DocumentCode
1163943
Title
A Limitation of the Series-Parallel Structure
Author
Fialkow, Aaron D.
Volume
15
Issue
2
fYear
1968
fDate
6/1/1968 12:00:00 AM
Firstpage
124
Lastpage
132
Abstract
This paper disproves Darlington\´s conjecture that every 
-grounded two-port is equivalent to a series-parallel two-port. The proof depends upon the construction of a counterexample. This counterexample is a six-node -grounded two-port, whose admittance functions 
written without common factors, have compact poles at the zeros of 
and for which 
has a negative coefficient. In accordance with properties of series-parallel networks derived in an earlier paper, the network of the counterexample cannot be equivalent to any series-parallel two-port.
-grounded two-port is equivalent to a series-parallel two-port. The proof depends upon the construction of a counterexample. This counterexample is a six-node -grounded two-port, whose admittance functions written without common factors, have compact poles at the zeros of and for which has a negative coefficient. In accordance with properties of series-parallel networks derived in an earlier paper, the network of the counterexample cannot be equivalent to any series-parallel two-port.Keywords
Darlington´s conjecture; Two-ports; Admittance; Capacitance; Equations; Frequency; Helium; Impedance; Inductance; Network synthesis; Poles and zeros; Transfer functions;
fLanguage
English
Journal_Title
Circuit Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9324
Type
jour
DOI
10.1109/TCT.1968.1082803
Filename
1082803
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