volume | PIER Journals

Abstract

In classical electromagnetics textbooks, the microwave circuits such as circulators, couplers, and filters are solved by non-systematic approaches such as even-odd mode analysis. Hence an electrical engineering student coming from the conventional circuit theory background encounters difficulties in understanding and solving microwave circuits. In this paper, we propose a modified node voltage analysis method in which the circuit branches are represented by their forward transmission matrices so that the electromagnetic wave propagation is taken care of. The Kirchhoff's current rule, tailored for high frequencies, is applied to formulate the simultaneous node voltage equations which are subsequently solved by matrix inversion. The proposed forward transmission matrix (FTM) method is applied to evaluate the S-parameters of some well-known microwave devices including the recently-developed metamaterialbased circuits. The FTM node analysis is a natural extension of the classical node analysis which is taught in the early stages of an Electrical Engineering program. Hence we anticipate that the proposed method will ease up the conceptual transition of electrical engineering students and academicians from the low-frequency alternating current circuits to high frequency RF and microwave circuits.

1. Alexander, C. K. and M. N. Sadiku, Fundamentals of Electrical Engineering, 5th Ed., 82, Mc. Graw Hill, 2013.

2. Chen, W.-K., The Electrical Engineering Handbook, 8, El Sevier Academic Press, 2004.

3. Khalil, A. I. and M. B. Steer, "Circuit theory for spatially distributed microwave circuits," IEEE Trans Micro. Theory Tech., Vol. 46, 1500-1502, 1998.
doi:10.1109/22.721154

4. Smith, C., "Frequency domain analysis of RF and microwave circuits using SPICE," IEEE Trans Micro. Theory Tech., Vol. 42, 1904-1909, 1994.
doi:10.1109/22.320772

5. Pozar, D., Microwave Engineering, 3rd Ed., 49-55, 183–187, 257–260, 318–358, John Wiley & Sons, 2005.

6. Collin, R. E., Foundations of Microwave Engineering, 2nd Ed., 85-96, 413–449, IEEE Press, 2001.
doi:10.1109/9780470544662

7. Shelby, R. A., D. R. Smith, S. Shultz, and S. C. Nemat-Nasser, "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial," App. Phys. Lett., Vol. 78, 489-491, 2001.
doi:10.1063/1.1343489

8. Smith, D. R., W. Padilla, , D. Vier, S. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett., Vol. 84, 4184-4187, 2000.
doi:10.1103/PhysRevLett.84.4184

9. Caloz, C. and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, 1st Ed., John Wiley & Sons, 2006.

10. Eleftheriades, G. V. and K. G. Balmain, Negative Refraction Metamaterials: Fundamental Principles and Applications, 1st Ed., John Wiley & Sons, 2005.
doi:10.1002/0471744751

11. Nader, E. and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations, 3-30, 37, 143–150, 215–234, 240–256, Wiley & Sons, 2006.

12. Zouhdi, S., A. Sihvola, and A. P. Vinogradov, Metamaterials and Plasmonics: Fundamentals, Modelling, Applications, Springer-Verlag, December, 2008.

13. Xu, H., G. Wang, and Q. Peng, Novel Resonant-Type Composite Right/Left Handed Transmission Line Based on Cascaded Complementary Single Split Ring Resonator In Electrical Engineering and Control, Vol. 2, 98-107, Springer-Verlag, 2011.

14. Bala, B. D., M. K. Rahim, and N. A. Murad, "Composite right/left-handed dual-band metamaterial antenna with improved gain and efficiency," Microw. Opt. Tech. Lett., Vol. 56, 1575-1579, 2014.
doi:10.1002/mop.28390

15. Siddiqui, O., A. Mohra, and G. Eleftheriades, "Quad-band power divider based on left-handed transmission lines," Elect. Lett., Vol. 46, 1441-1442, 2010.
doi:10.1049/el.2010.2511

16. Eleftheriades, G., "EM transmission-line metamaterials," Materials Today, Vol. 12, 30-41, 2009.
doi:10.1016/S1369-7021(09)70073-2

17. Antoniades, M. A. and G. V. Eleftheriades, "Compact, linear, lead/lag metamaterial phase shifters for broadband applications," IEEE Antenn. Wireless Propag. Lett., Vol. 2, 103-106, 2001.
doi:10.1109/LAWP.2003.815280

18. Hu, J., J. Xiong, T. Ling, and Y. Zou, "Design of a novel Wilkinson power splitter based on the left-handed transmission line," Microw. Opt. Tech. Lett., Vol. 49, 2975-2977, 2007.
doi:10.1002/mop.22896

19. Qureshi, F., M. A. Antoniades, and G. V. Eleftheriades, "A compact and low-profile metamaterial ring antenna with vertical polarization," IEEE Antenn. Wireless Propag. Lett., Vol. 4, 333-336, 2005.
doi:10.1109/LAWP.2005.857041

20. Siddiqui, O. and A. Mohra, "A harmonic-suppressed microstrip antenna using a metamaterialinspired compact shunt-capacitor loaded feedline," Progress In Electromagnetics Research C, Vol. 45, 151-162, 2013.
doi:10.2528/PIERC13070502

21. Siddiqui, O., M. Mojahedi, and G. V. Eleftheriades, "Periodically loaded transmission line with effective negative refractive index and negative group velocity," IEEE Trans. on Antenn. and Propag., Vol. 51, 2619-2625, 2003.
doi:10.1109/TAP.2003.817556

22. Siddiqui, O. and G. V. Eleftheriades, "Study of resonance-cone propagation in truncated hyperbolic metamaterial grids using transmission-line matrix simulations," Journal of Franklin Institute, Vol. 348, 1285-1297, 2011.
doi:10.1016/j.jfranklin.2010.02.005

23. Siddiqui, O., "Numerical investigation of phase and group propagation of time-domain signals in a novel band-reject metamaterial ring hybrid," Journal of Computer and Communications, Vol. 3, 10-17, 2015, doi: 10.4236/jcc.2015.36002.
doi:10.4236/jcc.2015.36002

24. Siddiqui, O., "Dispersion analysis of capacitive loaded negative-refractive-index transmission lines and associated applications," 8th International Symposium on Antennas, Propagation and EM Theory, (ISAPE 2008) , 698-701, Kunming, China, 2008.
doi:10.1109/ISAPE.2008.4735310

Dr. Omar F. Siddiqui