802 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



meaning the displacement current across space charge region S^ as a 

 function of time. 



In this section we shall treat J and j as circuit currents. In subsequent 

 sections, we shall be concerned with current densities and shall use the 

 same symbols. 



The complex impedance of the device is evidently 



Z(o:) = v/j, 



where v and j are the coefficients in the sinusoidal case. 



In terms of the system of notation introduced above, Z(co) may also 

 be expressed in terms of D(t) by expressing j exp icjot in terms of incre- 

 ments of charge 



dQ = ye'"' dt, 



and summing over all increments up to time t. This leads to 



Z{co) = I D{t) exp i-wt) dt. 

 Jo 



A negative resistance will occur if 



> / Dit) cos wtdt = (-l/oj) / D\t) sin cot dt, 

 Jo Jo 



the latter form coming from integration by parts for the case of Z)(oo) 

 = 0, the only situation treated in this article. 



The use of D(t) in analysing the potential merits of diode structures 

 from the point of view of negative resistance is illustrated in Fig. 2.1. 

 Here three cases of D(t) together with certain cosine waves are shown. 

 It is seen for case (a) that a negative real part of Z will be obtained. 

 For case (b), the real part of Z is zero for the frequency shown; this 

 represents a limit ; for other frequencies, a positive real part will be ob- 



Fig. 2.1 — Some hypothetical D{t) characteristics. 



