204 Mr. E. V. Appleton and Dr. B. van der Pol on 



It will be seen that the oscillation characteristic through- 

 out a large range of values of v a is a falling one, corre- 

 sponding to a case of so-called " negative resistance " to 

 current variations. It has been shown by one of the 

 writers* that free infinitesimal oscillations are possible in 



the circuit LjCi if the slope of this curve is -r— - when 



v a =0, in which case the oscillatory circuit approximately 



acts as a non-reactive resistance of value ri S to sinusoidal 



changes of its natural angular frequency, making the equi- 

 valent ohmic resistance of the whole circuit zero. As we know 

 that the current in the output circuit is practically sinusoidal 

 we may employ the same principle for finite oscillations*. 

 Thus if we assume an anode potential change r al sinpt 



(where p 2 = ^— -, ) we may, with the aid of the oscillation 

 characteristic, expand the value of i a as follows : 

 i a = i'ao + Li sin pt + i a2 sin 2pt .... 

 -\-i / a iCospt + i' a 2Cos2pt .... 



Finite oscillations of maximum value v al are then possible- 

 when 



^+-^-=0 



ial + C 1 R 1 



Further, we have 



ia ~ iao = $( Vao + V a , -- j- V a \ — <j) (v a0 , 0) 



= f(v a ) say, 



which function (yfr (v a )) is obtained by taking the line AR 

 (shown dotted in fig. 3) as the v a axis. 

 If it is now possible to write ^ (v a ) as 



f {ra) = -*V a + /3v a 2 + ry 



we may show f that 



where —a is the slope of the curve of fig. 3 at r a = 0. 



* Appleton, 'Electrician,' Dec. 27th, 1918. 



7 Of. van der Pol, ' Radio Review,' vol. i. p. 701, Nov. 1920. 



