Triple Frequency Impedance Matching by Frequency Transformation
The purpose of this chapter is to bring to the attention of students and teachers of circuit theory, as well as of practising design engineers, a recently reported technique for impedance matching at multiple frequencies. This will be done through a specific example, namely that of design of a lumped network for matching a given load resistance RL to a given source resistance RS at three given frequencies ω1, ω2 and ω3. The method is based on the application of the frequency transformation technique, commonly used in analog filter design, to a basic single-frequency matching network. By comparison with the existing approach of assuming a network configuration and solving a set of simultaneous equations, as reported in a recent paper, the new method is shown to have the advantages of design by synthesis, elegance and simplicity. Further, by virtue of the synthesis approach, the method allows a number of alternative networks to be designed, so that the best one can be selected on the basis of a predetermined criterion.
KeywordsFrequency transformation Network design Impedance matching Multiple frequency matching
This work was supported by the Indian National Science Academy through the Honorary Scientist scheme. The author thanks Shoubhik Dutta Roy and Yashwant V. Joshi for their help in the preparation of this chapter. Thanks are also due to the reviewer for constructive comments.
- 1.C. Monzon, A small dual frequency transformer in two sections. IEEE Trans. Microw. Theory Tech. 51, 1157–61 (2003)Google Scholar
- 2.Y. Wu, Y. Liu, S. Li, A dual frequency transformer for complex impedances with two unequal sections. IEEE Microw. Wirel. Compon. Lett. 19, 77–79 (2009)Google Scholar
- 3.X. Liu, Y. Liu, S. Li, F. Wu, Y. Wu, A three section dual band transformer for frequency dependent complex load impedance. IEEE Microw. Wirel. Compon. Lett. 19, 611–613 (2009)Google Scholar
- 4.F. Paredes, G. Gonzales, J. Bonache, F. Martin, Dual band impedance matching networks based on split-ring resonators for application in RF identification (RFID). IEEE Trans. Microw. Theory Tech. 58, 1159–1166 (2010)Google Scholar
- 5.M.L. Chuang, Dual band impedance transformer using two section shunt stubs. IEEE Trans. Microw. Theory Tech. 58, 1257–1263 (2010)Google Scholar
- 6.C.S. Lee, C.-L Yang, A coupling matrix based design of triple band matching network. IEEE Microw. Wirel. Compon. Lett. 23, 391–393 (2013)Google Scholar
- 8.Y. Liu, Y. Chen, Y.J. Zhao, Lumped triple-frequency impedance transformer. Electron. Lett. 48, 1193–1194 (2012)Google Scholar
- 9.N. Nallam, S. Chatterjee, Multi-band frequency transformations, matching networks and amplifiers. IEEE Trans. Circuits Syst.-I: Regular Papers. 60, 1635–1647 (2013)Google Scholar
- 10.S.C. Dutta Roy, Network design for multiple frequency impedance matching by the frequency transformation technique. IETE J. Res. 59, 698–703 (2013)Google Scholar
- 11.S.C. Dutta Roy, On the design of a multiple pass-band filter by frequency transformation. IETE J. Res. 58, 20–23 (2012)Google Scholar
- 12.L. Wienberg, Network Analysis and Synthesis (Wiley, Hoboken, NJ, 1962)Google Scholar
- 13.E.A. Guillemin, Synthesis of Passive Networks (Wiley, Hoboken, NJ, 1964)Google Scholar