The Proportioning of Shielded Circuits for Minimum 

 High-Frequency Attenuation 



By E. I. GREEN, F. A. LEIBE and H. E. CURTIS 



For given conditions of design there exists an optimum proportion- 

 ing or configuration which makes the high-frequency attenuation of a 

 given type of individually shielded circuit a minimum. Determination is 

 made of such optimum proportioning for a wide variety of types of in- 

 dividually shielded circuits including several novel types designed to make 

 the high-frequency attenuation low in comparison with the cross-sectional 

 area occupied by the circuit, and the attenuation of different types is com- 

 pared. The following topics and specific circuit structures are considered: 



Coaxial Circuits — Basic Coaxial Circuit; Effect of Dielectric; Effect 

 of Frequency- on Optimum Ratio; Thin Walls; Stranded Conductors; 

 Optimum Proportioning as a Function of Conductor Resistance. 



Balanced Shielded Circuits — Shielded Pair (Cylindrical Conductors 

 and Shield) — Condition for Minimum Attenuation, Condition for Maxi- 

 mum Characteristic Impedance, Effect of Dielectric, Effect of Frequency; 

 Pair in Space; Shielded Stranded Pair; Pair with Shield Return; Double 

 Coaxial Circuit; Shielded Pair (Round Conductors and Oval Shield); 

 Shielded Pair (Quasi-Elliptical Conductors); Shielded Quad. 



Introduction 



SINCE the very beginning of mathematics, problems of maximizing 

 and minimizing have possessed a marked fascination. The Greeks 

 were successful in solving a few geometric problems of this character. 

 Later, algebra was found to be another method of attack. Finally, 

 the powerful methods of the calculus became available for the deter- 

 mination of maxima and minima in manifold variety. The reasons 

 for the continued interest in such problems are not hard to find. It is 

 but natural to seek the ideal, and here, at least, is one phase of man- 

 kind's search for perfection in which a goodly measure of success may 

 be achieved. In addition, a knowledge of the optimum dimensioning 

 of things, or of the optimum relations between things, frequently holds 

 much practical significance. 



It is mainly with problems of maxima and minima that this paper is 

 concerned. These problems have to do with transmission circuits 

 which are surrounded by individual shields. Recent literature '-has 

 pointed out that circuits of this type have properties which render them 

 especially suitable for the transmission of broad bands of frequencies. 

 Such circuits are also finding application as "lead-ins" to connect radio 

 antennas with transmitting or receiving apparatus.'- * 



1 For numbered references, see end of paper. 



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