Regeneration Theory

H E N t h e o u t p u t o f a n amplifier i s connected t o t h e i n p u t t h r o u g h a t r a n s d u c e r t h e resulting c o m b i n a t i o n m a y be either s t a b l e or u n s t a b l e . T h e circuit will be said to be s t a b l e w h e n an impressed small d i s t u r b a n c e , which itself dies o u t , results in a response which dies o u t . It will be said to be u n s t a b l e w h e n such a d i s t u r b a n c e results in a response which goes on indefinitely, e i t h e r s t a y i n g at a relatively small v a l u e or increasing until it is limited by t h e n o n - l i n e a r i t y of t h e amplifier. W h e n t h u s limited, t h e d i s t u r b a n c e does n o t grow f u r t h e r . T h e n e t gain of t h e r o u n d t r i p circuit is t h e n zero. Otherwise s t a t e d , t h e more t h e response increases t h e more does t h e non-linearity decrease t h e gain until at t h e point of o p e r a t i o n t h e gain of t h e a m p l i f i e r is j u s t equal to t h e loss in t h e f e e d - b a c k a d m i t t a n c e . An oscillator u n d e r these conditions would ordinarily be called s t a b l e b u t it will s i m p l i f y t h e p r e s e n t p a p e r to use t h e definitions a b o v e a n d call it u n s t a b l e . Now, this f a c t as to e q u a l i t y of gain a n d loss a p p e a r s to be an accident connected w i t h t h e non-linearity of t h e circuit a n d f a r f r o m t h r o w i n g light o n t h e conditions for s t a b i l i t y a c t u a l l y d i v e r t s a t t e n t i o n f r o m t h e essential facts.