NEGATIVE RESISTANCE IX SEMICONDUCTOR DIODES 



803 



iMined. Case (c) represents an exponential fall such as might occur for a 

 capacitor and resistor in parallel. We shall discuss this example below. 



Tlie conclusions regarding (a) and (b) may be somewhat more easily 

 seen from the corresponding —D'(t) plots shown in Fig. 2.2. From part 

 (a) it can be seen that the negative maximum in the sine wave at the 

 end of the rectangular D(t) plot is particularly favorable. From part (b) 

 it is seen that no choice of co will result in more negative area of sine 

 wa^'e than positive. For (c) it is evident that each positive half cycle of 

 the sine wave gives a larger contribution than the following negative 

 half cycle and hence that a positive resistance will be obtained. 



For case (c), it is instructive to obtain the value of Z analytically by 

 using 



D(t) = Cr' exp (-t/RC). 



This leads correctly to 



Z(a;) = (R 



-' + io,C)~\ 



For small values of uRC, Z reduces to R; furthermore, for this case, the 

 decay of D(t) occurs while cos cot = I. Under these conditions 



Z(c.) = f 

 Jo 



D{t) dt. 



This result is useful for estimating the effect of quickly decajdng contri- 

 l)utions to Dit). These evidently contribute a positive resistance to Z 

 equal to the area under the D(t) curve. 



From these considerations it follows that an upward deviation from 

 the linear fall in Fig. 2.1(b) towards Fig. 2.1(a) will result in negative 

 resistance. In Sections 4 and 5 we shall see how particular structures 

 may lead to such favorable, con vex-upwards characteristics for D(t). 



Fig. 2.2 — The —D'(t) characteristic corresponding to fig. 2.1. 



