A novel synthesis method for a class of time-domain passive filters that compensates for waveform distortion caused by frequency dependencies of the transmission properties of signal propagation paths, is formulated. The method is based on the linear response theory and mathematical properties of scattering matrices for passive circuits. This paper focuses on the formulation and theoretical consistency of the method. The causal transfer functions for the filters can be extracted by "regularizing" the inverse of a transfer function of the path. To fulfill the necessary restrictions imposed on the causal functions, regularization is realized by multiplying the function of linear phase filters comprising a sufficient number of resonators by the inverse. The filter circuits are easily derived from the regularized transfer functions through numerical optimization techniques and the coupling matrix synthesis method to determine transmission poles and extract each lumped element value, respectively. The method is then applied to practically designing a filter that compensates for the frequency dependencies of a two-port radio propagation path having a pair of wideband antennas. In addition, applications of the filter and the scope of further developments of this technology are discussed.
2. Brogan, W. L., Modern Control Theory, 3rd Edition, Prentice Hall, New Jersey, 1990.
3. Collin, R. E., Foundation for Microwave Engineering, 2nd Edition, 254-255, Wiley, New York, 2001.
4. Cameron, R. J., "Advanced coupling matrix synthesis techniques for microwave filters ," IEEE Trans. on Microw. Theory and Tech., Vol. 51, No. 1, 1-10, Jan. 2003.
5. Cameron, R. J., "General coupling matrix synthesis methods for Chebyshev filtering functions," IEEE Trans. on Microw. Theory and Tech., Vol. 47, No. 4, 433-442, Apr. 1999.
6. Amari, S., "Direct synthesis of folded symmetric resonator filters with source-load coupling," IEEE Microw. Wireless Compon. Lett., Vol. 11, No. 6, 264-66, Jun. 2001.
7. Amari, S. and U. Rosenberg, "Direct synthesis of a new class of bandstop filters," IEEE Trans. on Microw. Theory and Tech., Vol. 52, No. 2, 607-616, Feb. 2004.
8. Bairavasubramanian, R. and J. Papapolymerou, "Fully canonical pseudo-elliptic bandpass filters on multilayer liquid crystal polymer technology," IEEE Microw. Wireless Compon. Lett., Vol. 17, No. 3, 190-192, Mar. 2007.
9. Helszajn, J., Synthesis of Lumped Element, Distributed and Planer Filters, McGraw-Hill, London, 1990.
10. Rhodes, J. D., "A low-pass prototype network for microwave linear phase filters," IEEE Trans. on Microw. Theory and Tech., Vol. 18, No. 6, 290-301, Jun. 1970.
11. Hong, J. G. and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications, Wiley, New York, 2001.
12. Henderson, R. K., L. Ping, and J. I. Sewell, "Extended Remez algorithms for filter amplitude and group delay approximation," IEEE Proceedings G, Vol. 138, No. 3, 289-300, Jun. 1991.
13. Jinno, T., Y. Saito, and M. Okuda, "A study on weighting scheme for rational Remez algorithm," IEICE Trans. on Fundamentals, Vol. E94.A, No. 4, 1144-1147, Apr. 2011.
14. Reich, J. G., C Curve Fitting and Modeling for Scientists and Engineers, McGraw-Hill, New York, 1991.
15. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd Edition, Cambridge University Press, Cambridge, 1995.
16. Deschrijver, D. and T. Dhaene, "Fully parameterized macromod-eling of S-parameter aata by interpolation of numerator & denominator," IEEE Microw. Wireless Compon. Lett., Vol. 22, No. 6, 309-311, Jun. 2012.
17. Silverman, R. A., Introductory Complex Analysis, Dover, 1984.
18. Tseng, C. C. and S. L. Lee, "Design of variable fractional order differentiator using infinite product expansion," Proc. 2011 20th European Conference on Circuit Theory and Design (ECCTD2011) , 17-20, Aug. 2011.
19. , , "IE3D user's manual: Release 11,", Zeland Software, Feb. 2005.
20. Wang, Y., J. Li, and L.-X. Ran, "An equivalent circuit modeling method for ultra-wideband antennas," Progress In Electromagnetics Research, Vol. 82, 433-445, 2008.