PROPORTIONING OF CIRCUITS FOR ATTENUATION 277 



mine the hiRh-frcquency attenuation of a circuit comprising? a pair of 

 conductors surrounded by a shield may be briefly examined. At high 

 frequencies, where the currents are crowded toward the surfaces of 

 the conductors, the attenuation is proportional to the product of the 

 resistance and capacitance of the circuit, both of which are functions 

 of the flux density in the dielectric. 



With a circular shield, and round conductors, the flux density is far 

 from uniform around the surfaces of the conductors, being relatively 

 high at points nearest the shield and also at points nearest the shield's 

 center, and a minimum at points about half-way between. Accord- 

 ingly, it appears that the high-frequency resistance of the conductors 

 can be reduced by reshaping them so as to make the flux distribution 

 more uniform. This can be accomplished by squeezing the conductors 

 at regions of maximum flux density and bulging them at regions of 

 minimum flux density, thereby producing a conductor of approxi- 

 mately elliptical cross-section. 



The flux distribution around the shield is also far from uniform, being 

 a maximum at points nearest the conductors and a minimum at points 

 90 degrees away. Making the enclosed conductors elliptical tends to 

 reduce this non-uniformity, thereby reducing the circuit resistance due 

 to loss in the shield. 



This process of reshaping the conductors can not be carried very far, 

 however, because it soon increases the circuit capacitance more than 

 it decreases the resistance. It is difficult to treat this problem by 

 rigorous mathematics, but an analysis can be made which yields an 

 approximate solution. 



For certain conductor shapes, the high-frequency attenuation of a 

 pair with circular shield may be determined by a method involving the 

 substitution of charged filaments for the conductors. Let any number 

 of positively and negatively charged filaments be included in the shield, 

 the net charge on the filaments being zero. The electrostatic potential 

 at any point of this system can readily be determined by known meth- 

 ods. Thus, for example, Fig. 15 shows the location of the equipo- 

 tential surfaces for the case of two oppositely charged filaments placed 

 within a circular shield, the distance from each filament to the center 

 of the shield being .46 times the shield radius. 



In any such system, a conducting cylinder whose external surface 

 corresponds to, and whose potential is equal to the potential of, a 

 particular equipotential surface may be substituted for the part of the 

 system contained within that surface without disturbing the flux 

 distribution external to it. Consequently, the capacitance of a 

 shielded circuit employing equal and oppositely charged conductors 



