Aville online t www.sienediret.om SieneDiret Proedi Engineering 10 (015 ) 887 891 EUROSENSORS 015 A Fesiility Study for Self-Osillting Loop for Three Degreeof-Freedom Coupled MEMS Resontor Fore Sensor Chun Zho, Grhm S. Wood, Sun H. Pu,, Mihel Krft, 0F* Nno Reserh Group, University of Southmpton, Southmpton, SO17 1BJ, United Kingdom University of Southmpton Mlysi Cmpus, Nusjy, Johor, 7900, Mlysi Montefiore Institute, University of Liege, Liege, B-4000, Belgium Astrt For the first time, we investigte self-osillting ontrol loop for three degree-of-freedom (DoF) wekly oupled MEMS resontor sensor for fore sensing pplitions. This is n importnt step towrds rel-time mesurements using suh sensor. The simulted results suessfully demonstrted tht, without ny externl drive signls, the proposed self-osillting loop is le to utomtilly lok to the desired mode frequeny for the sensing pplitions. The mplitude rtios from the simultion showed good greement with the theoretil vlues. 015 The The Authors. Pulished Pulished y Elsevier y Elsevier Ltd. This Ltd. is n open ess rtile under the CC BY-NC-ND liense (http://retiveommons.org/lienses/y-n-nd/4.0/). Peer-review Peer-review under under responsiility responsiility of the of orgnizing the orgnizing ommittee ommittee of EUROSENSORS of EUROSENSORS 015 015. Keywords: Self-osilltion loop; oupled resontor sensor; MEMS; simultions 1. Introdution MEMS oupled resontor sensors hve een studied y n inresing numer of reserhers in reent yers due to their distint dvntges, nmely enhned sensitivity [1] nd ommon mode rejetion ilities [], ompred to onventionl single resontor sensors [3]. Coupled resontor sensors utilize mode loliztion effet [4] tht requires the mesurement of the virtionl mplitudes hnge t prtiulr mode frequeny. A promising resontor sensor * Corresponding uthor. Tel.: +3-(0)-4-366-616 ; fx: +3-(0)-4-366-60. E-mil ddress: m.krft@ ulg..e 1877-7058 015 The Authors. Pulished y Elsevier Ltd. This is n open ess rtile under the CC BY-NC-ND liense (http://retiveommons.org/lienses/y-n-nd/4.0/). Peer-review under responsiility of the orgnizing ommittee of EUROSENSORS 015 doi:10.1016/j.proeng.015.08.766
888 Chun Zho et l. / Proedi Engineering 10 ( 015 ) 887 891 onsisting of three wekly oupled MEMS resontors [5] demonstrted four orders of mgnitude improvement in stiffness hnge sensitivity, y mesuring the mplitude rtios of the out-of-phse mode. However, to find the desired mode frequeny, e.g. the out-of-phse mode for the 3DoF resontor sensor, urrent pprohes inlude mnully djusting the frequeny of the drive signl [5], whih is time onsuming nd unsuitle for prtil pplitions. Implementing self-osilltion loop struture [6] is n importnt step to enle rel time mesurement for emerging oupled resontor sensors. In this pper, we shll illustrte the fesiility, through simultion results, of relizing suh self-osillting loop utilizing positive eletril feedk, sed on n osilltor loop struture for single MEMS resontor [7].. Trnsfer funtion of MEMS osilltors Fig. 1 Figure showing: () typil struture of self-osillting loop, where H(j ) nd G(j ) re the trnsfer funtions of the resonnt struture nd eletril feedk, respetively; () mss-dmper-spring model of 3DoF oupled resontor devie [8]. For self-sustined osilltor s shown in Figure 1, the osilltion strt-up ondition is derived from the Brkhusen riterion [9]: H(j 0 )G(j 0 ) 1, H(j 0 )G(j 0 ) 0 (1) where 0 is the osilltor's desired ngulr frequeny. For 3DoF wekly oupled resontor system modelled y Figure 1, we ssume wek oupling with K <K/10<K -K, nd symmetril physil prmeters exept: K 1=K+ K 1, K 3=K+ K, K 1>0, K<0 nd K K. These ssumptions re mde sed on our previous work on fore sensor (mesuring K 1) with negtive is stiffness perturtion K [8]. The detiled trnsfer funtions n e found in [8]. For our prtiulr interest, the out-of-phse mode frequeny, where idelly resontor 1 nd resontor 3 virte out-of-phse to eh other if dmping is negleted, n e derived: 1 1 K K op [ K K ( K1 K1 ( ) )] () M K K K K K K If we ssume K/K >10 nd K 1>0, nd suppose tht the veloity of resontor 1, v 1=d(x 1)/dt, is the input of the eletril feedk nd F 1 s the only tution fore, we n otin the following t the out-of-phse mode frequeny op: v1( j op) 1 H ( j op ) F1 ( j op) (3) / Q ( 1 / K) 4 H ( j op) rtn( ) rtn( ) 0 (4) / ( / ) Q K1 K 4
Chun Zho et l. / Proedi Engineering 10 ( 015 ) 887 891 889 Where =K(K -K+K )/(K) nd is the dmping of the resontors. Due to the similr onlusions of single resontor, we n trnsplnt the eletril feedk iruit struture in [7] to relize the self-osilltion loop for 3DoF resontor sensor. 3. Simultion K 1 Trnsimpedne mplifiers (TIAs) Veloity mplitude of resontor 1 Veloity mplitude of resontor 3 Equivlent RLC Feedk voltge 180 0 phse shifter +5V/-5V Power Bis for PMOS Vrile gin stge Control signl for vrile gin Amplifition stge Bis for diode Feedk voltge Amplitude detetion Veloity mplitude of resontor 1 Control signl for vrile gin Fig. Figure showing the shemtis inluding: equivlent eletril iruit model of the 3DoF MEMS resontor with stiffness perturtions K nd K 1. K/K=-0.001, K 1/K=0.001 nd hnges to K 1/K=0.000 from t=1s nd onwrds; vrile gin stge nd mplitude detetion.
890 Chun Zho et l. / Proedi Engineering 10 ( 015 ) 887 891 For the self-osilltion loop simultion, we hve modelled the 3DoF wekly oupled resontor sensor into equivlent RLC iruit [5], shown in Figure. The equivlent vlues used for the simultions re lso shown in Figure. The vlues re hosen lose to the rel physil devie [8]. The stndrd trnsimpedne mplifier (TIA) shown in Figure ws used to onvert the motionl urrents into voltges. The vlues of the feedk resistors nd pitors were hosen to e the sme s the hrteriztion iruit in our previous work [8]. A pulsed urrent soure lsting for 100ns ws used to injet the initil energy to strt the osilltion. The eletril feedk lso inludes vrile gin struture in onjuntion with n mplitude detetor, with oth shown in Figure. Due to the 180 phse shift of the TIA, further 180 phse shifter is required to ensure tht the phse dely of the eletril feedk is 0. The voltge ontrolled gin stge ws relized using p-hnnel enhnement mode trnsistor BSS84 due to the low on-stte resistne nd fst swithing. A is stge ws used to mke sure tht the PMOS is lwys in the triode region. In Figure, efore the mplitude detetion, n mplifition stge ws used to mke sure tht the inrese in mplitude n e deteted. The mplitude detetor tht followed genertes the ontrol signl for the vrile gin stge. This ontrol signl ensures tht the loop gin mgnitude H(j 0)G(j 0) dereses from pproximtely to 1 s the mplitude of the resontor 1 inreses, hieving the utomti gin ontrol (AGC) funtion for the self-osillting loop [7]. 4. Simultion results The simultion results in Figure 3 show tht the self-osilltion loop is ple of hieving self-osilltion without tution voltges, nd uto-djusting when stiffness perturtion K1 is introdued. It n e seen tht the resontors strt to osillte from pproximtely t=0.s, nd the mplitudes of the resontors n settle within pproximtely 0.5s. To ensure the resontors were osillting t the desired out-of-phse mode, the mode frequenies were lulted from the results nd ompred to the theory (Eqution ). The simulted period of one yle for eh stiffness perturtion K 1 ws lulted y evluting the time period for pproximtely 140 yles (whih is within 0.01 seond window) in the simultion, nd dividing tht time y the numer of yles. The osilltion frequenies were then lulted from the period of yle. The lulted vlues of the out-of-phse mode frequenies from the simultion results in Figure 4 show tht the proposed loop struture is le to trk the out-of-phse mode frequeny with different perturtions, with n error smller thn 5ppm. To verify the funtionlity of the fore sensor [8], mplitude rtios s n output signl re lso verified. The mplitude rtios from simultions n e lulted y tking the mplitudes of resontor 1 nd 3 fter 1s of the introdution of the stiffness perturtion, so tht the mplitudes re within 1% of differene ross 0.01 seond window. The otined simulted mplitude rtios nd theoretilly estimted vlues [8] re plotted in Figure 4. The simulted mplitude rtios greed well with the theoretil estimtions with reltive errors within %. Fig. 3 Simulted trnsient response of resontors 1 nd 3 within the self-osilltion loop, with the stiffness perturtion K1/K hnges from 0.001 to 0.000 from t=1s: () trnsient response of resontor 1; () trnsient response of resontor 3.
Chun Zho et l. / Proedi Engineering 10 ( 015 ) 887 891 891 Fig. 4 Figure showing: () Mode frequenies nd () mplitude rtios lulted from the simultions results (red dots) under different stiffness perturtions, ompre to the theoretil vlues (lk lines). 5. Conlusions nd outlook To onlude, in this pper, we hve demonstrted fesile self-osilltion loop struture for the emerging type of resontor sensor with 3DoF wekly oupled resontors. The simultion results showed tht the struture ws le to trk the out-of-phse mode frequeny of the 3DoF resontor sensor, while mintining the funtionlity of the sensor. The future work should e fousing on the implementtion of the physil self-osilltion loop struture disussed in this pper. The min design hllenges will e the time dely for the resontors to settle, s in urrent simultion results, the time dely for resontor 3 to settle is pproximtely 0.5s, whih still needs further improvements. Referenes [1] M. Spletzer, A. Rmn, A. Q. Wu, X. Xu, R. Reifenerger (006): Ultrsensitive mss sensing using mode loliztion in oupled mirontilevers. Applied Physis Letters, 88, 5410. [] P. Thiruvenktnthn, J. Yn, A. A. Seshi (010): Differentil mplifition of struturl perturtions in wekly oupled mems resontors, IEEE Trnstions on Ultrsonis, Ferroeletris, nd Frequeny ontrol, Vol. 57, No. 3, 690-697 [3] M. A. Shmidt, R. T. Howe (1987): Silion resonnt mirosensors, 14th Automotive Mterils Conferene: Cermi Engineering nd Siene Proeedings, Volume 8, Issue 9/10, 1019 1034 [4] P. W. Anderson (1958): Asene of diffusion in ertin rndom ltties. Physil Review, 109(5):149 1505 [5] C. Zho, G. Wood, J. Xie, H. Chng, S. Pu, M. Krft (015): A sensor for stiffness hnge sensing sed on three wekly oupled resontors with enhned sensitivity, Miro Eletro Mehnil Systems (MEMS), IEEE 8th Interntionl Conferene on, 881-884. [6] A. A. Seshi, M. Plnipn, T. A. Roessig, R. T. Howe, R. W. Gooh, T. R. Shimert, S. Montgue (00): A vuum pkged surfe miromhined resonnt elerometer, Journl of Miroeletromehnil Systems (MEMS), Vol. 11, No. 6, 784-793 [7] C. T. C. Nguyen, R. T. Howe (1999): An integrted mos miromehnil resontor high-q osilltor, IEEE Journl of Solid-Stte Ciruits, Vol. 34, No. 4, 440-455 [8] C, Zho, G. S. Wood, J. B. Xie, H. L. Chng, S. H. Pu nd M. Krft (015): A fore sensor sed on three wekly oupled resontors with ultrhigh sensitivity. Sensors nd Atutors A: Physil, 3, 151-16 [9] F. He, R. Ris, C. Lhue, M. Jezequel (009): Disussion on the generl osilltion strtup ondition nd the Brkhusen riterion. Anlog Integrted Ciruits nd Signl Proessing, 59():15-1