Experimental study on electromechanical performance decoupling and vibration suppression of crystal oscillator Zhangqi Gu 1 Nanjing Research Institute of Electronics Technology No.8, Guorui Road, Nanjing, China Qingqing Yu 2 Nanjing Research Institute of Electronics Technology No.8, Guorui Road, Nanjing, China

ABSTRACT In the mechanical vibration environment, the phase noise of crystal oscillator would deteriorate sharply, which would lead to the decline of the stability of crystal oscillator and affect the compre- hensive performance of the whole electronic equipment. In this paper, the mechanism of electrome- chanical coupling between mechanical vibration and phase noise is analyzed theoretically. The re- lationship between phase noise and vibration magnitude and the sensitivity of phase noise to different vibration frequencies and directions are studied experimentally, then the decoupling of mechanical performance and electrical performance is realized. Based on this, a vibration isolator for crystal oscillator is designed, which can achieve 15-2000Hz full frequency band random vibration attenua- tion, the vibration acceleration RMS value is reduced by 95%, and the phase noise degradation of crystal oscillator is less than 5dB. The research has a certain reference value for the vibration isola- tion design of electromechanical coupling vibration sensitive devices.

1. INTRODUCTION

With the development of electronic technology, the requirements of electronic components perfor- mance are getting higher and higher. As the core part in electronic components, the stability of crystal oscillator will directly affect the overall performance of the whole electronic equipment. Phase noise, as an important index for evaluating the frequency stability of crystal oscillators [1], its performance is related to factors such as material, temperature and vibration, among which the phase noise value is most sensitive to the influence of environmental vibration [2].

In general, the crystal oscillator has excellent phase noise performance in static environment. How- ever, it is inevitable for crystal oscillators to work in vibration environment. When the crystal oscil- lator is used as the reference frequency source of communication, radar and navigation systems, it will be carried on high-speed flying vehicles such as aircraft, missiles and satellites. At this time, the crystal oscillator will work in a very bad vibration environment, resulting in a sharp deterioration of its phase noise performance [3, 4].

1 gzq_19900628@126.com

2 yuqingqing@aliyun.com

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Therefore, how to make the phase noise performance of crystal oscillator meets the system require- ments under vibration conditions has become a very key engineering problem.

In this paper, we analyzed the mechanism of the effect of mechanical vibration on the phase noise of crystal oscillation, and decoupled the electromechanical performance of crystal oscillator based on experimental means. Then we designed and verified a variety of vibration isolators for crystal oscil- lation. The vibration isolator finally attenuates the total root mean square value of vibration acceler- ation by about 95%, and the phase noise deterioration of the crystal oscillator under random vibration does not exceed 5dB. 2. MECHANISTIC ANALYSIS OF THE ELECTRIMECHANICAL COUPLING BE- TWEEN VIBRATION AND PHASE NOISE

The crystal oscillator is an electromechanically coupled device that works by converting the mechan- ical vibrations of a wafer into electrical signals. The vibration of the external environment will alter the mechanical vibration of the wafer, thus causing the frequency of the output electrical signals to drift. This is manifested as the external vibration frequency will have a modulating effect on the crystal oscillator output frequency, thus causing a parasitic modulation component in the crystal os- cillator output spectrum. The modulation depends linearly on the acceleration sensitivity of the crystal itself and the magnitude of the vibration.

The output frequency of crystal oscillator under vibration condition is given as:

0 0 ( ) [1 cos(2 ( )] g p v f t f f f S A f t  = + = + (1)

0 f f  where is the resonant frequency of crystal oscillator at static state, is the difference between ( ) f t g S p A output frequency and carrier frequency, is the acceleration sensitivity, is the peak accel-

( ) v f t eration of vibration, is the ambient vibration frequency. The output signal of the crystal oscillator is expressed as:

0 ( ) cos[ ( )] V t V t = φ (2)

( ) t φ ( ) t φ where is the instantaneous phase of the output signal, in the case of frequency modulation, is the integral of frequency over time:

0 ( )=2 ( ) t t f t dt   φ (3)

In a simple harmonic vibration environment with a fixed frequency, the instantaneous phase of the output signal can be obtained by substituting equation (1) into equation (3):

f t f t f t f      +     φ (4)

0 ( )=2 sin(2 ) v v

Then substituting equation (4) into equation (2):

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f V t v f t f t f      = +    

(5)

0 0 ( ) cos[2 sin(2 )] v v

Equation (5) can be expanded by an infinite series of Bessel functions as ：

 

=

( ) { ( )cos(2 )

V t V J f t

0 0 0

 

+ +

( )cos[2 ( ) ]

J f f t

1 0

v

 

+ −

( )cos[2 ( ) ]

J f f t

(6)

1 0

v

 

+ +

( )cos[2 ( 2 ) ]

J f f t

2 0

v

 

+ − +

( )cos[2 ( 2 ) ] ...}

J f f t

2 0

v

 0 ( ) v v f f A f f =  =  where is modulation index, . From equation (6), it can be observed that the modulated output signal contains not only the first carrier frequency component, but also the side frequency components corresponding to frequencies (f 0 +f v ), (f 0 -f v ), (f 0 +2f v ), (f 0 -2f v ), etc., which are sidebands generated by vibration. The power ratio of the n-th sidebands to the carrier wave as:

2 0 ( ( ) ( )) n V n L J J   = (7)

0.1  When modulation index ， the main power is concentrated on the carrier frequency, a small amount is concentrated on the first pair of sidebands, the higher-order part can be neglected. There- fore, in the case of small modulation index, the single sideband phase noise can be expressed as:

  = = (8)

( ) ( ) 20log 20log( 2 ) ( ) V v g p v J L f dBc S A f f dBc J

1 1

0 0

For a random vibration with known power spectral density function G(f v ) ， the relation relative to the sinusoidal acceleration in a 1 Hz bandwidth can be expressed as ：

( ) 2 ( ) v v A f G f = (9)

Then substituting equation (9) into equation (8), in the case of small modulation index, the single sideband phase noise in the random vibration environment which power spectral density function is G(f v ) can be obtained as:

0 1 2 ( ) ( ) 20log( ) 2

S f G f L f dBc f = (10)

g v V v

v

As can be seen from the above equation, in the random vibration environment, the variation of crystal oscillator phase noise is related to the acceleration sensitivity of the crystal oscillator, the vibration frequency, the spectral density of random vibration and the crystal frequency. The coupling

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effect of mechanical vibration on the crystal oscillator phase noise is mainly reflected in the changes of vibration magnitude and frequency will lead to changes in the crystal oscillator phase noise. 3. DECOUPLING OF ELECTROMECHANICAL PERFORMANCE FOR CRYSTAL OSCILLATOR

3.1. Anti-vibration Performance Test of Crystal Oscillator An airborne electronic equipment works in the environment of wide-band strong vibration. The fre- quency range of random vibration is 15~2000Hz, and the total acceleration RMS value is 3.5g. The crystal oscillator used in this electronic equipment needs to meet the requirement of ultra-low phase noise in its operating band, and the phase noise deterioration in the random vibration environment needs to be less than 5dB.

We tested the phase noise of the two types of crystal oscillator at a given offset frequency under static condition, and then tested the phase noise change under vibration conditions.

In order to convert the electrical performance index of crystal oscillator into the allowable vibration requirement, we tested the anti-vibration performance of crystal oscillators. The vibration condition of the whole frequency band is attenuated step by step at an interval of -6dB, then the vibration at- tenuation when meeting the phase noise requirements is obtained.

The phase noise of crystal oscillator 1# and 2# under static and vibration conditions is shown in Table 1. The phase noise variation at an offset frequency for different vibration magnitudes is shown in Figure 1 and Figure 2.

Table 1: The phase noise of crystal oscillators under static and vibration conditions.

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The phase noise of crystal oscillator 1# (dBc/Hz)

The phase noise of crystal oscillator 2# (dBc/Hz) X Y Z X Y Z 0dB(full magnitude) -97 -90 -95 -103 -102 -100 -6dB -105 -97 -102 -107 -105 -104 -12dB -113 -102 -107 -111 -112 -108 -18dB -119 -108 -113 -116 -117 -114 -24dB -126 -117 -120 -119 -119 -118 -30dB -132 -125 -127 -120 -119 -119 Static -132 -120

Vibration Magnitude

Figure 1: The phase noise of crystal oscillator 1# at different vibration attenuation levels.

Phase Noise (dBeittz) Sate hae Nate Rtrece Line 40 a8 20 Vibration Attenuation Magnitude (4B) 25

Figure 2: The phase noise of crystal oscillator 2# at different vibration attenuation levels. According to the above data, it can be seen that the crystal oscillator is very sensitive to the vibra- tion, and a very small amount of vibration will cause a great deterioration of the crystal oscillator phase noise. At the same time, the attenuation of vibration magnitude can improve the deterioration of phase noise, but the improvement changes slowly.

Due to the different internal compositions and packaging of different types of crystal oscillator, the anti-vibration performance of crystal oscillators is also different. For crystal oscillator 1#, the overall vibration level needs to be attenuated by 24-30dB when the phase noise is close to the index require- ment. The crystal oscillator 2# is internally encapsulated with a vibration isolator, so its anti-vibration performance is better than crystal oscillator 1# under the same vibration condition. When the overall vibration level is attenuated by about 18dB, the phase noise of this crystal oscillator can meet the index requirement.

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3.2. Sensitivity Test of Crystal Oscillator Phase Noise to Vibration In order to guide the design of the crystal oscillator vibration isolator, we tested the phase noise of the two types of crystal oscillators in different vibration bands and directions to obtain the sensitivity of phase noise to different mechanical vibration parameters.

During the test, the vibration frequency range is divided into four bands: 15-50Hz, 50-150Hz, 150- 450Hz and 450-2000Hz. The vibration magnitudes of each band are attenuated separately, and the overall vibration magnitude is similar. The phase noise of the two crystal oscillators at a given offset frequency in different vibration directions is tested.

The sensitivity test results of the phase noise of crystal oscillator 1# and 2# to vibration are shown in Table 2. The phase noise variation of different vibration frequency bands and directions at an offset frequency is shown in Figure 3 and Figure 4.

Table 2: The phase noise of crystal oscillators in different vibration bands and directions .

The phase noise of crystal oscillator 1# (dBc/Hz)

The phase noise of crystal oscillator 2# (dBc/Hz) X Y Z X Y Z 15-50Hz -102 -93 -99 -106 -107 -101 50-150Hz -103 -105 -101 -106 -101 -97 150-450Hz -100 -93 -96 -102 -102 -96 450-2000Hz -104 -94 -99 -102 -101 -100

Frequency Band

Phase Noise (dBe/Hz) ‘Sate Phan Nie Rfoence Lie Vibration Attenuation Magnitude (dB)

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Figure 3: The phase noise variation of crystal oscillator 1# in different vibration bands and direc-

tions.

@ eee 8 @ x ey [ez 10 Frequency Band (Hz) 160.480 “502000

Figure 4: The phase noise variation of crystal oscillator 2# in different vibration bands and direc-

tions. Combined with the above test data, it can be seen that crystal oscillator 1# has a certain frequency band sensitivity, in the attenuation of the vibration level of the 50-150Hz frequency band can effec- tively improve the phase noise at the central offset frequency. In addition, the crystal oscillator 1# is most sensitive to Y-direction vibration, followed by Z-direction vibration, and the least sensitive to X-direction vibration. Therefore, when installing this crystal oscillator, it should be avoided to ar- range the Y direction of the crystal oscillator in the direction of large vibration magnitude.

For crystal oscillator 2#, it is most sensitive to Z-direction vibration, and the phase noise deterio- rates greatly. However, its phase noise and vibration frequency band have no obvious correlation, which is due to it is internally encapsulated with a vibration isolator, and the vibration attenuation of this isolator are superimposed and coupled with the vibration attenuation of external excitation.

Phase Noise (dBe/Hz) Frequency Band (12)

4. DESIGN AND VERIFICATION OF CRYSTAL OSCILLATOR ISOLATOR

4.1. Design of Crystal Oscillator Isolator Under the same vibration condition, the anti-vibration performance of crystal oscillator 2# is better than crystal oscillator 1#. However, due to its internal vibration isolator, it is difficult to realize the coupling design of internal and external vibration isolators. Therefore, crystal oscillator 1# is selected for the airborne electronic equipment and the vibration isolator is designed accordingly.

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In order to meet the requirement that the phase noise deterioration of the crystal oscillator under vibration condition does not exceed 5dB, the attenuation of external vibration value should reach 24 ~ 30dB. At this time, the root mean square value of acceleration of random vibration is only 3% ~ 6.3% of the original value.

According to the above results of the analysis of the vibration sensitivity of the phase noise, the isolator should also reduce the vibration magnitude in the low frequency range, so as to ensure its phase noise requirements at a certain central offset frequency and achieve the optimal electrical index. For this purpose, the stiffness of the isolator should be adjusted as low as possible in all three direc- tions to reduce the inherent frequency of the system. However, as the stiffness of the vibration isolator decreases, it will inevitably affect the overall performance under shock, and there are reliability prob- lems such as vibration isolation performance degradation and collision. So the crystal oscillator vi- bration isolator needs to be designed and optimized for attenuation performance, stiffness, and relia- bility [5].

Aiming at the crystal oscillator used in this airborne electronic equipment and its using environ- ment characteristics, three kinds of wire rope vibration isolators are designed, as shown in Figure 5.

(a) Vine type (b) Spider-leg type (c) Cage type Figure 5: Wire rope vibration isolators for crystal oscillator.

4.2. Performance Verification of Crystal Oscillator Isolator The comparative test results of the vibration isolation performance of the above three wire rope vi- bration isolators for crystal oscillator are shown in Table 3.

From the point of view of mechanical performance, the three vibration isolators can achieve vibra- tion attenuation below 15Hz, and can isolate vibration of full frequency range. From the point of view of electrical performance, only the cage type vibration isolator can achieve the requirement that the phase noise deterioration of crystal oscillator under vibration condition does not exceed 5dB.

Although the vibration attenuation of cage type vibration isolator is lower than spider-leg type vibration isolator, its electrical performance is the best, mainly due to its lower inherent frequency, which can attenuate more external vibration in the low frequency band sensitive to the crystal oscil- lator.

Table 3: Performance comparison of vibration isolators for crystal oscillator.

Vibration Attenuation Magni-

Phase Noise

Inherent Fre-

tude (dB)

Deterioration (dB)

Type

quency (Hz)

X Y Z X Y Z

Vine type 13.5 -20.9 -24.3 -17.1 18 13 18

Spider-leg type 9 -29.9 -27.6 -30.4 7 4 7

Cage type 7 -27.6 -25.3 -27.6 3 3 4

5. CONCLUSIONS

In view of the phase noise deterioration of crystal oscillator in mechanical vibration environment, the mechanism of mechanical vibration on crystal oscillator phase noise is studied and analyzed. The crystal oscillator phase noise index is decoupled from the mechanical vibration requirements by means of experiments to obtain the vibration conditions under the satisfaction of electrical perfor- mance index. The sensitivity of crystal oscillator phase noise to vibration frequency and direction is also studied to provide a basis for the design of three types wire rope vibration isolators for crystal oscillator. The results of vibration isolator performance verification test showed that the crystal os- cillator phase noise is significantly improved after the installation of the isolators, in which the cage type vibration isolator can reduce the root mean square value of acceleration by 25-27 dB, and the phase noise is only changed by 3-4 dB compared with the static condition. 6. ACKNOWLEDGEMENTS

The authors are very grateful to the Editor-in-Chief and the anonymous referees, for their constructive comments and suggestions that led to an improved version of this paper. 7. REFERENCES

1. Leeson DB. 2016 Oscillator Phase Noise: A 50-Year Review. IEEE Transactions on Ultrasonics

Ferroelectrics & Frequency Control, 63(8) , p 1208-1225. 2. Min SU, Yuan CH, Jin SC, Gao W, Zhang L. 2017 Research on Effect of the Phase Noise

Deterioration of Frequency Source in Vibration Condition. Journal of Microwaves . 3. Li C, Sridhar A. 2017 Vibration and Shock Sensitivity: A Comparative Study of Oscillators.

Texas Instruments, Dallas, TX, USA, Appl Note SNAA296 , p 1-11. 4. Kumar V, Jhariya S, Jayasheela CS, Shivakumar R, Manjunath R. 2019 Phase Noise Performance

Improvement of X-Band Airborne Radar System. 2019 IEEE 5th International Conference for Convergence in Technology (I2CT) . 5. Li MR, Peng C, Zhang YD. 2019 Vibration Reduction Method of Airborne Vibration-Sensitive

Equipment and Its Application. Radar Science and Technology, 017(001) , p 104-111,118.

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