# DYNAMIC TTL METHOD APPLIED TO THE FIN-LINE RESONATORS

## Authors

• Humberto César Chaves Fernandes
• Magno Cavalcante da Silva

## Keywords:

TTL Method, Millimeter Waves, Resonator, Finline

## Abstract

The full wave TTL method is used to calculate the complex resonance frequency of the rectangular finline resonator. Also is used Fortran PowerStation for the calculation of this resonance frequency. Beside, the results are still presented in graphs in three dimensions. A slot resonator in unilateral fin line is a basic circuit element that is extensively used as a building block in the design of fin-line filters. It is also useful in other millimeter-wave circuits, such as oscillators and mixers. In the direct and concise TTL method, the Maxwell's equations in Fourier transform domain are firstly used to obtain the electromagnetic fields in terms of the transversal electromagnetic fields. By applying the boundary conditions, the fields in all dielectric regions are determined as functions of the electric fields in the resonant slot. An inhomogeneous equation system is obtained, in which the current densities in the conductor fins are related to the electric fields in the slot. By expanding these fields in terms of suitable basis functions and using the moment method and the Parseval's theorem, the current densities are eliminated, and a homogeneous equation system is obtained with two variables. The complex resonant frequency is obtained by setting the determinant of the system matrix equal to zero. The results for the unilateral fin line resonator are presented for different parameters including substrate thickness, permittivity, length and width of the slot resonator.

## References

Meier, P. J., "Two new integrated-circuit media with special advantages at millimeter wavelengths``, IEEE MTT-S Digest, 221-223, 1972.

Meier, P. J., "Integrated fin-line millimeter components``, IEEE Trans. On Microwave Theory and Tech., Vol. MTT-22, 1209-1216, Dec. 1974.

Baht, B. and S. K. Koul, "Analysis, design and applications of finlines``, Artech House, 1987.

Fernandes, H. C. C., Sidney A. P. Silva and Luiz C. Freitas Jr. "A Coupler with Losses in Millimeter Waves``. SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference, Natal, Brazil, pp. 59-64, August 11 - 14, 1997.

Fernandes, H. C. C. and Sidney A. P. Silva. "The TTL Method Applied to the Fin Line Coupler``, IRMMW â€“ 22th International Conference on Infrared and Millimeter Microwave, Wintegreen, VA, USA, pp. 371-372, July 1997.

Schmidt, L. P., T. Itoh and H. Hoffmann, "Characteristics of unilateral finline structures with arbitrary located slots``, Trans. on Microwave Theory and Tech., Vol. MTT-29, 352-355, April 1981.

Fernandes, H. C. C., "Structures glide general in waveguide millimeters: lines of sheets", Doctoral Thesis, 189p., FEC, UNICAMP, Campinas â€“ SP, July 1984, Advisor: A. J. Giarola.

Fernandes, C. C., R. F. Souza and A. J. Giarola, "The ETL and simplified TTL method applied to the analysis of generalized finlines``, International Conference and Workshop on Electromagnetic Interference and Compatibility, Bangalore, India, pp. 221-224, September, 1987.

Mendonça, L. M., "Analysis of complete wave of the line of transverse transmission for lines of three-dielectrics arbitrary unilateral sheets``, Master's Thesis, PPgEE â€“ DEE â€“ CT â€“ UFRN, Natal â€“ RN, 68p. July 1987, Advisor: H. C. C. Fernandes.

Fernandes, H. C. C., A. J. Giarola, R. F. Souza, L. M. Mendonça, D. H. B. Miranda and R. M. R. P. Spinelli, "The use of the TTL method for calculation of dispersion in slot lines and tridielectric unilateral finlines``, International Microwave Symposium â€“ SBMO, Rio de Janeiro â€“ RJ, Brazil, Vol. I, 405-411, July 1987.

Fernandes, H. C. C., A. Queiroz, Sidney A. P. Silva and C. Laerte, "Dispersion in arbitrary bilateral, antipodal, and unilateral fin lines and edge-coupled slotlines with semiconductor regions.`` SPIE's International Symposium on Optical Science, Engineering, and Instrumentation - San Diego, California USA, SPIE Proceedings Vol. 2558, pp. 122-130, July 1995.

Fernandes, H. C. C., Sidney A. P. Silva (IC) and Carlos L. Rodrigues (IC), "3-D Applications In Fin Lines With Semiconductor Substrate``, Invited, PIERS 1996-The Progress in Electromagnetics Research Symposium, Innsbruck, Austria. Conf. Proc. p.254. July 1996.

Farias, A. R. N. and H. C. C. Fernandes, "Microstrip antenna design using the TTL method``, 1997 SBMO/IEEE International Microwave and Optoelectronics Conference, Natal-RN, pp. 291-296, Aug. 1997.

Agrawal, A. K. and B. Bhat, "Resonant Characteristics and End Effects of a Slot Resonator in Unilateral Fin Line``, Proc. IEEE, Vol. 72, 1416-1418, Oct. 1984.

Fernandes, H. C. C., Sidney A. P Silva and José P. Silva, ``Coupling Analysis at the Coupler and Edge-Coupled Unilateral Fin Line``, International Conference on Millimeter And Submillimeter Waves and Applications II, SPIE's 1998 International Symposium on Optical Science, Engineering and Instrumentation, San Diego, California, USA. Conf. Proc. 53-54, July de 1998.

Fernandes, H. C. C., S.A.P. Silva and L. C. de Freitas Junior, "Complex Propagation Results in 3-D of the Generic Arbitrary Bilateral Finlines``, 22th Intern. Conf. on Infrared and Millimeter Waves, Wintergreen, VA, USA, Conf. Proc. 340-341, July, 1997.

Fernandes, H. C. C, "Coupling Analysis, Thick Edge-Coupled and Asymmetric Unilateral Fin Line``. Piers2000 â€“ Progress In Electromagnetic Research Symposium, Cambridge â€“ MA, USA, p. 1160, July 2000.

Fernandes, H. C. C, "An Efficient Analysis of Superconducting Microstrip Patch Antennas Arrays``. Piers2000 â€“ Progress In Electromagnetic Research Symposium, Cambridge â€“ MA, USA, p. 1162, July 2000.

2001-05-04

## How to Cite

Humberto César Chaves Fernandes, & Magno Cavalcante da Silva. (2001). DYNAMIC TTL METHOD APPLIED TO THE FIN-LINE RESONATORS. Journal of Microwaves, Optoelectronics and Electromagnetic Applications (JMOe), 2(3), 57-66. Retrieved from http://www.jmoe.org/index.php/jmoe/article/view/65

Regular Papers