PROPORTIONING OF CIRCUITS FOR ATTENUATION 271 



transmitting over the two enclosed conductors in parallel with the 

 shield as the return. This latter circuit alone is less efficient than a 

 coaxial circuit formed by replacing the two inner conductors with a 

 single one. If, however, the two circuits obtainable from the shielded 

 pair structure can both be employed without excessive mutual inter- 

 ference, there will be a considerable increase in the usefulness of the 

 system, measured in terms of the total frequency range that can be 

 transmitted without exceeding a given attenuation. It is therefore of 

 interest to determine the conditions making the total transmitted 

 frequency range for the two circuits a maximum. ^^ 



The high-frequency attenuation of each circuit, assuming solid 

 conductors, can be written 



a = K^Tj, (51) 



where X is a constant, different for each circuit, which depends on the 

 size and material of the conductors, and the dielectric constant of the 

 insulation. Leakage is assumed negligibly small. 



Using subscripts 1 and 2, respectively, to designate the circuit 

 comprising the two enclosed conductors one as a return for the other 

 and the circuit comprising the two wires in parallel with shield return, 

 it follows that 



/.+/= = |4 + g- (52) 



Letting A = aijai 



/. +/2 = ar(^+^,)- (53) 



Equation (53) gives the sum of the frequency ranges that can be 

 transmitted in the above manner over any given shielded pair for any 

 given attenuation at the highest frequencies of the bands. To obtain 

 maximum total range, this equation must be maximized. 



The attenuation of the circuit comprising one enclosed conductor 

 as a return for the other is given by equation (32), from which the 

 value of Ki can be obtained immediately. An expression for K2 has 

 been given in an unpublished formula due to Mrs. vS. P. Mead, as 

 follows : 



u+v 1/7 



''^-[^^^]-l^('+-('^^"'^^^' " 



1 + 4^= 



in which 





