Broadband Matching Network Design via Explicit Solutions of Two-Variable Scattering Equations

Year 2019, Volume: 3 Issue: 2, 127 - 130, 23.12.2019

Metin Şengül , Göker Eker

Abstract

In many applications, circuits containing lumped elements are preferred because they are small in size. Also the

losses in the designed circuits should be kept as low as possible. Unfortunately, especially at microwave frequencies, it is not

possible to avoid the losses caused by the connections between the lumped elements. However, the use of these connections as

circuit elements will improve the performance of the circuit. Therefore, it is inevitable to use circuits containing mixed

(lumped and distributed) elements at microwave frequencies. Mixed lumped and distributed element two-port networks are

described by means of two-variable scattering equations. So it is necessary to obtain the solutions of these equations to design

this kind of networks. In literate, the solutions of these equations for some classes of low-order ladder networks are given

under some restrictions. But in this paper, a broadband matching network is designed by using explicit solutions of the

equations without any restrictions. Then the obtained results and the results obtained in the literature have been compared.

Keywords

Scattering equations, two-port networks, broadband networks, matching networks, ladder networks

References

• L. Zhu, and A. Fettweis, “Computer design of mixed lumped and distributed lossy networks in mmics,” Int J Circ Theor App., vol. 22(3), pp. 243-249, 1994.
• D. C. Youla, J. D. Rhodes, and P. C. Marston, “Driving-point synthesis of resistor terminated cascades composed of lumped lossless passive two-ports and commensurate tem lines,” IEEE Trans. Circuit Th., vol. 19(6), pp. 648-664, 1972.
• T. Koga, “Synthesis of a resistively terminated cascade of uniform lossless transmission lines and lumped passive lossless two-ports,” IEEE Trans. Circuit Th., vol. 18(4), pp. 444-455, 1971.
• S. O. Scanlan, and H. Baher, “Driving-point synthesis of resistor terminated cascade composed of lumped lossless two-ports and commensurate stubs,” IEEE Trans. Circuits Sys., vol. 26(11), pp. 947-955, 1979.
• J. D. Rhodes, and P. C. Marston, “Cascade synthesis of transmission lines and lossless lumped networks,” Electron. Lett., vol. 7(20), pp. 621-622, 1971.
• A. Aksen, “Design of lossless two-port with mixed, lumped and distributed elements for broadband matching,” PhD thesis, Ruhr University, Bochum, Germany, 1994.
• A. Sertbaş, “Description of generalized lossless two-port ladder networks with two-variable,” PhD thesis, İstanbul University, İstanbul, Turkey, 1997.
• A. Sertbaş, A. Aksen, and B. S. Yarman, “Construction of some classes of two-variable lossless ladder networks with simple lumped elements and uniform transmission lines,” in IEEE Asia-Pacific Conference. (Thailand), 1998, p. 295-298.
• A. Aksen, and B. S. Yarman, “A real frequency approach to describe lossless two-ports formed with mixed lumped and distributed elements,” Int. J. Electron. Commun. (AEÜ), vol. 55(6), pp. 389-396, 2001.
• A. Sertbaş, “Two-variable scattering formulas to describe some classes of lossless two-ports with mixed lumped elements and commensurate stubs,” Turk. J. Elec. Eng., vol. 13(2), pp. 231-240, 2005.
• B. S. Yarman, Design of Ultra Wideband Power Transfer Networks, West Sussex, John Wiley & Sons Ltd, 2010.
• B. S. Yarman, Design of Ultra Wideband Antenna Matching Networks via Simplified Real Frequency Techniques, Springer-Verlag, 2008.
• M. Şengül, “Construction of lossless ladder networks with simple lumped elements connected via commensurate transmission lines,” IEEE Trans. CAS II Exp. Briefs, vol. 56(1), pp. 1-5, 2009.
• M. Şengül, “Design of practical broadband matching networks with mixed lumped and distributed elements,” IEEE Trans. CAS II Exp. Briefs, vol. 61(11), pp. 875-879, 2014.
• S. Basu, and A. Fettweis, “On synthesizable multidimensional lossless two-ports,” IEEE Trans. Circuits Sys., vol. 35(12), pp. 1478-1486, 1988.
• M. Şengül, and G. Eker, “Explicit two-variable scattering equations describing lossless two-ports with mixed lumped and distributed elements,” Int. J. Circuit Theory and Appl., in press.
• (2019) Microwave Office homepage on AWR. [Online]. Available: www.awrcorp.com/products/ni-awr-design-environment/microwave-office-software
• R. M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst., vol. 249(1), pp. 57-83, 1950.
• D. C. Youla, “A new theory of broadband matching,” IEEE Trans. Circuit Theory, vol. 11, pp. 30-50, 1964.