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On real and complex normalizations

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Abstract

This paper presents a general expression relating the complex-normalized scattering matrix of ann-port network to that of its augmentedn-port network normalizing to then 1 −Ω resistances, where the Darlington equivalent network may be either reciprocal or nonreciprocal.

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References

  1. H. J. Carlin, A new approach to gain-bandwidth problems,IEEE Trans. Circ. Syst., vol. CAS-24, pp. 170–175, April, 1977.

    Google Scholar 

  2. H. J. Carlin and B. S. Yarman, The double matching problem: analytic and real frequency solutions,IEEE Trans. Circ. Syst., vol. CAS-30, pp. 15–28, January, 1983.

    Google Scholar 

  3. D. C. Youla, H. J. Carlin and B. S. Yarman, Double broadband matching and the problem of reciprocal reactance 2n-port cascade decomposition.Int. J. Circ. Theory Appl., vol. 12, pp. 269–281, July, 1984.

    Google Scholar 

  4. M. Uruski, Cascade decomposition of a passive 2n-port network,Int. J. Circ. Theory Appl., vol. 17, pp. 55–69, January, 1989.

    Google Scholar 

  5. R. Pauli, Darlington's theorem and complex normalization,Int. J. Circ. Theory Appl., vol. 17, pp. 429–446, October, 1989.

    Google Scholar 

  6. N. R. Wohlers,Lumped and Distributed Passive Networks, New York: Academic Press, 1969.

    Google Scholar 

  7. T. M. Chien, A theory of broadband matching of a frequency-dependent generator and load,J. Franklin Inst., vol. 298, pp. 181–221, September, 1974.

    Google Scholar 

  8. W. K. Chen,Broadband Matching: Theory and Implementations, Singapore: World Scientific, 1988.

    Google Scholar 

  9. Y. S. Zhu and W. K. Chen, A theorem on complex-normalized reflection coefficient and its applications,IEEE Trans. Circ. Syst., vol. CAS-36, pp. 1238–1244, September, 1989.

    Google Scholar 

  10. D. C. Youla, An extension of the concept of scattering matrix,IEEE Trans. Circ. Theory, vol. CT-11, pp. 310–312, June, 1964.

    Google Scholar 

  11. R. A. Rohrer, The scattering matrix: normalized to complexn-port load networks,IEEE Trans. Circ. Theory, vol. CT-12, pp. 223–230, June, 1965.

    Google Scholar 

  12. Y. S. Zhu and W. K. Chen, Realizability of lossless reciprocal and nonreciprocal broadband matching networks,J. Franklin Inst., vol. 319, pp. 325–340, March, 1985.

    Google Scholar 

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Zhu, YS., Chen, WK. On real and complex normalizations. Circuits Systems and Signal Process 12, 579–587 (1993). https://doi.org/10.1007/BF01188096

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  • DOI: https://doi.org/10.1007/BF01188096

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