THEORY OF NEGATIVE IMPEDANCE CONVERTER 97 



finite frequency band this negative resistance can be produced by a converter 

 circuit such as that of Fig. 4. However, in this case Bartlett's circuit becomes 

 in a sense, a converter within a converter. 



The Negative Impedance Locus 



Before the El type of converter is described, it would be well to con- 

 sider, in general, the impedance characteristic which can be produced by 

 a negative impedance converter. The shape of the impedance characteristic 

 over the frequency range, zero to infinity, looking into terminals 1 and 2 

 or into terminals 3 and 4 of a negative impedance converter will be called 

 the negative impedance locus. It is convenient to plot this locus in the polar 

 form with frequency as a ''running" parameter. The locus can be derived 

 for any circuit by means of the theory outlined by K. G. Van Wynen for 

 positive two- terminal impedances.® 



For example, consider the converter of Fig. 4. Assume that an impedance 

 such as that shown in Fig. 5(a) is connected to terminals 3 and 4 of Fig. 4; 

 assume Zi of Fig. 4 is a capacitance and that both Rp and Z\ are resist- 

 ances. Now Fig. 5(a) represents a two- terminal network made up of a 

 resistance shunted by an inductance. The locus of this positive impedance 

 plotted on the R and jX plane over the frequency range from zero to in- 

 finity is shown in Fig. 5(b). At zero frequency the impedance is zero; at 

 infinite frequency the impedance is i?i. If to the network of Fig. 5(a) a ca- 

 pacitance C is added, to represent Zi of Fig. 4, the impedance of the net- 

 work so formed. Fig. 5(c), follows the circle of Fig. 5(d). At zero frequency 

 the impedance is zero, at the resonant frequency the impedance is i?i, 

 and at infinite frequency the impedance is zero again. If the impedance 

 of this network. Fig. 5(c), were viewed through an ideal negative imped- 

 ance converter. Fig. 5(e), having a ratio of transformation of —k\\ where, 

 for the moment, k is assumed to be a numeric over the entire frequency 

 range, the impedance locus can be represented by Fig. 5(f). Of course, 

 k will always have an angle at high and low frequencies but, to a first 

 approximation, at least, it can be assumed that over most of the frequency 

 range shown in the impedance diagrams of Fig. 5(f) and Fig. 5(h) k ap- 

 proaches a numeric. If the circuit configuration of Fig. 5(g) is created by 

 adding resistance Ri in series with Fig. 5(e) the impedance locus looks 

 like that of Fig. 5(h). This is a series type of negative impedance and simulates 

 the impedance seen over a large portion of the frequency range looking into 

 terminals 1 and 2 of Fig. 4 with the two- terminal network of Fig. 5(a) con- 

 nected to terminals 3 and 4. 



^ Design of Two-Terminal Balanciner Networks — K. G. Van Wynen — B.S.TJ. — Oct., 

 1943. 



