THEORY OF NEGATIVE IMPEDANCE CONVERTER 95 



Thus the impedance Z12 equals the impedance Z\ in parallel with Rp 

 which combination is in series with impedance Zn multiplied by 

 1 — \ixZ\liRj, + Zi)]. An equivalent circuit for Z12 is illustrated in Fig. 3(c). 



Next, assume that Zl^ not shown on Fig. 3(b), is connected to terminals 

 1 and 2 of Fig. 3(b) and that Zn is removed from across terminals 3 and 4. 

 The mesh equations can be written as follows: 



-72= (Zi + Zz.)/i -Zi/o 



MF2 = -Zi/i +(i?p + Zi)/2 



The current /i can be written: 



J - - ^2 [Rp + Zi - fiZi] , V 



^' - (Z, + Z,KR, + zo - z\ ^- ^^^ 



The impedance looking into terminals 3 and 4, Fig. (3b), with the changes 

 listed above is: 



z. + ^-^' 



y _ ^2 Rp -\- Zi . . 



Z34 = -— = -, r Eq. (4) 



\ Rv + Zj 



Hence, if the circuit of Fig. 3(b) is redrawn as a four- terminal network as 

 shown in Fig. 4(a) with Z2 added to represent the input impedance of ampli- 

 fier A the equivalent circuit of this network can be represented by Fig. 4(b). 

 The equivalent circuit consists of two positive impedance networks, one 

 on each side of an ideal converter. The ratio of transformation of this ideal 

 converter is of the form — ()Ui — 1):1. Looking into terminals 1 and 2, 

 Fig. 4(b), a series type negative impedance will be seen and looking into 

 terminals 3 and 4 a shunt type negative impedance will be seen. The proof 

 that these impedances are negative and of the reversed voltage or reversed 

 current type has been established by H. W. Dudley, F. H. Graham and 

 R. C. Mathes for similar circuits and will not be taken up here, although the 

 fact could be derived simply from equations (1), (2), (3) and (4). The 

 purpose of this discussion is to illustrate the simplicity with which an 

 equivalent circuit can be derived, and to point out the value of the concept 

 of the ideal negative impedance converter. 



A well known circuit which can be used as a negative impedance converter 

 is the circuit of the 21 type repeater. In this circuit the output of the ampli- 

 fier is connected back to the input through a bridge type of arrangement 

 referred to as a hybrid coil. Negative feedback and positive feedback can 

 be developed across this coil between the amplifier output and the amplifier 

 input. This device was used as a negative impedance converter by Crisson 

 in his twin 21-type repeater. 



