1298 



be represented bv a constant tension e^ augmented by an alternating- 

 tension' ^1 ; for the current tlie division into i^ and / lias already 

 been made. 



For the oscillation-circuit, consisting of arc. seltindiiction and 

 capacity we have . 



di. ri.dt 



e + Ri, + ^ i + j c "" ^' ■ • • • • • ^^^ 



giving by diffei'entiation : 



d^i, f de \ di. i, 



'W \ dij dt C ^ ' 



Hence it follows that continual alternating currents can only 



exist, if: 



de 



TT - - ^ (7) 



It is thus necessary that an increase in the current involves a 

 decrease of tension and inversely, in other words: the condition for 

 the generation of alternating currenis is a falling arc-characteristic. 

 For the alterjiating curr-ent the arc behaves as a "negative resistance" 

 hence the quantity — e may be considered as the electromotive 

 force for the alternating current. 



Applying this to the audion. we see from the characteristics of 

 tig. 2, that foi' a coiL^ttint gridpotential, it has a /v'^/??^^ characteristic, 

 hence it is stable. Only by coupling the grid to the oscillatioi- 

 circuit it is |)Ossible to make the system unstable. 



The anode current i ') is a function of the anode-potential e and 

 the grid-potential v ; 



i =f{e,v) ......... (8) 



If here also we assume a liueai- relation between current and 

 tensions, the general solution of the differential equations for this 

 system consists of the sum of a "continuous-current-solution" /„, e„, v, 

 and an "alternating-current-solution" /j, e',, r,. Here again the qnantity 

 — «, is to be considered as the electromotive force for the alter- 

 nating current. 



From (8) it follows that 



^\= ^^i +^r, (9) 



Oe ov 



rutting ^ = and — =: /., this becomes: 

 oe r dt' 



') For the sake of convenience we henceforth leave out the index a. 



