Synthesis of Some Classes of Multivariable Cascaded Transmission-Line Networks
Isao Shirakawa, Hiroaki Takahashi, Hiroshi Ozaki · IEEE Transactions on Circuit Theory · 1968
Since the concept of multivariable positive real functions was introduced, the synthesis of these functions and matrices, concerning passive networks composed of lumped elements and of lumped and transmission-line elements, has been one of the most interesting problems in the field of circuit theory. This paper considers the synthesis of cascaded transmission-line networks of noncommensurate unit elements with the following structures: 1) a cascade connection ofmtransmission linesN_{i} (i= 1, 2, \cdots ,m)in a prescribed order, eachN_{i}being a transmission line with open-ended stubs, composed of unit elements of a single variablep_{i}; 2) a transmission line with open-ended stubs composed of unit elements ofP_{2}, connected in cascade between two transmission lines composed of unit elements ofp_{1}; 3) a cascade connection ofmtransmission linesN_{i} (i = 1, 2, \cdots ,m)in an arbitrary order, eachN_{i}being a transmission line composed of unit elements ofp_{i}; and 4) a transmission line composed of commensurate unit elements with open-ended stubs, partitioned from a multivariable network.