254 BELL SYSTEM TECHNICAL JOURNAL 



Here, at once, the dependence of sidetone balance upon the presence 

 of the inductively coupled third winding is apparent. Without 

 winding C the impedances Zac, Zbc and Zc in the above expression 

 would all be zero, the terms in which they occur would drop out, and 

 the requirement for elimination of sidetone would reduce to Zn = 0, 

 i.e., a short circuit across the receiver. 



The remainder of this discussion of sidetone balance can be carried 

 out more conveniently in terms of the mesh currents than in terms of 

 the above voltages. As already noted, the voltage balance just 

 examined is equivalent to requiring that I2A and /gj^ in Fig. 1A be 

 made equal and opposite. But I2A is the sum of the two components, 

 I^2A in Fig- 9vl and I^il in Fig. 8^ ; and, because of neutralizing balance, 

 ^ZA = -^3A in Fig. 8^. Furthermore, by the Reciprocity Theorem, 

 the component I2A always equals If^; and the latter, like the former, is 

 independent of Zn- The condition for sidetone balance may, there- 

 fore, be expressed in terms of the currents in Fig. 8^ as 



in + 1^1 + ifi = 0. (4) 



The question, then, is whether N can be so adjusted that the sum of 

 the three mesh currents in Fig. 8^ is made zero; and it is fairly evident 

 such an adjustment for any given value of Zl is theoretically possible. 

 Since Ifl is known to be independent of Zn, and because inspection 

 shows the circuit to be symmetrical with respect to L and N, it appears 

 that /g^^ must be independent of L — an intuitive inference which the 

 Reciprocity Theorem confirms. The value of I^2a depends, of course, 

 upon both Zl and Zn- Hence, with the value of Pi\ remaining fixed 

 as Zn is varied, and with Ifl independent of Zl but under the direct 

 control of Zn, it may be concluded possible to meet eq. (4) by a suitable 

 choice of Zn for any given value of Zl. The value of Zn required to 

 attain sidetone balance is shown by eq. (7) in the appendix. 



With N so adjusted that sidetone is zero, it is obvious the receiver 

 impedance may be changed in any way whatever without upsetting 

 the sidetone balance. The same is true of any change in the im- 

 pedance of the transmitter; because this, being equivalent to a com- 

 pensating change in the transmitter e.m.f., would cause all mesh 

 currents to change in the same proportion; thus leaving the balance 

 expressed by eq. (4) undisturbed. Hence, the impedance of N re- 

 quired to provide sidetone balance is independent of the receiver and 

 of the transmitter. But as has already been seen, the couplings of 

 winding C necessary to provide the neutralizing balance in eq. (2) do 

 depend upon the receiver and transmitter impedances. The sig- 

 nificance of this observation is that although the value of Zn required 



