Design of a Readout Scheme for a MEMS Microphone

Transcription

1 Design o a eadout Schee or a MEMS Microphone Aeng Cheng Subitted to the Electrical Engineering, Matheatics and Coputer Science Departent o Delt University o Technology, in Partial Fulillent o the equireents or the Degree o Master o Science in Electrical Engineering TU Delt Supervisor: Pro. Koi A.A. Makinwa NXP Supervisors: obert H.M. van Veldhoven Twan van Lippen Geert Langereis

2 II

3 Abstract This design ainly proposes a readout schee or MEMS icrophone with positive eedback to decrease the parasitic capacitance. It is designed in CMOS04 technology with a supply voltage o 3.3 V. The proposed architecture can increase the icrophone s sensitivity with a coparatively low bias voltage. It enables the icrophone to achieve high sensitivity even i it is loaded by an apliier with large input capacitance. In the ean tie, the SN and THD are not aected uch. The Spectre siulation shows that the syste can achieve 6 db SN (A-weighted), 0.5% THD (Pa sound pressure) and W power consuption. Several traditional readout schees or MEMS icrophone are also discussed and copared. The schee which is based on aplitude odulation is tested and easured on PCB level. I

4 II

5 Acknowledgeent I would like to express y gratitude to all those who give e the opportunity to coplete the research. The achieveent I have ade through this project would not have been possible without the enlightenent, support and encourageent ro a lot o people. I started the one-year research in NXP Seiconductors ro Septeber, 008 as y graduation project o Delt University o Technology. Thanks a lot to y proessor Koi A.A. Makinwa ro TUDelt, y supervisors obert H.M. van Veldhoven, Twan van Lippen and Geert Langereis ro NXP Seiconductors. They provided e this opportunity to have a close vision about MEMS world and the analog circuit design. Special thanks are given to y daily supervisor Mr. obert van Veldhoven, a talented and proessional engineer, who gave e a lot o iportant guidance in this research. He can point out y istakes in the very irst tie and in this way he helps e set up a strict attitude to science which is beneicial to y uture work. He gives e a ree atosphere to do the research without too uch pressure. His encourageents in the proper tie help e go through the darkest period o the project. I also want to thank y proessor Dr. Koi Makinwa who has provided e with a large nuber o iportant and stiulating suggestions which helps e to know the intrinsic nature behind the probles. Not only he gave e directions in the project but he also gave e instructions about how to be a good engineer. In addition, I want to thank Mr. Twan van Lippen and Mr. Geert Langereis who always provide e with the ost detailed and proessional answers to y questions. Their positive attitude to y work gives e a lot o conidence. I also want to thank Mr. Carel Dijkans or his valuable and experienced suggestions on this project. In the ean tie, I want to thank Ms. Agnese Bargagli-Stoi or her patience and riendly anners when dealing with y questions. Although I did not spend a lot o tie with y riends and group ebers in TUDelt in the past year, I still want to thank the or their help and valuable input to this project. Special thanks are given to ong Wu and Qinwen Fan who spend tie to review y thesis and give e iportant eedback. Thanks also go to y riends in Shanghai. Their caring between whiles ake e eel attached to each other. Last but no least, I would like to thank y parents and y little sister. Their unconditional love, support and encourageents enable e to inish this work. The thesis is dedicated to the. III

6 IV

7 Content CHAPTE.INTODUCTION.... What is a MEMS Microphone?.... Characteristics o the Microphone ro NXP Sensitivity VerilogA Model or Microphone ro NXP Speciication to be Achieved Sound Pressure Level A-weighted Motivation Outline o the Thesis... CHAPTE.EADOUT SCHEME.... ead-out schees or Capacitive Microphone.... DC Biasing Signal Level Noise Calculation Charge Apliier Signal Level Noise Calculation AC Biasing Signal Level Noise Calculation....5 Practical Measureent Aplitude Modulation AC Biasing Setup Noise Analysis Check Functionality Conclusion Conclusion... 3 CHAPTE 3.NEW EADOUT SCHEME WITH POSITIVE FEEDBACK Miller Eect Miller Eect in DC Biasing Syste Level Analysis Deine the Gain o the Preapliier Diode Connected MOSFET V

8 3.3.3 Stability Speciication or Preapliier Conclusion...43 CHAPTE 4.PEAMPLIFIE DESIGN Apliier Topology Noise Analysis in Folded-Cascode Apliier eerence Current Source Size o the Devices in the Preapliier...5 CHAPTE 5.SYSTEM IMPLEMENTATION Parasitic Capacitance Stability Check by AC Siulation Prograable C Conclusion...59 CHAPTE 6.SIMULATION ESULT Stability Check by Transient Siulation Signal-to-Noise atio Total Haronic Distortion Sensitivity Process Corners Siulation Corner Siulation without C Corner Siulation with C = 390 F Monte-Carlo Siulation Coparison Conclusion...68 CHAPTE 7 CONCLUSION AND FUTUE WOK Conclusion Future Work...69 APPENDIX A...7 VI

9 APPENDIX B... 7 APPENDIX C VII

10 VIII

11 List o Figures Figure. The cross-sectional view o a typical MEMS capacitive icrophone.... Figure. Cross-sectional view o Bourouina et al. s condenser icrophone [9]... Figure. 3 Spring supported ebrane []....3 Figure. 4 Topview on the back electrode side....3 Figure. 5 Cross section o the icrophone....3 Figure. 6 Force diagra o a icrophone in equilibriu...5 Figure. 7 Capacitance variance with dierent voltage...5 Figure. 8 Mebrane s delection without bias voltage....6 Figure. 9 VrilogA Model or Microphone...8 Figure. 0 A-weighting Curve...0 Figure. Traditional readout schee or ECM.... Figure. Typical voltage-readout schee or MEMS capacitive icrophone [0]....3 Figure. 3 Schee o the integrated capacitive icrophone with dc-dc voltage converter and preapliier [6]....3 Figure. 4 Scheatic o the preapliier used in []....4 Figure. 5 Schee o the integrated icrophone by using requency odulation [3].4 Figure. 6 DC biasing schee...5 Figure. 7 Noise sources in DC biasing schee...6 Figure. 8 Charge Apliier...7 Figure. 9 V out s aplitude versus radio requency...8 Figure. 0 Noise Source in Charge Apliier...9 Figure. AC biasing schee...0 Figure. Spectru o the aplitude odulated signal....0 Figure. 3 Mixer deodulation.... Figure. 4 (a) Schee or realizing aplitude odulation. (b) Frequency response o the transer unction....4 Figure. 5 Aplitude-odulated signal s spectru...4 Figure. 6 Magnitude o the side band under dierent bias voltage....5 Figure. 7 Magnitude o the ain tone under dierent bias voltage...5 Figure. 8 AC biasing schee realized on PCB...6 Figure. 9 The irst stage or AC biasing....7 Figure. 0 Noise versus requency or the irst stage o AC biasing...8 Figure. Coparison o the noise easureent and calculation result or AC biasing....8 Figure. esponse to oscillation requency with dierent oscillation aplitude in noral ode....9 Figure. 3 Equivalent voltage s waveor exerted on the icrophone under two cases....9 Figure. 4 Dierent average sensitivity in two cases...30 Figure. 5 Deodulated signal in noral ode...3 Figure. 6 Coparison o requency response between noral ode and collapse ode...3 Figure. 7 The nonlinear deodulated signal in collapse ode at 00KHz oscillation requency...3 IX

12 Figure. 8 The deodulated signal in collapse ode at 0KHz oscillation requency Figure 3. Ipedance connected ro input to output o an apliier Figure 3. Miller eect in DC biasing Figure 3. 3 Matlab siulation result o the DC biasing with positive eedback C Figure 3. 4 A non-inverting apliier with closed loop gain Figure 3. 5 A non-inverting apliier with AC-coupled closed loop gain Figure 3. 6 A non-inverting apliier with voltage regulator Figure 3. 7 DC biasing with positive eedback on syste level Figure 3. 8 I-V characteristic o a diode Figure 3. 9 (a) Cross section o a diode-connect PMOS. (b) Equivalent scheatic... 4 Figure 3. 0 (a) Cross section o a diode-connect NMOS. (b) Equivalent scheatic Figure 3. Positive eedback syste... 4 Figure 4. Input coon ode range or an NMOS input dierential apliier with (a) a current irror load (b) olded-cascode with current source load Figure 4. A olded-cascode apliier Figure 4. 3 Siple apliier with source degeneration at load Figure 4. 4 The basic topology o the preapliier Figure 4. 5 (a) Bootstrap current source. (b) I-V characteristic curves o and M Figure 4. 6 Equivalent odel or bootstrap current source Figure 4. 7 (a) Scheatic o preapliier. (b) Biasing scheatic Figure 5. The schee to decide the input capacitance o the preapliier Figure 5. Schee or loop gain siulation Figure 5. 3 AC siulation or Loop Gain with two dierent C Figure 5. 4 eadout schee with 4-bit DAC Figure 5. 5 Cross section o a Npoly-Nwell capacitor Figure 5. 6 Transission Gate Figure 5. 7 (a) The schee o unstable situation. (b) Oscillation waveor Figure bit DAC with switches to ground Figure 6. Schee or siulating ipulse response Figure 6. Ipulse response Figure 6. 3 Transient siulation result with C = 390 F Figure 6. 4 SN versus C (all available value o DAC)... 6 Figure 6. 5 THD versus dierent C. (all available value o DAC) Figure 6. 6 Signal Level versus dierent C Figure 6. 7 Corner siulation or SN when there is no C Figure 6. 8 Corner siulation or THD when there is no C Figure 6. 9 Corner siulation or SN when C = 390 F Figure 6. 0 Corner siulation or THD when C = 390 F Figure 6. Monte-Carlo siulation or SN with C = 390 F at 94dBSPL input Figure 6. Monte-Carlo siulation or SN with C = 390 F at 94dBSPL input X

13 List o Tables Table. Notation used in the equation (. 4) to (. 7)...7 Table. Notation used in the equation (. 8) and (. 9)...7 Table. 3 The speciication o the MEMS icrophone products on the arket...8 Table. 4 elation between sound pressure level and sound pressure [6]...0 Table. Measureent in DC biasing with dierent bias voltage Table. Coparison between three schees...33 Table. 3 Advantages and disadvantages or the three schees Table 4. Size o the devices....5 Table 4. Speciications or the preapliier...53 Table 6. Coparison between this design and the products on arket...68 XI

14

15 Chapter.Introduction A icrophone is an acoustic-to-electric transducer or sensor that converts an acoustical signal into an electrical signal. They are used in any applications such as telephones, hearing aids, obile phones and personal audio systes. Many transduction principles have been used, leading to the developent o transduction have been developed, including the piezoelectric, the piezoresistive, the capacitive and the contact icrophones. The irst icrophone abricated by silicon icroaching has been around or ore than 0 years []. The introduction o silicon technology allows high precision and batch abrication o the devices at low cost and with high reproducibility []. The ost coonly used icrophones are based on the capacitive principle or their lowpower and tolerance to high teperature [3]. They also have advantages o large bandwidth and high sensitivity [4]. The capacitive icrophone can be divided into two categories, naely the electret condenser icrophone (ECM) and the condenser icrophone. An ECM eploys an electret, a coponent with a built-in charge-accuulating layer, which has the unction o accuulating charges in the absence o an applied bias voltage. The irst ECM which is based on silicon technology was presented by jhoh and Gerhard-Multhaupt in 984 [5]. The charge on the electrets, however, was susceptible to teperature and suered ro long-ter drit, which aected the sensitivity o the icrophone [6]. The authors o[7] describe a proising telon electret or use in a silicon icrophone but the use o telon in a standard industrial production process gives rise to a lot o diiculties [8]. The condenser icrophone does not require an electret aterial. To accuulate charge, it requires an applied bias voltage. It has oderate sensing sensitivity and low sensitivity to teperature. They are usually abricated as Micro-Electro-Mechanical Syste (MEMS) because o this results in sall size, low cost and batch abrication. eading out such icrophones is the ain objective o this thesis and this topic will be explained in detail in the next section. Thereore, or siplicity, the ter MEMS icrophone quoted requently in the ollowing text reers to a condenser icrophone based on silicon.. What is a MEMS Microphone? The MEMS condenser icrophone is a design based on icroiniaturized echanical structures which can be integrated with CMOS process and other audio electronics. It can be viewed as a parallel plate capacitor that consists o a top ebrane and a botto back plate separated by a sall air gap acting as a dielectric aterial. The back chaber acts as a reerence chaber. Figure. shows a cross-sectional view o a typical MEMS capacitive icrophone. The acoustic holes on the back plate are used to alleviate air daping. An incident acoustic sound wave causes the ebrane to delect. As the ebrane vibrates in accordance with the requency and aplitude o the sound wave, the capacitance between the ebrane and backplate changes accordingly due to the variable air gap. The ai o the readout circuit is thus to transor the capacitance variations into electric signals.

16 Figure. The cross-sectional view o a typical MEMS capacitive icrophone. In the past 0 years, any researchers have investigated the abrication o MEMS icrophone with dierent structures or aterials to iprove their sensitivity and reduce their noise level. In 99, T. Bourouina et al. proposed a condenser icrophone with a p+ silicon ebrane without acoustic holes that is shown scheatically in Figure. [9]. Because o the absence o acoustic holes, the air gap is increased to 7.5u to alleviate the air daping eect which results in a lat requency response up to 0KHz. Figure. Cross-sectional view o Bourouina et al. s condenser icrophone [9]. Since the stress o the ebrane deines the icrophone s sensitivity [], the author in [0] proposes a icrophone with a sandwich structure ebrane which cobines layers o copressive stress and tensile stress together to decrease the stress in the ebrane. Another option to increase the sensitivity is to adjust the connection between back plate and ebrane. The author in [] reported that a spring type support rather than ully claping the ebrane at the whole circuerence will increase the sensitivity by a actor o two. The picture o the spring-supported ebrane is shown in Figure. 3. Although there are still any ways to optiize the icrophone s sensitivity by choosing dierent structures or aterials, the design in this report will ocus on the readout schee which is at the circuit level. Thereore, the ollowing sections describe a readout circuit or a MEMS icrophone abricated by NXP Seiconductors.

17 Figure. 3 Spring supported ebrane [].. Characteristics o the Microphone ro NXP The MEMS icrophone in this design is anuactured by NXP Seiconductors. The ebrane and perorated back plate are round in shape as shown in Figure. 4. The two electrodes are supported or connected by a silicon dioxide ring at the edge o the round plate. Figure. 5 illustrates the cross section o the icrophone. Figure. 4 Topview on the back electrode side. Figure. 5 Cross section o the icrophone. 3

18 Fro the diensions shown in Figure. 4 and Figure. 5, we can calculate the capacitance o the icrophone when the ebrane is not delected. It is given by: C ε ε π *8.85e = *3.4 *(460e 6 e 6 0 r ic =. 94 d gap ) pf (. ) whereε 0 is vacuu perittivity, ε ris relative static perittivity o air, is the radius o the ebrane and d gap is the quiescent air gap thickness. In noral operation, the ebrane and bulk are shorted together and biased at ground to eliinate C p. Thus C p shown in Figure. 5 is the ain contribution or parasitic capacitance. The value o C p is given by: C ε ε φ π ( ) d φ ( ) 0 r p = = 0. 7 gap pf (. ) where ε r is 4.5 which is the relative static perittivity o SiO, φis the diaeter o the ebrane and φ is the eective diaeter o the ebrane. A MEMS icrophone needs a bias voltage across its two plates. During operation, there are ainly our dierent types o orces exerted on the capacitor structure: the echanical input ro the acoustical wave, the elastic (restoring) orce generated in the vibrating ebrane in response to the delection, the electrostatic orce caused by the bias voltage on the two electrodes, and the daping orce generated by the air gap[]. They are illustrated in Figure. 6 without the daping orce since it can be neglected in equilibriu. And the electrostatic orce shown in Figure. 6 is given by: F es = ε AV 0 ( d x) gap (. 3) where A is the area o the capacitor plate and x represents the displaceent o the ebrane. Equation (. 3) indicates that the electrostatic orce varies quadratically with the distance between the ebrane and the back plate. This eect is the ain reason or the icrophone s nonlinearity. 4

19 Figure. 6 Force diagra o a icrophone in equilibriu. Thereore the orce acting on the ebrane is the su o the external echanical pressure, the electrostatic orce and the counterbalancing elastic orce. When the electrostatic orce exceeds the echanical restoring orce, we call the corresponding critical bias voltage the pull-in voltage. I the voltage is increased beyond this pull-in voltage, the ebrane will collapse onto the ixed back plate. Figure. 7 illustrates the capacitance o the icrophone with dierent voltages by inite-eleent siulation [ 3 ]. The pull-in voltage o the icrophone is around 8V by experient and 8.8V by siulation which can also be derived ro Figure C [pf] Vbias [V] Figure. 7 Capacitance variance with dierent voltage.3 Sensitivity When there is no bias voltage across the two electrodes, the delection o the ebrane with an acoustical pressure, which is shown in Figure. 8, can be expressed as 4 : P w( r, P) = ( 4 σ h r ) (. 4) 5

20 Figure. 8 Mebrane s delection without bias voltage. Consequently, the capacitance between ebrane and back plate is given: 0 r 0 A C( P) = ε π ε dr ( + P + d w( r, P) d 4 hd 6 4 hd 0 gap gap σ gap σ gap P +...) [ F] (. 5) 3 With =.38 0 /N, the third ter in the bracket on the right side o equation (. 4σ hd gap 5) can be neglected. Thus the sensitivity to acoustical pressure is: S d = C ( P ) P 4 ε 0 A ε 0π = [ F / Pa ] d 8σ hd 8σhd gap gap gap (. 6) I we substitute the value o 4σ hd gap into equation (. 5), it gives the linear relation between the icrophone s capacitance and the acoustical pressure which is given by: C ic ε A ( P) ( P) = C d ( + kp) [ F], or k = [ Pa 0 ic gap ] (. 7) where C ic is the quiescent capacitance o the icrophone which is calculated in equation (. ). For convenience and clarity, is replaced with a sybol k. Fro this chapter on, the requently entioned ter C represents the capacitance variance Δ in the tie doain and it is equal to C ic kp. I the acoustical pressure P can be represented as Pˆ sin( ω t), where Pˆ is the aplitude o the sound and ω is the requency o the sound, then the aplitude o the capacitance variance in the requency doain is C ic kpˆ and it is C sybolized as C v. Consequently, the rs value o the capacitance variance C v,rs is v Table. shows the notation used in the above equations. 6 Sybol w Explanation Delection o the ebrane []

21 adius o the ebrane [] r adial position [] σ Initial stress o ebrane [Pa], 30MPa h Thickness o ebrane [], 0.38e-6 P Acoustical Pressure [Pa] d const Quiescent air gap between ebrane and back plate [], e-6 ε Perittivity o ree space [F/], 8.854e- 0 A Area o the ebrane [ ] Table. Notation used in the equation (. 4) to (. 7) When there is a bias voltage, the author in [5] gives the sensitivity under this condition which is given by: S S ech el ac el Vbias = K cell [ V / ] [5] (. 8) d Vbias = K cell S d [ V / Pa] [5] (. 9) d Table. shows the notations used in the above equations. Since the ovable ebrane will be attracted to the ixed back plate when a bias voltage is exerted, the air gap distance becoes saller and results in a larger sensitivity. Consequently a larger signal will be generated by the icrophone with a larger bias voltage. Sybol Explanation S Mechanical sensitivity in electrical doain ech el ac S Acoustical sensitivity in electrical doain el K Holes in the cell and the ringing ields at the edges cell V Voltage exerted on the icrophone bias S Acoustical sensitivity without bias voltage which is shown in equation(. 6) d d Air gap between ebrane and back plate Table. Notation used in the equation (. 8) and (. 9).4 VerilogA Model or Microphone ro NXP Given the basic characteristics o the icrophone, a behavioral odel o the icrophone is essential or siulation. Ideally, this odel should be accurate and include the non-idealities o the sensor which liit the perorance. But a siple odel can speed up the siulation process and reduce the design tie. In this design, a proper unctionality is the ain objective or the odel. Thereore a very siple odel is coded in Verilog-A which does not consider the nonlinearity and electrostatic orce liit o the icrophone. The eect that sensitivity increases with increasing bias voltage is not included as well. I speciication can be achieved with the lowest sensitivity, it will also be achieved with higher sensitivity. 7

22 The basic principle behind the odel is regarding the icrophone as a variable capacitance and its capacitance variance is controlled by a voltage source which represents the acoustical signal. The related code can be ound in Appendix A. Figure. 9 VrilogA Model or Microphone.5 Speciication to be Achieved In the current MEMS icrophone products arket, the ajor anuacturers are Knowles Electronics, Analog Devices, Inineon, Akustica and Pulse MEMS. They produce both analog icrophones and digital icrophones. With the datasheets o these products, the ain characteristics o those analog icrophones are listed in Table. 3. There exists another design which is based on the icrophone ro NXP Seiconductors already. It adopts charge pup to ove the bias voltage across icrophone up to 5V. Its speciications are also listed in Table. 3. Speciication Product SPM004HE5 (Knowles Acoustics) ADMP40- (ADI) (dbv/pa) Current (ua) (V DD =.5~3.6V) (V DD =.5~3.6V) SN@Pa (db)(aweighted) Bandwidth (HZ) 4K K THD(%) %@00dBSPL 3%@05dBSPL AKU6 (Akustica) (V DD =.65~3.6V) N/A 5%@5dBSPL SMM30 (Inineon) (V DD =.V) 0K 0.%@04dBSPL TC00A (Pulse MEMS) (V DD =.64~.86V) 0K 0%@0dBSPL Previous Design K %@00dBSPL Table. 3 The speciication o the MEMS icrophone products on the arket. 8

23 The table shows a general idea about the behavior o the current MEMS icrophone products on the arket. It also indicates the ost iportant speciications when designing the interace circuit or MEMS icrophone. The data in bold type states that it exceeds the behavior o other products in this speciication. By coparing the data listed in Table. 3, we can have a rough idea about the speciications which are going to be satisied. SN at Pa should not be lower than 58 db. Sensitivity at Pa should not be lower than -4 db. The current consuption is supposed to be kept as sall as possible. The bandwidth which is ainly decided by the requency response o the icrophone should be the sae as the previous design. And the total haronic distortion (THD) is also expected not to exceed that o the previous design. Since the previous design uses charge pup to increase the bias voltage across the sensor which increases the coplexity o the circuit, the ai o this design is thus trying to achieve the sae speciication o the previous design with a lower bias voltage..5. Sound Pressure Level The dbspl shown in the last colun o Table. 3 is the unit o sound pressure level (SPL) which is oten denoted as sound level Lp. It is a logarith decibel scale easureent o the rs (oot Mean Square) sound pressure o a sound relative to a reerence value[6]. Fro this section on, i not explicitly entioned, sound pressure will be expressed in ters o its eective value (rs). The reerence value is 0uPa which is the threshold o hearing (roughly the sound o a osquito lying 3 eters away). The relation between sound pressure and sound pressure level is given by: prs p L p = 0log0 ( ) = 0log0 ( p p re rs re ) (. 0) where p rs is the rs value o the sound pressure being easured and p re is the reerence sound pressure. Table. 4 shows a coparison o sound pressure level and corresponding sound pressure which gives a general idea o the relation between the coon sound source in huan lie and the abstract sound pressure level. Exaples Sound Pressure Level Sound Pressure p (N/ =Pa) (dbspl) Jet aircrat, 50 away Threshold o pain Disco, ro speaker 00 Diesel truck, 0 away Kerbside o busy road, Vacuu cleaner, distance Conversational speech, Quiet library Quiet bedroo at night Background in TV studio

24 ustling lea Threshold o hearing Table. 4 elation between sound pressure level and sound pressure [6]..5. A-weighted When SN speciications are stated in Table. 3, the ter A-weighted is used. Since the huan ear is ost sensitive to sounds at requencies between KHz to 5 KHz, requencyweighting curves are oten incorporated with sound pressure level eters to produce a result which conors to what we hear [7]. The weighting curves were originally dierent with dierent sound level, but A-weighting, which was originally used or low level sounds, is now oten used or easuring environental noise and the output o audio systes. The A- requency-weighting curve is shown in Figure. 0. The gain curve crosses 0dB at KHz. The unction deining the A-weighting curve in ters o poles and zeros coes ro IEC/CD 67 (and ANSI S.4-00): G k s ( s + 9.4) ( s )( s )( s ) 4 A (. ) A ( s) = where k A *0 9 A-weighting Curve Gain (db) dba Frequency (Hz) Figure. 0 A-weighting Curve.6 Motivation As has been stated above, a large bias voltage exerted on the icrophone can generate large signal until the voltage exceeds the pull-in voltage. The act that ainstrea CMOS technology cannot handle voltages greater than a ew volts, however, indicates that realizing a high bias voltage will bring ore diiculties. Moreover, the signal generated ro the MEMS icrophone needs to be readout by an interace circuit. For a speciic icrophone, dierent interace circuits will drive the icrophone to have dierent speciications. 0

25 Thereore, the ain purpose o this project is to investigate the possible interace structures and inally develop an interacing principle which can drive a icrophone biased with a low bias voltage in such a way to achieve the speciication..7 Outline o the Thesis The thesis is coposed o seven chapters presenting dierent aspects o the investigation. Following this introduction chapter, Chapter describes the investigations o several possible readout schees or a capacitive MEMS icrophone sensor. These coparisons ainly ocus on the signal-to-noise ratio (SN), linearity and sensitivity. Chapter 3 proposes a new readout schee which can increase the sensitivity o the icrophone by the use o positive eedback capacitor. It ainly deals with the principle behind this schee. The speciication o the preapliier will also be given. Chapter 4 describes the process o designing a lownoise operation apliier (opap) on transistor level. The design o the current source used in the biasing circuit is included as well. In Chapter 5, the opap will be siulated with the icrophone odel in the whole schee. The practical ipleentation issues o the syste are discussed. The siulation results and the analysis o the are both presented in Chapter 6. Finally, in Chapter 7, the conclusion o the project and recoendations or uture iproveent are given.

26 Chapter.eadout Schee This section ainly analyzes the possible readout schees or MEMS icrophone. It starts with the background o soe coon readout schees in literature (section.). Then three dierent schees will be analyzed (section.~.4). Both the advantage and disadvantage o these schees will be explained in detail. The chapter ends with a coparison aong the three schees (section.5).. ead-out schees or Capacitive Microphone A typical MEMS icrophone ront-end interace has to transer the capacitive changes in the sensor to voltage or current variations. It has relatively ixed speciication driven by the characteristic o the icrophone. The interace circuit also has to iniize the ost critical non-idealities o the sensor (e.g. parasitic capacitance) to axiize its sensitivity [8]. In traditional design, a Junction-Field-Eect-Transistor (JFET) in the source-ollower coniguration is used to buer the signal ro the electret icrophone which is shown in Figure. [ 9 ]. The voltage source V ic represents the input sound which is also proportional to the sound pressure. The value o bias needs to be very large to ove the k B T/C noise corner generated by the icrophone and bias to low requency where it is o no iportance. Figure. Traditional readout schee or ECM. The icrophone in Figure. is an electret icrophone which has long-ter drit probles as entioned in Chapter. For a MEMS capacitive icrophone, i.e. without an electret, a typical voltage-readout schee is shown in Figure. [0]. The icrophone is biased with a dc voltage through a large resistor. The resulting large C tie constant can guarantee that the icrophone works under constant charge condition. However, the bias resistor needs to be very large (depending on the icrophone s capacitance and bandwidth) which is not easy to ipleent in a standard CMOS technology. The sensitivity is liited by the parasitic capacitances both o the sensor itsel and o the preapliier

27 Figure. Typical voltage-readout schee or MEMS capacitive icrophone [0]. The MEMS icrophone can achieve high sensitivity with high bias voltage. Thus the author in [6] proposed a schee which is shown in Figure. 3. A MEMS icrophone without an electret is biased by a dc-dc converter. The Dickson type dc-dc converter behaves like a charge pup and it builds up charge at the output by the two anti-phase oscillation clocks [].What akes this design novel is that the dc-dc converter enables the icrophone to achieve high sensitivity at a low supply voltage. The ain disadvantage o this design is the linearity. It has 0.% distortion under 0 Pa sound pressures. Figure. 3 Schee o the integrated capacitive icrophone with dc-dc voltage converter and preapliier [6]. ecently the authors in [] propose a solution which ipleents two icrophones biased by voltages having opposite polarities. The SN is thus increased by 3 db. The bias voltage or the icrophone is ± 0V which is generated ro a charge pup. A 6V PMOS dierential pair ors the basic gain stage. Another novel point o this design is the eedback apliier (FA). It not only speeds up the start up transient tie but also increases the insensitivity to the supply-induced noise and electro-agnetic intererence (EMI). The scheatic o the preapliier used in this design is shown in Figure. 4. One distinct disadvantage o the design is the cost since two icrophones are used. 3

28 Figure. 4 Scheatic o the preapliier used in []. Another option or readout capacitive icrophone adopted a dierent detecting principle, requency odulation. The schee is shown in Figure. 5. C represents the capacitive icrophone and it plays the role o tiing capacitance in the ring oscillator due to its variable capacitance. In this design, the icrophone does not need extra dc bias. Thereore the icrophone behaves ore linearly to the acoustic pressure due to the sall electrostatic orce between the ebrane and back plate. Moreover, the requency odulated output is convenient or urther digital signal processing. However, the ajor disadvantage o the design is its low SN (about 60 db SN under 0 Pa) and high power consuption (.96 W) [3]. Figure. 5 Schee o the integrated icrophone by using requency odulation [3]. Fro the above literature study, it can be seen that there are two designs use charge pup to bias the icrophone. Since a charge pup is not easy to ipleent and the distortion increases sharply as bias voltage approaches the pull-in voltage [4], the ai o the design is thus to ind out a suitable readout schee which will get rid o the charge pup and axiize the sensitivity o the icrophone under a low supply voltage. It starts with the ost traditional and typical schee and then oves on to a new schee by reducing the drawbacks o the old design. 4

29 . DC Biasing In DC biasing, which is shown in Figure. 6, there is a very large resistor b (in the order o Giga-Ohs) connected between the icrophone and a dc voltage source which is indicated as V re. The nae dc biasing coes ro the electrical characteristics o the reerence source V re. The charge accuulated on the icrophone does not change by uch because o the large C tie constant. The charging current is given by: V I = re b e t b Cic [A] (. ) I b is ininite, Q Vre I = = 0 which eans Q can be regarded as constant. The ollowing t b equation is based on constant charge assuption which is given by: V o Q = C ic ic Qic = d Aε [V ] (. ) where Q ic the total charge accuulated on the sensor, C ic is the static capacitance o the sensor, A is the area o the eective ebrane, ε is the perittivity o the ediu between the ebrane and the back plate and d is the distance between the ebrane and the backplate. V re b H V out C ic ±C C p Figure. 6 DC biasing schee... Signal Level Based on constant charge assuption, we can derive that: Q const = ( C + C )* V = ( C + C ± CΔ )( V ΔV ) [ F V ] (. 3) ic p re ic p re where C Δ is C ic kp which coes ro equation (. 7) and the value o C ic is denoted in equation (. ). Fro this section on, C p not only represents C p which is entioned in section (.3) but also includes the parasitic capacitance ro the preapliier. (Since it is ipossible to have a resistor with ininite large resistance, the calculation o the output signal without the constant charge assuption is included in Appendix B.) 5

30 As a result, the signal generated on the icrophone in the tie doain is: ΔV ( C = C ic ic + C ) * V + C p p C re Δ V re = C ic C Δ * V + C p re C Δ [ V ] (. 4).. Noise Calculation There are ainly two noise sources in DC biasing schee which are shown in Figure. 7. One is the theral noise ro the bias resistor which is represented by noise power spectru density v noise,. It is iltered by the icrophone and the parasitic capacitance. The other one is b the input-reerred noise density o the preapliier which is represented byv noise,in. Although the voltage source V re also contributes noise, its noise is iltered by the b and icrophone as well. Even though, a clean bias voltage is also deanded in DC biasing schee. For siplicity, the ollowing calculation is based on the assuption that the bias voltage is noise ree. Thereore the total input-reerred noise at the input o the preapliier is given by: v * ( C = vnoise, * + noise b + j * ωb ic + C p ) v noise, in [ V / Hz] (. 5) eerring the noise voltage power spectru to a capacitive noise power spectru by using the voltage-to-capacitance transer unction (assuing C Δ is uch saller than C ic +C p ) yields: C noise Cic + C = Vre p v noise, b + j * ω Cic + C p + vnoise, in [ F b *( Cic + C p ) Vre / Hz] (. 6) v noise,b v noise,in Figure. 7 Noise sources in DC biasing schee. Equation (. 6) indicates that or a certain capacitance variance C v, large value o V re and b will yield large SN. Although the DC biasing schee is siple, its doinant disadvantage is that the large resistor is diicult to ipleent in IC technology. Moreover, in the audio bandwidth which 6

31 is ro 0 Hz to 0 KHz the / noise o the opap doinates which is not beneicial to achieve a good SN. Equation (. 4) also shows that the electrical sensitivity o the icrophone is inversely proportional to the quiescent capacitance (C ic +C p ) o the icrophone. I the preapliier connected aterwards has large input parasitic capacitance (or low noise or coupling reason), the sensitivity o the icrophone is deteriorated even ore. As a result, the input-reerred noise o the preapliier has to be reduced to copensate or the sensitivity reduction. Another drawback o this schee is the nonlinearity. ewriting equation (. 4) into: ΔV = ( C ic C Δ * V re + C p ) C CΔ + C ic p [ V ] (. 7) In the ideal case, the signal should be linearly proportional to the capacitance variance o the CΔ icrophone. The actor in the denoinator o equation (. 7), however, aects the C ic + C p linearity. This actor is supposed to be sall which iplies that C ic +C p should be large. A large value o C ic +C p, however, will kill the signal level which is indicated ro equation (. 4). Thereore, there exists a trade o between the signal level and linearity when the DC biasing schee is used..3 Charge Apliier In order to avoid the ipact o parasitic capacitance, another interacing schee was investigated. This is shown in Figure. 8. Because o eedback, the voltages on the two inputs o the apliier will ollow each other and so the bias voltage across the icrophone will be stable. The voltage across the parasitic capacitor will also be stable. Consequently, C p can be neglected in the calculation o AC transer unction which is shown below Figure. 8 Charge Apliier..3. Signal Level When there is an acoustical signal exerted on the icrophone, the tie-varying capacitance will generate tie-varying current which turns out to be tie-varying voltage at the output because o the eedback network. The tie-varying current is expressed as: 7

32 i d( Cic + C dt ) V ε A = kv d Δ 0 ic( t) = re gap re dp( t) dt (. 8) The requency-varying current is then given by: i ε A ω) = kpˆ Vre ω (. 9) d 0 ic ( gap Thereore, the voltage on the output in the requency doain is given by: V ε A ω) = kpv ˆ d 0 out ( gap re ( ω + jω C ) = C v V re ( ω + jω C ) (. 0) The above calculations are all based on the assuption that the input acoustic signal is a pure sine wave and can be expressed as Pˆ sin( ω t), where Pˆ is aplitude o this sine wave signal. This assuption will also be used in the ollowing parts. Figure. 9 shows the aplitude o V out versus requency. Since the audio requency that huan being can hear is ro 0Hz to 0KHz, the pole which is decided by should π C be uch lower than 0Hz to avoid attenuation on the signal. Thus the aplitude o the output Cv Vre signal in the audio band is, assuing that this pole is uch lower than 0Hz. Since C C should be kept sall in order not to attenuate the signal, the only way to ove the pole downwards is to increase. Assuing C is pf, should be about 8 GΩ to ake the pole locate at 0Hz. And or noise consideration, the pole should be oved to even lower requencies to iniize the theral noise ro. Thereore DC biasing with virtual ground still can not avoid the ipleentation and noise issues associated with a huge resistor. C V v C re 8 C Figure. 9 V out s aplitude versus radio requency..3. Noise Calculation Copared to DC biasing, this schee can achieve high signal level at the output o the apliier i C is saller than C ic. While or noise consideration, both o these two schees

33 can not avoid the iltered huge resistance s noise, the / noise ro the preapliier and the noise ro the reerence voltage or bias voltage. For siplicity, the ollowing noise derivation will not take the reerence voltage noise into consideration. I we denote the input reerred noise o the apliier as v the output can be expressed as: noise,in which is shown in Figure. 0, the total noise at v noise + jω ( ) Cic + C p + C v v [ V / Hz], out noise, in noise, j C j C = + + ω + ω (. ) eerring the noise voltage power in equation (. ) back to a capacitive noise power at input by using the transer unction in equation (. 0) yields: C noise = v noise + jω ( Cic + C p + C ) v [ F / Hz], in noise, Vre Vre + (. ) ω ω v noise, v noise,in Figure. 0 Noise Source in Charge Apliier Equation (. ) shows that the input-reerred noise o apliier is apliied by the actor C ic + C p + C in audio bandwidth (assue is uch saller than 0Hz ). To get C π C higher signal level we need sall C while the noise o the apliier is apliied even ore. Moreover, the / noise o the apliier still doinates..4 AC Biasing The proble with the charge apliier schee is ainly caused by input-reerred noise o the apliier. Norally, the / noise o the apliier will be doinant in the audio bandwidth. I we want to avoid the / noise o the apliier, one option is to odulate the signal to higher requencies. That s why we introduce AC biasing to excite the icrophone in order to realize aplitude odulation (AM). It is also expected that the noise level at high requency is sall and it will beneit the SN result. The nae AC biasing is derived ro the property o the excitation source. 9

34 The AC biasing schee is shown in Figure.. The large resistor is not necessary any ore since the signal is oved to uch higher requency band and / noise does not doinate as well. Moreover, this schee is not sensitive to the parasitic capacitor since the voltage applied to the parasitic capacitor is constant due to the virtual ground. Figure. AC biasing schee. The principle behind the AC biasing is ainly about aplitude odulation and deodulation. The icrophone s capacitance varies with the sound signal. Meanwhile, the capacitor is excited by the AC source. Thereore, aplitude odulated current is generated. And with the eedback C network, the odulated current generates a voltage at the output o the apliier. The spectru o the voltage here is coposed o three coponents. One is carrier signal which is at the requency o AC source. The other two are odulated signal at both sides o the carrier signal. The distance between the sidebands and carrier signal is exactly equal to the requency o the sound. Figure. illustrates the spectru o the aplitude odulated signal with a square wave carrier. 0 Figure. Spectru o the aplitude odulated signal. Usually the carrier signal is uch higher than the sidebands. The large aplitude o the carrier signal ay cause saturation proble in the apliier. Since it does not contain the sound s inoration, it can be reduced by a capacitor connected in parallel with the

35 icrophone. The added capacitor has the sae capacitance as C ic and it is driven by the oscillation source which is 80 degrees out o phase with the source connected to the icrophone. Thereby the signal at the output o the apliier contains only the sidebands which have the inoration we want. In order to deodulate sound ro the signal, a synchronized ixer is added aterwards. The ixer is driven by the sae requency as the excitation source. Thereore, the two odulated sidebands are oved back and ixed together at the sound s requency. In ideal situation, the excitation source should generate a pure sinusoidal wave as carrier because it contains only one requency coponent which is good or linearity o the sensor and iltering ater deodulation. In IC design, however, it is uch ore diicult to ipleent a sinusoidal wave than generating a square wave. Thereore a square wave is chosen as excitation source. The spectru o a square wave, however, contains odd haronics o the base requency. As a result, the deodulated signal is coposed o several sidebands o the odd haronics at sound s requency and other higher requency coponents which is shown in Figure.. Thereore a low pass ilter (LPF) is necessary to ilter out the higher requency coponents to liit the deodulated signal as pure as possible in the audio bandwidth..4. Signal Level To ake the idea ore distinct, a atheatical derivation o the principle is given below. Assue the excitation source is a square wave with aplitude V osc and requency osc, the Fourier Transor o the square wave is shown below: Vosc V osc F( t) = + [cos( ωosct) cos(3ω osct) + cos(5ω osct)...], or ωosc = π osc (. 3) π 3 5 Since the higher odd haronics have decreasing aplitude and they will be iltered out in the end, the ollowing derivation will only consider the base requency coponent which is V osc cos( ωosct). π Then the current through the icrophone and the parallel capacitor is given by: Vosc ( t) V I ( t) = + Z Z = jw osc ic V π osc C v osc Co ( t) * [sin(( w osc + w) t) sin(( w osc w) t)], or C v = C ic kpˆ (. 4) Consequently, the aplitude o the sidebands at the output o the irst apliier can be expressed as: (A and A are shown in Figure..) V w osc osc A = A = I( t)* = Cv [ V ] (. 5) + jω C osc π + ( ω C ) osc

36 I is uch lower than the oscillation requency osc, the aplitude o A and A can π C Vosc Cv be expressed as which is about 0 db ( 0 log 0 π ) lower than the signal level o the π C charge apliier schee. When the ixer is added, the sidebands o all haronics are oved back and ixed together at the base requency. (So does the noise.) The ixer can be regarded as the input ultiplied with a syetric square wave which is indicates in Figure. 3[5]. The Fourier transor o the syetric square wave is given by: 4 F( ( t)) = [cos( ωosct) + cos(3ω osct) + cos(5ω osct) +...] π 3 5 (. 6) Then the deodulated signal at the output o the LPF is given by: A ' = * A 4 * + ( ) π 3 Vosc 3.43 * C v π * A w + ( ω osc osc 4 * + ( ) π 5 C ) * A [ V ] 4 * +... π (. 7) Figure. 3 Mixer deodulation..4. Noise Calculation The noise calculation o AC biasing beore adding the synchronized ixer is alost the sae as that o the charge apliier schee which is given by: v + jω ( * Cic + C p + C ) v [ V / Hz], in noise j C j C + + ω + ω noise, out = v noise, (. 8) (Although the excitation source has phase noise, the noise calculation above is based on the assuption that the excitation source is noise ree.) eer the output noise voltage power back to the capacitive noise power at input yields: C noise = v noise π + jω ( * ) Cic + C p + C ( ) v ( ) [ F / Hz], in noise, Vosc Vosc π + ω ω (. 9)

37 Equation (. 9) is siilar to equation (. ).The dierence is that the input reerred noise o the apliier in AC biasing is ainly theral noise rather than / noise and it is apliied by * C ic + C p + C around the oscillation requency since a copensation capacitor is added C to decrease the carrier signal. The noise calculation in equation (. 8), however, does not consider the / noise coing ro the oscillator. Since the bias voltage across the sensor is o square wave type and swings ro ground to supply voltage, the electrostatic orce between the ebrane and the back plate is changing ro now and then which will introduce nonlinearity proble..5 Practical Measureent Since we have the MEMS icrophone in hand, it is interesting to test how it behaves with electronics. Thus a PCB (Printed Circuit Board) level investigation is ade ainly or the AC biasing schee..5. Aplitude Modulation As has been explained in section.4, the principle behind the AC biasing schee is based on aplitude odulation. It is also indicated in section.4 that the oscillation source used to drive the icrophone should be o square wave type or considering a sine wave is ore diicult to be ipleented on transistor level. Since the easureent is at PCB level, a pure sine wave can be generated ro an outside signal generator to drive the icrophone. Consider the schee in Figure. 4 (a), the signal generator which is connected to the icrophone generates a pure sine wave with 0.5 voltage aplitude. The apliier labeled as A is opap NE55 coing ro the NXP Seiconductors. The sound is generated by PM538A unction generator through a speaker. It generates a sine wave with 0 V peak to peak aplitude and KHz requency. Due to the lack o a reerence icrophone, it is diicult to easure the actual sound pressure exerted on the ebrane. The easureent is undertaken by setting V re with dierent voltages to prove that the sensitivity o the icrophone is increased by increasing the equivalent bias voltage exerted on it. The transer unction ro the input to output o A behaves like a band-pass ilter which is shown in Figure. 4 (b). The lower liit o the requency is decided by which is about 4 π C KHz. And the higher liit o the requency is decided by the bandwidth o the NE55 which is about 3 MHz. 3

38 (0 KΩ) osc Cic V p-p = V Vre C (00 pf) A Vout Cic + CΔ + C Vout C Apliier s bandwidth ω (a) (b) Figure. 4 (a) Schee or realizing aplitude odulation. (b) Frequency response o the transer unction. Due to the aplitude odulation, the signal at the output o A is coposed o a ain tone at the oscillation requency with two relatively sall sidebands which can be noticed on the spectru analyzer. It is illustrated in Figure. 5 where osc represents the oscillation requency; sound eans the requency o the input sound, A represents the agnitude o the ain tone and A s eans the agnitude o the sidebands. I the pure oscillation sine wave can be represented by V osc *sin(π osc t) with V osc as its aplitude, A and A s in the lat band are given by: C V A = ic osc [V ] (. 0) C and C V kpˆ A = ic osc s [ V ] (. ) C where C is the eedback capacitor, k has been entioned in equation (. 7) and P is the rs sound pressure exerted on the ebrane. Fro equation (. ), it can be seen that the output signal is proportional to the aplitude o the oscillation source. 4 Figure. 5 Aplitude-odulated signal s spectru.

39 Figure. 6 shows the agnitude o the side band versus oscillation requency under dierent bias voltages. The trend o these curves roughly perors like a band-pass ilter as has been entioned beore. These curves in the band (4 KHz - 3 MHz) are not unior as it is supposed to be. The peak sensitivity appears at MHz. -50 Sideband Magnitude(dB) Vre=5 Vre=3 Vre= Frequency (Hz) Figure. 6 Magnitude o the side band under dierent bias voltage. This eect ay caused by the sensor itsel. For a noral MEMS icrophone, the curve o the sensitivity versus acoustical requency is supposed to be lat at least in the audio band which is ro 0 Hz to 0 KHz. The icrophone used in the easureent can guarantee a lat requency response up to 00 KHz acoustic requency. When an oscillation source is exerted, the ebrane o the icrophone also vibrates with the oscillation requency. Since the 3 MHz oscillation requency has exceeded the lat requency response band, there is possibility that the icrophone dose not peror norally. Figure. 6 not only proves that the sensitivity increases with increasing bias voltage but also provides a rough idea about the perorance o the icrophone driven by a sine wave oscillation source o dierent oscillation requency. The agnitude o the ain tones versus oscillation requency with dierent bias voltage is shown in Figure. 7. The trends o these three curves are alost the sae with the side band in Figure. 6. Maintone Aplitude(dB) 4 0 Vre=5 Vre=3 Vre= req(log) Figure. 7 Magnitude o the ain tone under dierent bias voltage. 5

40 Coparing the agnitude in Figure. 6 and Figure. 7, we can see that the agnitude o the ain tone is alost 60 db higher than that o the side band. Thereore, it is necessary to reduce the ain tone otherwise it ay cause saturation proble o the preapliier..5. AC Biasing Setup Figure. 8 shows the AC biasing schee ipleented at PCB level. The chain coposed o NANDs and inverters is used to setup a two-phase non overlapping clock by decreasing the duty cycle o the square wave generated ro an external signal generator. Since the supply voltage o all the NANDs and inverters on the board are 4V, clock signal Φ and Φ swings ro 0 to 4V consequently. Thereore a resistive voltage divider is added to decrease the swing to a lower value. The potentioeter p and p are or the purpose o aking the swing o Φ and Φ ore tunable. The opaps which are labeled as A, A and A3 are opap NE55 coing ro the NXP Seiconductors which has 30 nv / Hz as input reerred noise and 3 MHz as sall signal unity gain bandwidth. The STM-3 Microphone Preapliier is or the purpose o apliying the deodulated signal ore easily by only tuning the ounted potentioeter. a(50ω) b(50ω) 3(0KΩ) C3(0.8nF) Figure. 8 AC biasing schee realized on PCB. The supply voltage is aected by the clock due to the act that all the devices on the board share the sae supply voltage. Thus, the syste generates ore haronics than we expected. The C network (&C, 3&C3 in Figure. 8) which provides 0 KHz irst-order cut-o requency is not enough to reduce the haronics. Thereore a 4 th -order LPF with 0 KHz cuto requency is placed ater to ilter out the unexpected intererences ro the clock and the higher haronics..5.3 Noise Analysis We are interested in the noise behavior on the irst stage o AC biasing which is shown in Figure. 9. The reason is that the irst stage ainly decides the sensitivity o the schee and the noise calculation is coparatively less coplicated which will reduce the dierence between the theoretical calculation and easureent. 6

41 (.5MΩ) p(0kω) Cic C (. pf) Φ A Vout Vre Trier Φ p(0kω) C0(.pF) Figure. 9 The irst stage or AC biasing. a(50ω) b(50ω) The total noise at the output is given by: V ntot a ( ) = * 4k BT p * ( ) + 4k T B a a + p + jω ( C C C + ic + + V ( n, opap, in + jω C + 4k T B ( + jω C ) [ V / Hz] p * ( + ic ) ) a p jω Cic ) ( ) + jω C (. ) where p = p =950 Ω (to decrease swing o the excitation voltage exerted on the icrophone to V), a = b and V is the input reerred noise o the apliier labeled as n, opap, in A. Equation (. ) was used to write a MATLAB script which yields Figure. 0. It shows the noise spectral density at the output o A. It gives a general idea about the noise distribution at dierent requencies. The plot shows that the noise level is low at high requencies. Thus the aplitude odulation is expected to operate at high requencies to get better signal-tonoise ratio. 7

42 Figure. 0 Noise versus requency or the irst stage o AC biasing. The noise at the output o A is also easured to check i the calculation in equation (. ) is correct. The noise easureent is undertaken by shorting the oscillation source to the ground. The result is shown in Figure.. The two curves agree to each other. We can also predict the input-reerred theral noise level o the preapliier by using equation (. 5) and equation (. ). Assuing the aplitude o the oscillation source is 3.3 V and the eedback capacitor is 00 F, the theral noise level o the preapliier is approxiately 7 nv / Hz to achieve 60 db SN on the irst stage without considering the theral noise generated ro the eedback resistor. It is not easy to realize such an apliier on transistor level Measured esult Calculated esult 60 Noise(nV/sqrt(Hz)) E+03.00E+04.00E+05.00E+06 Freq(Hz) Figure. Coparison o the noise easureent and calculation result or AC biasing..5.4 Check Functionality According to equation (. 8) and (. 9), the sensitivity o a icrophone is proportional to the bias voltage exerted on it. And as has been entioned in section., the pull-in voltage o the icrophone is around 8V by experient. Thus it is interesting to test the behavior o the icrophone with dierent bias voltage and especially with pull-in voltage. Thereore, two 8

43 odes are tested. One is the noral ode which eans that the equivalent bias voltage does not exceed the pull-in voltage. The other one is the collapse ode which eans equivalent bias voltage exerted on the icrophone is close or equal to the pull-in voltage. The collapse ode is expected to have high sensitivity because o the high bias voltage. Noral Mode Figure. illustrates the signal level to oscillation requency response with two dierent biasing setups. The lower curve is tested with V re =3 V and V osc = V. The higher curve is tested with V re = 5V and V osc = 5V. V osc is the aplitude o the oscillation source exerted on the icrophone. Since the DC value o a square wave is hal o its peak to peak aplitude, the equivalent DC voltage exerted across the icrophone are both.5 V under two cases. It is illustrated in Figure. 3. The ai is trying to keep the sensitivity o the icrophone sae under these two cases. Oscillation Frequency esponse -0-5 MS Signal Level (db) Freq(Hz) Vosc=,Vre=3 Vosc=5,Vre=5 Figure. esponse to oscillation requency with dierent oscillation aplitude in noral ode. Figure. 3 Equivalent voltage s waveor exerted on the icrophone under two cases. The two curves are lat when the oscillation requency is lower than 00 KHz. They drop suddenly at 400 KHz and 600 KHz respectively. It ay caused by the characteristic o the icrophone itsel. With oscillation source connected to the ixed back plate, the ebrane will vibrate at the oscillation requency without any acoustical signal input. It will cause nonlinearity and resonant issues. The icrophone ight behave badly under certain oscillation requency. The two curves also iply that the axiu oscillation requency o a 9

44 square wave type excitation source that the icrophone can handle is approxiately 00 KHz. Equation (. 5) indicates that the aplitude o the odulated signal which contains the sound s inoration is linear with the oscillator s aplitude. Thereore, the signal o the case 5 with V osc = 5 V should be 4 db ( 0 log ) larger than that o the case with V osc = V. Figure., however, shows that the upper curve is only about 0dB higher than the lower curve. I we look into the equivalent voltage exerted on the icrophone in two cases, it can be seen that in one case the voltage swings ro 0V to 5V and in another case the voltage swings ro V to 3V. It is illustrated in Figure. 3. Figure. 7 indicates that the icrophone has dierent sensitivity with dierent bias voltage. That is, in one cycle o the clock, the icrophone has two dierent sensitivities. Thereore the 4 db dierence ay coe ro the dierent average sensitivity under the two cases. Figure. 4 illustrates the eect. To test this, we can siply do the ollowing test. The DC biasing schee is the ost direct way to test the dierent sensitivity with dierent bias voltage. Thereore, easure the output signal level with bias voltage o 0.V (with 0V bias voltage, there will not be a signal coe ro the icrophone), V, 3V and 5V respectively in DC biasing setup. The results are listed in Table.. During this easureent, the distance between the speaker and the icrophone is kept constant Sensitivity [pf/pa] Vbias [V] Figure. 4 Dierent average sensitivity in two cases. DC Voltage(V) MS Signal Level (db) Average (db) Table. Measureent in DC biasing with dierent bias voltage. Table. iplies that with the sae sound pressure level input, the icrophone generates dierent signal with dierent bias voltage. The dierence between the average signal levels o the two cases explains the 4 db dierence between easureent and equation (.) because equation (. 5) does not take dierent sensitivity into consideration

45 Figure. 5 shows the waveor displayed on the oscilloscope with V re = 5 V and V osc = 5 V. The deodulated signal on the oscilloscope in this case is very stable and clear. Collapse Mode Figure. 5 Deodulated signal in noral ode The response to oscillation requency in collapse ode is shown in Figure. 6. The igure also includes the response in noral ode to copare with. Around 00 KHz, the collapse ode generates about 0 db larger signal than the noral ode. However, the response has soe resonant behaviors. Oscillation Frequency esponse -0-5 MS Signal Level (db) Freq(Hz) Vosc=,Vre=3 Vosc=,Vre=8.5 Figure. 6 Coparison o requency response between noral ode and collapse ode. The deodulated waveor at the highest peak appeared in Figure. 6, however, is highly distorted which is shown in Figure. 7. 3

46 Figure. 7 The nonlinear deodulated signal in collapse ode at 00KHz oscillation requency. The collapse ode can also behave norally at certain oscillation requency. Figure. 8 shows the result with 0 KHz oscillation requency. But the aplitude is lower than that in Figure. 5 and Figure. 7 which eans that the collapse ode does not have better perorance than the noral ode. Figure. 8 The deodulated signal in collapse ode at 0KHz oscillation requency..5.5 Conclusion This part investigates the AC biasing on PCB level. And the noral ode and collapse ode o AC biasing is investigated urther. The ai or biasing the icrophone in collapse ode is intended to ake the icrophone generate large signal. The results, however, show that the behavior o the collapse ode does not exceed the noral ode as uch as we expected. And the non-linearity and instability o collapse ode counteracts its advantages..6 Conclusion Table. shows a coparison between the three dierent readout schees in signal and noise. 3

47 DC Biasing Charge Apliier AC Biasing Input (F) Input ( F / Hz Cic + C p C C C ic + p v, rs v + v noise V b re V re C v, rs C v, rs v, noise, in,/ + jω ( ),, Cic + C p + C + v noise in noise V re ω Vre ω π + jω ( * ) Cic + C p + C ( ) π + v ( ) noise in noise, V osc ω Vosc ω v, Table. Coparison between three schees where 4, ( ) v = kbtb, 4 noise b + jωb Cic + C p, v = kbt, v stands or noise + jω C noise, in, / the / noise doinated input reerred noise o an apliier and v stands or the noise, in, theral theral noise doinated input reerred noise o an apliier. k B is Boltzann constant which is equal to.38*0-3 J/K. T is teperature (K). Fro the above table and the explanation in section. to.4, we can not draw a conclusion that a certain schee will deinitely exceed the other two schees in certain speciication. They all have advantages and disadvantages. To suarize, the pros and cons o dierent schees are listed in Table. 3. For instance, the charge apliier schee has a higher sensitivity with a sall eedback capacitor while the noise o apliier is apliied by a large actor at the sae tie. The AC biasing schee sees to avoid the / noise o the apliier but the aplitude odulation decreases the signal level and AC excitation source exerted on the icrophone generates nonlinearity probles. ) DC Biasing Charge Apliier Advantages Siple topology Insensitive to the parasitic capacitance and have high signal level. Disadvantages Large resistor is needed or low noise and sall leakage current. Moderate sensitivity because o parasitics. / noise. Large eedback resistor is needed or low noise and sall leakage current. / noise. AC Biasing Get rid o / Noise, insensitive to the parasitic capacitance and large eedback resistor is unnecessary. Oscillator has phase noise. Changing Electrostatic orce between the two plates ay cause nonlinearity issues. Low side band level. Table. 3 Advantages and disadvantages or the three schees. The ain dierence between the DC biasing and the use o a charge apliier is the eect o parasitic capacitances. The virtual ground established by a charge apliier neutralizes the eect o parasitic capacitances. With DC biasing, however, another ethod can be used to 33

48 reduce the eect o parasitic capacitance. This ethod will be explained in detail in the ollowing chapters. 34

49 Chapter 3.New eadout Schee with Positive Feedback This chapter will introduce a new readout schee with which the parasitic capacitances o a DC biased icrophone can be reduced. First, the basic principle behind the schee will be explained (section 3.), ollowed by theoretical analysis o the output signal level and the noise o the new schee (section 3.). The syste level analysis described in section 3.3 decides the inal schee to be ipleented. Speciications or apliier in the interace circuit are proposed consequently (section 3.4). 3. Miller Eect The Miller eect is a coon phenoenon that occurs in any analog circuits. It is irst described by John M. Miller in [6]. The Miller eect reers to the act that the ipedance seen at the input o an apliier depends on the ipedance connected between input and output o the apliier. Consider an ideal apliier o gain -H with ipedance connected ro input to output which is shown in Figure 3. Figure 3. Ipedance connected ro input to output o an apliier The input current I i is calculated as: Vi Vo ( + H ) Vi (3. ) Ii = = Z Z Then the equivalent ipedance at the input o the apliier is: Z in Vi = I i Z = + H (3. ) Applying the sae calculation, the equivalent ipedance at the output o the apliier is: Z Z out = + H (3. 3) 35

50 Since ost apliiers have negative gain, the presence o the Miller eect eans that their eective input ipedance is (+H) ties saller i the ipedance is resistive or inductive. And i the ipedance is capacitive, the eective input capacitance is (+H) ties larger. For non-inverting apliiers, the Miller eect results in a negative capacitive ipedance at the input. Thereore, we can use the Miller eect o a non-inverting apliier to reduce the parasitic capacitance associated with DC biasing. 3. Miller Eect in DC Biasing A capacitor C is connected ro input to output o the preapliier in DC biasing which is shown in Figure 3. (a): Figure 3. Miller eect in DC biasing Figure 3. (b) shows the Miller eect o C. Fro Miller theory, we know that C is equal to (-H)C and C is (-/H)C. I H is larger than, C is negative. With this negative capacitive ipedance, the static capacitance o the sensor C ic and the parasitic capacitance o the preapliier and the sensor C p can be reduced. Based on the constant charge theory, the rs signal at the output is given by: ΔV rs = H C ic + C p C v, rs * V re + ( H ) C C v, rs [ V ] (3. 4) In this way, a proper cobination o H and C can ake the denoinator o the raction in equation (3. 4) extreely sall which results in a large signal. Although the signal is boosted with the positive eedback capacitor C, the noise is increased at the sae tie. The noise at the output o the preapliier is given by: 36

51 v noise, tot = 4k T v B b noise, in * + jω [ C b + ( H ) C H[ + jωb ( C + Cic + C p)] * + jω [ C + C + ( H ) C ] b ic ic H + C p p + ] (3. 5) where V noise,in is the input reerred noise o the preapliier. Equation (3. 4) and (3. 5) were used to write a MATLAB script with C ic + C p = 5 pf and H =. The resulting signal level, noise integrated in the audio bandwidth and the signal-tonoise ratio is shown in Figure 3. 3 by sweeping C ro 0 to 0.5 pf with 0.0pF step size. More details o the scripts can be ound in Appendix C. Figure 3. 3 Matlab siulation result o the DC biasing with positive eedback C. Figure 3. 3 shows that the signal and rs noise increases with C alost at the sae rate. But the SN curve indicates that SN drops draatically when (-H)C is equal to the value C ic + C p. The reason or the big drop is that the pole in the raction o equation (3. 5) becoes ininite when (-H)C = C ic + C p. At this point, the large theral noise ro the huge resistor b is not iltered any ore. And the transer unction o the preapliier will apliy the input reerred noise to ininity at high requencies. This will ake the integrated noise incredibly large. 37