On the problem of degree reduction of a scattering matrix by factorization

✍ Scribed by P. Dewilde; V. Belevitch; R.W. Newcomb

• Publisher: Elsevier Science
• Year: 1971
• Tongue: English
• Weight: 951 KB
• Volume: 291
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(71)90074-3

✦ Synopsis

Bebvitch

(1) haa shown that, starting from a given paseive, rational, n x n scattering muttix S( p) of degree 6, one can proceed to a realization by factoring it in the form S(P) = S,(P)S,(P), where S,(p) is an n x n, lorrslees acaltering matrix of degree one, while the degree of S1( ) is redwed to 6 -1. Some su.cient conditiona allowing the stated jactorizution were developed by Youlu (2) and Belevitch (3) but complete necessary and su.cient condiGons were not obtained. Complete conditions are derived here by two different and complementary methoda, one based on Hankel matrices, the other on the Smith-MacMillan form. Moreover, several errors of the above-mentioned papers are corrected. The resulting condilions are quite Bimpb and only involve the structure of the reaiativity matrix of the given network in the neighborhood of a singularity. Finally, the conditions clarify certain aqvecta of the cascade 8ynthesis of passive n-ports and &crease the similarity of this process with the Darlington one-port synthesis.