512 BELL SYSTEM TECHNICAL JOURNAL 



the phase might outweigh the increase due to the function ^ '^ . Asa 



CiV 



result the conductance niiglit have a maximum value for an amplitude 



greater than zero, leading to the conditions shown in Fig. 23, under which 



hysteresis can exist. 



The first order theory for the reflex oscillator does not predict such an 



effect, since the phase is independent of amplitude. The second order 



theory gives the admittance as 



_ ^ihO 2Ji(X) y(e_(^/2)) /., _ 1 



.. (8.21) 

 ■ I i\-(A- + 1) - X-' ^-^ - -^^ (2 - A-) - X ^1^ 



The quantity appearing outside the brackets is the admittance given by the 

 first order theory. The second order correction contains real and imaginary 

 parts which are functions of A" and hence of the amplitude of oscillation. 

 Thus, for fixed d-c conditions the admittance phase depends upon the am- 

 plitude of oscillation and hence hysteresis might occur. It should be ob- 

 served that the correction terms are important only for small values of the 

 transit angle 9. In particular, this explanation would not suffice for the 

 case described earlier since the design employed which eliminated the hys- 

 teresis left the variables of equation (8.21) unchanged. 



IX. Effect of Load 



So far we have considered the reflex oscillator chiefly from the point of 

 view of optimum performance; that is, we have attempted chiefly to evaluate 

 its performance when it is used most advantageously. There has been some 

 discussion of non-optimum loading, but this has been incidental to the 

 general purpose of the work. Oscillators frequently are worked into other 

 than optimum loads, sometimes as a result of incorrect adjustment, some- 

 times through mistakes in design of equipment and quite frequently by 

 intention in order to take advantage of particular properties of the reflex 

 oscillator when worked into specific non-optimum loads. 



In this section we will consider the effects of other than o])timum loads 

 on the performance of the reflex oscillator. We may divide this discussion 

 into two major subdivisions classified according to the type of load. The 

 first type we call fixed element loads, and the second variable element loads. 

 The first type is constructed of arbitrary passive elements whose constants 

 are independent of frequency. The second category includes loads con- 

 structed of the same tyi)e of elements but connected to the oscillator by 

 lines of suflicient length so that the frequency variation of the load admit- 

 tance is appreciably modified by the line. 



