224 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



works. One gets then a clearer view of the unique position occupied by 

 passive devices among all linear S3^stems. 



Third, there is a kind of semantic issue here: the assertion that any 

 finite passive network (sic) can be put in such a form that 1.1 applies 

 seems to this author to give a kind of circular characterization of such 

 devices. A characterization which did not itself involve the concept of 

 a network seems more satisfying. Logically, there is no circle here, but 

 this is a fact requiring proof. A careful reading of this paper will show 

 that it provides a proof. This particular subtlety does not of itself justify 

 the lengths to which we have gone. It is, however, no longer a subtlety 

 if one wishes to consider devices which do not have a representation in 

 terms of something non-degenerate to which ideal transformers have 

 been added. 



2.91 The present Part I of the paper is so organized that at the end of 

 Section 8 the reader is in possession of all of its principal results and its 

 basic ideas. The remaining Sections, 9 through 20, may then be regarded 

 as an Appendix containing the details of proofs. Indeed, Part II will be 

 largely devoted to further details of proof, though there will be there 

 one important idea not mentioned, save casually, in Part I — the idea 

 of degree for a matrix. 



In Sections 4 through 11, technical paragraphs have been distinguished 

 from explanatory or heuristic ones by starring the paragraph numeral. 



Part II of the paper contains the bulk of the proof of 1.1. This proof 

 is modelled after that of Brune for the realizability of two-poles. One 

 familiar with the Brune process will probably find Part II readable 

 without extensive reference to Part I. 



Let the reader be warned that the Brune process is not a practical 

 one for realizing networks because of its critical dependence upon a 

 difficult minimization and balancing operation. The same criticism 

 applies to the generalized Brune process of Part II. 



The Brune process is of theoretical importance because it does realize 

 a network with the minimum number of reactive elements. These facts 

 will be brought to light in Part II. 



The proofs of Oono and Bayard are different from ours. That of 

 Oono again follows the Brune model. 



III. INTRODUCTION TO PART I 



3.0 We keep before us first the problem of finding a mathematical de- 

 scription applicable to and characterizing the behavior of all finite pas- 



