Low Jitter Thin-Film Piezoelectric-on-Substrate Oscillators Mohsen Shahmohammadi, Mohammad Jafar Modarres-Zadeh, and Reza Abdolvand Department of Electrical and Computer Engineering, Oklahoma State University Tulsa, Oklahoma, USA [email protected] Abstract—In this paper we report a 27MHz oscillator with very low cycle-to-cycle jitter (7 psec standard deviation) based on a thin-film piezoelectric-on-substrate (TPoS) resonator driven beyond the bifurcation point. For the first time, our results seem to provide experimental validation for the speculated suppression of overall oscillator circuit noise through the operation of the resonator beyond the bifurcation. In our work the dependency of jitter on the resonator characteristics (i.e. quality factor and motional impedance) and oscillation power is studied. A phase-noise as low as -130dBc/Hz @ 1kHz offset from carrier is measured for these TPoS oscillators which is comparable with the results reported for quartz oscillators.

I.

INTRODUCTION

In data and wireless communication, the clock generator is an essential building block of the system. For many years, quartz crystal resonators have been commonly employed in clock generators since they offer high quality factor (Q) and excellent temperature frequency stability. The drawback of such scheme is the incompatible fabrication process of quartz resonators which hinders the complete integration of the highperformance oscillators with the rest of electronics. This issue will be of much greater importance for realization of future generations of portable devices in which several oscillators at different frequencies are demanded in an extremely small foot print area. MEMS resonator technology seems to gradually gain popularity as a solution for the integration problem and more high-performance MEMS-based oscillators are presented by researchers and companies [1, 2, 3]. In the past, our group has shown that thin-film piezoelectric-on-substrate (TPoS) MEMS resonators can yield superior power handling and Q (in air) due to the excellent power density and low acoustic loss of their silicon resonant body [4]. With such advantages, TPoS resonators are posed as great candidates to be employed in low-noise oscillator circuits. Noise in an oscillator is commonly characterized either in time (jitter) or frequency domain (phase-noise). The presence of jitter in oscillators introduces sampling error which confines the bit rate in the communication systems. Based on a linear model, the phase-noise and consequently the jitter in

978-1-4244-6400-5/10/$26.00 ©2010 IEEE

an oscillator are inversely proportional to the oscillation power [5]. However, increasing the power delivered to a mechanical resonator will eventually increase the vibration amplitude to an extent that the small high-order elastic constants of the material can't be neglected (onset of nonlinearity). This will introduce a shift in the resonance peak toward lower (spring softening) or higher frequencies (spring hardening). At large vibration amplitudes (relative to the resonator size) the resonator reaches to a point beyond which multi-stable vibration amplitudes exists for a single frequency (Duffing bifurcation point). It is traditionally believed that the oscillation power in an oscillator loop is limited by the maximum stored energy in the resonator at bifurcation point. A chaotic change in the frequency is expected at bifurcation and consequently the phase-noise performance is degraded [1]. This issue is of great concern in MEMS resonators because they can store less energy compared to bulky crystal resonator as a result of their very small size. On the other hand, there exists a body of theoretical work on the topic of nonlinear oscillators that suggests operation of the mechanical resonator at bifurcation yields improved overall oscillator circuit noise [6]. However, to the best of our knowledge this has never been demonstrated in practice. The results presented in this paper are believed to be the first validation for the possibility of suppressing oscillator noise by driving a MEMS resonator beyond the bifurcation point. Our measurement confirms that the oscillator jitter is scaled down after the TPoS resonator reaches the bifurcation and the close-to-carrier phase-noise of the oscillator doesn't seem to deteriorate. Also, we show that the jitter in the 27MHz oscillator based on TPoS resonator at any oscillation amplitude is lower for a device with the lower motional impedance. In depth investigation of the oscillator behavior at bifurcation is currently underway in order to better relate the resonator characteristic to the oscillator performance. II.

TPOS RESONATOR

As shown in the schematic of Fig. 1a, a TPoS resonator consists of a thin piezoelectric film (e.g. aluminum nitride, AlN) sandwiched between two metal electrodes (e.g. molybdenum, Mo) stacked on top of the device layer of a silicon-on-insulator (SOI) substrate [4]. The top Mo is dry

613

etched to form the top electrodes and the tracces while the AlN is wet etched to clear access to the bottom m electrode. The resonator body is defined in a stack dryy etch step. The backside handle layer silicon is etched iin an anisotropic etching step, which creates the cavity below tthe resonator. The final release step is done in buffered oxxide etch (BOE) solution to remove the buried silicon oxidee layer and create the free-standing structure (Fig.1b).

-10

S12 Magnitude (dB)

-15

fc

fs

Linear Response

Bifurcation point

-20

Nonlinear Response

-25 -30 -35 27.705

27.710

4.66dBm

3.75dBm

1.87dBm

-18dBm

5 27.715

27.720

27.725

Frequencyy (MHz) Fig. 2.

Frequency response of a typicaal TPoS resonator at different delivered poweer

IV. (a) Fig. 1.

(b)

a) The schematic of a 27MHz TPoS devicce, b) Process flow

III.

NONLINEARITY IN TPOS RESO ONATORS

In lateral-extensional TPoS resonators vvibrating at large amplitudes, elastic constants depend on strain and consequently the equivalent spring constant is represented as 1 where k and k are the first- and second- order anharmonic term ms and is the vibration amplitude. The equation of mottion for a forced vibration MEMS resonator is written as: cos

,

(1)

mass m and where γ is the damping coefficient of the m the magnitude of the force term at angular freequency ω.

is R5-G

The presence of the high order terms in k(x) results in an amplitude dependant resonance frequency in the device [8]: 1

1

OSCILLATOR R CIRCUIT

The schematic of the oscillator circuit c used in this work is shown in Fig. 3a. This circuit conssists of a trans-impedance amplifier (SA5211) which provides the t gain and a comparator (TVL3501) which is used to producee a square waveform (Fig. 3b). The comparator, which is a hig ghly nonlinear component, is included in the oscillation loop in order to create simple ge to the resonator over a means to control the applied voltag very wide range. In this circuit the amplitude of the applied voltage to the resonator is adjusted by the potentiometer R5. i also tuned to 50% by The duty cycle of the waveform is potentiometer R2 before collecting jitter at each applied voltage.

,

(2)

where is the shifted resonance frequencyy, is the linear resonance frequency, and x0 is the vibrration amplitude. Depending on the sign of the resonancee peak frequency shifts toward the lower (spring softenning) or higher frequencies (spring hardening). As it turns out (Fig. 2), the peak frequency shifts to the left in ouur devices which represents the spring softening.

(a)

In order to compare the nonlinearity of diifferent resonators in this study, we define a normalized frequenncy shift called SN which is a measure of relative peak frequuency shift as the vibration amplitude is altered: ,

(3)

where SN is calculated as the difference beetween the shifted peak frequency (fs) and the center frequenncy (fc) at linear operation divided by fc (Fig. 3b). Therefore,, SN is zero when the peak is perfectly symmetric.

614

(b) Fig. 3.

or circuit, b) Output waveform a) The schematic of the oscillato

V.

MEASUREMENTS

A. Resonator characterization By varying the design features such as top electrode pattern, TPoS resonators with different charracteristics can be fabricated at similar frequency. Three ~27MHz TPoS resonators with a range of various characteriistics (Table I) are fabricated and chosen to be used in the osciillators in order to enable investigation of the effect of resonattor characteristics on the oscillator performance. Frequency rresponses of each device as well as their SEM pictures are shoown in Fig. 4 (All measured quality factors are in air). TABLE I.

DEVICES PROPERTIIES

he resonator with smaller and C with almost the same Q, th motional impedance is more nonlinear. These observations are expected since both higher Q and lower impedance result in a wer to be absorbed by the larger portion of the delivered pow resonator. Considering similarity in i the size of all three resonators, larger amount of absorb bed energy will cause the resonator to behave nonlinearly at a lower l onset. In order to find the value of th he applied voltage to the device at bifurcation, upward an nd downward frequency sweeps are examined around th he resonant peak. The bifurcation is detected at a pointt the two corresponding frequency responses begin to deviatee from each other (Fig. 6.). -10

Device A Device B Device C

M Motional Imp pedance(Ω) 400 430 1073

S12 Magnitude (dB)

Quality factor 16041 28819 28904

S12 Magnitude (dB)

-10

-15 -20 Backward at a 2.64dBm

-25

Forward at 2.64dBm At -21.86dB Bm

-30

-30

Device B

Device C

Device A

26.870

-50

Fig. 6.

26.872

26.874 26.8766 26.878 Frequency (M MHz)

26.880

26.882

Frequency response of a 27MHz resonator at -21.86dBm (linear response) and 2.64dBm (nonlinear reesponse with hysteresis)

-70

B. Oscillator characterization Three oscillator boards were asseembled using the aforesaid resonators. The oscillator jitter is meeasured using a Tektronix oscilloscope model TDS5104B. The measured standard deviation (STD) of the cycle-to-cyclee jitter as a function of the voltage amplitude applied to the dev vice is plotted for the three oscillators in Fig. 7.

-90 26.3

26.8

27.3

27.8

28.3

Frequency (MHz) Fig. 4.

Frequency response and SEM’s of threee different 27MHz resonators

STD jitter (psec)

To study the nonlinearity in these resonators, the frequency responses of the resonators aare measured at different delivered power to the resonatoor using Agilent E8358A PNA network analyzer. Using (3), normalized frequency shift is calculated and shown in Figg. 5. 60 Device-A (Q=16041, R=400Ω)

50 SN (ppm)

Device B (Q=28819, Rm=430Ω)

100

40 20

Fig. 7.

VC(bifurcation) ~ 1.164V

0 -23

-18

--3 -13 -8 Delivered Power(dBm)

500

1000

1500

2000

2500

3000

Device voltagge (mV)

VA(bifurcation) ~ 1.31V

10

Unstable U operation o

60

0

VB(bifurcation) ~ 0.661V

20

Device C (Q=28904, Rm=1073Ω)

80

Device-C (Q=28904, R=1073Ω)

30

Fig. 5.

Device A (Q=16041, Rm=400Ω)

120

0

Device-B (Q=28819, R=430Ω)

40

140

2

Nonlinearity measurement of three differennt 27MHz resonators

As it is clear from this figure, between reesonators A and B with almost the same motional impedance, resonator B with ween resonators B higher Q is more nonlinear [7]. Also, betw

Jitter versus device voltage for thrree different 27MHz Oscillators

It is observed that in all three osccillators the jitter gradually decreases as the amplitude of thee resonator input voltage increases. This trend is disrupted at a specific voltage at which a chaotic behavior in the oscillatorr is triggered. There is a range of fractional resistances (labeled as R5-G in Fig. 3) at which the oscillator is not stable and a the measured jitter is extremely high (nano seconds rang ge). However, as R5-G is further increased the oscillator staabilizes again yielding a scaled down jitter value compared to the last stable point. Further increasing the applied voltaage beyond this point will

615

only cause slight improvement in the cycle-to-cycle jitter and the minimum value for all three resonators are very close (~7 psec STD ). It was observed that at any applied voltage, the oscillator built based on the resonator with the lowest motional impedance yields the lowest measured jitter. Device C Device voltage 456mV

In order to better understand the nature of discontinuity in the jitter vs. voltage curves, the experiment was repeated at more data points around the discontinuity region for the oscillator based on device B (Fig. 8).

Oscillator/Jitter

Peak-toPeak (psec)

Cycle-toCycle (psec)

Device A

145.5

138

Device B

200.5

196

Device C

268

245

Device B Device voltage 450mV

STD Jitter (Psec)

40

Unstable operation

30

Device A Device voltage 460mV

20 Fig. 10. 10 0 400

500

600

700

800

900

Device voltage (mV) Fig. 8.

Jitter versus device voltage for device B in a closer view

Results interestingly show (Fig. 9) that for a small range of R5-G, the applied voltage trend is reversed (i.e. voltage decreases as R5-G increases). This means that for this range the equivalent impedance seen from the input of the device is reducing. This change in the input impedance can be attributed to a sudden shift in the vibration amplitude occuring right at the bifurcation in the resonator. 900

Device voltage(mV)

Phase noise measurement of device A, B and C

Finally, a similar oscillator using a resonator with very low motional impedance (~267Ω) was assembled. This time the device voltage amplitude was intentionally set beyond the unstable region of the jitter vs. voltage curve and the phase noise measurement was repeated (Fig. 11). This curve shows improvement in both close-to-carrier and noise floor compared to the oscillators tested in Fig. 9. It should be noticed that the recorded standard deviation for the cycle-tocycle jitter in this oscillator is also the same as those recorded for the other three oscillators beyond the unstable region and therefore, similar noise floors are expected for all of these oscillators. The measured phase noise of -130dBc/Hz @ 1kHz offset from carrier for this oscillator is very promising for MEMS oscillators and is comparable with the results reported for quartz oscillators.

Unstable operation

800 700 600

Numbr of Acquistion

Std dev (psec)

Cycle-to-Cycle Jitter (psec)

Peak-to-Peak Jitter (psec)

4,533,590

7

42

47.5

500

-143dBc/Hz Noise floor

400 2 Fig. 9.

4

R5-G(kΩ)

6

8

-130dBc/Hz @1kHz

Device voltage versus fractional resistance R5-G

Phase noise for these three oscillators is also measured and overlapped in Fig. 10. These measurements are taken at similar applied voltages (~455mV) to ensure operation of the resonators below the unstable region (which is believed to correspond to the bifurcation point of the resonator). As it is clear, the oscillator with the lowest motional impedance device (device A) exhibits the lowest noise floor which agrees with the jitter measurement results. The maximum peak-topeak and cycle-to-cycle jitters are also recorded for these oscillators (inset table of Fig. 10) and they confirm similar superiority for the device with the lowest motional impedance.

Fig. 11.

Phase noise measurement of device A

I.

CONCLUSION

In this paper, the evidence of suppressed overall noise in a MEMS-based oscillator is reported as a result of operating the resonator beyond the bifurcation point. If solidly proven through ongoing in-depth investigations, this is the first time that such experimental proof for this speculated result is observed. Meanwhile, the motional impedance of the thin-film piezoelectric-on-substrate (TPoS) resonator was shown to have a dominant effect on the oscillator jitter. Resonators with

616

lower motional impedance seem to yield lower jitter at any given oscillation amplitude. However, cycle-to-cycle jitter for all oscillators assembled based on different TPoS resonators converged to the same level of ~7psec standard deviation at very large device applied voltages. ACKNOWLEDGMENT

[5]

This work was funded by Integrated Device Technology. Authors thank Brandon Harrington for his significant contribution in fabrication of TPoS resonators. REFERENCES [1]

[2]

[3]

[4]

[6]

[7]

S. Lee and C. T.-C. Nguyen, "Influence of automatic level control on micromechanical resonator oscillator phase noise," in Proc. IEEE Int. Frequency Control Symp , May 2003, pp. 341–349. W.-T. Hsu and M. Pai, “The New Heart Beat of Electronics - Silicon MEMS Oscillators,” in 2007 Proceedings 57th Electronic Components and Technology Conference (IEEE, 2007), pp. 1895-1899. H.M. Lavasani, et al., “A 76dBOhm, 1.7 GHz, 0.18um CMOS Tunable Transimpedance Ampflier Using Broadband Current Pre-Amplifier for

[8]

617

High Frequency Lateral Micromechanical Oscillators,” IEEE International Solid State Circuits Conference (ISSCC 2010), pp. 318320. R. Abdolvand, et al., “Thin-film piezoelectric-on-silicon resonators for high-frequency reference oscillator applications,” IEEE transactions on ultrasonics, ferroelectrics, and frequency control, vol. 55, pp. 2596606, 2008. A. Hajimiri and T. H. Lee, “A general theory of phase noise in electrical oscillators,” IEEE J. Solid-State Circuits, vol. 33, pp. 179194, Feb. 1998. B. Yurke, D.S. Greywall, A.N. Pargellis, and P.A. Busch, “Theory of amplifier-noise evasion in an oscillator employing a nonlinear resonator,” Physical Review A, vol. 51, 1995, pp. 4211 - 4229. M. Shahmohammadi, B.P. Harrington, and R. Abdolvand, “Concurrent Enhancement of Q and Power Handling in Multi-Tether High-Order Extensional Resonators,” in Proc. IEEE Int. Microwave Symp., May 2010, pp. 1452-1455. V. Kaajakari, et al., “Nonlinear mechanical effects in silicon longitudinal mode beam resonators,” Sensors and Actuators A: Physical, vol. 120, pp. 64-70, 2005.

I.

INTRODUCTION

In data and wireless communication, the clock generator is an essential building block of the system. For many years, quartz crystal resonators have been commonly employed in clock generators since they offer high quality factor (Q) and excellent temperature frequency stability. The drawback of such scheme is the incompatible fabrication process of quartz resonators which hinders the complete integration of the highperformance oscillators with the rest of electronics. This issue will be of much greater importance for realization of future generations of portable devices in which several oscillators at different frequencies are demanded in an extremely small foot print area. MEMS resonator technology seems to gradually gain popularity as a solution for the integration problem and more high-performance MEMS-based oscillators are presented by researchers and companies [1, 2, 3]. In the past, our group has shown that thin-film piezoelectric-on-substrate (TPoS) MEMS resonators can yield superior power handling and Q (in air) due to the excellent power density and low acoustic loss of their silicon resonant body [4]. With such advantages, TPoS resonators are posed as great candidates to be employed in low-noise oscillator circuits. Noise in an oscillator is commonly characterized either in time (jitter) or frequency domain (phase-noise). The presence of jitter in oscillators introduces sampling error which confines the bit rate in the communication systems. Based on a linear model, the phase-noise and consequently the jitter in

978-1-4244-6400-5/10/$26.00 ©2010 IEEE

an oscillator are inversely proportional to the oscillation power [5]. However, increasing the power delivered to a mechanical resonator will eventually increase the vibration amplitude to an extent that the small high-order elastic constants of the material can't be neglected (onset of nonlinearity). This will introduce a shift in the resonance peak toward lower (spring softening) or higher frequencies (spring hardening). At large vibration amplitudes (relative to the resonator size) the resonator reaches to a point beyond which multi-stable vibration amplitudes exists for a single frequency (Duffing bifurcation point). It is traditionally believed that the oscillation power in an oscillator loop is limited by the maximum stored energy in the resonator at bifurcation point. A chaotic change in the frequency is expected at bifurcation and consequently the phase-noise performance is degraded [1]. This issue is of great concern in MEMS resonators because they can store less energy compared to bulky crystal resonator as a result of their very small size. On the other hand, there exists a body of theoretical work on the topic of nonlinear oscillators that suggests operation of the mechanical resonator at bifurcation yields improved overall oscillator circuit noise [6]. However, to the best of our knowledge this has never been demonstrated in practice. The results presented in this paper are believed to be the first validation for the possibility of suppressing oscillator noise by driving a MEMS resonator beyond the bifurcation point. Our measurement confirms that the oscillator jitter is scaled down after the TPoS resonator reaches the bifurcation and the close-to-carrier phase-noise of the oscillator doesn't seem to deteriorate. Also, we show that the jitter in the 27MHz oscillator based on TPoS resonator at any oscillation amplitude is lower for a device with the lower motional impedance. In depth investigation of the oscillator behavior at bifurcation is currently underway in order to better relate the resonator characteristic to the oscillator performance. II.

TPOS RESONATOR

As shown in the schematic of Fig. 1a, a TPoS resonator consists of a thin piezoelectric film (e.g. aluminum nitride, AlN) sandwiched between two metal electrodes (e.g. molybdenum, Mo) stacked on top of the device layer of a silicon-on-insulator (SOI) substrate [4]. The top Mo is dry

613

etched to form the top electrodes and the tracces while the AlN is wet etched to clear access to the bottom m electrode. The resonator body is defined in a stack dryy etch step. The backside handle layer silicon is etched iin an anisotropic etching step, which creates the cavity below tthe resonator. The final release step is done in buffered oxxide etch (BOE) solution to remove the buried silicon oxidee layer and create the free-standing structure (Fig.1b).

-10

S12 Magnitude (dB)

-15

fc

fs

Linear Response

Bifurcation point

-20

Nonlinear Response

-25 -30 -35 27.705

27.710

4.66dBm

3.75dBm

1.87dBm

-18dBm

5 27.715

27.720

27.725

Frequencyy (MHz) Fig. 2.

Frequency response of a typicaal TPoS resonator at different delivered poweer

IV. (a) Fig. 1.

(b)

a) The schematic of a 27MHz TPoS devicce, b) Process flow

III.

NONLINEARITY IN TPOS RESO ONATORS

In lateral-extensional TPoS resonators vvibrating at large amplitudes, elastic constants depend on strain and consequently the equivalent spring constant is represented as 1 where k and k are the first- and second- order anharmonic term ms and is the vibration amplitude. The equation of mottion for a forced vibration MEMS resonator is written as: cos

,

(1)

mass m and where γ is the damping coefficient of the m the magnitude of the force term at angular freequency ω.

is R5-G

The presence of the high order terms in k(x) results in an amplitude dependant resonance frequency in the device [8]: 1

1

OSCILLATOR R CIRCUIT

The schematic of the oscillator circuit c used in this work is shown in Fig. 3a. This circuit conssists of a trans-impedance amplifier (SA5211) which provides the t gain and a comparator (TVL3501) which is used to producee a square waveform (Fig. 3b). The comparator, which is a hig ghly nonlinear component, is included in the oscillation loop in order to create simple ge to the resonator over a means to control the applied voltag very wide range. In this circuit the amplitude of the applied voltage to the resonator is adjusted by the potentiometer R5. i also tuned to 50% by The duty cycle of the waveform is potentiometer R2 before collecting jitter at each applied voltage.

,

(2)

where is the shifted resonance frequencyy, is the linear resonance frequency, and x0 is the vibrration amplitude. Depending on the sign of the resonancee peak frequency shifts toward the lower (spring softenning) or higher frequencies (spring hardening). As it turns out (Fig. 2), the peak frequency shifts to the left in ouur devices which represents the spring softening.

(a)

In order to compare the nonlinearity of diifferent resonators in this study, we define a normalized frequenncy shift called SN which is a measure of relative peak frequuency shift as the vibration amplitude is altered: ,

(3)

where SN is calculated as the difference beetween the shifted peak frequency (fs) and the center frequenncy (fc) at linear operation divided by fc (Fig. 3b). Therefore,, SN is zero when the peak is perfectly symmetric.

614

(b) Fig. 3.

or circuit, b) Output waveform a) The schematic of the oscillato

V.

MEASUREMENTS

A. Resonator characterization By varying the design features such as top electrode pattern, TPoS resonators with different charracteristics can be fabricated at similar frequency. Three ~27MHz TPoS resonators with a range of various characteriistics (Table I) are fabricated and chosen to be used in the osciillators in order to enable investigation of the effect of resonattor characteristics on the oscillator performance. Frequency rresponses of each device as well as their SEM pictures are shoown in Fig. 4 (All measured quality factors are in air). TABLE I.

DEVICES PROPERTIIES

he resonator with smaller and C with almost the same Q, th motional impedance is more nonlinear. These observations are expected since both higher Q and lower impedance result in a wer to be absorbed by the larger portion of the delivered pow resonator. Considering similarity in i the size of all three resonators, larger amount of absorb bed energy will cause the resonator to behave nonlinearly at a lower l onset. In order to find the value of th he applied voltage to the device at bifurcation, upward an nd downward frequency sweeps are examined around th he resonant peak. The bifurcation is detected at a pointt the two corresponding frequency responses begin to deviatee from each other (Fig. 6.). -10

Device A Device B Device C

M Motional Imp pedance(Ω) 400 430 1073

S12 Magnitude (dB)

Quality factor 16041 28819 28904

S12 Magnitude (dB)

-10

-15 -20 Backward at a 2.64dBm

-25

Forward at 2.64dBm At -21.86dB Bm

-30

-30

Device B

Device C

Device A

26.870

-50

Fig. 6.

26.872

26.874 26.8766 26.878 Frequency (M MHz)

26.880

26.882

Frequency response of a 27MHz resonator at -21.86dBm (linear response) and 2.64dBm (nonlinear reesponse with hysteresis)

-70

B. Oscillator characterization Three oscillator boards were asseembled using the aforesaid resonators. The oscillator jitter is meeasured using a Tektronix oscilloscope model TDS5104B. The measured standard deviation (STD) of the cycle-to-cyclee jitter as a function of the voltage amplitude applied to the dev vice is plotted for the three oscillators in Fig. 7.

-90 26.3

26.8

27.3

27.8

28.3

Frequency (MHz) Fig. 4.

Frequency response and SEM’s of threee different 27MHz resonators

STD jitter (psec)

To study the nonlinearity in these resonators, the frequency responses of the resonators aare measured at different delivered power to the resonatoor using Agilent E8358A PNA network analyzer. Using (3), normalized frequency shift is calculated and shown in Figg. 5. 60 Device-A (Q=16041, R=400Ω)

50 SN (ppm)

Device B (Q=28819, Rm=430Ω)

100

40 20

Fig. 7.

VC(bifurcation) ~ 1.164V

0 -23

-18

--3 -13 -8 Delivered Power(dBm)

500

1000

1500

2000

2500

3000

Device voltagge (mV)

VA(bifurcation) ~ 1.31V

10

Unstable U operation o

60

0

VB(bifurcation) ~ 0.661V

20

Device C (Q=28904, Rm=1073Ω)

80

Device-C (Q=28904, R=1073Ω)

30

Fig. 5.

Device A (Q=16041, Rm=400Ω)

120

0

Device-B (Q=28819, R=430Ω)

40

140

2

Nonlinearity measurement of three differennt 27MHz resonators

As it is clear from this figure, between reesonators A and B with almost the same motional impedance, resonator B with ween resonators B higher Q is more nonlinear [7]. Also, betw

Jitter versus device voltage for thrree different 27MHz Oscillators

It is observed that in all three osccillators the jitter gradually decreases as the amplitude of thee resonator input voltage increases. This trend is disrupted at a specific voltage at which a chaotic behavior in the oscillatorr is triggered. There is a range of fractional resistances (labeled as R5-G in Fig. 3) at which the oscillator is not stable and a the measured jitter is extremely high (nano seconds rang ge). However, as R5-G is further increased the oscillator staabilizes again yielding a scaled down jitter value compared to the last stable point. Further increasing the applied voltaage beyond this point will

615

only cause slight improvement in the cycle-to-cycle jitter and the minimum value for all three resonators are very close (~7 psec STD ). It was observed that at any applied voltage, the oscillator built based on the resonator with the lowest motional impedance yields the lowest measured jitter. Device C Device voltage 456mV

In order to better understand the nature of discontinuity in the jitter vs. voltage curves, the experiment was repeated at more data points around the discontinuity region for the oscillator based on device B (Fig. 8).

Oscillator/Jitter

Peak-toPeak (psec)

Cycle-toCycle (psec)

Device A

145.5

138

Device B

200.5

196

Device C

268

245

Device B Device voltage 450mV

STD Jitter (Psec)

40

Unstable operation

30

Device A Device voltage 460mV

20 Fig. 10. 10 0 400

500

600

700

800

900

Device voltage (mV) Fig. 8.

Jitter versus device voltage for device B in a closer view

Results interestingly show (Fig. 9) that for a small range of R5-G, the applied voltage trend is reversed (i.e. voltage decreases as R5-G increases). This means that for this range the equivalent impedance seen from the input of the device is reducing. This change in the input impedance can be attributed to a sudden shift in the vibration amplitude occuring right at the bifurcation in the resonator. 900

Device voltage(mV)

Phase noise measurement of device A, B and C

Finally, a similar oscillator using a resonator with very low motional impedance (~267Ω) was assembled. This time the device voltage amplitude was intentionally set beyond the unstable region of the jitter vs. voltage curve and the phase noise measurement was repeated (Fig. 11). This curve shows improvement in both close-to-carrier and noise floor compared to the oscillators tested in Fig. 9. It should be noticed that the recorded standard deviation for the cycle-tocycle jitter in this oscillator is also the same as those recorded for the other three oscillators beyond the unstable region and therefore, similar noise floors are expected for all of these oscillators. The measured phase noise of -130dBc/Hz @ 1kHz offset from carrier for this oscillator is very promising for MEMS oscillators and is comparable with the results reported for quartz oscillators.

Unstable operation

800 700 600

Numbr of Acquistion

Std dev (psec)

Cycle-to-Cycle Jitter (psec)

Peak-to-Peak Jitter (psec)

4,533,590

7

42

47.5

500

-143dBc/Hz Noise floor

400 2 Fig. 9.

4

R5-G(kΩ)

6

8

-130dBc/Hz @1kHz

Device voltage versus fractional resistance R5-G

Phase noise for these three oscillators is also measured and overlapped in Fig. 10. These measurements are taken at similar applied voltages (~455mV) to ensure operation of the resonators below the unstable region (which is believed to correspond to the bifurcation point of the resonator). As it is clear, the oscillator with the lowest motional impedance device (device A) exhibits the lowest noise floor which agrees with the jitter measurement results. The maximum peak-topeak and cycle-to-cycle jitters are also recorded for these oscillators (inset table of Fig. 10) and they confirm similar superiority for the device with the lowest motional impedance.

Fig. 11.

Phase noise measurement of device A

I.

CONCLUSION

In this paper, the evidence of suppressed overall noise in a MEMS-based oscillator is reported as a result of operating the resonator beyond the bifurcation point. If solidly proven through ongoing in-depth investigations, this is the first time that such experimental proof for this speculated result is observed. Meanwhile, the motional impedance of the thin-film piezoelectric-on-substrate (TPoS) resonator was shown to have a dominant effect on the oscillator jitter. Resonators with

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lower motional impedance seem to yield lower jitter at any given oscillation amplitude. However, cycle-to-cycle jitter for all oscillators assembled based on different TPoS resonators converged to the same level of ~7psec standard deviation at very large device applied voltages. ACKNOWLEDGMENT

[5]

This work was funded by Integrated Device Technology. Authors thank Brandon Harrington for his significant contribution in fabrication of TPoS resonators. REFERENCES [1]

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