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Symbolic analysis of immittance inverters - Telfor

Symbolic analysis of immittance inverters - Telfor

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L 4 C 4R g L 2 C 2V g. . . L 3 C 3 L 1 C 1 R loadFig. 11. Ladder LC realization <strong>of</strong> a bandpass filter.K n+1L 02 C 02K 2L 01 C 01 K 1R 0gV g. . .R 0,loadFig. 12. Impedance inverter realization <strong>of</strong> the bandpass filter from Fig. 10.J n+1J 2R 0g J 1V g. . . L 02 C 02 L 01 C 01 R 0,loadFig. 13. Admittance inverter realization <strong>of</strong> the bandpass filter from Fig. 10.VII. CONCLUSIONWe revisited definition, operation, and realization <strong>of</strong><strong>immittance</strong> <strong>inverters</strong>. By using Mathematica as acomputer algebra system we symbolically analyzed theinversion mechanism and presented exact equivalentnetworks for transformation <strong>of</strong> series impedance to shuntadmittance and vice versa. The equivalent networks areimportant for understanding practical implementations <strong>of</strong>bandpass and bandstop filters, particularly their phaseresponse, when starting from the realizations that use<strong>immittance</strong> <strong>inverters</strong>.ACKNOWLEDGMENTWe thank Ministry <strong>of</strong> Science and EnvironmentalProtection <strong>of</strong> the Republic <strong>of</strong> Serbia for partial support <strong>of</strong>our research on this topic (Project TR–6154).REFERENCES[1] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters,Impedance-Matching Networks, and Coupling Structures, McGraw-Hill, New York, 1964. Reprinted by Artech House, Norwood, MA,1980.[2] J. A. G. Malherbe, Microwave Transmission Line Filters, ArtechHouse, Dedham, Massachusetts, 1979.[3] R. W. Rhea, HF Filter Design and Computer Simulation, NoblePublishing, Norcross, GA, USA, 1994.[4] Jia-Sheng Hong, M. J. Lancaster, Microstrip Filters forRF/Microwave Applications, John Wiley, New York, 2001.[5] R. E. Collin, Foundations For Microwave Engineering, 2 nd Ed.,McGraw-Hill, New York, 1992.[6] D. M. Pozar, Microwave Engineering, 3 rd Ed., John Wiley, NewYork, 2005.[7] S. Wolfram, The Mathematica Book, Cambridge University Press,Cambridge, 2003.587

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