Distortion Correction in Electrical Circuits with Constant 

 Resistance Recurrent Networks 



By OTTO J. ZOBEL 



Synopsis: Constant resistance recurrent networks, that is, networks 

 whose iterative impedances are a pure constant resistance at all frequencies, 

 form here the basis of a method of distortion correction which is applicable 

 to any electrical circuit. The paper takes up first the general problem of 

 distortion correction, then this method of correction and its application in 

 the following Parts and supplementary Appendices. 



Part 1. Ideal Circuit Characteristics. Both ideal steady-state 

 attenuation and phase characteristics are formulated and then verified 

 as being necessary and sufficient for the preservation of signal-shape 

 under transient conditions. 



Part 2. Constant Resistance Recurrent Networks. These networks 

 are of three general types and are made possible by the introduction of 

 inverse networks of constant impedance product. Their propagation 

 characteristics are considered in some detail and various methods of 

 design are indicated. 



Part 3. Arbitrary Impedance Recurrent Networks. These net- 

 works are a generalization of those in Part 2. 



Part 4. Applications. The large variety of uses to which these 

 networks may be put is illustrated by specific designs made for com- 

 plementary distortion correcting networks, for a submarine cable 

 circuit, a loaded-cable program transmission circuit, and an open-wire 

 television circuit. In addition, networks are given for the equalization 

 of variable attenuation in carrier telephone circuits, for phase correc- 

 tion in the transatlantic telephone system and for the simulation of a 

 smooth line. 



Appendix I. Discussion of Linear Phase Intercept. 



Appendix II. Linear Transducer Theorems. 



Three theorems are proved which relate to the variation with 

 frequency over the entire frequency range of the propagation constants 

 and iterative impedances of certain passive linear transducers. 



Appendix III. Propagation Constant and Iterative Impedance 

 Formula for General Ladder, Lattice and Bridged-T Types. This 

 includes an improved formula for cosh~^ {x + iy). 



Appendix IV. Propagation Characteristics and Formulas for Various 

 Lattice Type Networks. These results can be applied quite readily to 

 many problems arising in the design of distortion correcting networks. 



438 



