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TWO-STAGE SELF-LIMITING SERIES MODE TYPE QUARTZ CRYSTAL OSCILLATOR EXHIBITING IMPROVED SHORT-TERM FREQUENCY STABILITY M. M. D r i s c o l l Westinghouse Electric Corporation Defense and Electronic Systems Center Summary A simplified model of t h e t r a n s i s t o r s u s t a i n i n g stage employed in common quartz crystal oscillators is presented.Examination of themodel,includingassociated noise sources, provides an explanation for general differences observed in the output frequency spectra of s e v e r a l t y p e s of w i d e l y u s e d s e l f - l i m i t i n g c r y s t a l oscillator circuits. A self-limiting quartz crystal oscillator circuit configuration is described that has been specifically designed to exhibit simultaneously each of t h e t h r e e i m portant circuit characteristics necessary for improved oscillator short-term frequencylphase stability; large value of o s c i l l a t o r r e s o n a t o r l o a d e d Q, adequate supp r e s s i o n of 1 /f flicker-of-phase type noise, and improvement in oscillator ultimate signal-to-noise ratio. l ( a ) a n d ( b ) a r e of the anti-resonant type; that is, the crystal unit is operated at a frequency slightly above series r e s o n a n c e , w h e r e t h e n e t r e a c t a n c e of t h e c r y s t a l unit is positive (inductive). The Butler and bridged-Tee type circuits illustrated in figure l(c) and (d), repecively, a r e of t h e s e r i e s r e s o n a n t o r s e r i e s m o d e t y p e , in which oscillator operation is a t t h e s e r i e s r e s o n a n t frequency of the crystal unit, and the crystal unit impedance is purely resistive. The circuit of figure l ( f ) may be considered a Pierce type oscillator, modified for operation at the crystal unit series resonant frequency by addition of a p p r o p r i a t e i n d u c t a n c e i n s e r i e s with the crystal unit. S e v e r a l m o d e l s of the oscillator circuit have been constructed employing high quality third overtone 5MHz AT a n d B T - c u t q u a r t z r e s o n a t o r s . M e a s u r e m e n t of o s c i l l a t o r s h o r t - t e r m f r e q u e n c y s t a b i l i t y u s i n g c o n ventional phaselock and sampling techniques confirm attainment of substantial improvement in o s c i l l a t o r s h o r t - t e r m f r e q u e n c y s t a b i l i t y when compared to conventional self-limiting oscillator circtiits. Introduction Requirements for HF - VHF s i g n a l s o u r c e s e x hibiting improved frequency stability for use in modern radar and communication systems have prompted recent studies conducted at Westinghollse for the purpose of accurate determination and definition of the causes of short-term frequency/phase instability exhibited by solid-stateoscillator,amplifier,andfrequencymultiplier circuits, including 1 / f flicker-of-phase type noise as defined by D. Halford in 1968. 1 Y1 (a) PIERCE Ibl H I L L E R , ( c l BUTLER I (dl BRIDGED-TEE The t h e o r i e s d e v e l o p e d a s