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BELL SYSTEM TECHNICAL JOURNAL 



formers, choke coils, and condensers whicli are so useful in assemblages 

 of apparatus which include vacuum tubes further limit the range of 

 frequency over which an approximately pure negative resistance may 

 be obtained. In some cases, this may not be a serious disadvantage. 

 Suppose, for example, it is desired to reduce the effective resistance of 

 a series resonant circuit in order to obtain more nearly ideal perform- 

 ance at the resonant frequency. It would be sufficient to arrange a 

 negative resistance in series with the resonant circuit which would 

 produce the desired result at and near the resonant frequency and 

 which would produce no harmful effect at other frequencies even though 

 it departed widely from the value at the resonant frequency. In 

 other cases the variation of the negative resistance with frequency and 

 the introduction of reactive components do no serious harm and may 

 even be quite useful as in the case of the twin 21 -type repeater to be 

 described below. In still other cases the difficulties of producing a 

 negative resistance of satisfactory characteristics may be very great. 



General Negative Impedance 



The arrangements described above produce under ideal conditions 

 pure negative resistances. 



It has been shown by R. C. Mathes and H. W. Dudley that it is 

 possible to produce any desired negative impedance provided that the 

 positive of this impedance can be constructed in the form of a network. 



e '^z- 



Fig. 8 — Series type negative impedance. 



Fig. 8 shows in simplified form the arrangement invented by Mathes, 

 and Fig. 9 shows the arrangement due to Dudley. Each of these 

 arrangements requires a distortionless one-way amplifier whose input 

 impedance (terminals 1, 2) is substantially infinite. This condition is 

 easily approximated by using vacuum tubes. In discussing the 

 behavior of such arrangements, it is necessary to use the ratio, AIv, of 



