252 BELL SYSTEM TECHNICAL JOURNAL 



upon the currents, and the circuit will thereby be reduced to the side- 

 tone circuit. Hence, with this ideal adjustment of the couplings, the 

 receiving efficiency of the anti-sidetone circuit will be the same as 

 that of its sidetone complement. 



Although equally satisfactory designs could be worked out with 

 other polings of the coil windings, the relative inductive directions 

 among windings A, B and C in the circuit here dealt with are such 

 that, if a current were passed through all three in series, windings 

 A and B would be inductively aiding; and C would be inductively 

 opposed to both A and B. Returning to the above condition for 

 maintaining the receiving efficiency, namely, that /g"^ be made zero, 

 the windings of the coil must be so adjusted that the sum of the 

 two voltages induced in winding C by its inductive couplings with 

 windings A and B is equal and opposite the voltage drop across the 

 receiver. With the windings poled as just stated, this requires that 



• (+ I'^IZac) + (- I'ilZsc) = -{- I^lZn). (2) 



This voltage balance expressed by eq. (2) will be referred to as neutral- 

 izing balance: its attainment requires the coil windings be adjusted to 

 meet the relation shown by eq. (6) in the appendix. 



It is important to note that neutralizing balance, and hence the 

 efficiency relations which depend upon it, are independent of the 

 impressed e.m.f. Ei, of the line impedance Zl and the self-impedance 

 of winding A , and of the network impedance Z.v and the self-impedance 

 of winding C. This of course follows from the fact that none of these 

 quantities is involved in eq. (2). 



Transmitting Efficiency 



It will now be shown that the transmitting efficiency of the anti- 

 sidetone circuit is the same as that of its sidetone complement; and 

 that this equality, like that of the receiving efficiencies, results from 

 the neutralizing balance effected by winding C. This is true if, with 

 equal transmitter e.m.f.'s in the top and bottom diagrams of Group IV, 

 the line currents are equal, viz., if 



ril2) _ 7'(12) 

 ^lA — ■'is • 



To prove this relation, refer to Fig. 7A at the bottom of Group IV and 

 move up step by step to Fig. 9A, observing the relations between 

 mesh currents indicated by the arrows. It will be seen that 



7(12) _ r(i) _1_ T(\) 



