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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 a r e s u l t of t h e s e s t u d i e s have been used successfully to accurately predict and verify short-term frequency stability limitations obs e r v e d f o r s e v e r a l t y p e s of crystal controlled HF and VHF oscillator circuits incommon usage at Westinghouse and throughout the industry.
In connection with these studies, an effort was undertaken to develop a q u a r t z c r y s t a l o s c i l l a t o r c i r cuit that would provide superior HF signal sources exhibiting best compromise between improved shortterm frequency stability and minimum circuit cost and complexity. This paper is a r e p o r t o n t h e r e s u l t s of that effort.

(el BRIDGED TEE. SHOWING RESEMBLANCE TO BUTLER

(11 MODIFIED PIERCE

72 0406 V B 1

F i g u r e 1.

CommonSingle-StageSelf-Limiting Quartz Crystal Oscillators

-Common

Self-Limiting Quartz Oscillator Circuits

Crystal

F i g u r e 1 shows the various types of commonly used single-stage self-limiting quartz crystal oscillator circuits.Thecircuitconfigurationsshowninfigure

F i g u r e 2 shows two commonly used two-stage self-limitingcrystaloscillatorcircuits.Thecathode (emitter)-coupled oscillator shown in figure Z(a) i s similar to the bridged-tee circuit, with oscillator operation at t h e c r y s t a l u n i t s e r i e s r e s o n a n t f r e q u e n c y . In

43

the cathode-coupled oscillator, the limiting function is usually provided as a result of c u r r e n t l i m i t i n g in t h e emitter follower stage, Q2. One of t h e c r y s t a l o s c i l l a t o r c i r c u i t s m o s t c o m monly used at Westinghouse i e t h e t w o - s t a g e P i e r c e oscillator shown in figure 2(b). Amplitude stabilization o c c u r s a s a r e s u l t of current limiting in the second stage. Although the output signal is n o r m a l l y t a k e n a t t h e e m i t t e r of QZ, it is possible to extract an output signal at the collector of Q2 t h a t i s i s o l a t e d f r o m t h e feedback path. If t h i s i s done, the output tank circuit a t t h e c o l l e c t o r m a y be tuned to the oscillator operating frequency, f , o r t o h i g h e r o r d e r h a r m o n i c s of fo.

Output F r e q u e n c y S p e c t r a of Common Crystal Oscillator Circuits It has been shown that the single-sided spectral density of phase E$(f) f o r t h e q u a r t z c r y s t a l o s c i l l a t o r m a y be e x p r e s s e d a s

w h e r e z&(f) = %@(f)denotes the single-sided spectral denaity of phaae exhiljited by the oscillator sustaining stage in the absence of an oscillator positive feedback loop connection. The Q, in equation denotes (1) the loaded Q of t h e o s c i l l a t o r r e s o n a t o r (i. e . , t h e c r y s t a l unit), w h e r e t h e r e s o n a t o r p h a s e s l o p e i n t h e v i c i n i t y of r e s o n a n c e i s a p p r o x i a m t e l y db Idf = 2Q11fo
(2)

Halford and others have shown that, excluding the effects of long-term drift, environmental effects, and burst or 'popcorn' noise. i s of the form

x(f)

E

K1 (1 -t K 2 / f )

(3)

W TWO-STAGE EMITTER-COUPLED
CRYSTAL OSCILLATOR

In addition, observation of t h e p h a s e n o i s e s p e c t r a e x hibited by solid-state amplifier, frequency multiplier, and oscillator circuits has been defined by Halford as having a nominal value of z - 1 1 5 dB /Hz for &f=1 Hz).
AUXILIARY 'ISOLATED' OUTPUT TERMINALS

Yl

E

OUTPUT TERMINALS NORMALLY USED

0 (8) WO-STAGE PIERCE OSCILLATOR
724408-'48-2

F i g u r e 3 s h o w s t h e r e s u l t s of m e a s u r e m e n t of short-term frequency stability exhibited by two differe n t t y p e s of q u a r t z c r y s t a l o s c i l l a t o r c i r c u i t s ; a twostage Pierce oscillator and a single-stage bridged-Tee oscillator. Both sources employ third overtone 47-MHz A T - c u t q u a r t z r e s o n a t o r s , w i t h c r y s t a l unit dissipation of i n t h e r a n g e 500 to 1000 microwatts. Examination the data depicted in figure 3, together with static meas u r e m e n t of oscillator working Q, reveals distinct simi l a r i t i e s a n d d i s s i m i l a r i t i e s b e t w e e n t h e s p e c t r a of the two sources:

F i g u r e 2. CommonTwo-StageSelf-Limiting Quartz Crystal Oscillators

The circuits shown in figures 1 and 2 together . with a variety of o t h e r l e s s c o m m o n o s c i l l a t o r c i r c u i t configurations, have been characterized in great detail with regard to recommended operating frequency range, usage in connection with prescribed types of q u a r t z r e s o n a t o r s , c r y s t a l u n i t Q degradation factor (usually assuming linear sustaining stage operation), ratio of oscillator power output to crystal dissipation, and sensitivity of oscillator frequency to lon -term changes in oscillator network element values. 3, Unfortunately, in many instances, decisions with regard to selection and design of a particular type of o s c i l l a t o r c i r cuit configuration a r e m a d e on the basis of e v e r y p e r formance requirement for the frequency source except short-term frequency stability. The device is fabricated, and subsequent measurements are made to determine whether or not t h e s h o r t - t e r m f r e q u e n c y s t a bility exhibited by t h e o s c i l l a t o r m e e t s t h e specification.

F i g u r e 3. S h o r t - T e r m S t a b i l i t y of T w o - S t a g e P i e r c e and Single-Stage Bridged-Tee Circuits

44

T h e v a l u e o b s e r v e d f o r X ( f ) i n t h e r e g i o n of l / f predominance is approximately the same for b o t h o s c i l l a t o r s , withd!(f= lOHz) zz 122 dB /Hz.

-

T h e v a l u e o b s e r v e d f o r r ( f ) i n t h e r e g i o n of white noise predominance is zz-152 dBjHz for the Pierce oscillator and 162 dB /Hz f o r t h e bridged/Tee circuit.

-

"n 1

The effective value for crystal unit loaded Q is a p p r o x i m a t e l y 1 2 0 , 000 f o r t h e P i e r c e c i r c u i t a n d 24, 000 f o r t h e b r i d g e d - T e e c i r c u i t . F o r fmrlO, 000 Hz, t h e b r i d g e d - T e e o e c i l l a t o r e x h i b i t s s u p e r i o r f r e q u e n c y s t a b i l i t y ; f o r fm i l 0 0 0 Hz h o w e v e r , t h e P i e r c e o s c i l l a t o r is superior. A d d i t i o n a l l y , c o m p i l a t i o n of r e s u l t s of s h o r t - t e r m frequency stability measurements for large numbers of Westinghouse and vendor self-limiting HF and VHF crystal-controlled frequency sources indicates that, in g e n e r a l , t h e s p e c t r a of t h e t w o - s t a g e P i e r c e o s c i l l a t o r is characterized by very little degradation in crystal u n i t u n l o a d e d Q, g ( f = lHz) x - 1 2 0 t o - 1 2 5 d B / H z , d e p e n d i n g o n s e l e c t i o n of RE, a n d u l t i m a t e S / N r a t i o > l0 k H z ) ) of a p p r o x i m a t e l y - 1 5 0 t o - 155 dB /Hz f o r c r y s t a l d r i v e l e v e l s o n t h e o r d e r of 5 0 0 m i c r o w a t t s . The spectra observed for the Butler and bridged-Tee series mode type oscillator circuits, on the other hand, are characterized byX(f=l Hz) 120dB /Hz, r e l a t i v e l y large crystal unit Q degradation factor, but extremely g o o d u l t i m a t e S / N r a t i o , on t h e o r d e r of z - 1 6 0 t o - 1 6 5 dB/Hz for crystal unit drive levels as low as 100 to 200 m i c r o w a t t s .

"C

'nl vn2

=

4KT RS df

VOLTSIHZ' VOLTSIHZX

J 4KTRgsdf
=

V d

4KT1dZdf

VOLTSIHZ' VOLTSlHZ'

v d

=

,/~ K T R E I ,

(x(f

'n

-

F i g u r e 4. Transistor Sustaining Stage Circuit Model with Noise Sources Figure 4 shows the simplified transistor equival e n tc i r c u i tw i t ha s s o c i a t e dn o i s es o u r c e s .T h e l/f type noise sources are not included in the model; the e f f e c t of t h e l / f c i r c u i t n o i s e o n o s c i l l a t o r f r e q u e n c y stabilitywillbesummarizedseparately.Thenoise s o u r c e s a s s o c i a t e d w i t h t h e c i r c u i t of f i g u r e 4 a r e

TransistorModelwithNoiseSources

A nt a l y s i s of t h e c i r c u i t of f i g u r e 4 y i e l d s t h e f o l lowing results: 1 ;

= Output current in transistor collector due to V,,, Vn,. Vn,, Vn4, o r V = Vin
sig

Vnl

= Thermal noise voltage associated with the s o u r c ei m p e d a n c e , 2s

Vn2 = T h e r m a l n o i s e v o l t a g e a s s o c i a t e d w i t h t h e
transistor base spreading resistance,

RBBI
Vn3

= Equivalentnoisevoltageduetoshot-effect
noise in the transistor emitter current,

I E
Vn4

= Thermal noise voltage associated with the
external emitter load impedance,

1 ;

ZE

= Outputcurrentintransistorcollectordue t o in x J ~ ~

i

n

Noise urrent ssociated ithhe educed c a w t r (uncorrelated) shot-effect noise i n the transistorcollectorcurrent,ICplusshot noise in the collector-base leakage current.

If we a s s u m e Z B t c i s l a r g e a n d i t s e f f e c t m a y b e neglected, solution of equations ( 4 ) and (5) f o r t h e c a s e w h e r e ZE i s a v e r y l a r g e r e a c t i v e ( n o i s e l e s s ) i m p e dance yields equation (4) r e d t o e s uc
1 ;

= 0

(6)
(7)

equation (5) reduces t o I" = i 3 n

Equations (4) through ( 7 ) s h o w v e r y c l e a r l y why properly designed series-mode crystal sources, such as t h e B u t l e r a n d b r i d g e d - T e e o s c i l l a t o r s , are able to exhibitexcellentultimatesignal-to-noiseratio. In these circuit configurations, ZE of figure 4 is t h e i m pedance exhibited by t h e q u a r t z c r y s t a l u n i t , a n d it becomes evident that because of t h e l a r g e r e a c t i v e i m p e dance exhibited by the crystal unit at frequencies other t h a n t h e c r y s t a l s e r i e s r e s o n a n t f r e q u e n c y , all of t h e sustaining stage noise sources of figure 4 can be made to have negligible effect (at modulation rates in excess of the effective crystal unit half-bandwidth) on the oscillator output signal short-term frequency stability. It should be noted that in most anti-resonant oscillator circuit configurations (such as the Pierce and Miller circuits shown in figures l(a), (b), and 2(b)), the out-of-band impedances (i. e . , Zs, Z E , Z L of figure 4 ) may become reactive due to the sharp reactance vs frequency characteristic exhibited by the c r y s t a l unit.It is usually found, however, that the r a t i o of the out-of-band reactive value for the external impedance to the resonant resistive value at the oscill a t o r o p e r a t i n g f r e q u e n c y i s not s o l a r g e a s i n t h e series mode circuits. Hence, the action of t h e c r y s t a l unit impedance function in reducing the oscillator high frequency (white) phase noise'bed'level is not so effective as in the series mode circuits. Flicker Noise of P h a s e In a d d i t i o n t o t h e t r a n s i s t o r n o i s e s o u r c e s p r e viously discussed, measurement of solid-state amplifier, frequency multiplier, and oscillator circuits rev e a l a 1 / f o r f l i c k e r - o f - p h a s e t y p e n o i s e e x i s t i n g a t low m o d u l a t i o n r a t e s on t h e d e v i c e c a r r i e r s i g n a l . R e c e n t investigations conducted at Westinghouse show that the p h e n o m e n a a r e c a u s e d by low frequency modulationofthe effective transistor transconductance magnitude and angle due to l / f n o i s e s o u r c e s i n t h e t r a n s i s t o r . In a d d i t i o n , i t h a s b e e n o b s e r v e d t h a t l o c a l R F negative feedback is effective in dramatically reducing both the modulation efficiency of the low frequency 1 /f noise and the AM-to-PM conversion efficiency. In t h e c a s e of a limiting transistor stage employed in oscillator service however, the use of R F negative feedback results in moderate reduction in AM-to-PM conversion efficiency, s o that typically, only E 10 dB d e c r e a s e i n n o m i n a l X(f=lH z ) = -115 dB/Hz is realized. Definition of Improved HF C r y s t a l Oscillator Circuit It is evident from the previous discussion that the series-mode circuits shown in figure l(c) and (d) and 2(a) are particularly advantageous in that the extremely s t e e p r e a c t a n c e v s f r e q u e n c y c h a r a c t e r i s t i c e x h i b i t e d by t h e c r y s t a l unit aids in effectively suppressing many of the dominant noise sources in the transistor sustaining stage. As stated previously, the main disadvantage of
46

these circuits is the large degradation in crystal unit unloaded Q, which seriously degrades the oscillator 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 at m o d u l a t i o n r a t e s l e s s than the effective oscillator resonator half-bandwidth. In addition, the degradation in crystal unit Q can be responsible for significant degradation in oscillator long-term frequency stability in that long-term changes in oscillator network elements (other than the crystal unit itself) that alter the sustaining circuit phase shift will have a more pronounced effect on o s c i l l a t o r f r e quency. This includes changes caused by environment (temperature, humidity) long-term power supply variation, and short-term effects (vibration and power supply ripple). Q d e g r a d a t i o n i n t h e c i r c u i t s of f i g u r e l ( c ) , ( d ) and 2(a) result principally from limiting in the transist o r . When l i m i t i n g o c c u r s , t h e t r a n s i s t o r i s t u r n e d 'off' for a portion of the signal waveform, s o t h a t t h e t i m e - v a r y i n g i m p e d a n c e s e e n by t h e c r y s t a l u n i t a t t h e t r a n s i s t o r e m i t t e r c o n t a i n s a large value component at the signal frequency. It i s t h i s c o m p o n e n t of t r a n s i s t o r impedance (which becomes increasingly large as the excess gain in t h e s u s t a i n i n g s t a g e i s i n c r e a s e d ) t h a t r e s u l t s in significant degradation in oscillator working

Q.
Clearly, superior HF source spectra could be obtained with the use of a c r y s t a l - c o n t r o l l e d s e r i e s - m o d e type circuit configuration employing class A nonlimiting action in the sustaining stage transistor. The limiting function may then be provided by means of (1) auxiliary low-noise AGC circuits (a portion of t h e amplified R F signal is rectified and used t o c o n t r o l t h e R F gain of the sustaining stage), ( 2 ) back-to-back Schottky barrier (hot carrier) diodes incorporated in t h e o s c i l l a t o r c i r c u i t s o that the diode R F impedance p r e s e n t e d t o t h e s u s t a i n i n g s t a g e ( a n d h e n c e R F gain) d e c r e a s e s w i t h i n c r e a s i n g R F level, and ( 3 ) i n c o r p o r a tion of a s e c o n d s e l f - l i m i t i n g t r a n s i s t o r s t a g e i n t h e oscillator sustaining circuit in a manner such that its effect on crystal unit loading insignificant. In t h i s paper, the results obtained with ( 3 ) only a r e r e p o r t e d .

Figures 5(a) and (b) show two types of s e r i e s mode crystal oscillator circuits similar to the bridgedTee and Butler circuits of f i g u r e s l ( c ) a n d ( d l , r e s p e c tively. In t h e c i r c u i t s of figure 5, t r a n s i s t o r s Q 1 a n d Q2 are connected in cascode (common emitter-common base) configuration, with the quartz crystal unit used as an unbypassed emitter load on Ql. Clearly, the effect i v e t r a n s c o n d u c t a n c e of t h e c a s c o d e s u s t a i n i n g s t a g e i s a maximum at precisely the series resonant frequency of the crystal unit. The combination L2-C2-C3 in figure 5(a) and the combination T1-C2 in figure 5(b) c o m p r i s e a low selectivity 180-degree phase shift feedback network tuned t o t h e o s c i l l a t o r o p e r a t i n g f r e q u e n c y ( t h e s e r i e s r e s o n a n t f r e q u e n c y of t h e c r y s t a l u n i t ) . Power is e x t r a c t e d i n t o l o a d r e s i s t o r RL. Unlike the common Butler or bridged-Tee circuits, in the circuit of figure 5, Q1 i s ' o n ' d u r i n g t h e f u l l c y c l e of the signal waveform since the limiting function is provided in the s e c o n d t r a n s i s t o r , Q2. T h i s i s a c c o m p l i s h e d by setting t h e d c q u i e s c e n t c u r r e n t i n Q 2 a t a s m a l l f r a c t i o n of that i n Q1. Amplitude stabilization occurs in the oscillator as a r e s u l t of current limiting in the second stage.

Since the dc quiescent current flowing in Q1 in t h e circuit of figure 5 can be made much larger than the peak signal current, the impedance presented to the crystal unit a t t h e e m i t t e r of Q1 can be made quite small, so that negligible loading occurs. Also, because of the small value of cascode output conductance, relatively large signal voltage swing at the collector of Q2 is possible, allowing large value of impedance transformation ratio in the o s cillator feedback network, further improving the crystal Q degradation factor. Local R F negative feedback exists in both Q1 and QZ. T h e e m i t t e r of Q1 is loaded (at the signal frequency) by the resonant resistance of t h e c r y s t a l unit, so that 20 dB effective R F negative feedback is typically obtained in t h e f i r s t s t a g e f o r m o d e r a t e c r y s t a l unit drive level. An e x t r e m e l y e x c e s s i v e a m o u n t of negative feedback is used in the second stage, since it is being d r i v e n f r o m t h e l a r g e c o l l e c t o r i m p e d a n c e a t Q1. Detailed calculations of the effect of the various noise sources associated with the circuits of figure 5 show that the oscillator output frequency spectrum should b e c h a r a c t e r i z e d by near minimum value for fo/2Qp corner frequency (see equation ( 1l ) , low value for high Fourier frequency (white) noise 'bed' level, and at least 10 dB reduction in n o m i n a l v a l u e o f R ( f ) i n t h e r e g i o n of of the limiting 1 /f predominance. The nonlinear behavior transistor in the sustaining circuit accounts for the fact that only moderate reduction in the 1 /f portion o f x ( f ) c a n be expected. F i g u r e 5. Series-ModeCrystalOscillatorwith Cascode Sustaining Stage Experimental Results Two models of t h e o s c i l l a t o r c i r c u i t d e s c r i b e d a b o v e were fabricated, employing very high inductance, high-Q third overtone 5-hfHz BT-cut quartz resonators designed by D. Neidig at the Piezo Crystal Company. A detailed s c h e m a t i c d i a g r a m i s shown in figure 7. The dc quiescent c u r r e n t i n Q1 was set at 5 mA; quiescent current in Q 2 was 0. 8 mA. C r y s t a l unit dissipation was approximately 8 5 microwatts, with t4 dBm oscillator output power. S t a t i c m e a s u r e m e n t of oscillator db/df was made for the circuit in figure 7 by m e a s u r e m e n t of Q1 b a s e - t o collector phase shift and resultant oscillator frequency shiftforslightdetuningof C7. M e a s u r e m e n t s i n d i c a t e d that a working oscillator Q equal to 8 0 percent of t h e c r y s t a l unit unloaded Q was achieved for the oscillator. Additionally, no measureable difference in Q degradation w a s o b s e r v e d as t h e o s c i l l a t o r e x c e s s g a i n w a s v a r i e d f r o m 3 to 12 dB. T o m e a s u r e t h e 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 of the models using conventional phaselock techniques, 8 one of the oscillators was modified for provision for electronic tuning. a s showninfigure 8. Tuning sensitivity of 0. 5 H z / V was obtained for the modified oscillator (VCXO). In the noise measurement test setup, the modified oscillator was phase-locked to the second model via a n a r r o w band b C = 2 rad/sec) phaselock loop. In the test set shown in figure 9, the combined phase instabilities of the two o s c i l l a t o r s u n d e r t e s t p r o d u c e a voltage at the phase detector output. The phase detector output voltage is amplified by means of a low-noise audio amplifier and fed to a wave analyzer for measurement of the individual frequency components of t h e o s c i l l a t o r ( s ) p h a s e instability. The test set is calibrated by m e a s u r e m e n t of t h e p h a s e d e t e c t o r s e n s i t i v i t y i n V / r a d . I n s t r u m e n t a tion noise level is determined by m e a s u r e m e n t of t h e

F i g u r e 6 shows a plot of typical effective transconductance magnitude and angle versus drive level for the cascode sustaining stage. As can be seen from the figure, a transconductance variation of nearly 20 dB is obtained as a function of sustaining stage drive level. This is due to the fact that increase in signal level results in a shift in the dc operating point in the second t r a n s i s t o r , s o that it conducts for only a s m a l l f r a c t i o n of thesignalcycle.Careshouldbetaken,however,to e n s u r e t h a t t h e peak instantaneous signal voltage developed at the emitter of the second stage does not e x ceed the rated value for transistor reverse baseemitter voltage. This is accomplished by proper selection of external R F i m p e d a n c e a t t h e e m i t t e r of t h e second stage and maximum sustaining stage signal current.

8 -

mm
&I

I ""I 111111 0"lYt , t * l ,
F i g u r e 6.

CascodeSustainingStageTransconductance vs Signal Level

47

combined noise voltages associated with the phase detector and loop amplifier appearing at the phase detector output, with the phase detector driven at phase quadr a t u r e f r o m a c o m m o n s o u r c e ( i . e . , o n e of the 5-MHz crystal oscillators).
L1 270 + l ( L I V D C B A T T E R Y SUPPLY

Results of short-term frequency stability measurement for the 5-MHz crystal oscillator circuit in f i g u r e 7 a r e shown in figure 10. As can be seen from t h e f i g u r e , e x t r e m e l y a c c u r a t e d e t e r m i n a t i o n of o s c i l l a tor Sb(f) at high modulation frequencies is difficult due t o t h e l e v e l of instrumentation noise level. However, figure 10 clearly indicates attainment of t h e o r e t i c a l short-term frequency stability for the oscillators. As can be seen from the figure, the oscillator frequency s p e c t r u m is characterized by 10 dB reduction in nominal level for 1 /f portion of and notably low level for white phase noise.

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5 MHz ModelOscillatorCircuitSchematic

F i g u r e 10.

5 MHz Model Oscillator Circuit Short-Term Frequency Stability

In a d d i t i o n t o t h e o s c i l l a t o r c i r c u i t s h o w n i n figure 7, two additional 5-MHz crystal sources were constructed employing the cascode sustaining stage with Colpitts oscillator type feedback network arrangement. A d e t a i l e d s c h e m a t i c f o r t h e o s c i l l a t o r c i r c u i t is shown in figure 11.
A Hewlett Packard Computing Counter was used for determination of the low frequency portion of SJ(f) for the oscillator circuit in figure11.Thecounteris p r o g r a m m e d ( b y m e a n s of a s t a n d a r d k e y b o a r d p r o g r a m supplied by Hewlett Packard) to compute and display the Fourier components of noise frequency modulation e x i s t i n g i n t h e s o u r c e u n d e r t e s t b y m e a n s of the Hadamard variance function. 9 Dead time between frequency measurements in the counter is fixed at 2. 3 msec. The oscillator output signals are frequency multiplied to 20 MHz by m e a n s of c l a s s C t r a n s i s t o r d o u b l e r s , as shown i n f i g u r e 12. The two 20-MHz signals (228-Hz) difference frequency) are beat together to obtain a 228 Hz beat note which is applied to the counter for analysis. Frequency multiplication of t h e s o u r c e s a n d l o w f r e quency input t o t h e c o u n t e r a r e n e c e s s a r y t o a v o i d limitations in computing counter resolution.

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F i g u r e 9.

Test Setup for Short-Term Frequency Stability Measurement

T h e r e s u l t s of t h e m e a s u r e m e n t u s i n g t h e s a m p l i n g technique described above a r e shown in figure 13. Although equivalent measurement bandwidth for the Hadamard variance program that was used is 10 percent, figure 13 shows the oscillator Si(f) referred to a l-Hz in figure 13 substantiate the bandwidth.Resultsshown results shown in figure 10, indicating achievement of approximately a 15 t o 20 dB reduction in the nominal v a l u e f o r x ( f ) i n the region of 1 /f predominance.

Conclusions A simple self-limiting quartz crystal oscillator circuit has been described that exhibits moderate reduction in the 1 /f p o r t i o n o f x ( f ) t oa level comparable to that reported by Brandenberger. l o Although further r e d u c t i o n i n d ( f ) s h o u l d b e a t t a i n a b l e t h r o u g h t h e u s e of o t h e r c i r c u i t m e a n s of providing the oscillator limiting function, the oscillator circuit configuration disclosed in this paper provides an inexpensive frequency source exhibiting improved short-term frequency stability, compared to crystal controlled frequency sources currently available. Although the models were operated at 5 MHz, m e a s u r e m e n t of tuned cascode amplifiers indicate that the oscillator circuit will be useful at frequencies in the 30 to 60 MHz range.

Additionally, proper use of appropriate phaselock and/or injection-lock techniques used in conjunction with the disclosed circuit as reference frequency will provide microwave frequency sources exhibiting superior frequency stability.

References D. J. Healey, 1 1 " F l i c k e r of Frequency and Phase 1, and White Frequency and Phase Fluctuation in Frequency Sources, I ' Proceedings of the 26th Annual Symposium on Frequency Control, Fort Monmouth, New J e r s e y , J u n e 1972. D. Halford, A. Wainwright,and J. B a r n e s ," F l i c k e r 2. Noise of P h a s e i n R F Amplifiers and Frequency I' Multipliers:Characterization,Cause,andCure, Proceedings of t h e 22nd Annual Symposium on Frequency Control, Fort Monmouth, New J e r s e y , April 1968, pp. 340-341. W. A. Edson, "Vacuum Tube Oscillators, John 3. WileyandSons,Inc., New York,1953. J. P. Buchanan,"Handbook of P i e z o e l e c t r i c 4. Crystals for Radio Equipment Designers. I ' Philco Corporation,October1956, WADC Technical Report 56-156. D. F i r t h , " Q u a r t z C r y s t a l O s c i l l a t o r C i r c u i t s De5. sign Handbook, l ' The Magnavox Co., Fort Wayne, Indiana,March1965, AD 460 377. 6. D. B. Leeson, "A Simple Model of Feedback Oscillator Noise Spectrum, I ' Proc. IEEE, Vol. 54, No. 2, F e b r u a r y 1966, pp. 329-330. 7. A. Van Der Zeil, "Noise in Solid State Devices and L a s e r s , I ' P r o c .I E E E , Vol. 58, No. 8. August 1970, pp. 1178-1206. M. Driscoll, "Design 8. D. J. Healey, I11 and M. Manual for Voltage Controlled Crystal Oscillators (VCXO), I ' Westinghouse Space and Defense Center TechnicalReport,December1967. R. A. Baugh, "Frequency Modulation Analysis with 9. the Hadamard Variance, ' ' Proceedings of the 25th Annual Symposium on Frequency Control, Fort Monmouth, New J e r s e y , A p r i l 1971, pp. 222-225. 10. H. Brandenbergerand F. Hadorn,"HighQuality Quartz Crystal Oscillators, Frequency Domain and Time Domain Stability, I t Proceedings of the 25th Annual Symposium on Frequency Control, Fort Monmouth, New J e r s e y , A p r i l 1971, pp. 226-230.
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