The Scattering Matrix in Network Theory

This paper gives an introductory treatment of the concept and uses of scattering methods in network problems. The scattering parameter description for linear networks is defined and the utility of this formalism for problems involving power flow in terminated networks is discussed. Examples of scattering computations for transformer 4-ports, transformerless impedance matching networks and transducers with parasitic capacitance are given. The physical realizability requirements for linear lumped networks in the frequency domain are presented in scattering terms, and some extensions to the realizability of distributed networks are briefly discussed.

[1]  J. Tiomno,et al.  On the Connection of the Scattering and Derivative Matrices with Causality , 1951 .

[2]  V. Belevitch Four-Dimensional Transformations of 4-Pole Matrices with Applications to the Synthesis of Reactance 4-Poles , 1956 .

[3]  G. Raisbeck A Definition of Passive Linear Networks in Terms of Time and Energy , 1954 .

[4]  V. Belevitch,et al.  Elementary Applications of the Scattering Formalism in Network Design , 1956 .

[5]  Vitold Belevitch Transmission Losses in 2n‐Terminal Networks , 1948 .

[6]  S. Tomonaga,et al.  A General Theory of Ultra-Short-Wave Circuits II , 1947 .

[7]  R. Fano Theoretical limitations on the broadband matching of arbitrary impedances , 1950 .

[8]  George A. Campbell,et al.  Maximum Output Networks for Telephone Substation and Repeater Circuits , 1920, Transactions of the American Institute of Electrical Engineers.

[9]  Y. Oono,et al.  Application of Scattering Matrices to the Synthesis of n Ports , 1956 .

[10]  H. J. Carlin,et al.  Gain-Bandwidth Limitations on Equalizers and Matching Networks , 1954, Proceedings of the IRE.

[11]  R. E. Collin Theory and Design of Wide-Band Multisection Quarter-Wave Transformers , 1955, Proceedings of the IRE.

[12]  W. Kahn Scattering Equivalent Circuits for Common Symmetrical Junctions , 1956 .

[13]  V. Belevitch,et al.  Topics in the Design of Insertion Loss Filters , 1955 .

[14]  R. H. Dicke,et al.  A Computational Method Applicable to Microwave Networks , 1947 .

[15]  W. H. Watson,et al.  Matrix methods in transmission-line and impedance calculations , 1946 .

[16]  Herbert J. Carlin,et al.  A General Theory of Wideband Matching with Dissipative 4 Poles , 1954 .

[17]  Herbert J. Carlin,et al.  On the Synthesis of Reactance 4‐Poles , 1953 .

[18]  M. Treuhaft Network Properties of Circulators Based on the Scattering Concept , 1956, Proceedings of the IRE.