DocumentCode :
1199499
Title :
On the Compactness of an RC Quadripole
Author :
Slepian, Paul
Volume :
5
Issue :
1
fYear :
1958
fDate :
3/1/1958 12:00:00 AM
Firstpage :
61
Lastpage :
65
Abstract :
Consider an RC quadripole with open-circuit impedances z_{11}(s) , z_{12}(s) , and z_{22}(s) , and let s_v be a pole of any of these functions. If k_{11}(v), k_{12}(v) , and k_{22}(v) are the respective residues of these three functions at s_v , then it is well-known that k_{11}(v)k_{22}(v) - [k_{12}(v)]^2 \\geq 0 . If the inequality is an equality, then s_v is called a compact pole; if every such pole is compact, the network is called compact. In this paper two new properties of compactness are exhibited and discussed. It is shown that if the network is grounded, noncompactness implies certain degeneracies in the determinant of the nodal admittance matrix and its cofactors. If the network is terminated with a resistance R , it is shown that for all but a finite number of values of R , the overall terminated network is compact. Thus, a noncompact resistance terminated RC quadripole can be approximated to any degree of accuracy by a compact network of this type, which implies that noncompactness is not detectable by terminal measurements of the open-circuit impedances.
Keywords :
Admittance; Capacitance; Circuit theory; Electrical resistance measurement; Frequency; Impedance measurement; Poles and zeros; Sufficient conditions; Terminology; Transfer functions;
fLanguage :
English
Journal_Title :
Circuit Theory, IRE Transactions on
Publisher :
ieee
ISSN :
0096-2007
Type :
jour
DOI :
10.1109/TCT.1958.1086424
Filename :
1086424
Link To Document :
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