NEGATIVE IMPEDANCES AND THE TWIN 21-TYPE REPEATER 495 



cannot reach it, while A remains finite. That is, the system shown in 

 Fig. 7 cannot sing. This is also obvious from the fact that the hybrid 

 coil is balanced. However, the resistance r does not depend upon 

 holding Rq at the terminals 5, 8 constant. If the resistance at the 

 terminals 5, 8 is reduced to a lower value Rq , while that at the terminals 

 6, 7 is held constant at i?o, the output energy of the amplifier is per- 

 mitted to reach the input terminals 1, 2 and when —Rq = r instability 

 or singing can occur. 



Throwing the reversing switch to give the reversed connection has 

 the effect of reversing the sign of the amplification A. The total 

 current Jo at the terminals 5, 8 decreases to zero, reverses and increases 

 as A increases, while r increases, passes discontinuously from + oo to 

 — CO and decreases in magnitude. Again r approaches — i?o as A 

 increases indefinitely, but cannot reach it. However, by increasing 

 the resistance connected to the terminals 5, 8 to a higher value R^' 

 such that —Rq — r, instability will occur. The reversed connection 

 thus gives a negative resistance of shunt characteristics. 



Referring to Fig. 7 and assuming that the switch is thrown to give 

 the directions of current flow indicated by the arrows, transfer the 

 e.m.f. E to the right-hand end of the diagram. This change will not 

 change the direction of /i in the input circuit of the amplifier or the 

 direction h at any point. The current /i will now be found at ter- 

 minals 6, 7 instead of 5, 8 and will be flowing in the direction opposite 

 to h. From this it will be seen that a 21-type circuit which is direct- 

 connected with reference to terminals 5, 8, giving a series type negative 

 resistance, will be reverse-connected, and give a shunt type negative 

 resistance at the opposite terminals 6, 7. Changing the reversing 

 switch reverses the conditions at both pairs of terminals. 



Non-Ideal Devices 



The discussion has so far been confined principally to certain ideal 

 conditions which can only be approximated in practice, but considera- 

 tion of these simple cases will serve to illustrate the important funda- 

 mental properties of negative resistances and the requirements that 

 must be met to insure stable operation. 



To obtain a pure negative resistance from a one-way amplifier or 

 from a 21-type repeater circuit requires that there shall be no phase 

 shift in the process of amplification. This can only be approximated in 

 practice because even a resistance coupled amplifier system involves 

 small inductances and capacitances in the tubes and wiring which pro- 

 duce phase shifts at high frequencies. Commercially practicable trans- 



