Belevitch V. Classical Network Theory

San Francisco : Holden-Day, 1968. — x, 440 p.A now classical work by a prominent Belgian mathematician and electrical engineer of Russian origin.
Belevitch produced a textbook, Classical Network Theory, first published in 1968 which comprehensively covered the field of passive one-port, and multiport circuits. In this work he made extensive use of the now-established S parameters from the scattering matrix concept, thus succeeding in welding the field into a coherent whole. The eponymous Belevitch's theorem, explained in this book, provides a method of determining whether or not it is possible to construct a passive, lossless circuit from discrete elements (that is, a circuit consisting only of inductors and capacitors) that represents a given scattering matrix.Elements and connectionsOne-port elements.
Inductance n-ports.
Transformer 2-ports.
Ideal transformer n-ports.
Connections.
Kirchhoff laws.
Loops.
Interconnection of subnetworks.
Kirchhoff networks.Network analysis.
The network equations.
Free solutions.
Stability.
Forced solutions.
Complex power.
Bilinear forms.
Duality.
Imaginary resistances.
Generalized networks.Analysis of n-ports
The elimination problem.
Well-defined n-ports.
Passivity and reciprocity of well-defined n-ports.
Dimensionality theorems.
Dimensionality of concrete n-ports.
Uncontrollable states.
Internal variables.
Examples.Basic structures and transformationsCongruence transformations.
Elementary 2-port structures.
Symmetric 2-ports.
Cascade connections.
Impedance transformations.
Networks without transformers.
Howitt transformations.
The degree of a Kirchhoff network.Synthesis of passive one-portsProperties of positive functions.
Lossless one-ports.
The Brune synthesis.
Partial specification of an immittance.
Scale transformations.Reflection and transmission
Reflection coefficient.
Scattering matrix.
Attenuation and phase.
Relations between scattering and hybrid matrices.
Change of reference.
Applications to 2-ports.
Image parameters.Positive matrices and bounded matrices
Properties of positive matrices.
Reduction of singular matrices.
Bounded matrices.
Synthesis by conjunctive transformations.
Circulators.
Biconjugate 4-ports.
Matched 2-ports.
Bridged-T networks.Chapter 8. Degree and canonic forms
The degree of an n-port.
Properties of the degree.
The McMillan form.
Kalman’s representation.
Similarity transformations.
Equivalence of lossless n-ports.
Explicit formulas for the degree.
The maximum number of parameters of n-ports of given degree.Lossless 2-ports
One-port synthesis by all-pass extraction.
Real one-ports.
Darlington’s synthesis.
One-port synthesis without transformers.
Uncontrollable and secular states in one-port synthesis.
The scattering matrix of a lossless 2-port.
Partial specifications of the scattering matrix.
The transfer matrix.
Halving a symmetric lossless 2-port.
Open-circuit behavior.Synthesis of passive n-ports
Principles of the iterative synthesis.
The section of degree 1.
Real n-ports.
Sections of degree 2.Factorization of scattering matrices
Factorization theorems.
All-pass 2n-ports.
Cascade n-port synthesis.
Reciprocal n-ports.Unitary bordering of scattering matricesThe equation G = HH.
The basic solution.
Physical solutions of minimum dimension.
Symmetric solutions of minimum dimension.
Solutions of nonminimum dimension.
Symmetric solutions of minimum degree.Appendix A. Matrix algebra
Terminology and notations.
Partitioned matrices.
Theorems on determinants.
Rank.
Linear equations.
Congruence transformations of hermitian matrices.
Unitary transformations.
Polynomial matrices.
Smith and Jordan forms.Appendix B. Properties of analytic functions
Extremal theorems.
Hilbert transforms.
The logarithm of a rational function.Notes

Index