492 BELL SYSTEM TECHNICAL JOURNAL 



the voltage e after E is removed, even though the current /o flows 

 against E and the source is receiving energy from the amplifier. 



If M becomes greater than the upper limit given by equation (10) 

 the system passes out of control by the e.m.f. E and becomes unstable 

 or sings. By short-circuiting the terminals 1, 2, it would be possible to 

 increase M until it is greater than the value given by equation (10) 

 which would make r numerically smaller than Rq. On removing the 

 short circuit, however, a disturbance would begin and grow until 

 checked by the limitations of the amplifier so that, in effect, M would 

 be reduced and r again made equal to —.Ro- 

 lf M is reversed in sign, for example, by interchanging the two wires 

 connected to the output terminals 3, 4, no negative resistance results. 

 As M increases, the current In increases. The resistance r decreases, 

 approaching zero as M becomes indefinitely great. 



From these facts it is seen that a negative resistance of any desired 

 value may be inserted in a circuit having any positive resistance Ra 

 provided that the inserted resistance has the characteristics of the 

 series type when the inserted negative resistance is numerically smaller 

 than the positive resistance or the characteristics of the shunt type 

 when the negative resistance is numerically larger than the positive 

 resistance. 



Other Forms of Negative Resistance 



All known devices for producing negative resistance fall into one 

 or the other of the two classes described above. 



Arrangements are known which exhibit one type of negative re- 

 sistance at one pair of terminals and the other type at a different pair 

 but not both types at the same pair of terminals at the same time. 



Certain apparatus involving gaseous conduction or electronic dis- 

 charge exhibit negative resistance effects. Fig. 6, for example, shows 

 an arc burning between two electrodes which are connected in series 

 with a resistance and inductance serving as ballast to a source of d-c. 

 power. The ballast serves to stabilize the arc and hold the current 

 drawn from the source constant and also to prevent the passage of 

 alternating current through the source from the arc. The arc has a 

 positive resistance with respect to the d-c. circuit, since it consumes 

 d-c. power, but this resistance varies with the current in such a way 

 that an increase of current is accompanied by a reduction of the po- 

 tential drop across the arc. 



If an alternating current is superimposed upon the direct current 

 through the arc by means of the taps a and h it encounters a negative 

 resistance. If a circuit consisting of a resistance R, inductance L and 



