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 On the synthesis of twoelementkind multiport networks
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On the synthesis of twoelementkind multiport networks Stein, Richard Adolph
Abstract
Procedures for the synthesis of a class of twoelementkind multiport networks are developed and illustrated by examples. In the RC case, the networks consist of the series connection of an R network and an RC network. The latter contains at least one capacitor tree so that its opencircuit impedance matrix vanishes at infinite frequency. It is shown that for a network within the class, the opencircuit impedance matrix and the normal form state model are equivalent in that, given one, the other can be written immediately. The synthesis problem then takes the form of the determination of a normal coordinate transformation such that the transformed state variables may be identified as capacitor voltage variables in a passive RC network. Two procedures are described for determining a transformation (modal) matrix which yields an irreducible realization of a given kxk, nͭʰ degree impedance matrix. There are ½(nk) (nkl) degrees of freedom in the modal matrix. General analytical solutions are possible when n≤k+2, one greater than in existing methods. The main procedure yields a network with, in general, n + ½k(k+1) capacitors. A set of necessary conditions, easily applied to the given impedance matrix, is derived. Necessary and sufficient conditions are given for the special case k=2, n=3 An alternative procedure yields a network with n capacitors. Using either procedure, it is possible to simultaneously minimize both the number of elements and the total capacitance in the network. By introducing additional equations into the main procedure, numerical solutions for the modal matrix may be determined for any value of n. With k=2, the procedure yields a new class of minimal, grounded twoport networks consisting of one πsection and n2 Tsections connected in parallel. The severity of the realizability conditions is approximately proportional to n. A given 2x2 impedance matrix may be realized exactly, or one drivingpoint impedance function may be realized, exactly and the transfer impedance function with a desired gain factor (within the limits of realizability). A computational procedure is given which minimizes the total capacitance and optimizes the voltage gain factor.
Item Metadata
Title  On the synthesis of twoelementkind multiport networks 
Creator  Stein, Richard Adolph 
Publisher  University of British Columbia 
Date Issued  1968 
Description 
Procedures for the synthesis of a class of twoelementkind multiport networks are developed and illustrated by examples. In the RC case, the networks consist of the series connection of an R network and an RC network. The latter contains at least one capacitor tree so that its opencircuit impedance matrix vanishes at infinite frequency. It is shown that for a network within the class, the opencircuit impedance matrix and the normal form state model are equivalent in that, given one, the other can be written immediately. The synthesis problem then takes the form of the determination of a normal coordinate transformation such that the transformed state variables may be identified as capacitor voltage variables in a passive RC network.
Two procedures are described for determining a transformation (modal) matrix which yields an irreducible realization of a given kxk, nͭʰ degree impedance matrix. There are ½(nk) (nkl) degrees of freedom in the modal matrix. General analytical solutions are possible when n≤k+2, one greater than in existing methods.
The main procedure yields a network with, in general, n + ½k(k+1) capacitors. A set of necessary conditions, easily applied to the given impedance matrix, is derived. Necessary and sufficient conditions are given for the special case k=2, n=3 An alternative procedure yields a network with n capacitors. Using either procedure, it is possible to simultaneously minimize both the number of elements and the total capacitance in the network.
By introducing additional equations into the main procedure, numerical solutions for the modal matrix may be determined for any value of n. With k=2, the procedure yields a new class of minimal, grounded twoport networks consisting of one πsection and n2 Tsections connected in parallel. The severity of the realizability conditions is approximately proportional to n. A given 2x2 impedance matrix may be realized exactly, or one drivingpoint impedance function may be realized, exactly and the transfer impedance function with a desired gain factor (within the limits of realizability). A computational procedure is given which minimizes the total capacitance and optimizes the voltage gain factor.

Subject  Electric networks 
Genre  Thesis/Dissertation 
Type  Text 
Language  eng 
Date Available  20110629 
Provider  Vancouver : University of British Columbia Library 
Rights  For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. 
DOI  10.14288/1.0104245 
URI  
Degree  Doctor of Philosophy  PhD 
Program  Electrical and Computer Engineering 
Affiliation  Applied Science, Faculty of; Electrical and Computer Engineering, Department of 
Degree Grantor  University of British Columbia 
Campus  UBCV 
Scholarly Level  Graduate 
Aggregated Source Repository  DSpace 
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For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.