Symbolic analysis of immittance inverters - Telfor

L 4 C 4R g L 2 C 2V g. . . L 3 C 3 L 1 C 1 R loadFig. 11. Ladder LC realization of a bandpass filter.K n+1L 02 C 02K 2L 01 C 01 K 1R 0gV g. . .R 0,loadFig. 12. Impedance inverter realization of 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 of the bandpass filter from Fig. 10.VII. CONCLUSIONWe revisited definition, operation, and realization ofimmittance inverters. By using Mathematica as acomputer algebra system we symbolically analyzed theinversion mechanism and presented exact equivalentnetworks for transformation of series impedance to shuntadmittance and vice versa. The equivalent networks areimportant for understanding practical implementations ofbandpass and bandstop filters, particularly their phaseresponse, when starting from the realizations that useimmittance inverters.ACKNOWLEDGMENTWe thank Ministry of Science and EnvironmentalProtection of the Republic of Serbia for partial support ofour 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