502 BELL SYSTEM TECHNICAL JOURNAL 



This gain is. of course, the gain which a booster having the impedance 

 Z, obtained from equation (26) would produce when connected be- 

 tween two impedances Zq. The actual gain of the booster, like that 

 of any other t>'pe of repeater approaches infinity as the singing condi- 

 tion is approached. 



The shunt booster (with shunt type negative impedance) will sing 

 when 



Zft + ^ = 0. (28) 



Substituting the value of Zb from this equation in equation (23) 

 shows that the relation given in equation (27) also holds for the shunt 

 type booster. 



It is well known that when a 22-type repeater giving the gain 6*22 in 

 each direction is connected between two lines having the return loss Si 

 singing will occur when 



G21 = Si, (29) 



if the worst combination of unbalances occurs. 



It is also well known that under similar conditions the gain of a 

 21 -type repeater is: 



Go, ^ Si- 6db, (30) 



because of the fact that waves reflected from the irregularities in both 

 lines combine in the input circuit of the amplifier. 



The curves of Fig. 13 show the singing gain as a function of line 

 return loss for boosters, 21-type and 22-type repeaters. These curves 

 together with the curves of Fig. 10 indicate that ideal boosters con- 

 sisting of series type negative impedances in series with the line or 

 shunt type negative impedances bridged across the line have properties 

 intermediate between those of 21 and 22-type repeaters with respect to 

 the amount of echo and margin against singing for a given transmission 

 gain. These properties are particularly favorable at low gains. 



In practice, however, it is usually necessary to limit the amplification 

 to a definite band of frequencies in order to avoid the effect of imped- 

 ance unbalances and interfering disturbances at frequencies outside 

 these limits. This must be accomplished by the use of inductance 

 and capacitance in the form of filters, transformers, choke coils or 

 condensers. It is also desirable to couple the series booster to the line 

 by means of a transformer having two equal windings, one in each line 

 conductor, to enable one booster mechanism to operate without 

 unbalancing the line and to permit the passage of low frequency signal- 

 ing waves from one part of the line to the other without interference 



