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Design considerations for an acoustic MEMS filter

S.-H. Shen, W. Fang, S.-T. Young

Abstract Microelectromechanical system (MEMS) devices

exhibit characteristics that make them ideal for use as ﬁlters

in acoustic signal processing applications. In this study, a

MEMS ﬁlter is constructed from multiple mechanical

structures (e.g. cantilever beams) and a differential ampli-

ﬁer. The outputs of the structures are then processed by the

differential ampliﬁer to achieve the ﬁlter functionality. The

important parameters of the mechanical structures and the

MEMS ﬁlters are investigated using a simulation approach,

including the structural damping factors, the normalized

frequency ratios (NFR) of the MEMS ﬁlters, the number of

mechanical structures required to construct individual

MEMS ﬁlter, and the spatial arrangement of the multiple

mechanical structures relative to the differential ampliﬁer.

Furthermore, the mutual coupling effects among these

parameters are evaluated by detailed simulations. The

simulation results show that a plot of the NFR versus the

damping factors can be used to determine the optimal

parameters for the mechanical structures. The number of

mechanical structures required to construct a MEMS ﬁlter

must equal 2

n

, with nas an integer, and these mechanical

structures should be arranged as a geometric series with

increasing resonant frequencies and with speciﬁc connec-

tions to the differential ampliﬁer.

1

Introduction

A crucial aspect for many signal-processing techniques,

including acoustic signal processing, is to divide the signal

into multiple frequency bands. With its powerful computing

capabilities, the digital signal processor (DSP) now forms

the core for such techniques [1, 2]. However, contemporary

DSPs still present limitations for some applications, in terms

of their power consumption and computation time. Where

these factors are crucial, the electromechanical ﬁlter – as a

passive device – provides a viable alternative. Electrome-

chanical ﬁlters have been well known for at least 5 decades

[3]. They can be used to extract signals from a speciﬁc fre-

quency band, and hence provide functionality similar to

electrical ﬁlters. Electromechanical ﬁlters also provide

excellent aging and thermal-stability characteristics [4].

With the introduction of microelectromechanical systems

(MEMSs), the application of electromechanical ﬁlters to

signal processing has become more feasible, from high-

frequency to radio-frequency regions [5–8]. An electrome-

chanical ﬁlter bank constructed from silicon beams for a

high-frequency communication system was recently inves-

tigated [9]. Each ﬁlter in this ﬁlter bank comprised a single

beam structure with a sharp frequency response. A sharp

frequency response always results in poor linearity for the

ﬁlter passband signals.

This study proposes a novel MEMS ﬁlter for acoustic

signal processing. Its characteristics and design param-

eters were investigated by simulations of ﬁlters com-

prising multiple mechanical structures. The simulation

approach enabled complete characterization of the crit-

ical parameters of the mechanical structures and the

MEMS ﬁlters, such as the structural damping factors, the

normalized frequency ratios (NFRs) of the MEMS ﬁlters,

the number of mechanical structures required to con-

struct an individual MEMS ﬁlter, and their spatial

arrangement. The simulations demonstrate that the

proposed MEMS ﬁlter can be implemented, and that it

would be an effective device for acoustic signal-pro-

cessing applications, such as in miniature hearing aids.

2

Theory and methods

2.1

Theory on MEMS filters

A mechanical structure has a preferred vibrating mode

referred to as resonance that depends on the conﬁguration

of the structure and its mechanical properties. This

vibrating mode can be characterized by the magniﬁcation

factor, which is taken as a normalized vibration amplitude

in this paper, and phase versus frequency in the ﬁrst mode

of vibration, expressed as Eqs. (1) and (2), respectively

[10]:

Microsystem Technologies 10 (2004) 585–591 ÓSpringer-Verlag 2004

DOI 10.1007/s00542-003-0335-6

Received: 20 November 2002 / Accepted: 19 September 2003

S.-H. Shen, S.-T. Young (&)

Bioelectronics Laboratory, Institute of Biomedical Engineering,

National Yang Ming University 155, Sec. 2, Li-Nung St,

Shih-Pai, Taipei 112, Taiwan

e-mail: Young@bme.ym.edu.tw

W. Fang

Micro Device Laboratory, Department of Power Mechanical

Engineering, National Tsing Hua University, Hsinchu 300,

Taiwan

This material is based (in part) upon work supported by the

National Science Council (Taiwan) under Grant NSC 91–2213-

E-010-008 and Delta Electronics Foundation. The authors would

like to express their appreciation to the NSC Central Regional

MEMS Center, Semiconductor Research Center of National Chiao

Tung University (Taiwan), and the NSC National Nano Device

Laboratories (Taiwan) in providing experimental facilities.

585

X

jj

Ds¼X

jj

F0=k¼1

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1x=xn

ðÞ

2

2þ2fx=xn

ðÞ

2

2

q

Magnification factor ð1Þ

/¼tan12fx

xn

1x

xn

2

2

6

43

7

5Phase shift ð2Þ

where X

jj

is the amplitude of the steady-state vibration,

Dsis the static displacement when the exciting force F

0

is slowly applied to the mechanical structure, kis the

spring constant of the structure, xnand xare the res-

onance and operating frequency of the structure, and f

is the damping factor. In this study, micromachined

cantilevers were employed to detect the acoustic waves.

Hence, the F

0

/k of these cantilevers with lin length and t

in thickness can be expressed as Eq. (3) [11].

F0

k¼3pl4

2Et3ð3Þ

where pis the acoustic pressure, and Eis the Young’s

modulus of cantilever. By dividing X

jj

into F

0

/kusing pre-

signal-processing tools, such as ampliﬁers or programs, we

can easily acquire the normalized signals.

The proposed MEMS ﬁlter is shown in Fig. 1, which

consists of multiple mechanical structures with sensing

circuits and a differential ampliﬁer. The MEMS ﬁlter had

designed with a bandpass characteristic. The mechanical

structures respond to acoustic stimulation, according to

their particular frequency responses, and cause the

sensing circuits to produce the associated electrical sig-

nals. The differential ampliﬁer processes the electrical

signals picked up from some parts of the mechanical

structures. The resulting signal can be a ﬁltered signal

when the mechanical structures are designed with

appropriate frequency responses and their outputs are

coupled in the differential ampliﬁer in an appropriate

arrangement. For a MEMS ﬁlter with multiple mechani-

cal structures, the output of each mechanical structures

is connected to either a positive or a negative port of the

differential ampliﬁer through a switching mechanism,

which is called as a positive and negative switch (PNS),

as shown in Fig. 1a. It is obvious that the variety of

possible PNS arrangements will increase with the num-

ber of mechanical structures in a MEMS ﬁlter. Besides,

the MEMS ﬁlter can be implemented by, for example,

micromachined cantilevers and piezoresistive sensing

circuitry as shown in Fig. 1b.

For unobvious effects from higher-order resonance

modes and convenient illustration, we only considered the

ﬁrst resonance mode of the mechanical structure. Com-

bining Eqs. (1) and (2), the vibration of a mechanical

structure can be presented by means of a cosine wave

equation, x

i

:

xi¼Xi

jj

Dsi

cosð2pxtþ/iÞ

¼1

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1x=xni

ðÞ

2

2þ2fx=xni

ðÞ

2

2

q

cos 2pxtþtan12fx

xni

1x

xni

2

2

6

43

7

5

0

B

@1

C

Að4Þ

The sufﬁx irepresents the label of an individual structure.

Multiple mechanical structures can be designed such that

their resonant frequencies increase sequentially, with their

responses x1;x2;...;xicoupled together to implement a

MEMS ﬁlter. The general response of such a MEMS ﬁlter

can be presented as

xtotal ¼xiþþxiMxiNx1

jj

;i2;

i1>M0;i1>N>0;M6¼ Nð5Þ

2.2

Performance definition and evaluation of MEMS filter

We evaluated the performance of the MEMS ﬁlter by

measuring certain ﬁlter parameters, including the pass-

band ripples and the ﬁlter shape. We wanted the passband

ripple to be less than 1 dB, and in any case ensure that it

did not exceed 3 dB to avoid violation of the cutoff-

frequency deﬁnition. The asymmetric ﬁlter shape is

assessed by a deﬁned shape factor. The shape factor of the

MEMS ﬁlter was divided into the lower shape factor (LSF)

and higher shape factor (HSF), which describe either side

of the bandpass ﬁlter’s shape. LSF and HSF are deﬁned in

Fig. 1a, b. Illustrations of MEMS ﬁlters: aa concept diagram of

the proposed MEMS ﬁlter; ba practical MEMS ﬁlter with

micromachined cantilevers and piezoresistive sensing circuitry

586

Eqs. (6) and (7), respectively, and the related deﬁnitions

are illustrated in Fig. 2. According to our deﬁnitions, a

MEMS ﬁlter with lower LSF and HSF values has a sharper

passband, and the ﬁlter is more symmetric when its LSF

and HSF values are similar:

LSF ¼The logarithmic bandwidth between f0and fL;40dB

The logarithmic bandwidth between f0and fL

¼log f0

ðÞlog fL;40dB

log f0

ðÞlog fL

ðÞ ð6Þ

HSF ¼The logarithmic bandwidth between f0and fH;40dB

The logarithmic bandwidth between f0and fH

¼log fH;40dB

log f0

ðÞ

log fH

ðÞlog f0

ðÞ ð7Þ

where f

L

is the lowest resonant frequency and f

H

is the

highest resonant frequency of the structures comprising

the MEMS ﬁlter; and f

0

is the center frequency, equal to the

average of f

L

and f

H

;fL;40dB and fH;40dB are the upper and

lower frequencies at which 40-dB attenuations occur.

2.3

Simulation approach

Using Eqs. (4) and (5), we developed simulation programs

to explore the optimized design parameters of the pro-

posed MEMS ﬁlter, using the following criteria:

(a) The damping factors of the mechanical structures are

the ﬁrst parameters to be investigated, since their

combination will determine the passband ripple and

resonant frequency of the MEMS ﬁlter. We simulated

different individual damping factors and different

combined ratios.

(b) The bandwidth is the second important parameter for

the MEMS ﬁlter. The bandwidth investigation is

achieved through the NFR. The NFR of a MEMS ﬁlter

constructed by multiple mechanical structures with

increasing resonant frequencies f

1

,f

2

.....f

n

is described

by the normalized interval between the lowest resonant

frequency f

L

(= f

1

) and the highest resonant frequency

f

H

(= f

n

) of the MEMS ﬁlter. The NFR is deﬁned as

NFR ¼Center frequency

The bandwidth between fHand fL

¼

1

2fHþfL

ðÞ

fHfL¼f0

fHfLð8Þ

The center frequency f

0

is the average of f

L

and f

H

.By

the deﬁnition, the NFR is inversely proportional to the

bandwidth for the same center frequency. How the

NFR effects the MEMS ﬁlter was also fully investigated

by the simulation program.

(c) Once the desired damping factors and ﬁlter bandwidth

were determined, the mechanical structures compris-

ing the MEMS ﬁlter were determined by simulations.

Different relationships between these structures and

the differential ampliﬁer were also analyzed. These

were implemented by conﬁguring the PNS shown in

Fig. 1. For clarity of illustration, when the PNS links

the mechanical structure to the positive port of the

differential ampliﬁer, the structure is symbolized as a

positive sign (‘‘+’’); whereas when the PNS switches to

the negative port, the structure is symbolized as a

negative sign (‘‘)’’). The sequential presentation of

these signs in the MEMS ﬁlter indicates the mechanical

structures with increasing resonant frequencies.

(d) The effects of the individual parameters on the char-

acteristics of the MEMS ﬁlter are not independent, and

hence their mutual effects on each other were also

investigated in the study. The simulations analyzed the

relationships between the damping factors and the

NFR to explore their trade-off whilst maintaining an

acceptable passband ripple. The simulations also

thoroughly investigated the effects on the ﬁlter shape

factors of NFR and number of structures simulta-

neously to determine a reasonable number of

mechanical structures for the MEMS ﬁlter.

3

Simulation results

The results of simulations into the effects of the damping

factor, the NFR, and the number of mechanical structures

comprising the MEMS ﬁlters are presented in Sects.

3.1–3.4, respectively. For illustrative simplicity, 2-structure

MEMS ﬁlters are used to show the effects of damping

factors and NFR in Sects. 3.1 and 3.2. The simulation

results for multiple-structure MEMS ﬁlters are only

depicted with an NFR of 2.50 and a damping factor of

0.123; for these values the 2-structure MEMS ﬁlter exhibits

a passband ripple of only 1 dB in Sect. 3.3. The resonant

frequencies of adjacent structures are arranged as a

geometric series in multiple-structure ﬁlters. The mutual

relationships among the parameters and performance of

MEMS ﬁlters are then illustrated in Sect. 3.4.

3.1

Effects of damping factor

Figure 3 illustrates how the damping factors of the struc-

tures affect the frequency response of the MEMS ﬁlter with

center frequency, f

0

, 1000 Hz. In Fig. 3a, the damping

factors of two structures, f

L

and f

H

, were assigned values

of 0.123 and 0.984 (f

H¼

8f

L

), 0.984 and 0.123 (f

L¼

8f

H

),

Fig. 2. Illustration of the deﬁnitions of MEMS ﬁlter parameters

587

and 0.123 and 0.123 (f

L¼

f

H

), respectively. Figure 3b

shows the response of MEMS ﬁlters that were comprised of

two structures with equal damping factors of 0.083, 0.123,

and 0.200. The resulting LSF, HSF, and passband-ripple

values for these MEMS ﬁlters were 6.37, 7.45, and 3 dB;

7.35, 8.38, and 1 dB; and 9.28, 9.56, and 0 dB; respectively.

3.2

Effects of normalized frequency ratio

Figure 4 shows the effect of different NFRs on the fre-

quency response of MEMS ﬁlters. Figure 4a shows that

NFR values of 1.69, 2.50, and 3.90 produce MEMS ﬁlters

with LSF, HSF, and passband-ripple values of 7.36, 8.39,

and 3 dB; 7.35, 8.38, and 1 dB; and 10.16, 11.04, and 0 dB;

respectively. Figure 4b illustrates the frequency responses

of different MEMS ﬁlters that have center frequencies of

500 Hz, 1000 Hz, and 3000 Hz, but the same NFR and

damping factors of 2.50 and 0.123, respectively. These

MEMS ﬁlters produce identical LSF, HSF, and passband-

ripple values, of 7.35, 8.38, and 1 dB, respectively.

3.3

Effects of number of mechanical structures and their

arrangement

Figure 5 illustrates the frequency responses of 4-structure

MEMS ﬁlters, whose structures had resonant frequencies

of 800 Hz, 916 Hz, 1048 Hz, and 1200 Hz (i.e., f

L

= 800 Hz

and f

H

= 1200 Hz). The ﬁgure shows the responses of the

4-structure MEMS ﬁlters for only some of the possible

structure arrangements, which were arranged with equal

structures to connect to both ports of the differential

ampliﬁer. The LSFs, HSFs, and passband-ripple values of

the 4-structure MEMS ﬁlters are 4.35, 5.10, and 0.32 dB, for

the ‘‘þþ’’ PNS arrangement; 7.04, 8.05, and 22.95 dB

for ‘‘þþ’’; and 6.75, 7.73, and 0 dB for ‘‘þþ’’.

Fig. 3a, b. The effect of damping factors on the frequency re-

sponses of MEMS ﬁlters comprised of two structures with: a

different damping factors and, bthe same damping factor

Fig. 4a, b. The effect of NFR on the frequency responses of

MEMS ﬁlters: awith various NFRs but with the same center

frequency and damping factor; bwith different center frequency

f

0

but with the same NFRs and damping factors

Fig. 5. The frequency responses of 4-structure MEMS ﬁlters with

different structure arrangements

588

Figure 6 shows the best frequency responses of 6-, 8-,

12-, and 16-structure MEMS ﬁlters, for PNS arrangements

of ‘‘þþþ’’, ‘‘þþþþ’’,

‘‘þþþþþþ’’, and

‘‘þþþþþþþþ’’, respectively. The

LSF and HSF values for 8-, 12-, and 16-structure MEMS

ﬁlters were 3.02 and 3.47; 2.88 and 3.3; and 2.46 and

2.78; respectively, while the passband-ripple values were 1

dB, 0 dB, and 3.43 dB, respectively. The responses of the

8- and 12-structure MEMS ﬁlters intersect around 380 Hz

and 2650 Hz. Due to the serious asymmetry to the central

frequency axis of its response, the passband-ripple values

and shape factors cannot be deﬁned in the 6-structure

MEMS ﬁlter.

Figure 7 depicts the responses of 8- and 16-structure

MEMS ﬁlters with different center frequencies and the

same NFR of 2.5. The center frequencies were set as

500 Hz, 1000 Hz, and 3000 Hz, and the PNS arrangements

were set as ‘‘þþþþ’’ and

‘‘þþþþþþþþ’’. The LSF, HSF,

and passband-ripple value of the 8-structure MEMS ﬁlters

are 3.02, 3.47, and 1 dB, and those of the 16-structure

MEMS ﬁlters are 2.46, 2.78, and 3.43 dB.

3.4

Mutual effects among crucial parameters

For passband-ripple values of 1 dB and 3 dB, Fig. 8 shows

that the damping factors and the NFRs were inversely

relationships irrespective of the number of the mechanical

structures used to construct the MEMS ﬁlter. The mutual

relationship of NFRs in 4-, 8-, and 16-structure MEMS

ﬁlters, and damping factors and ﬁlter shape factors are

illustrated in Fig. 9 for 1-dB and 3-dB passband ripples.

These ﬁgures show the trade-off between the shape factors

LSF and HSF with different desired NFRs.

4

Discussion

As designing a MEMS ﬁlter constructed from mechanical

structures, it is necessary to deﬁne its center frequency,

ﬁlter bandwidth, acceptable passband ripple, and desired

ﬁlter shape. The characteristics of a MEMS ﬁlter are

affected by many parameters, including the damping fac-

tors of the mechanical structures, the NFRs, and the

number and arrangement of mechanical structures con-

stituting the ﬁlter. This study investigated these parame-

ters by simulating various MEMS ﬁlters, and the results

provide certain guidelines for the design of such ﬁlter.

Fig. 6. The best frequency responses in 6-, 8-, 12-, and 16-

structure MEMS ﬁlters

Fig. 7a, b. The frequency responses of MEMS ﬁlters constructed

by multiple structures with the same damping factor and

NFR, but various center frequencies: a8-structure MEMS ﬁlters;

b16-structure MEMS ﬁlters

Fig. 8. The relationship between NFRs and damping factors with

differing numbers of structures and passband-ripple values

589

The damping factor of the mechanical structure is one

of these important parameters. The simulation results

showed that the damping factors of the mechanical

structures should be as similar as possible to ensure the

symmetry of the frequency response of the MEMS ﬁlter.

When a MEMS ﬁlter is made from structures with unbal-

anced damping factors, its ﬁlter proﬁle will skew to the

frequency response of the structure with the lower

damping factor. The more unbalanced the damping factors

are, the more asymmetric the ﬁlter proﬁle appears; and in

extreme cases the ﬁlter may lose its ﬁltering functionality,

with undeﬁned LSF and HSF values. Moreover, appropri-

ate damping factors are evidently necessary: a larger

damping factor decreases the passband ripples but

enlarges the LSF and HSF, when NFR is kept constant;

whereas a small damping factor produces a MEMS ﬁlter

with small LSF and HSF. However, damping factors that

are too small will produce a MEMS ﬁlter with individual

mechanical structures that do not exhibit mutual coupling.

The NFR of the MEMS ﬁlter is another important

parameter – it essentially determines the bandwidth of the

MEMS ﬁlter. Increasing the NFR both narrows the ﬁlter

bandwidth and makes the passband ripple smaller. The

simulation results also revealed the interesting character-

istic that MEMS ﬁlters with identical NFRs and damping

factors will have identical passband ripples and shape

factors, even though they can have different center

frequencies. This will simplify the design of MEMS ﬁlters

for use at different frequencies. Furthermore, the NFR and

the damping factor have mutual effects on the MEMS ﬁlter.

The simulation results (in Fig. 8) show that the damping

factor and the NFR are inversely related, which is impor-

tant information when designing for the allowable pass-

band ripple and desired shape factor of the MEMS ﬁlter: to

decrease the bandwidth of a MEMS ﬁlter it is necessary to

decrease the damping factor whilst simultaneously

increasing the NFR.

The number and arrangement of the structures is

especially important in the construction of multiple-

structure MEMS ﬁlters. The simulations showed that the

mechanical structures in a MEMS ﬁlter must be arranged

in a mirror relationship to the differential ampliﬁer (e.g.

‘‘þþþþ’’ for eight structures and

‘‘þþþþþþþþ’’ for 16 structures.

This arrangement can be explained with reference to logic.

A 2-structure MEMS ﬁlter has its basic arrangement as

‘‘þ’’ (or ‘‘þ’’). For a 4-structure MEMS ﬁlter, its best

PNS arrangement is ‘‘þþ’’, which can be considered

as two adjacent subsets, ‘‘þ’’ and ‘‘þ’’. Each subset can

be taken as a new structure, with the subset ‘‘þ’’ being

regarded as the inverse of ‘‘þ’’. The combination of the

two subsets can then be considered as another 2-structure

MEMS ﬁlter arranged with the mirror relation ‘‘þ’’.

Following this arranging rule, the best arrangement of an

8-structure MEMS ﬁlter is then derived from the combi-

nation of subset ‘‘þþ’’ and its inverse ‘‘þþ’’, and

the best arrangements of the 16-structure MEMS ﬁlter is

predicted as the combination of ‘‘þþþþ’’ and

‘‘þþþþ’’. The mirror relation in this best PNS

arrangement implies that the number of structures in a

MEMS ﬁlter must be equal to 2

n

, where nis an integer.

This also means that the train of the arrangement can be

folded up until it has its basic arrangement as ‘‘þ’’.

Although the multiple-structure MEMS ﬁlter can be

regarded as a pair of structures that process the incoming

signals, each virtual structure exhibits damping that is

different from that exhibited by the preceding structure

combination; therefore, this study has not provided a

complete comparison between 2-structure and multiple-

structure MEMS ﬁlters.

The mutual effects of all parameters on the MEMS ﬁlters

were very important when designing the ﬁlter proposed in

the study. The damping factor of each structure within the

ﬁlter is determined by both structural and environmental

factors, with changes in environmental conditions being

more signiﬁcant at micron dimensions. The squeezed-ﬁlm

effect is often taken as the critical solution for tuning the

damping factors in microstructures. Based on the

squeezed-ﬁlm theory, the gap depth and covered area of

the microstructure – as controlled by the fabrication

process – enables any damping factors to be obtained; for

instance, the stationary structures proposed in [12] can be

employed to tune the quality factor of bulk micro-

machined structures by incorporating with the squeezed-

ﬁlm damping. However, using a single damping factor for

all the structures is expected to simplify the fabrication of

the proposed MEMS ﬁlter on a wafer. In this case, the

Fig. 9a, b. The relationship between NFR and shape factors for a

response: awith a 1-dB passband ripple and different numbers of

structures and, bwith a 3-dB passband ripple and different

numbers of structures

590

number of structures becomes as a major selectable

parameter for obtaining the desired passband ripple and

bandwidth. Figure 8 shows that with a ﬁxed damping

factor, increasing the number of structures will increase

NFR and decrease passband ripple, except in the 2-struc-

ture MEMS ﬁlter. Increasing NFR decreases the band-

width. A large number of structures will also decrease LSF

and HSF values, as shown in Fig. 9, and the decreasing

LSFs and HSFs produces a sharper ﬁlter. A large number

of structures will then enhance the ﬁlter performance.

Another interesting phenomenon is that increasing NFR

will increase the LSF but decrease the HSF. This trend

brings the LSF and HSF closer, producing a more sym-

metrical ﬁlter. However, the advantages of increasing the

number of mechanical structures do not continue indeﬁ-

nitely: too many mechanical structures will complicate the

ﬁlter fabrication and decrease the yield rate. We therefore

propose that an 8-structure MEMS ﬁlter represents the

best compromise.

5

Summary and conclusions

This paper has proposed the design of a MEMS ﬁlter and

investigated its important parameters using a simulation

approach. In theory, all the requirements of MEMS ﬁlters

can be satisﬁed through the selection of appropriate

damping factors of the mechanical structures, NFR, and

the number and arrangement of the mechanical structures

that constitute the ﬁlter. For individual MEMS ﬁlter with

multiple mechanical structures, the structures should have

similar damping factors. The NFR of the MEMS ﬁlter is

another important parameter, which determines the ﬁlter

shape and bandwidth for different center frequencies.

Furthermore, the simulation results show that the number

of mechanical structures required to construct a MEMS

ﬁlter must be a power of 2, and the resonant frequencies of

these structures should be arranged as a geometric series.

These mechanical structures are connected to a differential

ampliﬁer, and their PNS arranged using a mirror rela-

tionship. The ﬁne tuning of these parameters allows the

desired ﬁlter characteristics to be realized step by step. The

ﬁlter designer can follow the design rules in this paper to

easily construct a MEMS ﬁlter with the desired function-

ality. The MEMS ﬁlter provides not only the advantages of

MEMS technology but also a creative and feasible concept

for acoustic signal processing which represents a viable

alternative to DSP implementations, with advantages of

lower power consumption and shorter computation time.

We ﬁrmly believe that these novel MEMS ﬁlters represent

promising new devices for acoustic signal processing.

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