Series-parallel grounded two-ports

Aaron Fialkow
1966 Quarterly of Applied Mathematics  
Introduction. The synthesis of grounded two-ports without mutual inductance has been an outstanding unsolved problem of electric network theory for many years. The principal structure that has been utilized in the study of this problem has been the series-parallel structure. The present paper derives a number of properties of seriesparallel two-ports. In particular a new realizability condition, independent of the residue and coefficient conditions, is obtained for RC series-parallel grounded
more » ... parallel grounded two-ports. These results are described below. As is well known, common factors play a decisive role in the synthesis of RC transfer functions when the reduced numerators of the transfer functions have some negative coefficients. Similarly, in two-port theory, a special position is occupied by those twoports-called factorable networks-for which the unsimplified numerators and denominators of all the admittance functions and impedance functions have a common factor. These networks are discussed in §4. The main purpose of the paper is to study the effect on a given RC factorable network of two basic operations: (i) removal of an impedance which is series connected to the rest of the network at one of its external nodes (ii) decomposition of the network into two parallel networks. This is accomplished
doi:10.1090/qam/99920 fatcat:4brbueox2rhcfmm6gocehy6fxi