Microelectronics Journal 44 (2013) 292–300

Contents lists available at SciVerse ScienceDirect

Microelectronics Journal

0026-26

http://d

n Corr

E-m

journal homepage: www.elsevier.com/locate/mejo

MEMS based oscillator for UHF applications with automaticamplitude control

Masoud Baghelani n, Habib Badri Ghavifekr, Afshin Ebrahimi

Microelectronics Research Lab., Department of Electrical Engineering, Sahand University of Technology, Tabriz, Iran

a r t i c l e i n f o

Article history:

Received 29 August 2012

Received in revised form

28 January 2013

Accepted 4 February 2013Available online 27 February 2013

Keywords:

MEMS

Resonator

RSACMDR

Transimpedance

Automatic amplitude controller

Oscillator

92/$ - see front matter & 2013 Elsevier Ltd. A

x.doi.org/10.1016/j.mejo.2013.02.008

esponding author. Tel.: þ98 918 343 7239.

ail address: m_baghelani@sut.ac.ir (M. Baghe

a b s t r a c t

This paper presents a MEMS based oscillator with automatic amplitude control. Previously demon-

strated ring shape anchored contour mode disk resonator is evaluated and some of its analytical aspects

are extracted as well as its equivalent electrical circuit for further transistor level simulations. Due to

1801 phase change of the resonator, the sustaining amplifier should provide another 1801 phase for

oscillation build up. As will be shown, the motional resistance of the resonator, which determines the

minimum required gain of the circuit, is very high and conventional techniques could not provide such

a gain in UHF frequencies. This paper proposes a trans-impedance amplifier satisfying mentioned

conditions just at the required frequency. In this case, traditional Automatic Amplitude Control (AAC)

method could not be applied and therefore this paper presents a novel AAC circuitry and technique. The

overall circuit including bias circuitry consumes 1128 mW from 1.8 V power supply implemented in

0.18 mm standard CMOS technology.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Most of electronic systems from RF transceivers to on-chipatomic clocks require a reference oscillator which determines thesize and cost of the overall system. Due to their high qualityfactor, low insertion loss, low power, integrability alongsidetransistors on a single chip and low fabrication costs micro-electro-mechanical resonators are excellent devices for suchapplications.

Recently demonstrated Ring Shape Anchored Contour ModeDisk Resonator (RSACMDR) introduced by [1] with suppressedspurious modes [2] and the ability to break GHz barrier forresonance frequency with relatively large size is an interestingdevice which can surmount problems of ordinary disk resonators[3], [4]. But, like the other disk resonators, since the electrostaticactuation mechanism through a capacitive gap is employed, it hasa very large motional resistance which makes design of thesustaining amplifier very problematic [5]. As will be shown inthe next section, electrical equivalent circuit of the RSACMDR has1801 of phase shift which puts another criterion on the sustainingcircuit design.

Considering the voltage to current conversion nature of MEMSresonators, amplification circuit must work in a reverse mannerand convert current to voltage for driving the resonator. One of

ll rights reserved.

lani).

the most popular circuits for implementing this conversion isTrans-Impedance Amplifier (TIA). But unfortunately, designing ofa TIA with the required high gain (more than 100 dB O) forsustaining UHF oscillators requires about 10 GHz of bandwidthand is not feasible with conventional methods. Therefore, anotherprocedure is required for implementing a TIA based oscillator.

Another problem involved with MEMS based oscillators is 1/f3

phase noise component as a result of device non-linearity [6–8].This noise component degrades the very critical close-to-carrierphase noise profile. Also, power handling problem in suchoscillators must be concerned [9]. The most sophisticated methodto remove these problems is using the AAC circuit. This paper alsointroduces a novel method for implementing AAC for MEMSoscillators in UHF range. The paper is organized as follows:RSACMDR design and characterization is described in Section 2.Design procedure of core oscillator is discussed in Section 3.Proposed AAC is introduced in Section 4 followed by a conclusionin Section 5.

2. RSACMD resonator

RSACMD resonator is utilized in this work as the high Q tankelement for the proposed oscillator. The insertion loss of such aresonator is reduced by locating the anchor at the stress-free ringarea which guarantees the reliability of the device. As shown inFig. 1, the structure is a hollow disk suspended 1 mm above thesubstrate and anchored at the ring shaped nodal area. In addition

Fig. 1. (a) The RSACMD resonator and its electrode and anchor configuration and (b) its contour plot, (c) harmonic analysis of the resonator showing its resonance

frequency.

Fig. 2. Electrical equivalent circuit of the resonator.

M. Baghelani et al. / Microelectronics Journal 44 (2013) 292–300 293

to suppressing the spurious modes, the crossed ring anchorprovides an excellent location for implementing low velocitycoupling for much more complex mechanical UHF signal proces-sing [10].

Fig. 2 shows the electrical equivalent circuit of RSACMDR to beused for simulation and characterization of the oscillator. Since apositive DC voltage is utilized for biasing of the resonator, whenthe AC exciting voltage increases, the voltage difference across thecapacitive gap decreases which consequently reduces the reso-nance amplitude of the device and output current. Therefore theoutput current of the resonator has 1801 phase difference withthe input voltage modeled by an inverse transformer in Fig. 2.

For fabrication of the resonator, thin adhesive silicon-nitridelayer is deposited over the silicon substrate. A very thin Cr/Aulayer is then deposited and patterned to form interconnections ofthe resonator and a via is stripped for future ground planeproviding a low impedance path for shunting away of the feed-through current [11]. Then, a 250 nm thick oxide layer is depos-ited by PECVD as a first sacrificial layer and patterned to createproper locations for anchor segments. These regions are thenfilled by polysilicon and construct the anchor. After patterning,a thick polysilicon layer is deposited to form the resonator’sstructural body.

After deposition of the structural polysilicon mass, a 100 nmoxide layer is deposited as the sidewall sacrificial spacer in bothinternal and external regions of the disk to form the electrodes toresonator transducer gap by LPCVD process. A photoresist layer isplaced over the sacrificial layer at the top of the structure to formthe connection between internal and external electrodes in bothsides of the resonator. A metal seed (Cr/Au) is then evaporated onthe wafer and removed from the top of structure and sidewalls inorder to prevent plating in these areas during electroplating steps.A thick photo-resist mold is then plated to determine that theelectrodes confined. Au electrodes are then plated using theelectroplating process. After all deposition processes the structureis released in Hydrofluoric acid to achieve the final cross-sectionof the resonator. For reducing parasitic and padding capacitances,a combined CMOS/MEMS chip could be achieved by flip-bond-and-tear process described in [12].

Although the precise resonance model of RSACMDR is pre-sented in [2], it is too complicated to be used for model extrac-tion. By neglecting the non-significant second order effects, theresonance equation of [1] could be employed:

r2 d2RðrÞ

dr2þrndRðrÞ

drþðk2r2�nÞRðrÞ ¼ 0 ð1Þ

where R(r) is a displacement as a function of radius, r is the radiusof the resonator, n is the Poisson ratio and k is

k¼2pls¼ 2pf

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir0ð1�n2Þ

E

rð2Þ

where f is the required resonance frequency, r0 and E are thedensity and the Young modulus of the structural material respec-tively. Eq. (1) is a Bessel type differential equation which could besolved by supposing a suitable value for inner radius and belowboundary conditions:

R ðrinÞ ¼ R0 andd R ðrÞ

d r

����r ¼ rin

¼ 0 ð3Þ

The value of R0 could be determined from Hooke’s law andconsidering the applied voltage and excitation electrodes of theresonator.

For a resonator with about 10 nm resonance amplitude andinner and outer radii of 12 mm and 16.8 mm respectively for940 MHz resonance frequency, the resonance equation becomes

RðrÞ ¼�1

14:4

aððk�1ÞYpðqÞÞþ3kðYpþ1ðqÞÞ�:::

2apYpðqÞ

" #� . . .

JpðkrÞþ

aðv�1ÞJpðqÞþ :::

3kðJpþ1ðqÞÞ�:::

2apðJpðqÞÞ

264

375� . . .

:::YpðkrÞ

8>>>>>>>>>><>>>>>>>>>>:

9>>>>>>>>>>=>>>>>>>>>>;� Crb ð4Þ

where Jx(.) and Yx(.) are the Bessel functions of types 1 and 2 andin the order of x and the other constants in the above equation are

p¼ 12

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi5v2�2vþ1p

q¼ 3k250000

a¼ 125000

m¼ 0:5ð1þvÞ

b¼ 0:5ð1�vÞ

C ¼ �ð1=14:4Þðð1=kÞ3m500�vÞ

ðJpþ 1ðqÞÞðYpðqÞÞ�ðYpþ 1ðqÞÞðJpðqÞÞ

8>>>>>>>>>><>>>>>>>>>>:

ð5Þ

The effective mass of the resonator could be achieved by

mr ¼2prh

R rrin

rR2ðrÞdr

R2ðrÞ

ð6Þ

M. Baghelani et al. / Microelectronics Journal 44 (2013) 292–300294

Also, the effective spring constant and the damping arecalculated by

kr ¼o2nmr ð7Þ

Cr ¼

ffiffiffiffiffiffiffiffiffiffiffikrmr

pQ

ð8Þ

Now, the equivalent electrical components of Fig. 2 could becalculated:

Lm ¼mr

Zem1Zem2

ð9Þ

Cm ¼Zem1Zem2

krð10Þ

Rm ¼Cr

Zem1Zem2

ð11Þ

where Zem1,2 are equal for symmetric sensing and actuatingdesigns and can be given by

Zem ¼ VP@C

@rð12Þ

Table 1RSACMD resonator design summary.

VP 12 V

h 2 mm

d 100 nm

E 160 Gpa

r 2330 Kg/m3

rin 12 mm

rout 16.8 mm

Electrodes overlap arc 5p/6

Zem 1.634712 mmr 0.533 ng

kr 18.61 MN/m

Q(supposed) 6000

Cr 0.5253 mNs/m

C0 13.35 fF

Lm 1.1489 H

Cm 0.0249 aF

Rm 196.5 KOResonance frequency (analysis) 940 MHz

Resonance frequency (simulation) 940.4 MHz

Fig. 3. Schematic of the proposed TIA RF MEMS reso

Calculation of the output current of the resonator could bevery useful in designing the AAC circuitry [13].

io ¼o0Q

krV2

Pvi@CexðsenÞ

@r

� �2

ð13Þ

where

@CexðrÞ

@r¼ C0,inside

�ð@RðrÞ=@rÞd

ðdþRðrÞÞ2

!r ¼ rin

þ . . .

C0,outsideð@RðrÞ=@rÞd

ðd�RðrÞÞ2

!r ¼ rout

ð14Þ

C0 ¼e0jhrinðoutÞ

dð15Þ

where C0 is the electrode to resonator static capacitance insideand/or outside of the resonator, e0 is the static permittivity ofthe air, d is the electrode to resonator gap, h is the resonatorthickness, and j is the overlapping arc between excitationelectrodes and the resonator’s body inside and outside of theresonator. RSACMDR design summary is given in Table 1.

Fig. 2 and Eq. (13) both neglect the effects of Duffing non-linearity of the resonator which occurs when applied voltageis increased [14]. This is because of large vibration amplitudesdue to large applied voltages. According to ultra-stiff structure ofRSACMDR, the required applied voltage to make this nonlinearitysignificant is pretty high and also as the result of AAC circuit, itwould not exceed its critical value.

3. Oscillator design

Fig. 3 illustrates the oscillator circuit including bias circuitry. Asmentioned in Section 2, the electrical equivalent circuit of RSACMDRposes 1801 phase shift between its input voltage and output currentand hence the sustaining circuit should provide 1801 phase shiftsatisfying the Barkhausen criteria. In addition, due to high motionalresistance of the resonator, the required trans-impedance gain isvery high. The sustaining circuit should comply these demands andstill have low input referred noise and consume low power.Achieving these specifications is very cumbersome and seems tobe impossible for standard CMOS technology.

The required circuit is a converting amplifier with more than200 KO trans-impedance gain and about 10 GHz bandwidth forpreventing excess phase to the circuit. For overcoming these pro-blems, based on the fact that the required conditions (high gain and1801 phase) should be obtained just at the required frequency, this

nator oscillator with biasing circuitry included.

M. Baghelani et al. / Microelectronics Journal 44 (2013) 292–300 295

paper proposes a non-inverting amplifier with too much larger gainat lower frequencies and several poles located at specific frequenciesto provide required phase shift at the desired oscillation frequency.

Another crucial requirement of the sustaining circuit is itsinput and output resistances, since they have a significant role indetermining the loaded Q of the resonator given by [15]

Ql ¼Rm

RiþRoþRmQ ð16Þ

Therefore the input and output resistances of the sustainingamplifier (Ri and Ro) should be as low as possible.

The proposed amplifier is constructed from three stages shownin Fig. 3. Due to their low noise nature, low input resistance, andlow power consumption, the first stage of the amplifier is selectedto be a modified current mirror based current amplifier (M1–M6)with an active feedback (M3–M4) for enhancement of bothbandwidth and input resistance.

The major input referred noise source is related to first stagewhere the input transistors noises (M1–M2) are directly added to theinput current and must be suppressed as much as possible. Thissuppression could be accomplished by reducing the gm of thesetransistors.

Noises of M5 and M6 refer to input after dividing by the currentgain of this stage which is calculated by

Ai �gm5

gm1þ1

ZBþð1þZC=ZBÞ=ðZAð1þgm3ZC ÞÞ

ZA ¼ rd199rd299 1ðCinþCgs3þCgd2Þs

ZB ¼ rd499 1ðCgs1þCgs5þCgd4Þs

ZC ¼ rd399 1Cgd1s

8>>>>>>><>>>>>>>:

ð17Þ

Ramp,RGC �½�rd9RF Cgd8CMGs2þfrd9RF ðCgd8ðgm8�gm10Þ�gm10Cgd9Þ�rd9CMGgsþ rd9ðgm8�gm10Þ�gm10RF �

½gm8rd9RF CMGCgd8s2þfrd9RF ðgm8Cgd8ðgm7þgm10Þþgm7gm10Cgd9Þþgm8CMGrd9gsþgm8ðgm7þgm10Þrd9þgm7gm10RF �

CMG ¼ ð1þgm10ðrd1099rd11ÞÞCgd10

Ai �gm5ðrd6RDACgd1CIAs2þðrd6Cgd1þRDACIAÞsþ1Þ

rd6RDACgd1CIAs2þðrd6Cgd1þRDACIA þRDArd3Cgd1Þsþgm3rd3RDA

RDA ¼ rd199rd2

CIA ¼ CinþCgs3þCgd2

Av ��gm12RDA

1þRDAðCGD12þCDBAÞs��ðgm14�ð1=RF2ÞÞRDB

1þRDBðZGDBþCDBBsÞ �gm16Rs

1þgm16RsþRsCLs

RDA ¼ rd1299rd13

CDBA ¼ CDB12þCDB13þCgd13

RDB ¼ rd1499rd15

ZGDB ¼1þRF2Cgd14s

RF2

CDBA ¼ CDB14þCDB15þCgd15

8>>>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>>>:

ð20Þ

Contributing noises of succeeding stages should be divided tothis gain and hence have minor effects on the overall inputreferred noise of the circuit. Noise contribution of M3 and M4 iscalculated by [16] and is repeated here for more convenience.

i2in,M3þM4 ,noise ¼ rd5 gm1þ1ZBþ

1þZC=ZB

ZAð1þgm3ZC Þ

� �� �2� . . .

½ðCinþCgs3Þ2o2þð1þgm3rd3Þ

2�i2n,M4

þr2d3ðCinþCgs3Þ

2o2i2n,M3

ðrd3þrd4Þ2ðCinþCgs3Þ

2o2þð1þgm1rd5Þ2ð1þgm3rd3Þ

2h i

ð18Þ

The second stage is a bandwidth improved regulated cascode(RGC) (M7–M11) which converts current to voltage and provides a

major part of the overall gain of the circuit achieved by

Ramp,RGC ¼Vo,RGC

Iin,RGC�

1�ðG3=G2Þ�ðgm10ZD=G2ZEÞ

ðG1G3=G2Þþ ð1=ZEÞþ ðZD=ZEÞðð1=ZF Þþgm10ðG1=G2ÞÞþ ð1=ZF Þ

ZD ¼ RF99 1Cgd8s

ZE ¼ rd999 1Cgd9s

ZF ¼ rd1099rd1199 1Cgs11s

ZG ¼ rd799 1ðCgs7þCgs10þð1þgm10ðrd1099rd11ÞÞCgd10Þs

G1 ¼ gm8þ1

rd8þ

ZD

rd8ZF

G2 ¼ gm7þgm8þ1

rd8þ 1

ZGþgm10

ZD

rd8

G3 ¼ gm7þgm10þ1

ZG

8>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>:

ð19Þ

This stage puts a dominant pole to the circuit far below theoscillation frequency and hence provides 901 phase shift at thedesired frequency. Two common-source voltage amplifiers areemployed as extra voltage gain stages (M12–M15) with a localresistive feedback for adjusting the excess phase required foroscillation. A source follower is considered as the output stage ofthe circuit for increasing the output swing and providing lowoutput resistance for the circuit to enhance the loaded Q of theresonator.

By considering Eqs. (17) and (19) and calculating the voltagegain from the gate of M12 to Vout the close form transfer functionis achieved (Eq. (20)).

Then the overall trans-impedance gain could be calculated by

Ramp,TIA ¼ Ai � Ramp,RGC � Av ð21Þ

The dominant pole of the circuit is located at the drain of M8

which poses 901 phase at the resonance frequency. The otherimportant poles are placed at the drains of M12 and M14 providingthe remaining 901 required phase shift at the oscillation fre-quency. Since the output impedance of the buffer circuit (M16) isvery small, its pole is very far from the oscillation frequency anddoes not play a significant role in the circuit.

Fig. 4 shows AC analysis of the proposed TIA loaded by a 0.5 pFcapacitor and results in 2.5 MO of trans-impedance gain and178.51 phase shift around the desired frequency satisfying theoscillation criteria.

Oscillation start-up of the described oscillator along with theelectrical equivalent circuit of the resonator (Fig. 2) is shown in

Fig. 5. Oscillation start up of the oscillator shown in Fig. 3.

Fig. 4. Result of AC analysis of the proposed TIA for RF2¼100 KO.

M. Baghelani et al. / Microelectronics Journal 44 (2013) 292–300296

Fig. 5. It is obvious that start-up time is inversely proportional tothe resonator’s Q. It can be seen that the start-up dynamics is veryfast and the required settling time is less than 5 ns. One of themost important characteristics of oscillators is their phase noise.Fig. 6 illustrates the phase noise of the proposed oscillator.Characteristics of the oscillator are summarized in Table 2.

4. AAC design

In MEMS based oscillators, both sustaining amplifier andMEMS resonator non-linearities are significant sources of thephase noise. A sophisticated solution to this problem is amplitudelimiting. As mentioned in [17] AAC circuits could remove the 1/f3

phase noise component. This component arises from Duffing non-linearity which changes the vibration equation of the resonatorfrom a linear conventional mass-damper-stiffness equation to anon-linear below given equation [15]:

m€rþc_rþkrþer3 ¼ 0 ð22Þ

It can be seen that, as the vibration amplitude increases, theimpact of this non-linearity arises and therefore the related phasenoise component becomes more significant. Phase noise equationof the series resonant oscillator is as follows [18]:

L f m

� ¼

2kTð1þFRampÞ

0:5ðRiþRoþRmÞi2o

RiþRoþRm

Rm

� �1þ

f o

2Qlf m

� �2 !

ð23Þ

where k is Boltzmann’s constant, fm is the offset from theoscillation frequency and FRamp is the noise factor of thesustaining amplifier [19]. It is obvious from Eq. (23) that,increasing the output power and loaded Q, and decreasing theinput and output resistances of the amplifier could reduce thephase noise of the oscillator.

Another problem, which must be concerned for MEMS reso-nator based oscillators, is Q reduction due to the aging of a tinymechanical structure that expands and contracts about billiontimes per second. Reduction of Q results in increasing themotional resistance and decreasing the output current of theresonator which must be compensated. This problem is alsoremoved by AAC circuit.

Most of reported AAC circuits in literatures are accomplishedby gain controlling of the sustaining amplifier by changing avariable resistance [20], [21]. This method could not be employedby this work, because changing any parameter (such as resis-tances) of the circuit causes changing in the location of 1801phase shift-frequency which may drastically reduce Q of the tankcircuit. Any deviation from the fixed 1801-phase frequency causesfrequency pulling of the oscillator. Frequency pulling determinesthe dependency of the oscillating frequency to the low qualitysustaining circuit rather than ultra high quality resonator, andtherefore decreases the purity of the output voltage from an idealsinusoidal wave which translates to increase the phase noise. It isimportant to note that the resonator provides a high Q only at itsnatural frequency and poses great amount of insertion loss atnearby frequencies. This high insertion loss increases themotional resistance and even may prevent the oscillation, soother techniques should be utilized for implementing AAC for theproposed oscillator.

The employed method in this paper is changing the biasvoltage of the resonator and controlling its motional resistancedynamically, leaving the sustaining circuit untouched. As studiedin [22], by varying the DC bias voltage of such a resonator from0 to 50 V, the resonance frequency changes less than 0.0014% or14 ppm which is too small to change the 1801-phase frequencysignificantly.

The dependency of the motional resistance of the resonator toits bias voltage is calculated as below. The output current of theresonator is given by

io ¼ VP@Csen

@r

� � @uðr,tÞ9r ¼ rin,out

@tð24Þ

uðr,tÞ ¼QFi

jkrð25Þ

The input electrostatic force at the resonance frequency is

Fi ¼�VPvi@Cinside

@rþ@Coutside

@r

� �ð26Þ

Table 2Oscillator and TIA circuit specifications.

VDD 1.8 V

Technology CMOS, 180 nm

Power consumption 1080 mW

BW of TIA 130 MHz

Supporting frequency range satisfying oscillation

by adjusting RF1 and employing suitable resonator

660–1300 MHz

Startup time 3.8 ns

Phase noise @ 100 KHz �146 dBc/Hz

Phase noise @ 1 KHz �101 dBc/Hz

Phase noise @ 100 Hz �59 dBc/Hz

Phase noise @ 10 Hz �25 dBc/Hz

Fig. 7. Top level schematic of the proposed oscillator including TIA and AAC.

Fig. 6. Phase noise diagram of the proposed oscillator.

M. Baghelani et al. / Microelectronics Journal 44 (2013) 292–300 297

And therefore

io ¼o0Q

krV2

Pvi@CexðsenÞ

@r

� �2

ð27Þ

Since the motional resistance of the resonator could beconsidered as

Rm ¼vi

io¼

kr

o0QV2Pð@CexðsenÞ=@rÞ2

ð28Þ

This shows a square dependency of the inverse of motionalresistance to the bias voltage. It can be seen from Eq. (28) thatsmall changes in bias voltage cause larger changes in the motionalresistance.

Fig. 7 shows the top level design of the proposed oscillator.The envelope detector of [15] is employed here which is a

combination of a conventional differential amplifier with acapacitive peak detector and a current source (MED6) with propervalues to track the sinusoidal input voltage. As vin becomes largerthan the voltage across the capacitor (VCPD), MPD forces VCPD to beequal with vin. When vino VCPD, Mpd becomes off and thecurrent source discharges CPD with a proper rate.

A very simple 11 stages charge pump circuit with a loadcurrent source for establishing the feedback loop for AAC isemployed in this work. Needless to say that much more compli-cated charge pump structures with better functionality have beenreported in literature [23–25], but a simple one is used to explainthe concept of the proposed AAC. The operation of the utilizedcharge pump could be studied in any standard book or reviewpaper concerning the concepts of charge pumps [26]. Theemployed charge pump circuit is shown in Fig. 8 along with otherAAC parts. Biasing supply of the circuit, VDD, is applied as theinput of the charge pump. The output of the envelope detectorcontrols the current source. Steady state value of the outputvoltage of the charge pump is given by [26]

Vout,ss ¼ ðNþ1ÞVDD�NILT

Cð29Þ

with the ripple of

Vr ¼ILT

CLð30Þ

where N is the number of stages, IL is the load current, T is theperiod of sampling signal (VCK), C is the tail capacitances and CL isthe load capacitance of the charge pump. As the output voltage ofthe envelope detector increases so do the voltage at the gate ofMcpcs and therefore IL, based on Eq. (29), and the bias voltage ofthe resonator reduces which based on Eq. (27) causes thereduction of the output current of the resonator and consequentlyoutput voltage of the oscillator. The same procedure occurredwhen the output voltage of the oscillator reduced. Figs. 9 and 10show the output of envelope detector and the settling of theoutput of the charge pump respectively. Fig. 11 provides thesimulated output until the amplitude is settled. It can be seen thatwhen the output of AAC achieves a special value corresponding tospecific motional resistance of the resonator, the oscillationstarts up.

As mentioned before, AAC reduces the overall phase noise ofthe oscillator by protecting the output of the oscillator fromMEMS nonlinearities. Since the input resistance of the envelopedetector is very much higher than the output impedance of theTIA, the AAC does not induce significant noise to the overall phasenoise of the oscillator. On the other hand, the output of the AAC iselectrically isolated from the oscillator and therefore could not

Fig. 8. Schematic of the proposed AAC circuit; transistors MCP13-MCP28 are designed with long channel length to provide sufficient voltage drop to avoid extra channel

length modulation over the current source transistor (MCPCS). Load capacitor is chosen 10 times greater than switching capacitors to reduce the ripple of the output of the

charge pump power supply.

Fig. 9. Output of the envelope detector for oscillator’s output amplitude equals

0.3 V.

M. Baghelani et al. / Microelectronics Journal 44 (2013) 292–300298

degrade the phase noise performance of the circuit. But unfortu-nately, 1/f noise at the AAC output is added to VP, causingelectrical stiffness stiffening at the resonator. This phenomenonchanges the resonance frequency of the resonator and causes anincrease in the close-to-carrier phase noise performance which isrelated to [17]

L f m

� 9VP

pke

kr

� �2

ð31Þ

where ke is the electrical stiffness. In comb and beam resona-tors, ke is relatively large and is comparable to kr, but asmentioned before, it is completely ignorable in contour modedisk resonators according to their ultra stiff mode shape. This isthe reason of non-tunability of this kind of resonators throughelectrical methods. Therefore, this AAC induced phase noisecomponent is automatically suppressed by the resonator.

Design summary of the proposed AAC is reported in Table 3.The overall required variation in VP for compensating the changeof the amplitude of oscillator from 0.7 V to 1 VP�P is 1 V, whichcould be achieved by changing the bias current from 1.1 mA to2.2 mA.

The output of the envelope detector is 885.7 mV for zero inputvoltage level and 1080 mV for the maximum input voltage level.Size of the current source transistor, Mcpcs, is so chosen that thecharge pump provides 12.5 V for desired output voltage level ofthe oscillator and therefore the comparator of conventional AAC

circuits is removed here. The settling time of the AAC loop isabout 5.2 ms as shown in Fig. 11. But the actual settling time forAAC is more important which is the consumed time by the AACloop for compensating changes in the oscillator’s output. Fig. 12illustrates this test, where a rapid change is carried out manuallyat the output of the oscillator and one can see the reaction of theAAC loop for compensating this change. The dynamic settlingtime of the AAC loop is around 500 ns.

The overall circuit including oscillator, AAC and biasing cir-cuitry is 48 mW. The charge pump ripple magnitude is about 1 mVand could be reduced to 500 mV by employing more sophisti-cated methods such as double charge pumps. The output rippleof charge pump has some effects on oscillator phase noise,but since their frequency is very much far from the oscillationfrequency they are not able to degrade close-to-carrier phasenoise performance. Based on our knowledge, this work is the firstdesign of MEMS based oscillator with AAC in such high frequencyand gain.

Comparison of different oscillators is difficult. Since differentoscillators operate at different frequencies and power levels. So anormalized phase noise has been defined as a figure of merit(FOM) for oscillators [27]:

FoM¼ L f of f set

n oþ10log

f of f set

f osc

� �2PDC

1mW

" #ð32Þ

Table 4 provides a comparison between this oscillator andsome of other high Q oscillators. Since close-to-carrier stability ismore crucial in MEMS based oscillators, FoMs are calculated at100 Hz offset from the oscillation frequency. It can be seen fromTable 4 that, the presented oscillator has acceptable performanceagainst competitors.

5. Conclusion

Analytical evaluation and design of the RSACMDR have beenaccomplished for UHF application. The electrical equivalent cir-cuit has been extracted based on calculated mechanical lumpedelements. A novel design of TIA has been presented, designed andsimulated to satisfy the Barkhausen criteria for oscillation at thedesired frequency. A new AAC technique has been introduced bychanging the motional resistance of the resonator by controlling

Fig. 11. The outputs of AAC and oscillator since settling of the oscillator.

Table 3Proposed AAC design summary.

VDD 1.8 V

Technology CMOS, 180 nm

Power consumption (envelope detector(ED)) 23 mW

Power consumption (charge pump) 25 mW (static)

Envelope detector output range 0.8857–1.08 V

Charge pump output range for full range variation of ED 12.43–13.2 V

Charge pump tail current range for full range variation of ED 1.1 mA-2.2 mA

Fig. 10. (a) Input of the Mcpcs (the output of envelope detector), (b) output of the charge pump; though the input changes by a step-like variation at the full scale output for

the envelope detector, the output of the charge pump reaches to its steady state value in both smooth and fast manner.

Fig. 12. Dynamic settling time of the AAC loop: (top) the output of AAC as a result of manual changing at the output of oscillator, (bottom) the output of oscillator is

instantaneously forced to an arbitrary value and recovered by the AAC loop.

M. Baghelani et al. / Microelectronics Journal 44 (2013) 292–300 299

Table 4Comparison between the proposed oscillator and some oscillators presented in

literature.

Ref. Frequency Motional resistance FoM

[5] 8.29 MHz 26 KO �157.97

[15] 60 MHz 1.5 KO �196.64

[16] 1.006 GHz 150 O �192

This work 940 MHz 196.5 KO �197.93

M. Baghelani et al. / Microelectronics Journal 44 (2013) 292–300300

its bias voltage. This work paves the way for commercializing theGHz, high Q with high motional resistance disk resonators. Ourresearches on micro-electro-mechanical signal processors are on-going.

Acknowledgment

This paper is a part of a project supported by Iranian NationalScience Foundation (INSF).

References

[1] M. Baghelani, H.B. Ghavifekr, Ring shape anchored RF MEMS contour modedisk resonator for UHF communication applications, Microsystem Technolo-gies 16 (12) (2010) 2123–2130.

[2] M. Baghelani, H.B. Ghavifekr, A. Ebrahimi, Analysis and suppression ofspurious modes of the ring shape anchored RF MEMS contour mode diskresonator, Microsystem Technologies 17 (11) (2011) 1599–1609.

[3] J. Wang, Z. Ren, C.T.-C. Nguyen, 1.14-GHz self-aligned vibrating micromecha-nical disk resonator, Tech. Digest, 2003 Radio Frequency Integrated CircuitsSymposium, Philadelphia, Pennsylvania, June 8–10 2003, pp. 335–338.

[4] S.-S. Li, Y.-W. Lin, Y. Xie, Z. Ren, C.T.-C. Nguyen, Micromechanical hollow-diskring resonators, in: Proceedings of the MEMS Conference, Maastricht, TheNetherlands, January 25–29 2004, pp. 821–824.

[5] F. Nabki, M.N. El Gamal, A high gain-bandwidth product transimpedanceamplifier for MEMS based oscillators, 34th European Solid State CircuitsConference, Edinburgh, September 15–19 2008, pp. 454–457.

[6] H.M. Lavasani, R. Abdolvand, F. Ayazi, A 500 MHz low phase-noise AlN-on-silicon reference oscillator, IEEE Custom Intergrated Circuits Conference(CICC), San Jose, California, September 16–21, 2007, pp. 599–602.

[7] M. Abdelsalam, M. Wahba, M. Abdelmoneum, D. Duarte, Y. Ismail, Supportingcircuitry for a fully integrated MicroElectro Mechanical (MEMS) oscillator in45 nm CMOS technology, 18th IEEE/IFIP VLSI System on Chip Conference(VLSI-SoC), Madrid, September 27–29, 2010, pp. 259–263.

[8] M. Akgul, B. Kim, L.-W. Hung, Y. Lin, W.-C. Li, W.-L. Huang, I. Gurin, A. Borna,C.T.-C. Nguyen, Oscillator far-from-carrier phase noise reduction via nano-scale gap tuning of micromechanical resonators, International Solid-StateSensors, Actuators and Microsystems Conference, Transducers, Denver,Colorado, June 21–25, 2009, pp.798–801.

[9] M. Agrawal, K. Park, R. Candler, M. Hopcroft, C. Jha, R. Melamud, B. Kim,B. Muramann, T.W. Kenny, Non-linearity cancellation in MEMS resonators forimproved power-handling, IEEE International Electron Devices Meeting,IEDM Technical Digest, Washington, December 5–7, 2005, pp. 286–289.

[10] M. Baghelani, H.B. Ghavifekr, A. Ebrahimi, A. New, Approach for design of lowvelocity coupling for the ring shape anchored contour mode disk resonators,Microsystem Technologies 18 (12) (2012) 2003–2016.

[11] J. Wang, Z. Ren, C.T.-C. Nguyen, 1.156-GHz self-aligned vibrating microme-chanical disk resonator, IEEE Trans. Ultrason. Ferroelectrics Freq. Control 51(12) (2004) 1607–1628.

[12] A.-C. Wong, Y. Xie, C.T.-C. Nguyen, A bonded micro-platform technology formodular merging of RF MEMS and transistor circuits, Tech. Dig., 11thInternational Conference on Solid-State Sensors Actuators (Transducers ’01),Munich, Germany, June 10–14 2001, pp. 992–995.

[13] C.T.-C. Nguyen, Micromechanical Signal Processors, Ph.D. Dissertation,Department of Electrical Engineering and Computer Sciences, University ofCalifornia at Berkeley, December 1994.

[14] L. He, Y.P. Xu, M. Palaniapan, A state-space phase-noise model for nonlinearMEMS oscillators employing automatic amplitude control, IEEE Trans.Circuits Syst.—I: Regular Pap. 57 (1) (2010) 189–199.

[15] Y.-W. Lin, S. Lee, S.-S. Li, Y. Xie, Z. Ren, C.T.-C. Nguyen, Series-resonant VHFmicromechanical resonator reference oscillators, IEEE J. Solid-State Circuits39 (12) (2004) 2474–2491.

[16] H.M. Lavasani, W. Pan, B. Harrington, R. Abdolvand, F. Ayazi, A 76 dB O1.7 GHz 0.18 mm CMOS tunable TIA using broadband current pre-amplifierfor high frequency lateral MEMS oscillators, IEEE J. Solid-State Circuits 46 (1)(2011) 224–235.

[17] S. Lee, C.T.-C. Nguyen, Influence of automatic level control on micromecha-nical resonator oscillator phase noise, Proceedings of the IEEE InternationalFrequency Control Symposium, Tampa, Florida, May 5–8 2003, pp. 341–349.

[18] D.B. Leeson, A simple model of feedback oscillator noise spectrum, Proceed-ings of the IEEE 54 (1966) 329–330.

[19] C.T.-C. Nguyen, R.T. Howe, An integrated CMOS micromechanical resonatorhigh-Q oscillator, IEEE J. Solid-State Circuits 34 (1999) 440–455.

[20] O. Robert, G. Amendola, H. Chen, A 200 1C automatic gain controlledoscillator for MEMS resonator with an MRC transimpedance, 15th AnnualIEEE International ASIC/SOC Conference, Rochester, New York, September25–28 2002, pp. 171–175.

[21] H.-Y. Hwang, J.-C. Chien, T.-Y. Chen, L.-H. Lu, A CMOS tunable transimpe-dance amplifier, IEEE Microwave Wireless Components Lett. 16 (12) (2006)693–695.

[22] M. Baghelani, H.B. Ghavifekr, A new high reliable structure of micro-electro-mechanical radial contour mode disk resonators for UHF application, 18thIranian Conference on Electrical Engineering (ICEE), May 11–13 2010,pp. 386–390.

[23] B.R. Gregoire, A compact switched-capacitor regulated charge pump powersupply, IEEE J. Solid-State Circuits 41 (8) (2006) 1944–1953.

[24] J.-Y. Lee, S.-E. Kim, S.-J. Song, J.-K. Kim, S. Kim, H.-J. Yoo, A regulated chargepump with small ripple voltage and fast start-up, IEEE J. Solid-State Circuits41 (2) (2006) 425–432.

[25] Hoi-Jun Yoo, K.I. Hwu, W.C. Tu, C.F. Chuang, Two types of voltage-boostingconverters based on PWM control strategy, Int. Rev. Electr. Eng. (IREE) 6 (5)(2011) 2178–2187.

[26] G. Palumbo, D. Pappalardo, Charge pump circuits: an overview on designstrategies and topologies, IEEE Circuits Syst. Mag. 10 (2010) 31–45.

[27] M. Tiebout, Low-power low-phase-noise differentially tuned quadrature VCOdesign in standard CMOS, IEEE J. Solid-State Circuits 36 (2001) 1018–1024.