Nonlinear analysis of high Q oscillator phase noise

Abstract

Silicon Valley Engineering 2 1 2 9 Hoover Court Santa Clara, Ca.. 95051 ( 4 0 8 ) 2 9 6 -8 8 7 2 1 . 0 A b s t r a c t T h i s p a p e r u s e s n o n -l i n e a r a n a l y s i s t o t r a n s l a t e between c i r c u i t n o i s e and h i g h Q o s c i l l a t o r phase n o i s e . The o s c i -l l a t o r 6 concept i s used t o s e p a r a t e t h e r e s o n a n t c i r c u i t f r o m t h e r e s t o f t h e system. Analysis i s based on t h e l l a t o r c h a r a c t e r i s t i c s . I t i s shown t h o The f i n a l r e s u l t reduces t o Leeson's model' f o r z e r o n o n -l i n e a r i t y . The r e s u l t s o f AGC a r e a1 so analyzed and it i s shown how o u r f o r m u l a s r e l a t e t o t h e " n o i s e ampl i f i e r " model discussed i n 1 0 , 1 1 , and 2 . If AGC i s n o t p r a c t i c a l , t h i s paper can be used t o e s t i m a t e t h e c o n t r i b u t i o n of each c i r c u i t component t o t h e Q tuned c i r c u i t o s c i 11 a t o r r e g a r d 1 ess o f c i r c u i t c o n f i g u r a t i o n . F o u r i e r a n a l y s i s i s used t o f o c u s on one noise frequency and t h e n i n t e g r a t e t h e r e s u l t o v e r t h e e n t i r e spectrum. (as i s done w i t h t h e i n v e r s e F o u r i e r t r a n s f o r m g ) E u l e r ' s i d e n t i t y f o r s i n u s o i d s s i m p l i f i e s t h e m a t h e m a t i c s . An analysis program such as Spice i s used t o o b s e r v e t h e " h i d d e n n o n -l i n e a r i t i e s " o f a p a r t i c u l a r l l a t o r . The r e s u l t s a r e t h e n plugged i n t o t h e t h e o r e t i c a l f o r m u l a s t o c r e a t e a n o i s e s p e c t r u m . S i n c e t h e a c t u a l computations are complicated, it i s recommended t h a t t h e e n t i r e p r o c e d u r e be computer i zed. A numerical example f o r t h e d i s t o r t i o n l i m i t e d l l a t o r i s i n c l u d e d f o r c l a r i t y and completeness.The AGC case i s discussed i n d e t a i 1.