250 BELL SYSTEM TECHNICAL JOURNAL 



when transmitting (see Fig. 5 of Group III), it will be looked upon as 

 the same passive impedance in tandem with an impedanceless generator 

 whose e.m.f. equals the variations in voltage drop (of the battery sup- 

 ply current) across the transmitter due to the changes in its impedance 

 which occur when the transmitter is agitated by sound. This e.m.f. 

 thus replaces in the circuit the sound engendered variations in the 

 transmitter impedance, thereby permitting this impedance to be 

 treated as a constant. Being impedanceless, this generator may, 

 without effect upon the circuit, be replaced by two impedanceless 

 generators — each having the same e.m.f. as the first — connected in 

 parallel as shown in Fig. 6. The direct connection between points 

 a and h, however, is shunted by the impedanceless path ach, so that the 

 direct connection ah may, without effect, be broken as in Fig. 7. 

 Hence, the two equal e.m.f. 's in Fig. 7, acting simultaneously, are 

 equivalent to the single e.m.f. in Fig. 5; and the mesh currents in the 

 two figures are, therefore, identical. Hereafter, Fig. 7, rather than 

 Fig. 5, will be considered the transmitting condition. 



This transmitting condition may, however, be broken into two com- 

 ponent conditions. By the fundamental principle known as the Super- 

 position Theorem, the currents in Fig. 7 are equal to the sum of the 

 currents which would result from each of the two e.m.f.'s acting alone. 

 In other words, the transmitting currents in Fig. 7 are equal to the sum 

 of the corresponding currents in Figs. 8 and 9. But by a second 

 fundamental principle called the Reciprocity Theorem, the current at 

 any point Z in a circuit, due to an e.m.f. at any other point Y, is equal 

 to the current which would result at Y from an equal e.m.f. at X. 

 Applying this to Figs. 8 and 9, in which Ei = £2, the mesh currents 

 pointed out by the arrows joining these two schematics are equal, 

 viz.: 



Ifl = I^s and m = m. (1) 



Of the above components of the transmitting currents, those in 

 Fig. 9 are due to an e.m.f. acting in mesh 1, i.e., in series with the line 

 impedance. This, however, is also the condition when receiving, as 

 will be seen by comparing Figs. 9 and 4. 



Neutralizing Balance — ^Receiving Efficiency 



Consider next the purpose of winding C. It is, of course, desirable 

 that the transmitting and receiving efficiencies be undiminished by the 

 anti-sidetone arrangement. If it is possible so to adjust the couplings 

 among windings A, B and C that the current If^ in Fig. 4 or 9 is 

 zero, the balancing branch can then be disconnected without effect 



