IEEE Transactions on Advanced Packaging, Vol. 24, No. 3, 334-346, 2001.
doi:10.1109/6040.938301

6. Ye, X., M. Y. Koledintseva, M. Li, and J. L. Drewniak, "DC power-bus design using FDTD modeling with dispersive media and surface mount technology components," IEEE Trans. Electromagn. Compat., Vol. 43, No. 4, 579-587, Nov. 2001.

7. Ege Engin, A., K. Bharath, and M. Swaminathan, "Multilayered finite-difference method (MFDM) for modeling of package and printed circuit board planes," IEEE Trans. Electromagn. Compat., Vol. 49, No. 2, 441-447, May 2007.
doi:10.1109/TEMC.2007.893331

8. Arcioni, P., M. Bozzi, M. Bressan, G. Conciauro, and L. Perregrini, "The BI-RME method: An historical overview," 2014 International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO), May 14-16, 2014.

9. Tsang, L. and D. Miller, "Coupling of vias in electronic packaging and printed circuit board structures with finite ground plane," IEEE Transactions on Advanced Packaging, Vol. 26, No. 4, 375-384, Nov. 2003.
doi:10.1109/TADVP.2003.821081

10. Zhang, Y.-J. and J. Fan, "A generalized multiple scattering method for dense vias with axially-anisotropic modes in an arbitrarily-shaped plate pair," IEEE Trans. on Microw. Theory and Tech., Vol. 60, No. 7, 2035-2045, Jul. 2012.
doi:10.1109/TMTT.2012.2195195

11. Chang, X. and L. Tsang, "Fast and broadband modeling method for multiple vias with irregular antipad in arbitrarily shaped power/ground planes in 3-D IC and packaging based on generalized Foldy-Lax equations," IEEE Trans. Compon. Packag. Manuf. Technol., Vol. 4, No. 4, 685-696, Apr. 2014.
doi:10.1109/TCPMT.2013.2290897

12. Tsang, L. and S. Huang, "Full wave modeling and simulations of the waveguide behavior of printed circuit boards using a broadband Green's function technique,", Provisional U.S. Patent No. 62/152.702, Apr. 24, 2015.

13. Huang, S., "Broadband Green's function and applications to fast electromagnetic analysis of high-speed interconnects,", Ph.D. dissertation, Dept. Elect. Eng., Univ. Washington, Seattle, WA, Jun. 2015.

14. Huang, S. and L. Tsang, "Broadband Green’s function and applications to fast electromagnetic modeling of high speed interconnects," IEEE International Symposium on Antennas and Propagation, Vancouver, BC, Canada, Jul. 2015.

15. Ishimaru, A., Electromagnetic Wave Propagation, Radiation, and Scattering, Prentice-Hall, 1991.

16. Tsang, L., J. A. Kong, K. H. Ding, and C. Ao, Scattering of Electromagnetic Waves, Volume 2, Numerical Simulations, Wiley, New York, NY, USA, 2001.
doi:10.1002/0471224308

17. Tsang, L., H. Chen, C. C. Huang, and V. Jandhyala, "Modeling of multiple scattering among vias in planar waveguides using Foldy-Lax equations," Microw. Opt. Tech. Lett., Vol. 31, 201-208, Nov. 2001.

18. Chen, H., Q. Li, L. Tsang, C. C. Huang, and V. Jandhyala, "Analysis of large number of vias and differential signaling in multi-layered structures," IEEE Trans. on Microw. Theory and Tech., Vol. 51, 818-829, Mar. 2003.
doi:10.1109/TMTT.2003.808616

19. Gu, X., B. Wu, C. Baks, and L. Tsang, "Fast full wave analysis of PCB via arrays with model-to-hardware correlation," IEEE 18th Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS'09), 175-178, 2009.

20. Wu, B. and L. Tsang, "Modeling multiple vias with arbitrary shape of antipads and pads in high speed interconnect circuits," IEEE Microwave and Wireless Comp. Lett., Vol. 19, 12-14, 2009.

21. Tsang, L. and X. Chang, "Modeling of vias sharing the same antipad in planar waveguide with boundary integral equation and group T matrix method," IEEE Trans. Compon. Packag. Manuf. Technol., Vol. 3, No. 2, 315-327, Feb. 2013.
doi:10.1109/TCPMT.2012.2220771