THEORY OF NEGATIVE IMPEDANCE CONVERTER 93 



From a practical engineering viewpoint there is a simple criterion for 

 judging stability. It can be stated as follows: The ideal negative impedance 

 converter will be unconditionally stable provided that the magnitude of 

 ^Zat/Zl is less than unity at any frequency where the angle of this ratio is 

 zero. 



These same conditions for stability apply to any practical (i.e., real or 

 actual) converter circuit, Fig. 1(d). However, Zl must be taken as the im- 

 pedance seen looking into the network N\ from the position of the ideal 

 converter C, and Zs must be taken as the impedance seen looking into the 

 network .Vo from the ideal converter C. In other words, the effect of N\ 

 must be included in Zl and the effect of Ni must be included in Zjv. 



Negative Impedance Converter Circuits 



Negative impedance can be produced by connecting the output of an 

 amplifier back in series or in shunt with the input in the right phase rela- 

 tionship. This type of circuit can be considered as a negative impedance 

 converter similar to Fig. 1(d) where the ratio of transformation — ^ is of the 

 form — (/ii — i), in which ii\ represents a function of the voltage amplifica- 

 tion of the amplifier. The disadvantage of a transformation ratio of this kind 

 is that it changes markedly with variations in tube constants and battery 

 supply voltage. Such circuits present a stability problem. One solution to 

 this problem has been described by E. L. Ginzton^. He reduced variations 

 in the amplifier gain by stabilizing the amplifier itself with negative feed- 

 back and thus reduced variation in /xi. Note that if jUi is set equal to 2, then 



— k becomes equal to —1. 



There is another method of using negative feedback to stabilize a circuit 

 for producing negative impedance. This method was used in the El circuit 

 and will be described in detail in connection with it. Essentially, here nega- 

 tive feedback is arranged together with positive feedback to produce a trans- 

 formation ratio for the ideal converter of the form — {\i\ — 1)/(m2 + !)• 

 The symbol /X2 represents a voltage ratio. Furthermore, /X] equals /3du2. If 

 |3 approximates unity and if y.^ is very much larger than one, — k approaches 



— 1 in value and is relatively independent of variations in tube constants 

 and battery supply voltage. 



In order to illustrate how the equivalent circuit of a negative impedance 

 converter can be derived, consider a circuit credited to Marius La tour about 

 the year 1920, Fig. 3(a). Figure 3(b) is a schematic representation of Fig. 

 3(a) in the manner originated by G. Crisson. With reference to Fig. 3(b), the 

 polarity of amplifier A is assumed such that, at the instant the a-c current 

 /i flows in the direction indicated, the current /o will flow in the direction 



^ E. L. Ginzton — Stabilized Negative Impedances — Electronics — July, 1945. 



