Cauer W. Synthesis of Linear Communication Networks. Volumes 1 and 2

2nd edition. — McGraw-Hill, 1958. — 866 p.This is a translation by G.E. Rnausenberger and J.N. Warfield of Wilhelm Cauer’s classical work ‘Theorie der linearen Wechselstromschaltungen’. The translation has been well prepared and reads easily. Furthermore, the book has been brought up to date by the addition of editorial notes and a valuable appendix which, with the aid of a detailed bibliography, summarizes the advances since Cauer’s time.
To some readers the notation may seem a little strange, for example the use of A, instead of p or s, for the complex frequency variable. However, this reviewer was fortunate in having been taught the subject by a lecturer who drew extensively from Cauer, including notation, and many other readers will no doubt be in a similar position.
The book provides a comprehensive treatment, in virtually all aspects, of single- and two-terminal-pair networks. The approach, pioneered by Cauer himself, involves three principal topics, namely realizability, equivalence, and the approximation to a prescribed characteristic by a realizable network function. In the process, all the necessary mathematical tools, e.g. linear algebra, topology, and function theory, are developed, while practical application is assisted by many worked examples and graphical data.
This has always been regarded as the classical work on network synthesis and is likely to remain so for many years. Both the translators and the publishers are to be congratulated on having introduced it to a wider audience.Volume IIntroductory Chapter
Four-terminal Networks; Reactance Theorem.
The Image-parameter Theory of Low-pass Filters.
Image-parameter Theory of Filters.
Treatment of Losses.
Reactance Two-terminal-pair Networks Having Prescribed Operating Parameters.
Frequency-band-separation NetworksStatement of the Problem and Examples
“Linear” Problems in Electrical Communications.
The “Circuit” (Network).
Frequency Characteristics of Two-terminal Networks and Four-terminal Networks.
The Relation between Frequency Characteristics and Transients.
The Statement of the Problem of Linear-circuit Theory.
Examples of the Concepts of Positive-real Functions, Equivalent Networks, and Interpolation and Approximation Problems.Circuit Analysis
Network Topology: The Line Complex, the Complete Tree, and the System of Independent Branches.
The Branch Equations and the Kirchhoff Rules of Combination for Determining the Network Properties.
The Relation between Branch Currents and Loop Currents; Analytic Representation of Complete Trees and Circuits.
The Loop Equations and the Relations between the Circuit Elements in the Branches and Loops.
Other Forms of the Fundamental Network Equations and the Characteristic Equations.
The Energy Conditions for Circuit Elements in Current Branches.
The Energy Conditions for Circuit Elements in Current Loops.
Invariant Expression of the Fundamental Equations; Analogy with Mechanics.
The Determination of Frequency Characteristics from the Fundamental Equations.
Special Cases and Supplementary Remarks.
Appendix. Geometric Interpretation of the Solutions of Kirchhoff Loop and Node Equations for a Network in l-dimensional Space.Two-terminal-pair Networks
Different Forms of the Two-terminal-pair-network Equations and the Relations between the Two-terminal-pair-network Parameters.
Cascade Connections of Two-terminal-pair Networks.
Series and Parallel Connections of Two-terminal-pair Networks.
Parallel Connections of Two-terminal-pair Networks for the Case of a Linear Relation between the Input and Output Currents of a Two-terminal-pair Network.
Generalizations of the Series- and Parallel-connection Rules and Applications.
The Equivalence Theorem for Symmetric Two-terminal-pair Networks.
The Symmetry Theorems of Bartlett and Brune.
Some Applications of the Two-terminal-pair Network Equations.
The Image Parameters of the Symtnetric Two-terminal-pair Network.
The Image Parameters of the Unsymmetric Two-terminal-pair Network.
Operating and Insertion Parameters.
The Propagation Functions for Cascade Circuits.
The Reflection Function.Positive-real Functions and Positive Matrices
Proof of the Theorem that the Impedance Function of Every Passive Two-terminal Network is a Positive-real Function.
Proof of the Theorem that the Impedance or Admittance Matrix of Every Passive Two-terminal-pair Network is a Positive (or Semipositive) Matrix.
Properties of a Positive Matrix, Especially for Symmetric Two-terminal-pair Networks.
Proof and Application of the Theorem: The Inverse t/-1 of a Positive Matrix if U is Positive.
Special Cases (Semipositive Matrices).
Realization of Semipositive Two-terminal-pair-network Impedance or Admittance Matrices by Circuits Formed from an Ideal Transformer and a Two-terminal network.
Partitioning of Positive-real Functions by Separation of Pole Parts for Poles at Imaginary Values of λ.
Behavior of the Non-Euclidean Distance between Two Points in the Mapping of a Positive-real Function.
Appendix. Ideal Transformers.Reactance Theorems
Two-terminal-network Reactance Theorem and Two-terminal Partial-fraction Circuits.
Equivalent Two-terminal Reactance Networks; Two-terminal Continued-fraction Circuits.
Zeros and Poles of a Reactance Function.
The Determinant Conditions for the Coefficients of a Rational Reactance Function.
Relation between Reactance Functions and Hurwitz Polynomials.
Transformation from Reactance Two-terminal Networks to Arbitrary Two-terminal Networks with Two Kinds of Circuit Elements.
Two-terminal-pair Impedance Partial-fraction Circuit and Two-terminal-pair Reactance Theorem.
Two-terminal-pair Admittance Partial-fraction Circuits.
Symmetric Reactance Two-terminal-pair Networks.
Reactance Theorem for /г-terminal-pair Networks.
Example of a Transcendental Reactance Function (Reactance Network with Infinitely Many Circuit Elements with Application to Delay Networks).Image Parameter Theory of the Low-pass Reactance Filter
Interpretation of the Term “Filter”; Normalized Frequency.
The Symmetric Low-pass Filter as a Problem in Approximation with Q Functions.
Properties of Q Functions (Image-impedance or Attenuation Functions).
Classification of Symmetric Low-pass Filters; Examples.
Composition of Q Functions.
Symmetric Low-pass Filters with Prescribed Attenuation Poles (or Prescribed One-points of the Normalized Image Impedance).
Proof that the Ideal Requirements for Symmetric Low-pass Filters Can Be Approximated Arbitrarily Well.
Propagation (Image) Phase Functions of Symmetric Filters as Related to the Determination of Zeros and Poles of an Attenuation Function (Image-impedance Function) from Its One-points.
The Choice of the Parameters of Attenuation Functions and Image-impedance Functions for Symmetric Filters. Parameters for Symmetric Low-pass Filters According to K. W. Wagner.
Chebyshev Parameters for Symmetric Low-pass Filters.
Frequency Transformations for Symmetric Low-pass Filters.
Unsymmetric Filters as Related to Symmetric Filters.
Relations between Attenuation Functions and Image-impedance Functions of Unsymmetric Reactance Two-terminal-pair Networks.
“Admissible Q Functions” with Prescribed One-points; “Matching” Two-terminal-pair Networks.
Matching Low-pass Filters with Left-side Image Impedance of the Class α(α*) and Right-side Image Impedance of the Class β*(β).
Antimetric Low-pass Filters; Inverter Two-terminal-pair Networks; Antimetric Cascade Filters.
Description of the Attenuation Behavior of the Antimetric Filters by Q' Functions.
Attenuation Functions q'_s, q'_a, and q' with Chebyshev Behavior.
Filter with Vacuum Tubes.Generalized Image-parameter Theory
Classification and Designation of Networks with Arbitrary Band Assignments.
Reactance Transformations.
Reactance Transformations for Filters with Arbitrary Band Separations; Determination of Rational Functions with Prescribed ±i-points.
Additional Frequency Transformations.
The Chebyshev Nature of Q Functions Derived by Frequency Transformations.
Applications of the Frequency Transformations.
Cascade-type High-pass Filters.
Cascade-type Bandpass Filters.
Approximate Consideration of Resistive Losses in Reactance Filters.
Methods for Avoiding or Compensating for the Influence of Resistance in Reactance Filters.
Filters and Band-separation Networks with Resistances as Essential Circuit Elements.
Connection of Filters to Form Band-separation Networks.
Appendix. Two-terminal-pair-network Formula Collection.
Appendix. Practical Filter-design Techniques Based on the Image-parameter Theory.Volume IIReactance Two-terminal-pair Networks with Prescribed Operating Conditions
Current- and Voltage-transfer Factors.
Reactance Two-terminal-pair Networks with Prescribed Current or Voltage Transfer Loss.
Open-circuited Reactance Two-terminal-pair Networks with Prescribed Open-circuit Attenuation Factor.
Reactance Two-terminal-pair Networks with Prescribed Current and Voltage Transfer Factors.
Reactance Two-terminal-pair Networks with Prescribed Operating Attenuation Function.
Properties of Symmetric and Antimetric Reactance Two-terminal-pair Networks.
Realization of Symmetric Reactance Two-terminal-pair Networks with Prescribed Operating Attenuation by Lattice Networks; Realization of Antimetric Reactance Two-terminal-pair Networks by Partial-fraction Networks.
Chebyshev Parameters of the Current, Voltage, Open-circuit, and Operating Attenuation for Filters.
Supplementary Remarks on Filters.
Brune’s Method for Realization of an Impedance Which Is Prescribed as a Rational Function of A.
Two-terminal Networks with Only One Resistance and Cascade Network.
Examples of Cascade Networks.
Design of Cascade Networks from Open-circuit or Short-circuit Impedances.
Mutual Inductance-free Antimetric Filters and Band-separation Networks.
Practical Determination of the Roots of Equations of a Higher Degree Which Occur in the Calculation of Circuit Elements.
Filter with Chebyshev Behavior in the Pass Band and Prescribed Attenuation Poles in the Stop Band.
The Lee-Wiener Networks.Frequency Band-separation Networks
Band-separation Networks of the Bridge (Differential) Type Which Contain Two Filters Reciprocal to Each Other.
The Characteristic Matrices of Frequency Band-separation Networks of the Bridge Type, and the Conditions for Existence of Equivalent Band-separation Networks which Consist of Front-series or Front-parallel Connections of Two-terminal-pair Networks.
Generalization of the Symmetry Theorems of A.C. Bartlett and O. Brune with Application to Equivalent Four-terminal-pair Band-separation Networks.
Frequency Band-separation Networksof Constant Driving-point Impedance Resulting from Front-series Connection and Front-parallel Connection of Two Two-terminal-pair Reactance Networks.
The Characteristic Matrices of the Frequency Band-separation Networks of Constant Driving-point Impedance Which Result from Front-series or Front-parallel Connections.
Low-high Band-separation Networks of Constant Driving-point Impedance.
Representation of General Symmetric and Antimetric Two-terminal-pair Reactance Networks and Band-separation Networks of Constant Driving-point Impedance by Q and Q' Functions.
Examples of Low-high Band-separation Networks Obtained from Q and Q' Functions with One Branch Point.
Bifurcated Band-separation Networks with an All-stop Band; Bifurcated Band-separation Networks with More Than Two Side Terminal Pairs; Ring Band-separation Networks.
Appendix. Determination of g(Λ) from f(Λ) and h(Λ).Equivalence of Reactance Networks
Principle of Linear Transformation for General Two-terminal Networks
Equivalence of Two-terminal-pair Networks with a Different Number of Independent Current Loops.
Equivalence of Reactance «-terminal-pair Networks.
Partial-fraction Networks for Reactance Two-terminal Networks.
Partial-fraction Realizations for Reactance n-terminal-pair Networks.
Referring the Equivalence of Two-terminal-pair Networks to the Equivalence of Two-terminal Networks.
Derivation of Equivalent Networks by Matrix Multiplication.
Stieltjes Continued-fraction Development of an n-terminal-pair Reactance-network Matrix.
Two-terminal-pair Continued-fraction Network Developments.
Numerical Example of the Two-terminal-pair-network Continued-fraction Development.
Example of a Mixed Development.Appendix. Aids in Linear Algebra
Determinants and Matrices.
Laplace Expansion of Determinants, Determinant Multiplication Theorem.
Linear Dependence.
Linear Systems of Equations.
Linear Homogeneous Transformations and Their Decomposition into Elementary Transformations.
Quadratic Forms.
Positive Quadratic Forms.
Principal-axis Transformations.
Summary of the Important Definitions and Theorems.Appendix. Elements of the Theory of Analytic Functions
Fundamental Properties of Analytic Functions.
Linear Functions; Stereographic Projection of the Gaussian Plane onto the Number Sphere.
Some Relations from the Geometry of Circles in the Plane and on the Sphere.
Power Function and Exponential Function.
Integration of Analytic Functions; Cauchy’s Integral Theorem; Taylor’s Formula.
Maximum-modulus Theorem; Identity Theorem.
The Schwarz Principle of Reflection.
The Schwarz Lemma.
Isolated Singularities; Residues; Liouville’s Theorem; Rational Functions.
Application of the Residue Theorem to the Partial-fraction Expansion of 1/sin z and cot z.
Infinite Series of Analytic Functions.
The Function In z; Riemann Surface; Power Functions with Noninteger Exponents.
An Example of Conformal Mapping and of a Two-sheet Riemann Surface.
Summary of the Most Important Definitions and Theorems.Appendix. Solution of Some Chebyshev Extremal Problems
Chebyshev Approximation and Chebyshev Polynomials.
The Extremal Problems of Chapter 8 as a Transformation Problem in Elliptic Functions.
The Elliptic Function sn u.
Solution of the Differential Equation (12).
Reduction of the Extremal Problems of Chap. 6 to Those of Chap. 8.Appendix. Practical Filter Design Techniques Based on the Operating-parameter Theory
Explanatory Remarks.
Tables of Design Formulas.
Examples.
Charts for Selection of Parameters to Give Chebyshev Behavior.Appendix. Recent Advances; Supplementary References

Index