90 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 



Zl is connected to terminals 1 and 2, a negative impedance Zl/— ^ will be 

 seen at terminals 3 and 4, Fig. 1(c). 



George Crisson stated^ that there are two types of negative impedance 

 which he defined as the series type and the shunt type respectively. His 

 series type is the reversed voltage type of negative impedance — kZt^ equiva- 

 lent to — F//; and his shunt type is the reversed current type Zif—k 

 equivalent to V/—I. This is a logical development considering that impe- 

 dance Z equals F//, and therefore negative impedance (— Z) equals either 

 — V/I or V/—I where V is the voltage measured across the impedance and 

 / is current flowing through it. 



(b) 



(c) 



(d) 



Fig. 1 — The negative impedance converter. 



It is important to note that k, the ratio of transformation, is of the form 

 A/Q where both the magnitude A and the angle 9 are changing, however 

 slowly, with frequency This follows from the fact that, as will be shown, k 

 contains a term (/xi — 1) where jui is a voltage ratio the magnitude and phase 

 of which can change with frequency. 



The ratio of transformation k can be made to have a magnitude closely 

 approaching unity, and at some frequency or frequencies the angle can be 

 made zero. If k equals 1/0 the series type negative impedance seen at ter- 

 minals 1 and 2, Fig. 1(b), will be equal to — Zn, — V/I, where the voltage V 

 is reversed by 180 degrees from the voltage which would appear across ter- 

 minals 1 and 2 were the impedance here the positive impedance Zjv- and the 

 voltage to current ratio the conventional V/I. Likewise, the shunt type 

 negative impedance seen at terminals 3 and 4, Fig. 1(c), would be ZJ — 1^ 

 V/—I, where here it is the current which is reversed by 180 degrees from the 

 current which would flow through the positive impedance Zl. Thus a strange 

 fact is noted: multiplying a positive impedance by — / does not yield the 



' George Crisson — Negative Impedance and the Twin 21-Type Repeater — B.S.T.J.- 

 July, 1931. 



