Vol. 107
Latest Volume
All Volumes
PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2022-02-01
An Analytic Model for Stripline/Microstrip Potential Using Infinite Series with Mixed Boundary Conditions
By
Progress In Electromagnetics Research M, Vol. 107, 231-242, 2022
Abstract
This paper derives an infinite series solution to the Laplace equation for the electric scalar potential of a stripline/microstrip transmission line. Due to the presence of a mixed Dirichlet/Neumann boundary condition, traditional solution methods involving mode orthogonality cannot be applied. Instead, three new solution methods are explored, which are collocation, minimum discrete-squared error (MDSE), and minimum mean-squared error (MMSE). Results yield excellent agreement compared to numerical simulation of capacitance per unit length. However, the Gibbs phenomenon appears to bias the outcome with a small (≈ 0.5%) under-estimation of the true result.
Citation
James R. Nagel , "An Analytic Model for Stripline/Microstrip Potential Using Infinite Series with Mixed Boundary Conditions," Progress In Electromagnetics Research M, Vol. 107, 231-242, 2022.
doi:10.2528/PIERM21081604
http://www.jpier.org/PIERM/pier.php?paper=21081604
References

1. Maloratsky, L. G., "Reviewing the basics of microstrip lines," Microwaves & RF, No. 3, 79-88, 2000.

2. Edwards, T. C. and M. B. Steer, Foundations for Microstrip Circuit Design, 4th Ed., Wiley-IEEE Press, 2016.
doi:10.1002/9781118936160

3. Khater, M. A., "High-speed printed circuit boards: A tutorial," IEEE Circuits and Systems Magazine, Vol. 20, No. 3, 34-45, 2020.
doi:10.1109/MCAS.2020.3005484

4. Ulaby, F. T. and U. Ravaioli, Fundamentals of Applied Electromagnetics, 7th Ed., Prentice Hall, Essex, 2015.

5. Pozar, D. M., Microwave Engineering, 4th Ed., Wiley, Hoboken, NJ, 2011.

6. Cohn, S. B., "Characteristic impedance of the shielded-strip transmission line," Transactions of the IRE Professional Group on Microwave Theory and Techniques, Vol. 2, No. 2, 52-57, 1977.
doi:10.1109/TMTT.1954.1124875

7. Rao, J. S. and B. N. Das, "Analysis of asymmetric stripline by conformal mapping," IEEE Transactions on Microwave Theory and Techniques, Vol. 27, No. 4, 299-303, 1979.
doi:10.1109/TMTT.1979.1129619

8. Homentcovschi, D., A. Maolescu, A. M. Manolescu, and L. Kreindler, "An analytical solution for the coupled stripline-like microstrip line problem," IEEE Antennas and Propagation Magazine, Vol. 36, No. 6, 1002-1007, 1988.

9. Cattaneo, P. W., "Capacitances in micro-strip detectors: A conformal mapping approach," Solid-State Electronics, Vol. 54, No. 1, 252-258, 2010.
doi:10.1016/j.sse.2009.09.030

10. Bahl, I. J. and D. K. Trivedi, "A designer's guide to microstrip line," Microwaves, Vol. 16, No. 5, 174-182, 1977.

11. Nagel, J. R., "Numerical solutions to Poisson equations using the finite difference method," IEEE Antennas and Propagation Magazine, Vol. 56, No. 4, 209-224, 2014.
doi:10.1109/MAP.2014.6931698

12. Chang, T.-N. and C.-H. Tan, "Analysis of a shielded microstrip line with finite metallization thickness by the boundary element method," IEEE Transactions on Microwave Theory and Techniques, Vol. 38, No. 8, 1130-1132, 1990.
doi:10.1109/22.57340

13. Peric, M., A. N. V. Sasa, S. Ilic, and N. B. Raicevic, "Improving the efficiency of hybrid boundary element method for electrostatic problems solving," ACES Journal, Vol. 35, No. 8, 872-877, 2020.
doi:10.47037/2020.ACES.J.350804

14. Powers, D. L., Bounadry Value Problems and Partial Differential Equations, 6th Ed., Elsevier, Burlington, 2010.

15. Read, W. W., "An analytic series method for laplacian problems with mixed boundary conditions," Mathematics and Statistics, Vol. 209, No. 1, 22-32, 2007.

16. Bryant, T. G. and J. A. Weiss, "Parameters of microstrip transmission lines and of coupled pairs of microstrip lines," IEEE Transactions on Microwave Theory and Techniques, Vol. 16, No. 12, 1021-1027, 1968.
doi:10.1109/TMTT.1968.1126858

17. Bahl, I. J. and P. Bhartia, "The design of broadside coupled stripline circuits," IEEE Transactions on Microwave Theory and Techniques, Vol. 29, No. 2, 165-168, 1981.
doi:10.1109/TMTT.1981.1130315

18. Trefethen, L. N., Spectral Methods in MATLAB, SIAM, Philadelphia, 2001.

19. Maloratsky, L. G., "Reviewing the basics of suspended striplines," Microwave Journal, 82-98, October 2002.