**Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications**

M. El Hassan, E. Kerherve, Y. Deval, K. Baraka, J.B. David and D. Belot

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/55131

## **1. Introduction**

In telecommunication systems, all filters and resonators that constitute the RF part have the tendency to be integrated on the same chip that contains the information treatment.

In order to achieve miniaturization, bulk acoustic wave (BAW) technology is presented. BAW filters are very sensitive to surface contamination, and can exhibit very small sizes. In addition, BAW resonators could be fabricated using compatible material CMOS and BiCMOS [1]. In this context and in order to compensate the variation due to the fabrication process, the work presented in this paper focuses on the tuning of BAW-SMR resonators and filters.

This work is divided in two parts. The first part consists of designing BAW-SMR (Solidly Mounted Resonator) filters. In the second part, we propose the use of two methods to tune this type of filters. Thus, we present the design methodology, the study, and the experimental realization of the BAW-SMR tunable filters.

## **2. BAW impedance behavior**

## **2.1. SMR impedance behavior**

The bulk acoustic wave resonator is basically constituted by a piezoelectric layer sandwiched between two electrodes (Fig.1). The application of an electric field between the two electrodes generates a mechanical stress that is further propagated through the bulk of the structure (acoustic wave). The resonance condition is established when the acoustical path (in thickness direction) corresponds to odd integer multiples of the half acoustic wavelength. The bulk acoustic wave resonator is basically constituted by a piezoelectric layer sandwiched between two electrodes (Fig.1) [2, 3].

The bulk acoustic wave resonator fabrication over silicon substrates imposes its acoustical isolation, confining the acoustic waves into the main resonant structure. Two configurations are proposed: the membrane suspended structure (FBAR – Film Bulk Acoustic wave Resonator) [3], where the resonator is suspended by an air-bridge (Fig.1a); and the solidlymounted structure (SMR – Solidly Mounted Resonator), where the resonator is mounted over a stack of alternating materials (Fig.1b). This stack is built on a Bragg reflector basis and it has an acoustic mirror behavior [2-3]. Both, air and acoustic mirror, present an optimum discontinuity for reflecting the acoustic waves at the interface with the bottom electrode, confining waves into the main resonant structure.

Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications 423

An important effect of the reflector layers, as demonstrated by Newell [4], is a partial lateral stiffening of the piezoelectric plate that minimizes plate wave generation and spurious resonances normally observed in free plates. However, real resonator structures are inherently 3D and some form of radiation beyond the simple thickness dimension is to be expected. If energy leaves the resonator structure, through radiation, then it counts as a loss mechanism. Reflections of lateral waves at the edge of the resonator can lead to standing waves and spurious responses. The SMR approach requires that the substrate be smooth in order to proceed with the fabrication of reflectors, electrodes, and piezoelectric film [5].

The Modified Butterworth-Van-Dyke (MBVD) model is an electrical schematic around resonance (Fig.2). The elements Ra, La, Ca present the series resonance and the insertion losses. The capacity C0 represents the piezoelectric material between the two electrodes.

The impedance characteristic of a measured BAW-SMR is shown in Fig.3. In this graph, it can be observed that the SMR presents mainly two resonance pulsations: the series resonance (fs), when the electrical impedance approaches to zero, and the parallel resonance (fp), when the electrical impedance approaches to infinity. For all other frequencies far from

**2.2. The Butterworth-Van-Dyke (BVD) model** 

**Figure 3.** Impedance characteristic of a measured BAW-SMR.

**Figure 2.** SMR-MBVD model.

In the solidly mounted resonator (SMR), the piezoelectric is solidly mounted to the substrate (Fig.1.b). Some means must be used to acoustically isolate the piezoelectric from the substrate if a high quality factor (Q) resonance is to be obtained. In effect, the quarter wavelength layers act as a reflector to keep waves confined near the piezoelectric transducer film [4]. The effect of the reflector on mechanical displacement is to cause the wave amplitude to diminish with depth into the reflector. The number of layers required to obtain a satisfactory reflection coefficient is dependent on the mechanical impedances between layers and, to a lesser extent, the substrate [5]. The number of layers is best determined by an analysis of the resonance response as a function of the number of layers versus resonator 'Q' and coupling coefficient.

**Figure 1.** (a) Film Bulk Acoustic Resonator (FBAR). (b) Solidly Mounted Resonator (SMR).

An important effect of the reflector layers, as demonstrated by Newell [4], is a partial lateral stiffening of the piezoelectric plate that minimizes plate wave generation and spurious resonances normally observed in free plates. However, real resonator structures are inherently 3D and some form of radiation beyond the simple thickness dimension is to be expected. If energy leaves the resonator structure, through radiation, then it counts as a loss mechanism. Reflections of lateral waves at the edge of the resonator can lead to standing waves and spurious responses. The SMR approach requires that the substrate be smooth in order to proceed with the fabrication of reflectors, electrodes, and piezoelectric film [5].

#### **2.2. The Butterworth-Van-Dyke (BVD) model**

The Modified Butterworth-Van-Dyke (MBVD) model is an electrical schematic around resonance (Fig.2). The elements Ra, La, Ca present the series resonance and the insertion losses. The capacity C0 represents the piezoelectric material between the two electrodes.

**Figure 2.** SMR-MBVD model.

422 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

confining waves into the main resonant structure.

Substrate

*2 d n* 

'Q' and coupling coefficient.

The bulk acoustic wave resonator fabrication over silicon substrates imposes its acoustical isolation, confining the acoustic waves into the main resonant structure. Two configurations are proposed: the membrane suspended structure (FBAR – Film Bulk Acoustic wave Resonator) [3], where the resonator is suspended by an air-bridge (Fig.1a); and the solidlymounted structure (SMR – Solidly Mounted Resonator), where the resonator is mounted over a stack of alternating materials (Fig.1b). This stack is built on a Bragg reflector basis and it has an acoustic mirror behavior [2-3]. Both, air and acoustic mirror, present an optimum discontinuity for reflecting the acoustic waves at the interface with the bottom electrode,

In the solidly mounted resonator (SMR), the piezoelectric is solidly mounted to the substrate (Fig.1.b). Some means must be used to acoustically isolate the piezoelectric from the substrate if a high quality factor (Q) resonance is to be obtained. In effect, the quarter wavelength layers act as a reflector to keep waves confined near the piezoelectric transducer film [4]. The effect of the reflector on mechanical displacement is to cause the wave amplitude to diminish with depth into the reflector. The number of layers required to obtain a satisfactory reflection coefficient is dependent on the mechanical impedances between layers and, to a lesser extent, the substrate [5]. The number of layers is best determined by an analysis of the resonance response as a function of the number of layers versus resonator

Piezoelectric layer

(a)

(b)

**Figure 1.** (a) Film Bulk Acoustic Resonator (FBAR). (b) Solidly Mounted Resonator (SMR).

Air cavity

support layer Electrodes

The impedance characteristic of a measured BAW-SMR is shown in Fig.3. In this graph, it can be observed that the SMR presents mainly two resonance pulsations: the series resonance (fs), when the electrical impedance approaches to zero, and the parallel resonance (fp), when the electrical impedance approaches to infinity. For all other frequencies far from

**Figure 3.** Impedance characteristic of a measured BAW-SMR.

the resonances, the SMR presents static capacitor behavior. fs is adjusted according to the thickness of the piezoelectric layer and it is spaced by the parallel resonance fp. The instantaneous frequency deviation between the two resonances is determined by the electromechanical coupling coefficient of the piezoelectric layer. The quality factor of the measured BAW-SMR is 192.5 and its active area is 16800 µm2. This relatively small quality factor is due to some technological problems.

The electrical impedance of an SMR is obtained by solving the acoustic boundary problem and applying the transmission line theory [6]. The electrical SMR impedance can be simplified and expressed by the following equation:

$$Z\_{\rm SMR} = \frac{1}{s\mathcal{C}\_0} \frac{\left(f^2 - f\_s^2\right)}{\left(f^2 - f\_p^2\right)}\tag{1}$$

Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications 425

0

*a a*

(3)

(5)

(6)

(4)

*aa aa*

*CCC*

0 0

*C C*

From (2), it is possible to notice the insertion of a pole and zero to the frequency response of the simple resonator. The extraction of the poles and zeroes values of (2), will lead us to (3)

0

1 2

**Figure 4.** Impedance response of the measured BAW-SMR with series capacitor.

2

measured BAW-SMR are shown in Fig.4.

*2.3.1.2. Parallel capacitor association* 

lead us to (5), presented below.

From (3) & (4), it may be noted that the capacitor added in series with the BAW resonator affects only the series resonance frequency. It is inversely proportional to fs. To illustrate this theoretical study, responses with different values of capacitors added in series with the

The analysis of the frequency response of the parallel capacitor associated to the SMR will

2

<sup>2</sup> *<sup>f</sup> s π C L*

*s s L C (C C) C C C a a <sup>a</sup> Yin sLCa a* 

1 1

0 0

*a a*

1

( )

*a f s π CC L C C L*

> 1 2

*a f p π CCL*

& (4) shown below.

where 's' is the complex variable: s = *jw*.

### **2.3. Addition of external passive elements**

The association of external passive components (L, C) to the resonators was made in two parts. First, the resonators analyses have been carried out using on-wafer measurements. Then, these results have been associated with the capacitors and inductors. The combination of experimental results and modeling of passive elements constitutes the final response of the tuned resonators.

#### *2.3.1. Addition of capacitors*

The addition of the capacitors (having an intrinsic quality factor 'Q' > 140) to the SMR circuitry doesn't affect severely the quality factor of the overall design. The resonator's electromechanical coupling coefficient is described indirectly by the capacitor ratio C0/Ca as determined by the resonator physical configuration and piezoelectric material properties [7]. When changing the electromechanical coefficient of the piezoelectric material, the bandwidth changes. Our goal is to tune the capacitor ratio C0/Ca by adding series or parallel capacitors to the resonator. Thus, controlling this ratio will enable us to control the electromechanical coefficient, and as a sequence the bandwidth of the resonator.

#### *2.3.1.1. Series capacitor association*

The performance analysis of the association of series capacitor to the SMR is based on the BVD model (Fig.4). The analysis of the frequency response of the series capacitor associated to the SMR will lead us to (2) presented below:

$$Z\_{in} = \frac{s^2(\mathcal{C}\mathcal{C}\_a L\_a + \mathcal{C}\_0 \mathcal{C}\_a L\_a) + \mathcal{C}\_0 + \mathcal{C}\_a + \mathcal{C}}{s\mathcal{C}(s^2 \mathcal{C}\_0 \mathcal{C}\_a L\_a + \mathcal{C}\_0 + \mathcal{C}\_a)}\tag{2}$$

Where's' is the complex variable: s = *jw*.

From (2), it is possible to notice the insertion of a pole and zero to the frequency response of the simple resonator. The extraction of the poles and zeroes values of (2), will lead us to (3) & (4) shown below.

$$f\_S = \frac{1}{2\pi} \sqrt{\frac{\mathcal{C}\_0 + \mathcal{C}\_a + \mathcal{C}\_a}{\mathcal{C}\mathcal{C}\_a\mathcal{L}\_a + \mathcal{C}\_0\mathcal{C}\_a\mathcal{L}\_a}}\tag{3}$$

$$f\_p = \frac{1}{2\pi} \sqrt{\frac{C\_0 + C\_a}{C\_0 C\_a L\_a}}\tag{4}$$

**Figure 4.** Impedance response of the measured BAW-SMR with series capacitor.

From (3) & (4), it may be noted that the capacitor added in series with the BAW resonator affects only the series resonance frequency. It is inversely proportional to fs. To illustrate this theoretical study, responses with different values of capacitors added in series with the measured BAW-SMR are shown in Fig.4.

#### *2.3.1.2. Parallel capacitor association*

424 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

factor is due to some technological problems.

where 's' is the complex variable: s = *jw*.

the tuned resonators.

*2.3.1. Addition of capacitors* 

*2.3.1.1. Series capacitor association* 

to the SMR will lead us to (2) presented below:

Where's' is the complex variable: s = *jw*.

**2.3. Addition of external passive elements** 

simplified and expressed by the following equation:

the resonances, the SMR presents static capacitor behavior. fs is adjusted according to the thickness of the piezoelectric layer and it is spaced by the parallel resonance fp. The instantaneous frequency deviation between the two resonances is determined by the electromechanical coupling coefficient of the piezoelectric layer. The quality factor of the measured BAW-SMR is 192.5 and its active area is 16800 µm2. This relatively small quality

The electrical impedance of an SMR is obtained by solving the acoustic boundary problem and applying the transmission line theory [6]. The electrical SMR impedance can be

0

The association of external passive components (L, C) to the resonators was made in two parts. First, the resonators analyses have been carried out using on-wafer measurements. Then, these results have been associated with the capacitors and inductors. The combination of experimental results and modeling of passive elements constitutes the final response of

The addition of the capacitors (having an intrinsic quality factor 'Q' > 140) to the SMR circuitry doesn't affect severely the quality factor of the overall design. The resonator's electromechanical coupling coefficient is described indirectly by the capacitor ratio C0/Ca as determined by the resonator physical configuration and piezoelectric material properties [7]. When changing the electromechanical coefficient of the piezoelectric material, the bandwidth changes. Our goal is to tune the capacitor ratio C0/Ca by adding series or parallel capacitors to the resonator. Thus, controlling this ratio will enable us to control the

The performance analysis of the association of series capacitor to the SMR is based on the BVD model (Fig.4). The analysis of the frequency response of the series capacitor associated

0 0

(2)

0 0 ( )

<sup>2</sup>

*s CC L C C L C C C aa aa a Zin sC s C C L C C aa a* 

2

electromechanical coefficient, and as a sequence the bandwidth of the resonator.

*<sup>f</sup> <sup>f</sup> <sup>Z</sup> sC f f*

*SMR*

*p*

(1)

1 ( ) ( ) *s*

> The analysis of the frequency response of the parallel capacitor associated to the SMR will lead us to (5), presented below.

$$Y\_{\rm int} = \frac{s(s^2 L\_d C\_d (C\_0 + C) + C\_0 + C + C\_d)}{s^2 L\_d C\_d + 1} \tag{5}$$

$$f\_S = \frac{1}{2\pi} \sqrt{\frac{1}{C\_a L\_a}}\tag{6}$$

**Figure 5.** Impedance response of the measured BAW-SMR with parallel capacitors.

$$f\_p = \frac{1}{2\pi} \sqrt{\frac{\mathcal{C}\_0 + \mathcal{C}\_a + \mathcal{C}}{L\_a \mathcal{C}\_a (\mathcal{C}\_0 + \mathcal{C})}}\tag{7}$$

Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications 427

From (8), it is possible to notice the insertion of a zero to the resonator frequency response. The extraction of the poles and zeroes values from (8), will bring (9) & (10). Based on these equations, we can see that the values of the poles are not deteriorated. However, from (9), we notice that the association of series inductors to the SMR will modify the zeroes, and

only the series resonance frequency is affected. It is inversely proportional to fs.

**Figure 6.** Impedance response of the measured BAW-SMR with series inductors.

different values of inductors associated in series is shown in Fig.6.

*s CC LL*

2 2

*2.3.2.2. Parallel inductor association* 

(11), will lead us to (12) & (13).

To illustrate this theoretical study, impedance behavior of the measured BAW-SMR with

() 4 <sup>1</sup>

1 2

parallel inductors associated to the SMR will lead us to (11), presented below.

0 0

*sCCLL s CL CL CL a a a aa Yin sL s C La a* 

*a f p C LC*

Based on the same procedure used above, the analysis of the frequency response of the

4 2

From (11), it is possible to notice the insertion of a pole to the resonator frequency response and the displacement of another. Also, we can notice the composition of a double pole near the frequency response of the device. The extraction of the poles and zeroes values from

2

(1 )

*aa a aa a aa <sup>f</sup>*

0 00

*a a*

0

*C L CL C L C L CL C L CC LL*

0

0

*C C*

*a a*

 (9)

2

(10)

1

(11)

From (5), it is possible to notice the displacement of the poles of the device's resonance frequency. The extraction of the poles and zeroes values of (5), will guide us to (6) & (7) as shown below.

It is noticed from (6) & (7) that the capacitor added in parallel with the BAW resonator affects only the parallel resonance frequency. It is inversely proportional to fp. Fig.5 presents the final responses of the measured BAW-SMR with different values of capacitors added in parallel.

#### *2.3.2. Addition of inductors*

The association of inductors to the BAW resonators could be realized in series or parallel. We should note that in the case of VLSI-CMOS, these inductors are characterized by a small quality factor with respect to the BAW (400 to 1000) which degrades the quality factor of the overall circuitry, and they occupy a relatively large size.

#### *2.3.2.1. Series inductor association*

The performance analysis of the assembly of the inductors in series with the SMRs is based on the BVD model. The analysis of the frequency response of the series inductors associated to the SMR will lead us to (8).

$$Z\_{\rm int} = \frac{\mathrm{s}^4 \mathrm{C}\_0 \mathrm{C}\_d L\_d L + \mathrm{s}^2 \left( \mathrm{C}\_d L\_d + \mathrm{C}\_0 L + \mathrm{C}\_d L \right) + 1}{\mathrm{s} \left( \mathrm{s}^2 \mathrm{C}\_d L\_d \mathrm{C}\_0 + \mathrm{C}\_0 + \mathrm{C}\_d \right)} \tag{8}$$

From (8), it is possible to notice the insertion of a zero to the resonator frequency response. The extraction of the poles and zeroes values from (8), will bring (9) & (10). Based on these equations, we can see that the values of the poles are not deteriorated. However, from (9), we notice that the association of series inductors to the SMR will modify the zeroes, and only the series resonance frequency is affected. It is inversely proportional to fs.

**Figure 6.** Impedance response of the measured BAW-SMR with series inductors.

To illustrate this theoretical study, impedance behavior of the measured BAW-SMR with different values of inductors associated in series is shown in Fig.6.

$$f\_S = \frac{1}{2\pi} \sqrt{\frac{(\mathbf{C}\_a L\_a + \mathbf{C}\_0 L + \mathbf{C}\_a L) \pm \sqrt{\left(\mathbf{C}\_a L\_a + \mathbf{C}\_0 L + \mathbf{C}\_a L\right)^2 - 4\mathbf{C}\_0 \mathbf{C}\_a L\_a L}}{2\mathbf{C}\_0 \mathbf{C}\_a L\_a L}}\tag{9}$$

$$f\_p = \frac{1}{2\pi} \sqrt{\frac{C\_0 + C\_a}{C\_a L\_a C\_0}}\tag{10}$$

#### *2.3.2.2. Parallel inductor association*

426 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**Figure 5.** Impedance response of the measured BAW-SMR with parallel capacitors.

shown below.

*2.3.2. Addition of inductors* 

*2.3.2.1. Series inductor association* 

to the SMR will lead us to (8).

overall circuitry, and they occupy a relatively large size.

parallel.

1 2

*a f p π L C (C C) a a* 

0

From (5), it is possible to notice the displacement of the poles of the device's resonance frequency. The extraction of the poles and zeroes values of (5), will guide us to (6) & (7) as

It is noticed from (6) & (7) that the capacitor added in parallel with the BAW resonator affects only the parallel resonance frequency. It is inversely proportional to fp. Fig.5 presents the final responses of the measured BAW-SMR with different values of capacitors added in

The association of inductors to the BAW resonators could be realized in series or parallel. We should note that in the case of VLSI-CMOS, these inductors are characterized by a small quality factor with respect to the BAW (400 to 1000) which degrades the quality factor of the

The performance analysis of the assembly of the inductors in series with the SMRs is based on the BVD model. The analysis of the frequency response of the series inductors associated

> 4 2 0 0 2

*sCCLL s CL CL CL aa aa a Zin ssC LC C C aa a* 

0 0

( )

1

(8)

0

(7)

*CCC*

Based on the same procedure used above, the analysis of the frequency response of the parallel inductors associated to the SMR will lead us to (11), presented below.

$$Y\_{\rm int} = \frac{s^4 C\_0 C\_{d} L\_{d} L + s^2 \left(C\_0 L + C\_{d} L + C\_{d} L\_{d}\right) + 1}{s L (1 + s^2 C\_{d} L\_{d})} \tag{11}$$

From (11), it is possible to notice the insertion of a pole to the resonator frequency response and the displacement of another. Also, we can notice the composition of a double pole near the frequency response of the device. The extraction of the poles and zeroes values from (11), will lead us to (12) & (13).

From (12) & (13), we can see that that the inductor added in parallel with the BAW resonator affects only the parallel resonance frequency. It is inversely proportional to fp. Fig.7 presents the final responses of the measured BAW-SMR with different values of inductors associated in parallel.

**Figure 7.** Impedance response of the measured BAW-SMR with parallel inductors.

$$f\_{p} = \frac{1}{2\pi} \sqrt{\frac{\left(\mathbf{C}\_{0}L + \mathbf{C}\_{a}L + \mathbf{C}\_{a}L\_{a}\right) \pm \sqrt{\left(\mathbf{C}\_{0}L + \mathbf{C}\_{a}L + \mathbf{C}\_{a}L\_{a}\right)^{2} - 4\mathbf{C}\_{0}\mathbf{C}\_{a}L\_{a}L}}{2\mathbf{C}\_{0}\mathbf{C}\_{a}\frac{L}{a}L}}\tag{12}$$

$$f\_s = \frac{1}{2\pi} \sqrt{\frac{1}{C\_a L\_a}}\tag{13}$$

Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications 429

The addition of inductors to the BAW-SMR increases the insertion losses and degrades the quality factor of the overall circuitry. Fig.8 illustrates the influence of inductors added in

Bulk acoustic wave filters are basically divided in three topologies: ladder, lattice and

**Figure 9.** Bulk acoustic wave resonator filter topologies: (a) ladder stage, (b) lattice stage and (c) ladder-

Ladder filter are characterized by an unbalanced operation mode and very small size able to deliver very high selectivity filtering responses, however presenting low rejection or isolation out-of-band. Typically, ladder bulk acoustic wave filters are quite effective for

On the other hand, lattice bulk acoustic wave filters are characterized by a balanced operation mode. In contrast to the first one, this topology presents typically a low selectivity close to the passband, followed by a high rejection out-of-band. They present slower roll off coefficient and higher rejection. Thus, lattice networks are not interesting to block signals

Ladder-lattice bulk acoustic wave filters are also characterized by a balanced operation mode. Ladder-lattice filters ally advantages of both network types, enabling high isolation at undesired bands and steep responses close to the passband [3]. This topology is able to strongly reduce the linearity constraints of the receiver RF chain. Fig.10 shows a comparison between the typical theoretical transmission responses (S21) of these three network types.

blocking signals close to the passband, but poor at rejecting undesired bands [3-4].

close to the passband, but they are more effective for rejecting undesired bands [3].

series with the SMR on the overall quality factor of the assembly.

**3.1. Bulk Acoustic Wave (BAW) filters topologies** 

**3. BAW filter design** 

ladder-lattice (Fig.9) [3].

lattice stage.

**Figure 8.** Impact of the quality factor of the inductors added in series with the BAW resonator on the series quality factor 'Qs' of the overall resonator circuitry (SMR+L).

The addition of inductors to the BAW-SMR increases the insertion losses and degrades the quality factor of the overall circuitry. Fig.8 illustrates the influence of inductors added in series with the SMR on the overall quality factor of the assembly.

## **3. BAW filter design**

428 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**Figure 7.** Impedance response of the measured BAW-SMR with parallel inductors.

2 2

157

137

192.5

0

50

100

**Quality Factors**

 Quality Factor 150

200

series quality factor 'Qs' of the overall resonator circuitry (SMR+L).

*p CCLL*

<sup>2</sup> *<sup>f</sup> s C L*

<sup>4</sup> <sup>1</sup>

*a aa a aa aa <sup>f</sup>*

122

98

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 **Inductors (nH)**

Inductors (nH)

**Figure 8.** Impact of the quality factor of the inductors added in series with the BAW resonator on the

000

*CL CL CL CL CL CL CCLL*

*a a*

*a a*

(12)

0

1 1

2

(13)

62

47 34

76

in parallel.

From (12) & (13), we can see that that the inductor added in parallel with the BAW resonator affects only the parallel resonance frequency. It is inversely proportional to fp. Fig.7 presents the final responses of the measured BAW-SMR with different values of inductors associated

## **3.1. Bulk Acoustic Wave (BAW) filters topologies**

Bulk acoustic wave filters are basically divided in three topologies: ladder, lattice and ladder-lattice (Fig.9) [3].

**Figure 9.** Bulk acoustic wave resonator filter topologies: (a) ladder stage, (b) lattice stage and (c) ladderlattice stage.

Ladder filter are characterized by an unbalanced operation mode and very small size able to deliver very high selectivity filtering responses, however presenting low rejection or isolation out-of-band. Typically, ladder bulk acoustic wave filters are quite effective for blocking signals close to the passband, but poor at rejecting undesired bands [3-4].

On the other hand, lattice bulk acoustic wave filters are characterized by a balanced operation mode. In contrast to the first one, this topology presents typically a low selectivity close to the passband, followed by a high rejection out-of-band. They present slower roll off coefficient and higher rejection. Thus, lattice networks are not interesting to block signals close to the passband, but they are more effective for rejecting undesired bands [3].

Ladder-lattice bulk acoustic wave filters are also characterized by a balanced operation mode. Ladder-lattice filters ally advantages of both network types, enabling high isolation at undesired bands and steep responses close to the passband [3]. This topology is able to strongly reduce the linearity constraints of the receiver RF chain. Fig.10 shows a comparison between the typical theoretical transmission responses (S21) of these three network types.

Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications 431

The acoustical performance of the fully dielectric stack is comparable to the traditional SiO2- W reflectors; however, it strongly reduces the coupling between resonators through the Bragg reflector. Furthermore, the filter stack was realized on a high resistive silicon

In order to optimize the filter performance, a double resonator and apodized geometries have been used. Indeed, double resonators present large electrodes' areas, which results in lower resistive losses. Also, the filter resonators present apodized geometries in order to avoid spurious resonances caused by the parasitic lateral acoustic modes [11]. Fig.11 and 12 show the microphotography and a comparison between the measured and simulated results of the tunable ladder BAW-SMR filter, respectively. The filter occupies a small area and has reduced dimensions (1035\*1075 µm2). Electromagnetic simulation of the overall filter structure has been performed using the ADS-Momentum software. Next, the acoustical effects have been considered using the Mason Model [12] and included in the simulations.

**Figure 12.** Comparison between measured and simulated results of the 802.11b/g ladder BAW-SMR

The filter design was realized for implementation in SiP context. The performances of the tunable BAW-SMR filter are in concordance with the simulation results. Mainly, the filter fulfills the requirements for the WLAN 802.11 b/g standard, presenting -3.3 dB of insertion loss, -12.7 dB of return loss and a selectivity higher than 33 dB at ± 30 MHz of the bandwidth. The filter high insertion losses are mainly due to the low resonators quality factor obtained in the fabrication (Q = 200). Therefore, these losses can be strongly reduced using mechanical energy concentration techniques in the resonator acoustical cavity [13].

The shunt resonators of the ladder filter determine the position of the zeroes at the left of the center frequency and the series resonators determine the position of the zeroes at the right of

filter.

**4. Tunability of the ladder filter** 

substrate in order to reduce losses due to the capacitive coupling [10].

**Figure 10.** Theoretical transmission responses for main bulk acoustic wave (BAW) filter topologies.

#### **3.2. Ladder BAW-SMR filter design**

The ladder filter is an association of resonators in series and in parallel. The shunt resonators are loaded and their resonance frequencies are smaller than the series resonators. Ladder BAW topology presents a good selectivity which enables to block undesired signals near the pass band. In this context, and in order to support the theoretical study, a tunable BAW-SMR ladder filter was designed for the 802.11b/g standard (2.40 – 2.48 GHz). The resonators and filters were fabricated at the CEA-Leti in the framework of the project '*EPADIM*'. The filter is composed of five SMRs, associated in ladder topology. The filter stack can be divided into resonators' layers and Bragg reflector's layers. The resonator's layers are composed by the classical couple AlN-Mo [8]. However, in contrast to [8], the Bragg reflector was implemented using an exclusive dielectric stack composed by SiOC:H and SixNy [9].

**Figure 11.** Microphotography of the Ladder BAW-SMR for the 802.11b/g standard.

The acoustical performance of the fully dielectric stack is comparable to the traditional SiO2- W reflectors; however, it strongly reduces the coupling between resonators through the Bragg reflector. Furthermore, the filter stack was realized on a high resistive silicon substrate in order to reduce losses due to the capacitive coupling [10].

In order to optimize the filter performance, a double resonator and apodized geometries have been used. Indeed, double resonators present large electrodes' areas, which results in lower resistive losses. Also, the filter resonators present apodized geometries in order to avoid spurious resonances caused by the parasitic lateral acoustic modes [11]. Fig.11 and 12 show the microphotography and a comparison between the measured and simulated results of the tunable ladder BAW-SMR filter, respectively. The filter occupies a small area and has reduced dimensions (1035\*1075 µm2). Electromagnetic simulation of the overall filter structure has been performed using the ADS-Momentum software. Next, the acoustical effects have been considered using the Mason Model [12] and included in the simulations.

**Figure 12.** Comparison between measured and simulated results of the 802.11b/g ladder BAW-SMR filter.

The filter design was realized for implementation in SiP context. The performances of the tunable BAW-SMR filter are in concordance with the simulation results. Mainly, the filter fulfills the requirements for the WLAN 802.11 b/g standard, presenting -3.3 dB of insertion loss, -12.7 dB of return loss and a selectivity higher than 33 dB at ± 30 MHz of the bandwidth. The filter high insertion losses are mainly due to the low resonators quality factor obtained in the fabrication (Q = 200). Therefore, these losses can be strongly reduced using mechanical energy concentration techniques in the resonator acoustical cavity [13].

### **4. Tunability of the ladder filter**

430 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**Figure 10.** Theoretical transmission responses for main bulk acoustic wave (BAW) filter topologies.

The ladder filter is an association of resonators in series and in parallel. The shunt resonators are loaded and their resonance frequencies are smaller than the series resonators. Ladder BAW topology presents a good selectivity which enables to block undesired signals near the pass band. In this context, and in order to support the theoretical study, a tunable BAW-SMR ladder filter was designed for the 802.11b/g standard (2.40 – 2.48 GHz). The resonators and filters were fabricated at the CEA-Leti in the framework of the project '*EPADIM*'. The filter is composed of five SMRs, associated in ladder topology. The filter stack can be divided into resonators' layers and Bragg reflector's layers. The resonator's layers are composed by the classical couple AlN-Mo [8]. However, in contrast to [8], the Bragg reflector was implemented

using an exclusive dielectric stack composed by SiOC:H and SixNy [9].

**Figure 11.** Microphotography of the Ladder BAW-SMR for the 802.11b/g standard.

**3.2. Ladder BAW-SMR filter design** 

The shunt resonators of the ladder filter determine the position of the zeroes at the left of the center frequency and the series resonators determine the position of the zeroes at the right of

the center frequency. Thus, changing the impedance of the parallel and series resonators leads to a change in the zeroes' positions.

Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications 433

L2=5.6 nH 40 L3=4.7 nH 45

**Table 1.** Values of the passive elements used to shift the center frequency of the tunable BAW-SMR

The tunable BAW-SMR filter and the passive components are mounted on a FR4 substrate

Fig.16 shows the simulation results of the tunable filter. The insertion loss (IL = -2.4 dB) obtained in the simulation is due to quality factors of resonators (Q = 500). The return loss (RL) is -10 dB, and the out of band rejection is 26 dB at 2.0 GHz. The simulation results

**Figure 16.** Simulation of tunable BAW filter with inductors added in parallel with the series resonators

Comparisons between the measurements of the tunable filter with the original one are

and capacitors added in series with the shunt resonators.

shown in Fig.17 and Fig.18.

Capacitors C1= C2=2.2 pF 140 Inductors L1=3.9 nH 47.7

**Figure 15.** Tunable BAW-SMR filter and passive elements mounted on FR4 PCB.

shows that a shift of +1% of the initial central frequency (2.44 GHz) is obtained.

filter towards higher frequencies and their quality factors.

as shown in Fig.15.

Value Quality Factor 'Q'

**Figure 13.** Ladder BAW-SMR filter.

Based on this theory and in order to tune the BAW-SMR filter (Fig.13), we propose to add passive elements to the shunt and series resonators that constitute the filter.

## **4.1. Shift towards higher frequencies**

To shift the center frequency of the filter towards higher frequencies we have to move all the zeroes towards these frequencies. Thus, we have added inductors in parallel with the series resonators and capacitors in series with the shunt resonators that constitute the ladder BAW-SMR filter (Fig.14).

**Figure 14.** Tunable BAW-SMR filter with inductors added in parallel with the series resonators and capacitors added in series with the shunt resonators.

Table 1 presents the values and the quality factor of the external passive elements used in the circuitry designed to move the center frequency of the tunable BAW-SMR filter towards higher frequencies.



**Table 1.** Values of the passive elements used to shift the center frequency of the tunable BAW-SMR filter towards higher frequencies and their quality factors.

The tunable BAW-SMR filter and the passive components are mounted on a FR4 substrate as shown in Fig.15.

**Figure 15.** Tunable BAW-SMR filter and passive elements mounted on FR4 PCB.

432 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

leads to a change in the zeroes' positions.

**Figure 13.** Ladder BAW-SMR filter.

BAW-SMR filter (Fig.14).

higher frequencies.

**4.1. Shift towards higher frequencies** 

capacitors added in series with the shunt resonators.

the center frequency. Thus, changing the impedance of the parallel and series resonators

Based on this theory and in order to tune the BAW-SMR filter (Fig.13), we propose to add

To shift the center frequency of the filter towards higher frequencies we have to move all the zeroes towards these frequencies. Thus, we have added inductors in parallel with the series resonators and capacitors in series with the shunt resonators that constitute the ladder

**Figure 14.** Tunable BAW-SMR filter with inductors added in parallel with the series resonators and

Table 1 presents the values and the quality factor of the external passive elements used in the circuitry designed to move the center frequency of the tunable BAW-SMR filter towards

passive elements to the shunt and series resonators that constitute the filter.

Fig.16 shows the simulation results of the tunable filter. The insertion loss (IL = -2.4 dB) obtained in the simulation is due to quality factors of resonators (Q = 500). The return loss (RL) is -10 dB, and the out of band rejection is 26 dB at 2.0 GHz. The simulation results shows that a shift of +1% of the initial central frequency (2.44 GHz) is obtained.

**Figure 16.** Simulation of tunable BAW filter with inductors added in parallel with the series resonators and capacitors added in series with the shunt resonators.

Comparisons between the measurements of the tunable filter with the original one are shown in Fig.17 and Fig.18.

Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications 435

Lbond

This time and in order to shift the center frequency of the filter towards lower frequencies,

Lbond

**Figure 19.** Tunable BAW-SMR filter with capacitors added in parallel with the series resonators and

**Table 2.** Values of the passive elements used to shift the center frequency of the tunable BAW-SMR

As same as before, the tunable BAW-SMR filter and the passive components are mounted

The insertion loss (IL = -2.4 dB) obtained by simulation is due to quality factors of resonators (Q = 500). In addition the return loss (RL) is -9.5 dB, and the out of band rejection is 16 dB at 2.0 GHz (Fig.20). The simulation results shows that a shift of -1% of the initial central frequency (2.44 GHz) is obtained. A comparison between the measurements of the tunable

Based on the measurements of the tunable filter, we can note -4.5 dB of insertion losses and a shift of -1.3% of the center frequency (2.44 GHz) towards the lower frequencies (Fig.21). In addition, the parasitic capacitors generated by the FR4 PCB and the bonding wires used to connect the tunable filter with the passive elements caused a reduction of 13 MHz to the

presents the values and the quality factor of the external passive elements used.

Capacitors C1=2.2 pF 140

Inductors L1=L2=2.2 nH 57

on a FR4 substrate. Fig.20 shows the simulation results of the tunable filter.

Thus, we have added capacitors in parallel with the series resonators and inductors in series with the shunt resonators that constitute the ladder BAW-SMR filter (Fig.19). Table 2

> C2=1 pF 200 C3=2 pf 150

Value Quality Factor 'Q'

**4.2. Shift towards lower frequencies** 

inductors added in series with the shunt resonators.

filter towards lower frequencies and their quality factors.

filter with the original one is shown in Fig.21.

bandwidth of the tunable filter.

we have to move all the zeroes towards these frequencies.

**Figure 17.** Shift towards higher frequencies: Comparison of transmission characteristic (S21)between the tunable BAW-SMR filter (passive elements added) and the original one.

Based on the measurements of the tunable filter, we can note -4.5 dB of insertion losses and a shift of +0.6% of the center frequency (2.44 GHz) towards the higher frequencies (Fig.17). As well, a return loss of -7 dB is obtained (Fig.18). The filter high insertion losses are mainly due to the low resonators quality factor obtained in the fabrication (Q = 200) and to the low quality factor of the passive element used. Moreover, the parasitic capacitors generated by the FR4 PCB and the bonding wires used to connect the tunable filter with the passive elements caused a reduction of 15 MHz to the bandwidth of the tunable filter.

**Figure 18.** Shift towards higher frequencies: Comparison of reflexion characteristic (S11) between the tunable BAW-SMR filter (passive elements added) and the original one.

## **4.2. Shift towards lower frequencies**

434 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

tunable BAW-SMR filter (passive elements added) and the original one.

**Figure 17.** Shift towards higher frequencies: Comparison of transmission characteristic (S21)between the

Based on the measurements of the tunable filter, we can note -4.5 dB of insertion losses and a shift of +0.6% of the center frequency (2.44 GHz) towards the higher frequencies (Fig.17). As well, a return loss of -7 dB is obtained (Fig.18). The filter high insertion losses are mainly due to the low resonators quality factor obtained in the fabrication (Q = 200) and to the low quality factor of the passive element used. Moreover, the parasitic capacitors generated by the FR4 PCB and the bonding wires used to connect the tunable filter with the passive

**Figure 18.** Shift towards higher frequencies: Comparison of reflexion characteristic (S11) between the

tunable BAW-SMR filter (passive elements added) and the original one.

elements caused a reduction of 15 MHz to the bandwidth of the tunable filter.

This time and in order to shift the center frequency of the filter towards lower frequencies, we have to move all the zeroes towards these frequencies.

**Figure 19.** Tunable BAW-SMR filter with capacitors added in parallel with the series resonators and inductors added in series with the shunt resonators.

Thus, we have added capacitors in parallel with the series resonators and inductors in series with the shunt resonators that constitute the ladder BAW-SMR filter (Fig.19). Table 2 presents the values and the quality factor of the external passive elements used.


**Table 2.** Values of the passive elements used to shift the center frequency of the tunable BAW-SMR filter towards lower frequencies and their quality factors.

As same as before, the tunable BAW-SMR filter and the passive components are mounted on a FR4 substrate. Fig.20 shows the simulation results of the tunable filter.

The insertion loss (IL = -2.4 dB) obtained by simulation is due to quality factors of resonators (Q = 500). In addition the return loss (RL) is -9.5 dB, and the out of band rejection is 16 dB at 2.0 GHz (Fig.20). The simulation results shows that a shift of -1% of the initial central frequency (2.44 GHz) is obtained. A comparison between the measurements of the tunable filter with the original one is shown in Fig.21.

Based on the measurements of the tunable filter, we can note -4.5 dB of insertion losses and a shift of -1.3% of the center frequency (2.44 GHz) towards the lower frequencies (Fig.21). In addition, the parasitic capacitors generated by the FR4 PCB and the bonding wires used to connect the tunable filter with the passive elements caused a reduction of 13 MHz to the bandwidth of the tunable filter.

Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications 437

When a transistor is ON, the capacitor is short circuited, and when a transistor is OFF, the capacitor will be considered in series with the shunt resonator. Thus, the bandwidth and the characteristics of the filter will be modified. The circuitry of the filter, capacitors, transistors

The BAW-SMR filter used in this study is a fifth order filter designed for the W-CDMA standard in the ladder topology. This topology is composed by the resonator in series and parallel, the parallel resonators are loaded and their resonance frequencies are smaller than the series resonators. The die photography of the tunable BAW-SMR filter is shown in Fig.23. The filter has reduced size, and the die area is 1450\*985 µm². Moreover, many

passive pads connecting the filter with the active chip were taken in consideration.

**Figure 23.** Microphotography of ladder BAW-SMR for the W-CDMA standard.

Fig.24 presents the comparison between the measurement and the simulation of the BAW-SMR filter. Electromagnetic simulation of the overall filter structure has been accomplished by using the ADS-Momentum software, where the acoustical effects have been included using the Mason Model. The filter is designed for implementation in SiP context. As shown

and the associated "bonding wires" are shown in Fig.22.

**Figure 22.** Tunable BAW-SMR using CMOS transistors.

**Figure 20.** Simulation of tunable BAW filter with capacitors added in parallel with the series resonators and inductors added in series with the shunt resonators.

**Figure 21.** Shift towards lower frequencies: Comparison between the tunable BAW-SMR filter (passive elements added) and the original one.

As a conclusion, one should note that in contrast to [13], where lumped elements (inductors or capacitors) were proposed to be added at a time, in this paper the use of capacitors and inductors together have shown how to shift the center frequencies towards higher or lower frequencies.

### **5. Digitally tuning BAW filters**

To validate the concept of digitally tuning BAW filters using passive elements controlled by CMOS transistors, we present in this part the use of CMOS switches at the terminals of capacitors (Fig.22) [6].

When a transistor is ON, the capacitor is short circuited, and when a transistor is OFF, the capacitor will be considered in series with the shunt resonator. Thus, the bandwidth and the characteristics of the filter will be modified. The circuitry of the filter, capacitors, transistors and the associated "bonding wires" are shown in Fig.22.

**Figure 22.** Tunable BAW-SMR using CMOS transistors.

436 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

and inductors added in series with the shunt resonators.

elements added) and the original one.

**5. Digitally tuning BAW filters** 

frequencies.

capacitors (Fig.22) [6].

**Figure 20.** Simulation of tunable BAW filter with capacitors added in parallel with the series resonators

**Figure 21.** Shift towards lower frequencies: Comparison between the tunable BAW-SMR filter (passive

As a conclusion, one should note that in contrast to [13], where lumped elements (inductors or capacitors) were proposed to be added at a time, in this paper the use of capacitors and inductors together have shown how to shift the center frequencies towards higher or lower

To validate the concept of digitally tuning BAW filters using passive elements controlled by CMOS transistors, we present in this part the use of CMOS switches at the terminals of The BAW-SMR filter used in this study is a fifth order filter designed for the W-CDMA standard in the ladder topology. This topology is composed by the resonator in series and parallel, the parallel resonators are loaded and their resonance frequencies are smaller than the series resonators. The die photography of the tunable BAW-SMR filter is shown in Fig.23. The filter has reduced size, and the die area is 1450\*985 µm². Moreover, many passive pads connecting the filter with the active chip were taken in consideration.

**Figure 23.** Microphotography of ladder BAW-SMR for the W-CDMA standard.

Fig.24 presents the comparison between the measurement and the simulation of the BAW-SMR filter. Electromagnetic simulation of the overall filter structure has been accomplished by using the ADS-Momentum software, where the acoustical effects have been included using the Mason Model. The filter is designed for implementation in SiP context. As shown

in Fig.24, the measurements are in concordance with the simulations. However, the filter fulfills the requirements for the W-CDMA standard, exhibiting -2.77 dB of insertion loss, - 8.75 dB of return loss and selectivity higher than 38 dB at 40MHz offset from the operating frequency.

Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications 439

Fig.26 shows the layout of the tuning circuit. In symbolize the pad for connection with ladder filter. VG, Vdd1, Vdd2 and GND correspond to the gate voltage, the command of

The tuning is attained by controlling the MOS transistors and capacitors in series with shunt resonators. Each transistor is open or short circuited by obtaining different outputs of the 2 to 4 decoder. Table 3 shows the truth table of the realized decoder. A, B, E symbolize the input of a decoder commanded by Vdd1, Vdd2 and VG respectively, Sn (n = 0, 1, 2 or 3) represent the output of this decoder used to control Qn. All transistors used in the tuning mechanism are provided by STMicroelectronics (CMOS 65 nm). The width and length of the gate are: W = 50 µm and L = 0.06 µm. The main parasitic elements are taken into account in the simulation (Cgs, Cgd, Cds and Ron). The length of bonding wire is 2 mm. It represents an inductive effect of approximately 2 nH at 2 GHz. Ron of the MOS transistor is function of its dimensions and of the gate voltage (VG). Thus, with an external adjustment of VG, Ron value

A B E S0 S1 S2 S3

0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 X X 0 0 0 0 0

Fig.27 shows the microphotography of the association of the ladder filter with the active chip. The devices are connected with bonding wires. The capacitors C1, C2 and C3 values are

0 1 0 0 0 1

decoder and the ground respectively. The size of the Silicon area is 335\*330µm².

**Figure 26.** Layout of the tuning mechanism.

**Table 3.** Truth table of the 2 to 4 decoder.

**5.2. Co-design: BAW filter- 65nm CMOS chip** 

is regulated.

**Figure 24.** Simulation and measurement results of the W-CDMA ladder BAW-SMR filter.

## **5.1. Switches design**

To adjust the bandwidth of the BAW filter, a chip is realized in 65nm CMOS technology. This chip is composed by the capacitors mounted in series with the MOS transistor, and these transistors are controlled by a 2 to 4 decoder (Fig.25).

**Figure 25.** Circuitry of the tuning mechanism.

Fig.26 shows the layout of the tuning circuit. In symbolize the pad for connection with ladder filter. VG, Vdd1, Vdd2 and GND correspond to the gate voltage, the command of decoder and the ground respectively. The size of the Silicon area is 335\*330µm².

**Figure 26.** Layout of the tuning mechanism.

438 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**Figure 24.** Simulation and measurement results of the W-CDMA ladder BAW-SMR filter.

these transistors are controlled by a 2 to 4 decoder (Fig.25).

**Figure 25.** Circuitry of the tuning mechanism.

To adjust the bandwidth of the BAW filter, a chip is realized in 65nm CMOS technology. This chip is composed by the capacitors mounted in series with the MOS transistor, and

frequency.

**5.1. Switches design** 

in Fig.24, the measurements are in concordance with the simulations. However, the filter fulfills the requirements for the W-CDMA standard, exhibiting -2.77 dB of insertion loss, - 8.75 dB of return loss and selectivity higher than 38 dB at 40MHz offset from the operating

> The tuning is attained by controlling the MOS transistors and capacitors in series with shunt resonators. Each transistor is open or short circuited by obtaining different outputs of the 2 to 4 decoder. Table 3 shows the truth table of the realized decoder. A, B, E symbolize the input of a decoder commanded by Vdd1, Vdd2 and VG respectively, Sn (n = 0, 1, 2 or 3) represent the output of this decoder used to control Qn. All transistors used in the tuning mechanism are provided by STMicroelectronics (CMOS 65 nm). The width and length of the gate are: W = 50 µm and L = 0.06 µm. The main parasitic elements are taken into account in the simulation (Cgs, Cgd, Cds and Ron). The length of bonding wire is 2 mm. It represents an inductive effect of approximately 2 nH at 2 GHz. Ron of the MOS transistor is function of its dimensions and of the gate voltage (VG). Thus, with an external adjustment of VG, Ron value is regulated.


**Table 3.** Truth table of the 2 to 4 decoder.

## **5.2. Co-design: BAW filter- 65nm CMOS chip**

Fig.27 shows the microphotography of the association of the ladder filter with the active chip. The devices are connected with bonding wires. The capacitors C1, C2 and C3 values are

fixed to achieve 12, 9 and 6 MHz tuning range, respectively. When the output S0 of the decoder is ON, the transistor Q0 is ON and all of the capacitors are short circuited. When the output Sn (n = 1, 2 or 3) is ON, the transistor Qn is ON and the capacitor Cn will be considered in series with the shunt resonators.

Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications 441

In this paper, the impedance behavior of the BAW-SMR has been shown. Also, the effects of the addition of passive elements (L, C) to this type of resonators have been illustrated. In addition, a tunable BAW-SMR filter realized in a ladder topology used for the 802.11b/g standard (2.40 - 2.48 GHz) was shown. Mainly, the filter fulfilled the requirements for the WLAN 802.11 b/g standard, presenting a measured -3.3 dB of insertion loss, -12.7 dB of return loss and selectivity higher than 33 dB @ ± 30 MHz of the bandwidth. This tunable BAW-SMR filter has reduced dimensions (1035\*1075 µm2). Moreover, the center frequency of this tunable filter was shifted towards higher and lower frequencies by adding passive elements. Measured shifts of -1.3% of the center frequency (2.44 GHz) towards lower frequency and +0.6% of the center frequency towards higher frequencies were obtained. Furthermore, digitally tunable BAW-SMR filter implementation was shown. The tunable filter was designed for the W-CDMA standard. The filter fulfilled the requirements for the WCDMA standard, presenting a measured -2.77 dB of insertion loss, -8.75 dB of return loss and selectivity higher than 38 dB @ ±40 MHz of the bandwidth. Moreover, the center frequency of this tunable filter is digitally shifted towards higher frequencies by adding capacitors in series with transistors that act as switches. These switches are controlled by a

2to4 decoder, and they are added to the shunt resonators.

*IMS Laboratory – UMR 5218 CNRS – University of Bordeaux, France* 

are acknowledged for the technology access and filter fabrication.

Applications", *IEEE MTT-S*, pp.367–370, 2001.

IMS laboratory is acknowledged for all facilities offered and the access to obtain the filter measurements. Also, CEA-LETI (Grenoble, France) and STMicroelectronics (Crolles, France)

[1] Bradley, P. et al. "A Film acoustic bulk resonator (SMR) duplexer for USPCS Handset

*University of Balamand –Al Kura, Lebanon* 

E. Kerherve, Y. Deval and K. Baraka

*CEA-Leti – Minatec – Grenoble, France* 

*ST Microectronics – Crolles, France* 

**Acknowledgement** 

**7. References** 

**6. Conclusion** 

**Author details** 

M. El Hassan

J.B. David

D. Belot

**Figure 27.** Microphotography of the digitally tunable ladder BAW-SMR for the W-CDMA standard.

The comparison between the simulation and the measurement results is shown in Fig.28. of the tunable BAW-SMR filter combined with the active chip presents a tuning range of 12 MHz, when the output S3 of the decoder is ON. It show also -1.52 dB of insertion loss and 12 dB of the out-band rejection at 1.85 GHz. This out-band rejection is improved by 3 dB. This degradation is due to the length of bonding wire associating the active chip and PCB [10].

**Figure 28.** Comparison between the simulation and the measurement of the digitally tunable BAW filter.

## **6. Conclusion**

440 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

in series with the shunt resonators.

filter.

fixed to achieve 12, 9 and 6 MHz tuning range, respectively. When the output S0 of the decoder is ON, the transistor Q0 is ON and all of the capacitors are short circuited. When the output Sn (n = 1, 2 or 3) is ON, the transistor Qn is ON and the capacitor Cn will be considered

**Figure 27.** Microphotography of the digitally tunable ladder BAW-SMR for the W-CDMA standard.

**Figure 28.** Comparison between the simulation and the measurement of the digitally tunable BAW

The comparison between the simulation and the measurement results is shown in Fig.28. of the tunable BAW-SMR filter combined with the active chip presents a tuning range of 12 MHz, when the output S3 of the decoder is ON. It show also -1.52 dB of insertion loss and 12 dB of the out-band rejection at 1.85 GHz. This out-band rejection is improved by 3 dB. This degradation is due to the length of bonding wire associating the active chip and PCB [10].

In this paper, the impedance behavior of the BAW-SMR has been shown. Also, the effects of the addition of passive elements (L, C) to this type of resonators have been illustrated. In addition, a tunable BAW-SMR filter realized in a ladder topology used for the 802.11b/g standard (2.40 - 2.48 GHz) was shown. Mainly, the filter fulfilled the requirements for the WLAN 802.11 b/g standard, presenting a measured -3.3 dB of insertion loss, -12.7 dB of return loss and selectivity higher than 33 dB @ ± 30 MHz of the bandwidth. This tunable BAW-SMR filter has reduced dimensions (1035\*1075 µm2). Moreover, the center frequency of this tunable filter was shifted towards higher and lower frequencies by adding passive elements. Measured shifts of -1.3% of the center frequency (2.44 GHz) towards lower frequency and +0.6% of the center frequency towards higher frequencies were obtained. Furthermore, digitally tunable BAW-SMR filter implementation was shown. The tunable filter was designed for the W-CDMA standard. The filter fulfilled the requirements for the WCDMA standard, presenting a measured -2.77 dB of insertion loss, -8.75 dB of return loss and selectivity higher than 38 dB @ ±40 MHz of the bandwidth. Moreover, the center frequency of this tunable filter is digitally shifted towards higher frequencies by adding capacitors in series with transistors that act as switches. These switches are controlled by a 2to4 decoder, and they are added to the shunt resonators.

## **Author details**

M. El Hassan *University of Balamand –Al Kura, Lebanon* 

E. Kerherve, Y. Deval and K. Baraka *IMS Laboratory – UMR 5218 CNRS – University of Bordeaux, France* 

J.B. David *CEA-Leti – Minatec – Grenoble, France* 

D. Belot *ST Microectronics – Crolles, France* 

## **Acknowledgement**

IMS laboratory is acknowledged for all facilities offered and the access to obtain the filter measurements. Also, CEA-LETI (Grenoble, France) and STMicroelectronics (Crolles, France) are acknowledged for the technology access and filter fabrication.

## **7. References**

[1] Bradley, P. et al. "A Film acoustic bulk resonator (SMR) duplexer for USPCS Handset Applications", *IEEE MTT-S*, pp.367–370, 2001.

	- [2] Carpentier, J. F. et al. "A SiGe:C BICMOS WCDMA zero-IF RF front-end using an above-IC BAW filter", *IEEE ISSCC,* 2005, pp. 394-395.

**Chapter 19** 

© 2013 Filipiak and Steczko, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Filipiak and Steczko, licensee InTech. This is a paper distributed under the terms of the Creative Commons

The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Seismic Vibration Sensor** 

Jerzy Filipiak and Grzegorz Steczko

http://dx.doi.org/10.5772/55445

**1. Introduction** 

with vibration sensors.

piezoelectric acceleration sensors,

geophones,

At present practically three types of seismic sensors are used:

micro-mechanical silicone acceleration sensors.

**with Acoustic Surface Wave** 

Additional information is available at the end of the chapter

Mechanical vibrations are a movement of particles around the state of equilibrium in a solid environment. Vibrations are a common phenomenon in our daily life. These vibrations are often parasite effects threatening our existence. Vibrations of the ground, machines, or a number of technical devices present a process, which require a continuous or a long-term

Mechanical vibrations serve as a source of information in medicine, diagnostics of the structure of many machines and in perimeter protection (monitoring). The knowledge of vibration parameters allows evaluating the technical condition of machines, the quality of their design and manufacture and their reliability. Early detection of ground vibrations serves to predict and warn of earthquakes. Ground vibrations serve to monitor explosions and are used in the reflexive seismology (prospecting for mineral deposits). Detection of ground vibrations in systems of perimeter protection allows detecting an intrusion into an area under surveillance. Mechanical vibrations are characteristic for their differing frequencies and amplitude. The frequency of mechanical vibrations ranges usually from a hundredth of Hz to a dozen or so kHz. Parameters of mechanical vibrations are measured

Geophones belong to the simplest and most inexpensive vibration sensors. They feature a low mechanical resonance frequency, which ranges usually between 4Hz and 14Hz. They

and reproduction in any medium, provided the original work is properly cited.

monitoring. In many sectors vibrations are a working factor in a production process.


## **Chapter 19**

## **Seismic Vibration Sensor with Acoustic Surface Wave**

Jerzy Filipiak and Grzegorz Steczko

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/55445

## **1. Introduction**

442 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

piezoelectric resonators", Proc. IEEE, Vol 53, June 1965, pp.575-581.

above-IC BAW filter", *IEEE ISSCC,* 2005, pp. 394-395.

GA, USA, pp.827-831, October 9, 2001.

*UFFC Symposium*, Honolulu, Hawaii, pp. 174-177, 2003.

*Proceedings*, Maastricht, Netherlands, pp. 186-190, 2006.

581.

1993.

pp. 93-96, 2005.

Jersey, Van Nostrand, 1948.

[2] Carpentier, J. F. et al. "A SiGe:C BICMOS WCDMA zero-IF RF front-end using an

[3] Shirakawa, A. A. Jarry, P. Pham, J-M. Kerherve, E. Dumont, F. David, J-B. Cathelin, A. "Ladder-Lattice Bulk Acoustic Wave Filters: Concepts, Design and Implementation", *RF and Microwave Computer Aided Engineering*, 2007.Newell, "Face-mounted

[4] Newell, "Face-mounted piezoelectric resonators", Proc. IEEE, Vol 53, June 1965, pp.575-

[5] Lakin, K.M. Kline, G. McCarron, K.T. "High-Q microwave acoustic resonators and filter", *IEEE Trans. On Microwave Theory and Techniques*, vol. 41, pp. 2139-2146, Dec.

[6] Lakin, K.M. Belsick, J. McDonald, J.F. McCarron, K.T. "Improved bulk wave resonator coupling coefficient for wide bandwidth filters", *IEEE Ultrasonics Symposium*, Atlanta,

[7] Fattinger G. G. et al. "Thin Film Bulk Wave Devices for Applications at 5.2 GHz", *IEEE* 

[8] Ancey, P. "Above IC RF MEMS and BAW filters: fact or fiction", *IEEE BCTM* 

[9] Shirakawa, A. A. Pham, J-M. Jarry, P. Kerherve, E. Dumont, F. David, J-B. Cathelin, A."A High Isolation and High Selectivity Ladder-Lattice BAW-SMR Filter", *36th European Microwave Conference,* 2006, Manchester, UK, pp. 905 – 908, 10-15 September. [10] Tsutsumi, J. Iwaki, M. Iwamoto, Y. Yokoyama, T. Sakashita, T. Nishihara, T. Ueda, M. Satoh, Y. "A Miniaturized FBAR Duplexer with Reduced Acoustic Loss for the W-CDMA Application", *IEEE Ultrasonics Symposium Proceedings,* Rotterdam, Netherlands,

[11] Lakin, K. M. Lakin, K. G. "Numerical Analysis of Thin Film BAW Resonators", *Proceedings of Ultrasonics Symposium*, Honolulu, Hawaii, Vol. 1, pp. 74-79, 2003. [12] Mason, W. P. "Electromechanical Transducers and Wave Filters", Princeton, New

[13] El Hassan, M. Kerherve, E. Deval, Y. David, J.B. Belot, D. "Reconfiguration of Bulk Acoustic Wave Filters Using CMOS Transistors: Concept, Design and Implementation", 2010 IEEE RFIC Symposium, Anaheim, CA, USA, 23 - 25 May, 2010. pp. 241 – 244.

Mechanical vibrations are a movement of particles around the state of equilibrium in a solid environment. Vibrations are a common phenomenon in our daily life. These vibrations are often parasite effects threatening our existence. Vibrations of the ground, machines, or a number of technical devices present a process, which require a continuous or a long-term monitoring. In many sectors vibrations are a working factor in a production process.

Mechanical vibrations serve as a source of information in medicine, diagnostics of the structure of many machines and in perimeter protection (monitoring). The knowledge of vibration parameters allows evaluating the technical condition of machines, the quality of their design and manufacture and their reliability. Early detection of ground vibrations serves to predict and warn of earthquakes. Ground vibrations serve to monitor explosions and are used in the reflexive seismology (prospecting for mineral deposits). Detection of ground vibrations in systems of perimeter protection allows detecting an intrusion into an area under surveillance. Mechanical vibrations are characteristic for their differing frequencies and amplitude. The frequency of mechanical vibrations ranges usually from a hundredth of Hz to a dozen or so kHz. Parameters of mechanical vibrations are measured with vibration sensors.

At present practically three types of seismic sensors are used:


Geophones belong to the simplest and most inexpensive vibration sensors. They feature a low mechanical resonance frequency, which ranges usually between 4Hz and 14Hz. They

are used in mining, for safety perimeter protection [1] and in the reflexive seismology (Figure 1).

**Figure 1.** Reflexive seismology and geophones [1]

Micro mechanical silicone acceleration sensors (MEMS) [2-3] are mass-produced and used in many fields (e.g. deploying air bags, laptops). They are characterised by small dimensions. Due to their miniature dimensions their mechanical resonance frequency is very high, usually a dozen or so kHz or a few dozen kHz. With piezoelectric acceleration sensors [4] one can measure variable accelerations. Their mechanical resonance frequency is higher than that of MEMS.

Seismic Vibration Sensor with Acoustic Surface Wave 445

**Figure 3.** Basic structure of a SAW vibration sensor

deformations and stresses occurring in it.

surface wave in a delaying line including the SAW.

Figure 3 presents the idea of the structure of an SAW-based sensor. The main element of this sensor is an anisotropic plate of a piesoelectric material. One end of the piesoelectric plate is made fast to the sensor housing, while on the other free end a seismic mass can be placed. An SAW-delaying line in the form of a four-terminal-network is made on the top surface of the sensor. The movement of the sensor housing causes its plate to vibrate and the SAWbased delaying line delay to change. This is why the phase of a high frequency signal passing thru such a line changes. The magnitude of a signal pahse change will be

proportional to the change in the delay of an SAW-based delaying line.

The presented sensor design presents three different issues, which must be solved:

the SAW (first of all of the delay) due to distortions and stresses in the plate

modeling of the sensor mechanical system, which amounts to the description of plate

 modeling of the sensor mechanical-electrical converter – delaying line with the SAW, which amounts to the description of the change in parameters of a delaying line with

 modeling of the electric circuit cooperating with the sensor, which amounts to the analysis and synthesis of an electric circuit measuring the changes in the delay of the

The work presents a solution of the mentioned problems, which were further analysed. The work presents executed models of SAW-comprising sensors and the results of a study of their parameters. The use of realised sensors in a system of perimeter protection is described. The structure of an SAW-comprising sensor (Fig. 3) is a combination of a continous system in the form of a piesoelectric, anisotropic support plate and a discrete system in the form of a concentrated mass. In theory such a system can feature an infinite number of free vibration frequencies. Writing a description of the mechanics of the plate of an SAW-based vibration sensor is a complicated proces; what makes it dificult is the tensor description of the plate mechanical properties. The knowledge of the value of an attenuation tensor (viscosity tensor) poses a problem. Therefore an analysis was conducted, which allows to simplify the sensor model presented in Figure 3 and next as a result of this analysis the movement of a piesoelectric, anisotropic plate with a concentrated mass was described with the aid of a discrete system of one degree of freedom. Elastic and viscous properties of the plate material were taken into account. This model was introduced by way of an isotropic descritpion of anisotropic material properties. The model accuracy was evaluated. Explicit realtionships between sensor plate movement parameters and its geometey and parameters describing its elastic an viscous properties were determined, thus

**Figure 2.** Seismometers offered by MEROZET 1 - portable broadband seismometer, 2 - very broadband seismometer 3 - triaxal seismic accelerometer.

Figure 2 shows seismometers offered by MEROZET: a portable one, a wide-band and a triaxial one; all these 3 models are based on and include piezoelectric acceleration sensors. Vibration sensors can be built using sensors with the acoustic surface wave (SAW).

These SAW-based sensors are used to measure a number of physical quantities: gas concentration [5-8], temperature, pressure [9-13], and mechanical quantities: torque of a rotating shaft [14], stress [15-17], acceleration [18-19] and vibrations [20-21]. All these SAW–based sensors work on the basis of measuring changes in the delay of a surface wave due to the impact of a physical quantity being measured on its speed and the propagation path. However, depending on the kind of a measured physical quantity, a number of problems occur, which are characteristic for the group of sensors used for measuring that quantity.

**Figure 3.** Basic structure of a SAW vibration sensor

**Figure 1.** Reflexive seismology and geophones [1]

seismometer 3 - triaxal seismic accelerometer.

(Figure 1).

than that of MEMS.

quantity.

are used in mining, for safety perimeter protection [1] and in the reflexive seismology

Micro mechanical silicone acceleration sensors (MEMS) [2-3] are mass-produced and used in many fields (e.g. deploying air bags, laptops). They are characterised by small dimensions. Due to their miniature dimensions their mechanical resonance frequency is very high, usually a dozen or so kHz or a few dozen kHz. With piezoelectric acceleration sensors [4] one can measure variable accelerations. Their mechanical resonance frequency is higher

**Figure 2.** Seismometers offered by MEROZET 1 - portable broadband seismometer, 2 - very broadband

Figure 2 shows seismometers offered by MEROZET: a portable one, a wide-band and a triaxial one; all these 3 models are based on and include piezoelectric acceleration sensors.

These SAW-based sensors are used to measure a number of physical quantities: gas concentration [5-8], temperature, pressure [9-13], and mechanical quantities: torque of a rotating shaft [14], stress [15-17], acceleration [18-19] and vibrations [20-21]. All these SAW–based sensors work on the basis of measuring changes in the delay of a surface wave due to the impact of a physical quantity being measured on its speed and the propagation path. However, depending on the kind of a measured physical quantity, a number of problems occur, which are characteristic for the group of sensors used for measuring that

Vibration sensors can be built using sensors with the acoustic surface wave (SAW).

Figure 3 presents the idea of the structure of an SAW-based sensor. The main element of this sensor is an anisotropic plate of a piesoelectric material. One end of the piesoelectric plate is made fast to the sensor housing, while on the other free end a seismic mass can be placed. An SAW-delaying line in the form of a four-terminal-network is made on the top surface of the sensor. The movement of the sensor housing causes its plate to vibrate and the SAWbased delaying line delay to change. This is why the phase of a high frequency signal passing thru such a line changes. The magnitude of a signal pahse change will be proportional to the change in the delay of an SAW-based delaying line.

The presented sensor design presents three different issues, which must be solved:


The work presents a solution of the mentioned problems, which were further analysed. The work presents executed models of SAW-comprising sensors and the results of a study of their parameters. The use of realised sensors in a system of perimeter protection is described. The structure of an SAW-comprising sensor (Fig. 3) is a combination of a continous system in the form of a piesoelectric, anisotropic support plate and a discrete system in the form of a concentrated mass. In theory such a system can feature an infinite number of free vibration frequencies. Writing a description of the mechanics of the plate of an SAW-based vibration sensor is a complicated proces; what makes it dificult is the tensor description of the plate mechanical properties. The knowledge of the value of an attenuation tensor (viscosity tensor) poses a problem. Therefore an analysis was conducted, which allows to simplify the sensor model presented in Figure 3 and next as a result of this analysis the movement of a piesoelectric, anisotropic plate with a concentrated mass was described with the aid of a discrete system of one degree of freedom. Elastic and viscous properties of the plate material were taken into account. This model was introduced by way of an isotropic descritpion of anisotropic material properties. The model accuracy was evaluated. Explicit realtionships between sensor plate movement parameters and its geometey and parameters describing its elastic an viscous properties were determined, thus a simple analysis and synthesis of the sensor plate movements were possible. The main feature of the sensor mechanical system (a continous system combined with a discrete one) is the occurence of pratically only one resonance frequency. A simple description of this magnitude by design parameters of the system and elastic and viscous plate parameters allow a simple modelling, how these sensors function, and as well to determine elastic and viscous parameters of a plate empirically. These parameters in the form : an equivalent Young's modulus and an equivalent material damping coefficient for a selected direction of a piezoelctric substrate (i.e. the direction of the surface wave propagation) were determined in works [22][23]. In available bibliography they are not knowen or utilised. The above considerations are presented in the work [21]. For a full description of the SAW-comprising vibaration sensor designing process in Section 2 we present a modelling process of its mechanical system.

## **2. Model of mechanical unit for SAW vibration sensor**

The object of consideration has been presented in Figure 4. One end of the plate is stiffly attached, and the other is free and without any concentrated mass. The piezoelectric properties of sensor plate will be omitted in the analysis.

**Figure 4.** The plate of a vibration sensor.

The equation of a movement of an anisotropic body with the mass density ρ is:

$$\frac{\partial \sigma\_{ij}}{\partial \mathbf{x}\_{j}} + \rho \frac{\partial^{2} \mathbf{u}\_{i}}{\partial t^{2}} = \mathbf{0} \tag{1}$$

Seismic Vibration Sensor with Acoustic Surface Wave 447

1122 1122

1122 2323 1122 2323

1122 2323 1122 2323

(5)

 

*c c c c* 

The description of viscous properties of an isotropic body done by material damping tensor

2323 1122 1122

The Young's modulus *E* is described as a proportion of a longitudinal stress to longitudinal strain for the direction of the functioning of a stress. To describe the mechanical properties of anisotropic materials taking into account a particular direction of the stress an effective Young's modulus may be used *E* [24][25](Its magnitude is described by overt dependence). An exemplary expression for a inverse effective Young's modulus for a trigonal unit

22 4 2 2 2 2

where: *sij*—is an element of an compliance matrix, *lj*—is a cosine of an angle between the chosen direction and the axis − *j*, in Cartesian coordinates. The compliance matrix *sij* is

It is possible to calculate the values of material damping coefficients in a chosen crystallographic direction, too. The presented approach allows to model the anisotropic material by the isotropic model. In a such model the stresses are the sum of elastic and

*E E*

We consider equivalent isotropic model of cylindrically bent plate [19]. Equation of free

 

*t* 

(7)

3 11 3 33 3 3 13 44 2 3 1 2 14 1 / (1 ) *E l s ls l l s s ll l l s* (1 )(2 ) 2 (3 ) (6)

2 , *<sup>E</sup>* <sup>2</sup>

*ijkl* has an identical

, and elasticity tensor

(4)

problem. The causes of the complications are huge number of non-vanishing modules of an

symmetry as the elasticity tensor *Cijkl*. For materials used in SAW devices (quartz, lithium niobate), the value of damping constants are difficult to experimental verification. For higher class of symmetry of an anisotropic materials, equations (2, 3) are simple. For the isotropic material the elasticity tensor has only two independent components C1111=λ+2μ, C1122=λ, C2323=μ. Therefore the elastic properties of an isotropic substance describe two quantities (λ, μ). They are often shown in form of a Young's modulus *E* and a Poisson

> 2 , <sup>2</sup> *<sup>c</sup> <sup>c</sup> E c*

 

elasticity and material damping tensor. The material damping tensor

ratio *ν*. The following relations occur between quantities *E*,

2323

is analogical. It is usually described by two quantities [24]:

reverse to the stiffness elasticity matrix *cij*.

(lithium niobate, quartz) is:

dissipative components:

vibrations has the form:

components [24]:

The stress tensor σ*ij* depends on the strain tensor *k l* through Hook-Voight equation:

$$
\sigma\_{ij} = \mathbb{C}\_{i\ jkl}\varepsilon\_{kl} + \Sigma\_{i\ jkl}\varepsilon\_{kl,t} \tag{2}
$$

where: *Cijkl*—is a elasticity tensor, *ijkl*—is a material damping tensor, *ui*—is a displacement vector,

$$\varepsilon\_{kl} = \frac{1}{2} \left( \frac{\partial u\_k}{\partial \mathbf{x}\_l} + \frac{\partial u\_l}{\partial \mathbf{x}\_k} \right) \quad - \text{ is a strain tensor} \tag{3}$$

The mathematical description of this issue will be closed if the initial and boundary conditions are added to the aforementioned equations. It is complicated to solve the problem. The causes of the complications are huge number of non-vanishing modules of an elasticity and material damping tensor. The material damping tensor *ijkl* has an identical symmetry as the elasticity tensor *Cijkl*. For materials used in SAW devices (quartz, lithium niobate), the value of damping constants are difficult to experimental verification. For higher class of symmetry of an anisotropic materials, equations (2, 3) are simple. For the isotropic material the elasticity tensor has only two independent components C1111=λ+2μ, C1122=λ, C2323=μ. Therefore the elastic properties of an isotropic substance describe two quantities (λ, μ). They are often shown in form of a Young's modulus *E* and a Poisson ratio *ν*. The following relations occur between quantities *E*, , and elasticity tensor components [24]:

446 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**2. Model of mechanical unit for SAW vibration sensor** 

The equation of a movement of an anisotropic body with the mass density ρ is:

 <sup>1</sup> is a strain tensor 2

*kl*

*k l*

 

*l k u u x x*

*j*

*x t*

 

*ij ijkl kl ijkl kl t C* ,

where: *Cijkl*—is a elasticity tensor, *ijkl*—is a material damping tensor, *ui*—is a displacement

The mathematical description of this issue will be closed if the initial and boundary conditions are added to the aforementioned equations. It is complicated to solve the

2 <sup>2</sup> <sup>0</sup> *ij <sup>i</sup>*

*u*

 

(1)

(3)

through Hook-Voight equation:

(2)

properties of sensor plate will be omitted in the analysis.

**Figure 4.** The plate of a vibration sensor.

vector,

The stress tensor σ*ij* depends on the strain tensor *k l*

mechanical system.

a simple analysis and synthesis of the sensor plate movements were possible. The main feature of the sensor mechanical system (a continous system combined with a discrete one) is the occurence of pratically only one resonance frequency. A simple description of this magnitude by design parameters of the system and elastic and viscous plate parameters allow a simple modelling, how these sensors function, and as well to determine elastic and viscous parameters of a plate empirically. These parameters in the form : an equivalent Young's modulus and an equivalent material damping coefficient for a selected direction of a piezoelctric substrate (i.e. the direction of the surface wave propagation) were determined in works [22][23]. In available bibliography they are not knowen or utilised. The above considerations are presented in the work [21]. For a full description of the SAW-comprising vibaration sensor designing process in Section 2 we present a modelling process of its

The object of consideration has been presented in Figure 4. One end of the plate is stiffly attached, and the other is free and without any concentrated mass. The piezoelectric

$$E = c\_{2323} \left( 2 + \frac{c\_{1122}}{c\_{1122} + c\_{2323}} \right), \quad \nu = \frac{c\_{1122}}{2 \left( c\_{1122} + c\_{2323} \right)} \tag{4}$$

The description of viscous properties of an isotropic body done by material damping tensor is analogical. It is usually described by two quantities [24]:

$$\tau = \frac{\Sigma\_{2323}}{E} \left( \mathbf{2} + \frac{\Sigma\_{1122}}{\Sigma\_{1122} + \Sigma\_{2323}} \right), \quad \eta = \frac{\Sigma\_{1122}}{2 \left( \Sigma\_{1122} + \Sigma\_{2323} \right)} \tag{5}$$

The Young's modulus *E* is described as a proportion of a longitudinal stress to longitudinal strain for the direction of the functioning of a stress. To describe the mechanical properties of anisotropic materials taking into account a particular direction of the stress an effective Young's modulus may be used *E* [24][25](Its magnitude is described by overt dependence). An exemplary expression for a inverse effective Young's modulus for a trigonal unit (lithium niobate, quartz) is:

$$1/E = (1 - l\_3^2)^2 s\_{11} + l\_3^4 s\_{33} + l\_3^2 (1 - l\_3^2) (2s\_{13} + s\_{44}) + 2l\_2 l\_3 (3l\_1^2 - l\_2^2) s\_{14} \tag{6}$$

where: *sij*—is an element of an compliance matrix, *lj*—is a cosine of an angle between the chosen direction and the axis − *j*, in Cartesian coordinates. The compliance matrix *sij* is reverse to the stiffness elasticity matrix *cij*.

It is possible to calculate the values of material damping coefficients in a chosen crystallographic direction, too. The presented approach allows to model the anisotropic material by the isotropic model. In a such model the stresses are the sum of elastic and dissipative components:

$$
\sigma = E\varepsilon + E\tau \frac{\partial \varepsilon}{\partial t} \tag{7}
$$

We consider equivalent isotropic model of cylindrically bent plate [19]. Equation of free vibrations has the form:

$$
\rho \frac{\partial^2 w(\mathbf{x}, t)}{\partial t^2} + E\_e \frac{h^2}{12} \left( \mathbf{1} + \tau \frac{\partial}{\partial t} \right) \frac{\partial^4 w(\mathbf{x}, t)}{\partial \mathbf{x}^4} = \mathbf{0} \tag{8}
$$

Seismic Vibration Sensor with Acoustic Surface Wave 449

**y** (t)

3 3

*E bh E bh*

 (14)

*z*

, (16)

, (17)

(18)

*<sup>r</sup>* , (19)

. (15)

**c z**

**k z**

**Figure 5.** The equivalent circuit of sensor plate with one degree of freedom.

2

The solution of an equation for natural vibrations:

0 <sup>2</sup> 3.5172

model with one degree of freedom (17) are in fulfils relation:

1 0.9996

*m bhl k c*

Parameters in the model are as follows [18]:

where: b — plate width

where:

mass movement is as follows:

**F** 

3 3 0.25196 , 3.1169 , 3.1169 *e e zzz*

*l l*

The model with one degree of freedom has only one resonance frequency. The equation of

2 2 2 0 0

*d y t dy t F t y t dt dt <sup>m</sup>* 

> 2 0 <sup>2</sup> ( ) sin( ) *t <sup>r</sup> y t Ae t*

 

() () ( ) ( )

 

12 *<sup>e</sup> h E*

> 2 2 0

 

*l*

<sup>0</sup> 1 4 *<sup>r</sup>*

It is analogical to the Equation (10) obtained with the use of an isotropic model of sensor plate. Comparison of the first frequency of damped vibrations of the plate obtained in an isotropic model (11) and the frequency of damped vibrations obtained with the use of a

First frequency of damped vibrations calculated in an isotropic model is 0.5 per cent lower than frequency calculated with the use of a discrete model. This difference could be smaller

**m <sup>z</sup>**

where: —mass density, *h*—plate thickness, *L*—plate length, τ—equivalent material damping coefficient , 2 <sup>1</sup> *<sup>E</sup> <sup>E</sup> e* 

*Ee* is an equivalent Young's modulus.

At the boundaries we have:

$$w(0,t) = 0, \quad \frac{\partial w(0,t)}{\partial \mathbf{x}} = 0, \quad \frac{\partial^2 w(L,t)}{\partial \mathbf{x}^2} = 0, \quad \frac{\partial^3 w(L,t)}{\partial \mathbf{x}^3} = 0,\tag{9}$$

The solution to the boundary problem (8), (9) has the form:

$$\text{cov}(\mathbf{x}, t) = \sum\_{n=1}^{\infty} \mathcal{W}\_n(\mathbf{x}) \cdot A\_n \ e^{-\frac{\left\| \overline{\sigma}\_n^2 t \right\|}{2}} \cdot \sin(\overline{\sigma}\_n t + \varphi\_n) \tag{10}$$

where: constants An and φn are determined by initial conditions.

The angular frequency of non-damped vibrations is equal to:

$$
\rho \alpha\_n = k\_n^2 \frac{h}{l^2} \sqrt{\frac{E\_\epsilon}{12\rho}} \,\, . \tag{11}
$$

The angular frequency of damped vibrations is equal to:

$$
\overline{\phi}\_m = \phi\_m \sqrt{1 - \frac{\phi\_m^2 \pi^2}{4}} \tag{12}
$$

$$\text{where:}\,\text{:}\,\mathbf{k}\_1 = 1, 875, \,\mathbf{k}\_2 = 4, 694, \,\mathbf{k}\_3 = 7, 855\tag{13}$$

The orthonormal set of function Wn (eigenfunctions) is taken from [26]. Only some elements in the sum (10) represent vibrations. For *N* < n where *N* is the greatest natural number for chich ωn < 2/τ , the element of sum represents very strongly dumped movement and there is no resonance at this frequency. Each of the harmonics n=1,2,3… has part of energy. How great is the part depends on the unit (normal vibrations, ωn, *w(x)* ) and depends on activation. In the paper [18][19][27][28] a simplified model with one degree of freedom was presented and it is shown in Figure 5. It has been used to describe the dynamics of sensor plate movement. It was derived according to the Rayleigh method. This method is based on a simplified modeling of a plate with the use of an equivalent circuit with one degree of freedom which is energetically equivalent. The free end of sensor plate has been taken as a point of reduction. The equivalent circuit present Figure 5

**Figure 5.** The equivalent circuit of sensor plate with one degree of freedom.

Parameters in the model are as follows [18]:

$$m\_z = 0.25196 \,\rho b \, hh \, , \quad k\_z = 3.1169 \frac{E\_e \, b \, h^3}{l^3} , \quad c\_z = \tau \, 3.1169 \frac{E\_e \, bh^3}{l^3} \tag{14}$$

where: b — plate width

The model with one degree of freedom has only one resonance frequency. The equation of mass movement is as follows:

$$\frac{d^2y(t)}{dt^2} + \alpha\_0^2 \tau \frac{dy(t)}{dt} + \alpha\_0^2 y(t) = \frac{F(t)}{m\_z} \,. \tag{15}$$

The solution of an equation for natural vibrations:

$$y(t) = Ae^{-\frac{\alpha\_0^2 \tau}{2}t} \sin(\alpha\_r t + \phi) \,. \tag{16}$$

where:

448 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

*<sup>E</sup> <sup>E</sup> e*

 

The solution to the boundary problem (8), (9) has the form:

1

*n*

where: constants An and φn are determined by initial conditions.

The angular frequency of non-damped vibrations is equal to:

The angular frequency of damped vibrations is equal to:

point of reduction. The equivalent circuit present Figure 5

where:

damping coefficient , 2 <sup>1</sup>

At the boundaries we have:

*Ee* is an equivalent Young's modulus.

2 24

12 *<sup>e</sup> wxt h wxt <sup>E</sup> t x t*

2 4 ( ,) ( ,) 1 0

(0, ) ( , ) ( , ) (0, ) 0, 0, 0, 0, *w t wLt wLt w t*

( , ) ( ) sin( )

*wxt W x A e t*

2

*n n*

*m m*

 

<sup>2</sup> 12 *e*

2 2

4 *m*

 

*<sup>h</sup> <sup>E</sup> <sup>k</sup> l*

1

where : k 1,875, k 4,694, k 7,855 <sup>123</sup> (13)

The orthonormal set of function Wn (eigenfunctions) is taken from [26]. Only some elements in the sum (10) represent vibrations. For *N* < n where *N* is the greatest natural number for chich ωn < 2/τ , the element of sum represents very strongly dumped movement and there is no resonance at this frequency. Each of the harmonics n=1,2,3… has part of energy. How great is the part depends on the unit (normal vibrations, ωn, *w(x)* ) and depends on activation. In the paper [18][19][27][28] a simplified model with one degree of freedom was presented and it is shown in Figure 5. It has been used to describe the dynamics of sensor plate movement. It was derived according to the Rayleigh method. This method is based on a simplified modeling of a plate with the use of an equivalent circuit with one degree of freedom which is energetically equivalent. The free end of sensor plate has been taken as a

*x x x*

2 2

*n t n n n n*

 

—mass density, *h*—plate thickness, *L*—plate length, τ—equivalent material

2 3

2 3

 . (11)

(12)

(10)

(9)

(8)

$$
\rho\_0 = 3.5172 \left( \frac{h}{l^2} \right) \sqrt{\frac{E\_e}{12 \,\rho}} \,\, \, \, \tag{17}
$$

$$
\alpha\_r = \alpha\_0 \sqrt{1 - \frac{\alpha\_0^2 \tau^2}{4}} \tag{18}
$$

It is analogical to the Equation (10) obtained with the use of an isotropic model of sensor plate. Comparison of the first frequency of damped vibrations of the plate obtained in an isotropic model (11) and the frequency of damped vibrations obtained with the use of a model with one degree of freedom (17) are in fulfils relation:

$$
\alpha\_1 = 0.9996 \alpha\_{r'} \tag{19}
$$

First frequency of damped vibrations calculated in an isotropic model is 0.5 per cent lower than frequency calculated with the use of a discrete model. This difference could be smaller

in case of a sensor construction with the concentrated mass attached to the movable end of the plate. That is why the model with one degree of freedom may be used to describe the movement of sensor plate. It allows relatively easy simulation of vibrations of the plate with the mass attached to its movable end. Free vibrations of sensor plate are a definite as a sum of damped harmonic frequency vibrations. But, in free vibration damped vibrations with first harmonic frequency will dominate. The amplitudes of the superior harmonic vibrations will be extremely small. As it is shown in [18] their quantity is 40 dB smaller than the first harmonic amplitude. This is the reason why a model with one degree of freedom [18][27][28] has been used to analyze the movement of the plate with concentrated mass. Vibrations of the plate have been activated by the movement of the sensor casing *Y(t)*. The equation of movement is as following:

$$\frac{d^2y(t)}{dt^2} + \alpha\_0^2 \tau \frac{dy(t)}{dt} + \alpha\_0^2 y(t) = \alpha\_0^2 \tau \frac{dY(t)}{dt} + \alpha\_0^2 Y(t) \tag{20}$$

Seismic Vibration Sensor with Acoustic Surface Wave 451

(24)

ST-cut quartz

It will always have a factor in form of a harmonic function with the frequency equal to the resonance frequency of sensor plate and with variable amplitude. That is why the frequency response of sensor plate may be quantity identifying the sensor. Frequency response of the sensor plate is the ratio of the amplitude of the deflection plate sensor to the harmonic amplitude of its case The frequency response of the sensor plate calculated from the

1( ) ( )

*H*

Equivalent material damping coefficient[ ]

**Table 1.** Material parameters of quartz.

of 22 Hz and 100 Hz**.**

**0.01**

**0.1**

**1**

**10**

**Magnitude**

**100**

**1000**

Equivalent Young's modulus [GPa] 76 Dynamic critical compressive stress [MPa] 80

Density [kg/m3] 2650

selectivity of the sensor is high. It decreases with increased resonance frequency.

**Figure 6.** Theoretical resonance characteristics of plates with resonance frequencies

2 22 2

*s* 29.3

[1 ( ) ] ( ) *r*

Parameters in relation (24) depends on mechanical properties of the sensor plate material. The quantities of elastic and viscous parameters for quartz are shown in Table 1 [22][23].

Theoretical frequency response for plates made of ST-cut quartz with the resonance frequencies of 22 Hz and 100 Hz are shown in Figure 6. The most important is that for low frequency the frequency response has narrower band and higher magnitude so the

**22Hz 100Hz**

**0 50 100 150 200**

**Frequency [Hz]**

Equation (20) is as follow:

where:

$$
\alpha\_0 = 3.5172 \left(\frac{h}{l^2}\right) \sqrt{\frac{E\_e}{12\,\rho}} \sqrt{\frac{1}{1 + r\,3.9689}}\tag{21}
$$

r is a ratio between seismic mass and mass of sensor plate.

The solution of the Equation (20) is a function:

$$\begin{split} y(t) &= A \exp\left[ -\frac{\alpha\_0^2 \tau t}{2} \right] \sin\left[ \alpha\_r \left( t + \varphi \right) \right] - \\ &- \frac{4\alpha\nu}{4 - \alpha\_0^2 \tau^2} \int\_0^t \left( \tau \frac{dY(\xi)}{dt} + Y(\xi) \right) \cdot \exp\left[ -\frac{\alpha\_0^2 \tau}{2} (t - \xi) \right] \cdot \sin\left[ \alpha\_r \left( t - \xi \right) \right] d\xi \end{split} \tag{22}$$

where: constants *A* and are determined by initial conditions.

Relations between ω0 and ωr are as in identity (18). In both components of the solution (22) appears the following function:

$$\varphi\_{\boldsymbol{\phi}}(t) = A e^{-\frac{\alpha\_0^2 \tau}{2} t} \sin(\alpha\_r t + \boldsymbol{\phi}) \tag{23}$$

It is a product of a harmonic and damping (exponentially decay with time) function. The frequency of a harmonic function is the resonance frequency of the unit. This function describes sensor impulse response and its natural vibrations. It is a sum of:


It will always have a factor in form of a harmonic function with the frequency equal to the resonance frequency of sensor plate and with variable amplitude. That is why the frequency response of sensor plate may be quantity identifying the sensor. Frequency response of the sensor plate is the ratio of the amplitude of the deflection plate sensor to the harmonic amplitude of its case The frequency response of the sensor plate calculated from the Equation (20) is as follow:

$$H(\phi) = \sqrt{\frac{1 + \left(\alpha \tau\right)^2}{\left[1 - \left(\frac{\partial}{\partial \rho\_r}\right)^2\right]^2 + \left(\alpha \tau\right)^2}}\tag{24}$$

Parameters in relation (24) depends on mechanical properties of the sensor plate material. The quantities of elastic and viscous parameters for quartz are shown in Table 1 [22][23].


**Table 1.** Material parameters of quartz.

450 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

equation of movement is as following:

where:

2

r is a ratio between seismic mass and mass of sensor plate.

4 2

 

describes sensor impulse response and its natural vibrations. It is a sum of:

damped vibrations with the resonance frequency of a sensor plate.

2 0

 

exp sin <sup>2</sup>

 

*dY*

*dt*

*<sup>t</sup> yt A <sup>t</sup>*

The solution of the Equation (20) is a function:

2 2 0 0

*t*

4

where: constants *A* and

appears the following function:

 

movement of the sensor casing,

0 2

*r*

 

are determined by initial conditions.

Relations between ω0 and ωr are as in identity (18). In both components of the solution (22)

2 0 <sup>2</sup> ( ) sin( ) *<sup>t</sup> <sup>r</sup> t Ae t* 

It is a product of a harmonic and damping (exponentially decay with time) function. The frequency of a harmonic function is the resonance frequency of the unit. This function

convolution of an impulse response of the plate and the component of describing

in case of a sensor construction with the concentrated mass attached to the movable end of the plate. That is why the model with one degree of freedom may be used to describe the movement of sensor plate. It allows relatively easy simulation of vibrations of the plate with the mass attached to its movable end. Free vibrations of sensor plate are a definite as a sum of damped harmonic frequency vibrations. But, in free vibration damped vibrations with first harmonic frequency will dominate. The amplitudes of the superior harmonic vibrations will be extremely small. As it is shown in [18] their quantity is 40 dB smaller than the first harmonic amplitude. This is the reason why a model with one degree of freedom [18][27][28] has been used to analyze the movement of the plate with concentrated mass. Vibrations of the plate have been activated by the movement of the sensor casing *Y(t)*. The

> 2 22 2 2 0 00 0 () () ( ) ( ) ( ) *d y t dy t dY t*

> > <sup>1</sup> 3.5172

*l r*

*<sup>e</sup> h E*

 

*dt dt dt* 

  *y t Y t*

12 1 3.9689

 

exp sin

*Y t td*

2 0

   

(21)

*r*

  (22)

 

(23)

. (20)

Theoretical frequency response for plates made of ST-cut quartz with the resonance frequencies of 22 Hz and 100 Hz are shown in Figure 6. The most important is that for low frequency the frequency response has narrower band and higher magnitude so the selectivity of the sensor is high. It decreases with increased resonance frequency.

**Figure 6.** Theoretical resonance characteristics of plates with resonance frequencies of 22 Hz and 100 Hz**.**

The maximum value of the frequency response of the plate will occur for ω = ωr. It has been described with the relationship:

$$H(\phi\_r) = \sqrt{\frac{1 + \left(\phi\_r \tau\right)^2}{\left(0, 5\phi\_0 \tau\right)^4 + \left(\phi\_r \tau\right)^2}}\tag{25}$$

Seismic Vibration Sensor with Acoustic Surface Wave 453

**r=0**

**r=1**

**r=2**

**Figure 8.** The influence of a change of a concentrated mass on sensor plate resonance frequency.

Figure 9.

**Resonance frequency [Hz]**

**1**

**10**

**100**

**1000**

**10000**

**0**

**0.2**

**0.4**

**Decrease of resonance frequency**

**0.6**

**0.8**

**1**

It is visible that the use of concentrated mass quantities exceeding two times the mass of the plate enables and triple decrease of resonance frequency of a plate. It is the most effective place to decrease the resonance frequency of a plate. Continuous increase of a concentrated mass does not substantially decrease the resonance frequency of sensor plate. The further analysis of sensor parameters will be limited to such range of concentrated mass quantities. The relationship between the value of resonance frequency of a plate made of ST-cut quartz and length of the plate determined by three different concentrated mass values is shown in

**0 2 4 6 810**

**Concentrated mass (r)**

**Figure 9.** The relationship between sensor plate resonance frequency made of ST-cut quartz 0.5 mm

**Length [mm]**

**0 20 40 60 80 100**

thick, and plate length (l) and the quantity of concentrated mass (r).

Its value exceeds repeatedly the value of static deflection. (e.g., for the resonance frequency of 22 Hz it is 246 times higher).

**Figure 7.** Maximum magnitude of frequency response versus the resonance frequency of the sensor plate.

The change in maximum magnitude of frequency response as a function of resonance frequency of the plate is shown in Figure 7 For the resonance frequency of a plate of 10Hz the vibrations amplitude multiplication is 1,600 higher than static deflection. This property may be used to construct sensors with high sensitivity level. But it is necessary to answer one question beforehand: what is the lowest possible resonance frequency of a plate that we can manufacture? The answer is accessible on the basis of the described model and the length of available plates. The resonance frequency of sensor plate is described by the relation (21). It depends on plate length (l) and on quantity of a concentrated mass (r) attached to the free end of sensor plate. The increase of the concentrated mass lowers resonance frequency of the plate, simultaneously increasing stresses of the plate.

The influence of a change of concentrated mass on resonance frequency of the sensor plate is shown in Figure 8.

*r*

*H*

described with the relationship:

of 22 Hz it is 246 times higher).

1

10

100

**Magnitude**

1000

plate.

stresses of the plate.

shown in Figure 8.

The maximum value of the frequency response of the plate will occur for ω = ωr. It has been

0 1( ) ( ) (0,5 ) ( )

 

Its value exceeds repeatedly the value of static deflection. (e.g., for the resonance frequency

**Figure 7.** Maximum magnitude of frequency response versus the resonance frequency of the sensor

The change in maximum magnitude of frequency response as a function of resonance frequency of the plate is shown in Figure 7 For the resonance frequency of a plate of 10Hz the vibrations amplitude multiplication is 1,600 higher than static deflection. This property may be used to construct sensors with high sensitivity level. But it is necessary to answer one question beforehand: what is the lowest possible resonance frequency of a plate that we can manufacture? The answer is accessible on the basis of the described model and the length of available plates. The resonance frequency of sensor plate is described by the relation (21). It depends on plate length (l) and on quantity of a concentrated mass (r) attached to the free end of sensor plate. The increase of the concentrated mass lowers resonance frequency of the plate, simultaneously increasing

0.1 1 10 100 1000

**Frequency resonanse [Hz]**

The influence of a change of concentrated mass on resonance frequency of the sensor plate is

2 4 2

 

*r*

(25)

*r*

 

**Figure 8.** The influence of a change of a concentrated mass on sensor plate resonance frequency.

It is visible that the use of concentrated mass quantities exceeding two times the mass of the plate enables and triple decrease of resonance frequency of a plate. It is the most effective place to decrease the resonance frequency of a plate. Continuous increase of a concentrated mass does not substantially decrease the resonance frequency of sensor plate. The further analysis of sensor parameters will be limited to such range of concentrated mass quantities. The relationship between the value of resonance frequency of a plate made of ST-cut quartz and length of the plate determined by three different concentrated mass values is shown in Figure 9.

**Figure 9.** The relationship between sensor plate resonance frequency made of ST-cut quartz 0.5 mm thick, and plate length (l) and the quantity of concentrated mass (r).

From the figure presented above may conclude that it is relatively easy to create plates of resonance frequency form 20 Hz do 4 kHz. For the 0.5 mm thick plates it is necessary to use the concentrated mass up to 1.5 g. The relation between the concentrated mass and the plate length is shown in Figure 10. The sensor impulse response presented by the relation (23) has a damped character. Its fast fading can impose an upper limit of the resonance frequency. The damping value depends on the geometry of the plate and the equivalent damping coefficient. In order to simplify the illustration the impulse response damping measure has been introduced as a relative decrease of its quantity after one period.

Seismic Vibration Sensor with Acoustic Surface Wave 455

**r=0 r=1 r=2**

damping of free vibrations of the plate is relatively slow. The impulse response of shorter plates is dampened relatively fast. This is why it seems to be beneficial to use possibly long plates loaded by concentrated mass equal to plate mass. The value of resonance frequencies of plates possible to manufacture has changed. It seems that the range of resonance frequency plates available to use is limited to the scope from 20 Hz to 250 Hz. The parameters of resonance frequencies of the plates in the aforementioned range are shown in

**Figure 12.** The relation between resonance frequency of a sensor plate and plate length and the value of

**40 50 60 70 80 90 100**

**Length [mm]**

From the above considerations one can draw a conclusion that working with SAW vibration sensors one can utilise their pulse responses or forced vibrations. The sensor resonance characteristics is a basic parameter of the first operation mode. On 0.5 mm thick quartz plates with a concentrated mass equalling the mass of a plate we can achieve plate own vibration frequencies from 20 Hz thru 250Hz. In the second operation mode the vibration sensors with SAW will operate like classical acceleration sensors. The plate resonance

The knowledge of the resonance characteristic curve is required for both sensor operation modes. That characteristic can be easily calculated with the aid of the presented model. In the Section 4 we will present experimental examples of the operation of a seismic vibration sensor with SAW, which will enable to evaluate the precision of this model and its

In order to ensure the transmission of test and supply signals through one coaxial cable there must be a system at the sensor input separating the test signal (74MHz) and supply signal 12VDC (separator). At the output there must be a system summing up the test signal

frequency should be above the measuring range of a sensor.

**3. Vibration sensor electronic components** 

Figure 12.

**Resonanse frequency [Hz]**

concentrated mass.

**0.0**

**50.0**

**100.0**

**150.0**

**200.0**

**250.0**

**300.0**

usefulness.

**Figure 10.** The concentrated mass quantities used in the considered sensor constructions.

The relation of impulse response damping in form of a function of length of ST-cut quartz plate for three different concentrated mass values is presented in Figure 11. For plates longer than 40 mm loaded by the concentrated mass equal to the mass of the plate (r = l) the

**Figure 11.** Relative decrease of impulse response amplitude after the time equal to its period in form of a function of plate length for different concentrated mass quantities (r).

damping of free vibrations of the plate is relatively slow. The impulse response of shorter plates is dampened relatively fast. This is why it seems to be beneficial to use possibly long plates loaded by concentrated mass equal to plate mass. The value of resonance frequencies of plates possible to manufacture has changed. It seems that the range of resonance frequency plates available to use is limited to the scope from 20 Hz to 250 Hz. The parameters of resonance frequencies of the plates in the aforementioned range are shown in Figure 12.

454 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

been introduced as a relative decrease of its quantity after one period.

**0**

**0.0**

**0.2**

**0.4**

**Decrease of impulse response**

**0.6**

**0.8**

**1.0**

**0.5**

**1**

**1.5**

**Concentrated mass [g]**

**2**

**Figure 10.** The concentrated mass quantities used in the considered sensor constructions.

than 40 mm loaded by the concentrated mass equal to the mass of the plate (r = l) the

The relation of impulse response damping in form of a function of length of ST-cut quartz plate for three different concentrated mass values is presented in Figure 11. For plates longer

**0 20 40 60 80 100**

**r=0 r=1 r=2**

**r=1 r=2 r=3**

**Length [mm]**

**Figure 11.** Relative decrease of impulse response amplitude after the time equal to its period in form of

**10 30 50 70 90**

**Length [mm]**

a function of plate length for different concentrated mass quantities (r).

From the figure presented above may conclude that it is relatively easy to create plates of resonance frequency form 20 Hz do 4 kHz. For the 0.5 mm thick plates it is necessary to use the concentrated mass up to 1.5 g. The relation between the concentrated mass and the plate length is shown in Figure 10. The sensor impulse response presented by the relation (23) has a damped character. Its fast fading can impose an upper limit of the resonance frequency. The damping value depends on the geometry of the plate and the equivalent damping coefficient. In order to simplify the illustration the impulse response damping measure has

**Figure 12.** The relation between resonance frequency of a sensor plate and plate length and the value of concentrated mass.

From the above considerations one can draw a conclusion that working with SAW vibration sensors one can utilise their pulse responses or forced vibrations. The sensor resonance characteristics is a basic parameter of the first operation mode. On 0.5 mm thick quartz plates with a concentrated mass equalling the mass of a plate we can achieve plate own vibration frequencies from 20 Hz thru 250Hz. In the second operation mode the vibration sensors with SAW will operate like classical acceleration sensors. The plate resonance frequency should be above the measuring range of a sensor.

The knowledge of the resonance characteristic curve is required for both sensor operation modes. That characteristic can be easily calculated with the aid of the presented model. In the Section 4 we will present experimental examples of the operation of a seismic vibration sensor with SAW, which will enable to evaluate the precision of this model and its usefulness.

### **3. Vibration sensor electronic components**

In order to ensure the transmission of test and supply signals through one coaxial cable there must be a system at the sensor input separating the test signal (74MHz) and supply signal 12VDC (separator). At the output there must be a system summing up the test signal with a constant supply voltage (adder). Test signal (high frequency) after going through SAW delay line must be amplified to input quantity. It will ensure loss compensation caused by SAW delay line. In the entire line of high frequency test signal (74MHz) a characteristic impedance of 50Ω should be retained. Input and output impedance must have the value of 50Ω. Figure 13 shows the basic functional elements of SAW vibration sensor. Depending on the function in the whole system the following components may be distinguished:

Seismic Vibration Sensor with Acoustic Surface Wave 457

**Figure 15.** Inductance equivalent system diagram

impedance of such a system in frequency function.

**Figure 17.** Actual system separating the test and supply signal.

In reality, the chosen inductance is a parallel resonant circuit. Figure 16 presents change in

**Figure 16.** Relationship between impedance and frequency of a system presented in Figure 15

For frequency equal to 74MHz the system impedance value amounts to 400kΩ. It is relatively high in comparison with characteristic impedance of the test signal transmission line (50Ω). It is then possible to obtain considerable attenuation of the test signal entering the supply circuit and it practically eliminates reflections at the point of signal separation or


**Figure 13.** Block diagram of SAW vibration sensor.

The method of making the aforementioned components will be discussed in the next Section.

## **3.1. System separating or summing up electrical signals (separator/adder)**

A system separating test and supply signals is placed at the sensor input. A system summing up these signals is placed at the sensor output. Figure 14 shows a system separating or summing up test and supply signals. The system is in a form of a circulator. It is connected to the line of high frequency signal with a characteristic impedance of 50Ω. A point of separation (or summation) of signals is the place where additional impedance is added to a line of characteristic impedance of 50Ω by inductance L1. It may change the characteristic impedance of the line and be the reason of signal reflections. In order to avoid this the quantity of added impedance must be much larger than line characteristic impedance (50Ω). In order to fulfill this requirement inductance L1=4,7uH of its own parallel resonance frequency of 74MHz has been chosen. Figure 15 shows inductance equivalent system diagram.

**Figure 14.** System separating or summing up test and supply signals.

**Figure 15.** Inductance equivalent system diagram

system separating and summing up the test and supply signals;

systems adjusting the impedance of SAW line to 50Ω;

**Figure 13.** Block diagram of SAW vibration sensor.

amplifier compensating losses caused by SAW delay line.

SAW delay line;

Section.

with a constant supply voltage (adder). Test signal (high frequency) after going through SAW delay line must be amplified to input quantity. It will ensure loss compensation caused by SAW delay line. In the entire line of high frequency test signal (74MHz) a characteristic impedance of 50Ω should be retained. Input and output impedance must have the value of 50Ω. Figure 13 shows the basic functional elements of SAW vibration sensor. Depending on

The method of making the aforementioned components will be discussed in the next

A system separating test and supply signals is placed at the sensor input. A system summing up these signals is placed at the sensor output. Figure 14 shows a system separating or summing up test and supply signals. The system is in a form of a circulator. It is connected to the line of high frequency signal with a characteristic impedance of 50Ω. A point of separation (or summation) of signals is the place where additional impedance is added to a line of characteristic impedance of 50Ω by inductance L1. It may change the characteristic impedance of the line and be the reason of signal reflections. In order to avoid this the quantity of added impedance must be much larger than line characteristic impedance (50Ω). In order to fulfill this requirement inductance L1=4,7uH of its own parallel resonance frequency of 74MHz

**3.1. System separating or summing up electrical signals (separator/adder)** 

has been chosen. Figure 15 shows inductance equivalent system diagram.

**Figure 14.** System separating or summing up test and supply signals.

the function in the whole system the following components may be distinguished:

In reality, the chosen inductance is a parallel resonant circuit. Figure 16 presents change in impedance of such a system in frequency function.

**Figure 16.** Relationship between impedance and frequency of a system presented in Figure 15

**Figure 17.** Actual system separating the test and supply signal.

For frequency equal to 74MHz the system impedance value amounts to 400kΩ. It is relatively high in comparison with characteristic impedance of the test signal transmission line (50Ω). It is then possible to obtain considerable attenuation of the test signal entering the supply circuit and it practically eliminates reflections at the point of signal separation or

summation. Figure 17 presents an actual system separating the test and supply signals. Impedance of connected in series: C1 capacity and RF output impedance is equal to characteristic impedance of 50Ω. A diagram presented in Figure 17 enables to analyze test signal attenuation in supply circuit. It allows to calculate the change in line characteristic impedance made by the separating system.

Seismic Vibration Sensor with Acoustic Surface Wave 459

and line impedance equals 50Ω. A separating or summing up system prepared in such a manner does not influence the test signal transmission through SAW vibration sensor.

The design of SAW-comprising delaying lines used for vibration sensors (Figure 20A) differ from those used for sensors of other physical quantities (Figure 20B). Since the sensor plate moves, electrodes applying electric signals to converters (bus bar) should be situated on the immobile part of the plate. (Thus a proper strength of electric contacts for these electrodes will be ensured.) Electrodes are long and their resistance is specific. As the plate moves its housing is greater than that of classic filters comprising the SAW. This causes the signal passing directly between the SAW-comprising delaying line inlet and outlet to increase.

The line was designed in the form of two cooperating, identical, simple, periodical, doubleelectrode interdigital transducers. Figure 21 shows a system of converter electrodes. Such a structure of converters enables their operation on the third harmonic. The lines were

Due to a low value of the electro-mechanical coupling factor for a ST-cut quartz losses for a mismatch its inlet impedances to 50Ω are significant. In order to cut on these losses

**3.2. Delaying line and adapting system** 

**Figure 20.** SAW delay lines: for vibration sensor (A), classic (B)

designed to fabricate them with a ST-cut quartz.

**Figure 21.** Structure of delaying line converters

Figure 18 shows attenuation of the test signal at DC output and change in line impedance in frequency function for R1=1Ω.

**Figure 18.** Attenuation of test signal at DC output vs. frequency

Calculations of transmission line impedance change have been done on the assumption that the test signal line has the impedance equaling 50Ω in the entire frequency range. This assumption is correct in the range of line frequency. It substantially simplifies modelling of the system. Figure 19 shows the change line characteristic impedance vs. frequency for R1 = 1Ω.

**Figure 19.** Change in test signal line characteristic impedance in frequency function.

This simplification does not influence the results in the system frequency range. For the sensor frequency equalling 74MHz the test signal attenuation at DC output equals –78dB, and line impedance equals 50Ω. A separating or summing up system prepared in such a manner does not influence the test signal transmission through SAW vibration sensor.

## **3.2. Delaying line and adapting system**

458 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

impedance made by the separating system.

**Figure 18.** Attenuation of test signal at DC output vs. frequency

frequency function for R1=1Ω.

1Ω.

summation. Figure 17 presents an actual system separating the test and supply signals. Impedance of connected in series: C1 capacity and RF output impedance is equal to characteristic impedance of 50Ω. A diagram presented in Figure 17 enables to analyze test signal attenuation in supply circuit. It allows to calculate the change in line characteristic

Figure 18 shows attenuation of the test signal at DC output and change in line impedance in

Calculations of transmission line impedance change have been done on the assumption that the test signal line has the impedance equaling 50Ω in the entire frequency range. This assumption is correct in the range of line frequency. It substantially simplifies modelling of the system. Figure 19 shows the change line characteristic impedance vs. frequency for R1 =

**Figure 19.** Change in test signal line characteristic impedance in frequency function.

This simplification does not influence the results in the system frequency range. For the sensor frequency equalling 74MHz the test signal attenuation at DC output equals –78dB, The design of SAW-comprising delaying lines used for vibration sensors (Figure 20A) differ from those used for sensors of other physical quantities (Figure 20B). Since the sensor plate moves, electrodes applying electric signals to converters (bus bar) should be situated on the immobile part of the plate. (Thus a proper strength of electric contacts for these electrodes will be ensured.) Electrodes are long and their resistance is specific. As the plate moves its housing is greater than that of classic filters comprising the SAW. This causes the signal passing directly between the SAW-comprising delaying line inlet and outlet to increase.

**Figure 20.** SAW delay lines: for vibration sensor (A), classic (B)

The line was designed in the form of two cooperating, identical, simple, periodical, doubleelectrode interdigital transducers. Figure 21 shows a system of converter electrodes. Such a structure of converters enables their operation on the third harmonic. The lines were designed to fabricate them with a ST-cut quartz.

**Figure 21.** Structure of delaying line converters

Due to a low value of the electro-mechanical coupling factor for a ST-cut quartz losses for a mismatch its inlet impedances to 50Ω are significant. In order to cut on these losses

operation of interdigital transducers under conditions of matching to impedance of 50Ω at a frequency of 74MHz was selected [29-32]. Figure 22 shows a converter matching system. The element for matching a converter having the conductance of Gp and the capacity Cp to the impedance Rg = 50Ω is the inductance L1. The matching takes place on the condition that the available power derived from a voltage source Eg of the internal impedance Rg = 50Ω is distributed released/emitted on the converter conductance Gp.

**Figure 22.** Interdigital transducer matching system to 50Ω impedance..

This condition is met for a conductance resulting from the relationship [29]:

$$L\_1 = \frac{\mathcal{C}\_P}{\mathcal{G}\_P^{\;\;\;2} + o^2 \mathcal{C}\_P^{\;\;2}} \tag{26}$$

Seismic Vibration Sensor with Acoustic Surface Wave 461

**Figure 24.** Coefficient of reflection from a matched converter versus frequency.

Figure 26 presents the frequency amplitude curve for the fabricated SAW delaying line. The measurement was conducted after the line was mounted in an SAW-based vibration

Figure 25 shows the mounting of the sensor plate.

**Figure 26.** Attenuation frequency diagram of SAW vibration sensor.

**Figure 25.** Mounting of the sensor plate

converter.

With the help of the (26) relationship the converter geometry for a ST-cut quartz was determined. The aperture of the converter A= 2,5 mm was adopted. To fulfill the purpose converters operated on the third harmonic at 74MHz. For such parameters a converter consisting of N=25 pairs of electrodes was received. The electrode width and the gap between electrodes were 16 μm, and the surface length 37 μm. The results of theoretical calculations of conductance and converter capacity versus frequency are presented in Figure 23.

**Figure 23.** Theoretical dependence of conductance and capacity of simple transducer composed of 25 double electrode pairs on ST-cut quartz.

At 74MHz frequency the converter conductance is 0.74mS and the capacity 3.13pF. For these quantities the inductance L1= 900nH was calculated, at which value the condition of matching the converter to the impedance 50 Ω is satisfied. Practically, the matching of interdigital transducers to the impedance of 50 Ω was carried out by measurement of the coefficient of reflection Figure 24 shows the change in the coefficient of reflection from a matched converter versus frequency in a system of an impedance of 50 Ω.

Seismic Vibration Sensor with Acoustic Surface Wave 461

**Figure 24.** Coefficient of reflection from a matched converter versus frequency.

Figure 25 shows the mounting of the sensor plate.

**Figure 25.** Mounting of the sensor plate

460 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

distributed released/emitted on the converter conductance Gp.

**Figure 22.** Interdigital transducer matching system to 50Ω impedance..

This condition is met for a conductance resulting from the relationship [29]:

conductance and converter capacity versus frequency are presented in Figure 23.

1 2 22 *P P P*

With the help of the (26) relationship the converter geometry for a ST-cut quartz was determined. The aperture of the converter A= 2,5 mm was adopted. To fulfill the purpose converters operated on the third harmonic at 74MHz. For such parameters a converter consisting of N=25 pairs of electrodes was received. The electrode width and the gap between electrodes were 16 μm, and the surface length 37 μm. The results of theoretical calculations of

**Figure 23.** Theoretical dependence of conductance and capacity of simple transducer composed of 25

At 74MHz frequency the converter conductance is 0.74mS and the capacity 3.13pF. For these quantities the inductance L1= 900nH was calculated, at which value the condition of matching the converter to the impedance 50 Ω is satisfied. Practically, the matching of interdigital transducers to the impedance of 50 Ω was carried out by measurement of the coefficient of reflection Figure 24 shows the change in the coefficient of reflection from a

matched converter versus frequency in a system of an impedance of 50 Ω.

double electrode pairs on ST-cut quartz.

*G C* 

(26)

*<sup>C</sup> <sup>L</sup>*

operation of interdigital transducers under conditions of matching to impedance of 50Ω at a frequency of 74MHz was selected [29-32]. Figure 22 shows a converter matching system. The element for matching a converter having the conductance of Gp and the capacity Cp to the impedance Rg = 50Ω is the inductance L1. The matching takes place on the condition that the available power derived from a voltage source Eg of the internal impedance Rg = 50Ω is

> Figure 26 presents the frequency amplitude curve for the fabricated SAW delaying line. The measurement was conducted after the line was mounted in an SAW-based vibration converter.

**Figure 26.** Attenuation frequency diagram of SAW vibration sensor.

## **3.3. Amplifier**

The role of an amplifier is to compensate losses caused by SAW delay line. An amplifier has been built on a monolithic system MAR-6 manufactured by Mini-Circuits. Figure 27 shows a diagram of an amplifier being a part of an electronic system of SAW vibration sensor.

Seismic Vibration Sensor with Acoustic Surface Wave 463

coupling the inductances should be placed perpendicularly to each other and placed at a distance. These elements define the manner of making of the printed circuit plates. Any

The fundamental problem is an occurrence of electromagnetic coupling between the transducers and SAW delay line. Bus-bars delivering electric signal to transducers are placed on an immobile part of the plate. They are long and they are placed close to each other. It causes an increase in capacity between IDTs. The direct signal going through this way is also strengthened. Because of sensor plate motion its casing is larger than those used in traditional SAW filters. It also causes an increase in direct signal strength in the delay line. This problem and possible solutions are known in literature [29-31]. The most effective solution is symmetrical supply of one of transducers and their functioning in a bridge circuit [34]. Such a solution has been used in the presented SAW vibration sensor. The signal strength at the level of –35dB has been achieved. The second mechanism causing increase in direct signal strength is the ground current coupling [33]. Figure 29 shows the mechanism of

Ground current couplings occur only when the connection between component mass and joint mass is not perfect. A diagram in Figure 29 shows this effect by introduced impedances. An ideal connection is characterised by a null value of all impedances. Introduced impedances change current distribution in the entire system. Values of these impedances are small (fractions of ohm). That is why they are difficult to model. A physical making of component mass connection to the system joint mass must be considered during the design stage of the system. Reduction of this value by careful preparation of the system

problems are solved individually, in accordance with a chosen construction.

**Figure 28.** Electromagnetic coupling in electronic system of SAW vibration sensor.

this coupling.

**Figure 29.** The mechanism of ground current coupling.

**Figure 27.** A diagram of an amplifier for SAW vibration sensor.

The amplifier is supplied at the output side by an R1 resistor. The R1 value is selected according to the DC supply voltage. For a supply voltage of 12V the resistance R1 equaled 560Ω. An amplification of 22dB was achieved for test signal frequency of 74MHz. It is the highest amplification value possible to achieve in this system. The value of current input equaled 16mA. Figure 26 shows an experimental frequency characteristics of SAW vibration sensor. Measurement of attenuation frequency diagram of SAW vibration sensor has been conducted on a spectrum analyzer HMS 1010. A supply voltage system has been put at line input. A supply voltage blocking system has been put before the analyzer at line output. Losses of 0.75dB consist of line losses and losses in the connection wiring and discussed separation systems. The value of these losses has been estimated at the level of 1dB. A conclusion may be drawn that an amplifier compensates the losses caused by SAW delay line. A theoretical shape of attenuation frequency diagram of a sensor should be described by the function (sin(x)/x). An experimental characteristic has high-frequency irregularities. Their reasons are the signals going from sensor output to input, omitting sensor electronic components. This signal amplitude is around –36dB lower than useful signal amplitude. The reason of occurrence of signal going from sensor input to output will be discussed in the next Section.

## **3.4. Parasitic signals**

Parasitic signals are the signals going from electronic system input to output, omitting any component which is a part of the test signal transmission line. It is possible due to the occurrence of a parasitic coupling between any place of electronic system. There are two mechanisms leading to the occurrence of couplings [18][33]. The first one is electromagnetic coupling. The second one is ground current coupling. Figure 28 shows the mechanism of electromagnetic coupling. Red lines indicate paths of electromagnetic coupling which may occur in the electronic system of SAW vibration sensor. Electromagnetic couplings occur in all the electronic components constituting a sensor system. Paths of printed circuit are matched to the impedance of 50Ω. They are simultaneously transmitting and receiving aerials. Their efficiency depends on the path length. A similar role is played by inductances occurring in the system and capacities between paths. In order to reduce the electromagnetic coupling the inductances should be placed perpendicularly to each other and placed at a distance. These elements define the manner of making of the printed circuit plates. Any problems are solved individually, in accordance with a chosen construction.

**Figure 28.** Electromagnetic coupling in electronic system of SAW vibration sensor.

462 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**Figure 27.** A diagram of an amplifier for SAW vibration sensor.

The role of an amplifier is to compensate losses caused by SAW delay line. An amplifier has been built on a monolithic system MAR-6 manufactured by Mini-Circuits. Figure 27 shows a

The amplifier is supplied at the output side by an R1 resistor. The R1 value is selected according to the DC supply voltage. For a supply voltage of 12V the resistance R1 equaled 560Ω. An amplification of 22dB was achieved for test signal frequency of 74MHz. It is the highest amplification value possible to achieve in this system. The value of current input equaled 16mA. Figure 26 shows an experimental frequency characteristics of SAW vibration sensor. Measurement of attenuation frequency diagram of SAW vibration sensor has been conducted on a spectrum analyzer HMS 1010. A supply voltage system has been put at line input. A supply voltage blocking system has been put before the analyzer at line output. Losses of 0.75dB consist of line losses and losses in the connection wiring and discussed separation systems. The value of these losses has been estimated at the level of 1dB. A conclusion may be drawn that an amplifier compensates the losses caused by SAW delay line. A theoretical shape of attenuation frequency diagram of a sensor should be described by the function (sin(x)/x). An experimental characteristic has high-frequency irregularities. Their reasons are the signals going from sensor output to input, omitting sensor electronic components. This signal amplitude is around –36dB lower than useful signal amplitude. The reason of occurrence of signal going from sensor input to output will be discussed in the

Parasitic signals are the signals going from electronic system input to output, omitting any component which is a part of the test signal transmission line. It is possible due to the occurrence of a parasitic coupling between any place of electronic system. There are two mechanisms leading to the occurrence of couplings [18][33]. The first one is electromagnetic coupling. The second one is ground current coupling. Figure 28 shows the mechanism of electromagnetic coupling. Red lines indicate paths of electromagnetic coupling which may occur in the electronic system of SAW vibration sensor. Electromagnetic couplings occur in all the electronic components constituting a sensor system. Paths of printed circuit are matched to the impedance of 50Ω. They are simultaneously transmitting and receiving aerials. Their efficiency depends on the path length. A similar role is played by inductances occurring in the system and capacities between paths. In order to reduce the electromagnetic

diagram of an amplifier being a part of an electronic system of SAW vibration sensor.

**3.3. Amplifier** 

next Section.

**3.4. Parasitic signals** 

The fundamental problem is an occurrence of electromagnetic coupling between the transducers and SAW delay line. Bus-bars delivering electric signal to transducers are placed on an immobile part of the plate. They are long and they are placed close to each other. It causes an increase in capacity between IDTs. The direct signal going through this way is also strengthened. Because of sensor plate motion its casing is larger than those used in traditional SAW filters. It also causes an increase in direct signal strength in the delay line. This problem and possible solutions are known in literature [29-31]. The most effective solution is symmetrical supply of one of transducers and their functioning in a bridge circuit [34]. Such a solution has been used in the presented SAW vibration sensor. The signal strength at the level of –35dB has been achieved. The second mechanism causing increase in direct signal strength is the ground current coupling [33]. Figure 29 shows the mechanism of this coupling.

**Figure 29.** The mechanism of ground current coupling.

Ground current couplings occur only when the connection between component mass and joint mass is not perfect. A diagram in Figure 29 shows this effect by introduced impedances. An ideal connection is characterised by a null value of all impedances. Introduced impedances change current distribution in the entire system. Values of these impedances are small (fractions of ohm). That is why they are difficult to model. A physical making of component mass connection to the system joint mass must be considered during the design stage of the system. Reduction of this value by careful preparation of the system

joint mass is a proper solution. Similarly to the first mechanism, SAW delay line plays an important part. Impedance of bus-bars and impedance of contacts leading the signal to transducer are crucial elements in SAW vibration sensor delay line. The joint mass of the discussed system has been made of 5 mm copper plate to which a printed-circuit board has been soldered. This side of the plate was completely bonded. The electronic system joint mass has been connected to component masses. Figure 30 shows SAW vibration sensor. Only supply voltage of the amplifier system goes through printed circuit paths. Longer segments of test signal line have been made by means of coaxial cables. It allowed to reduce an electromagnetic couplings value in the system. Attenuation frequency diagram of this sensor is presented in Figure 26.

Seismic Vibration Sensor with Acoustic Surface Wave 465

directly between interdigital transducers of SAW delay line. In order to explain the origin of the signal, it is important to learn about its delay time. It has been made in a system

At sensor input a signal in form of wave packet at frequency of 74MHz has been delivered. The length of the packet is smaller than line delay. In this way a temporary separation of the

Figure 33 presents timing of signals at the output of SAW vibration sensor. There are five signals at the sensor output. The first signal is going directly from sensor output to its input. The second one is a useful signal. Next three signals are reflected from the plate edge. Reflected signals will be attenuated by a damping paste. The amplitude of direct signal is – 35dB below the useful signal. It leads to conclusion that the signal shown in Figure 31 is a signal going directly between SAW delay line IDTs. When the electronic system is properly made, the elimination of this signal is the most fundamental problem in SAW vibration

SAW-based vibration sensors with SAW were made as described in Section 3. Delaying lines of a 74MHz middle frequency and various delay quantities of 4.2μs, 6.2μs, 8.2μs were

presented in Figure 32.

**Figure 32.** Meter circuit for parasitic signals in SAW delay line.

direct and useful signals has been ensured.

**Figure 33.** Time run of signals in SAW delay line.

**4. Measurements of vibration sensor parameters** 

sensor design.

**Figure 30.** SAW vibration sensor

**Figure 31.** Attenuation frequency diagram of SAW vibration sensor after shut-down of amplifier supply.

Figure 31 presents this characteristic after a shut-down of amplifier supply. Shapes of characteristics in delay line operation band are similar in both figures. It suggests that signal source at the sensor output is situated behind SAW delay line. This signal strength is –35dB below the sensor frequency characteristic signal. Beyond the operation band the signal strength equals –40dB. Conducted measurements make use of the time trace of stationary signals. The lack of information about the delay of these signals does not allow to determine their source. IDTs are selectively matched to the impedance of 50Ω. It can be a signal going directly between interdigital transducers of SAW delay line. In order to explain the origin of the signal, it is important to learn about its delay time. It has been made in a system presented in Figure 32.

**Figure 32.** Meter circuit for parasitic signals in SAW delay line.

464 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

sensor is presented in Figure 26.

**Figure 30.** SAW vibration sensor

supply.

joint mass is a proper solution. Similarly to the first mechanism, SAW delay line plays an important part. Impedance of bus-bars and impedance of contacts leading the signal to transducer are crucial elements in SAW vibration sensor delay line. The joint mass of the discussed system has been made of 5 mm copper plate to which a printed-circuit board has been soldered. This side of the plate was completely bonded. The electronic system joint mass has been connected to component masses. Figure 30 shows SAW vibration sensor. Only supply voltage of the amplifier system goes through printed circuit paths. Longer segments of test signal line have been made by means of coaxial cables. It allowed to reduce an electromagnetic couplings value in the system. Attenuation frequency diagram of this

**Figure 31.** Attenuation frequency diagram of SAW vibration sensor after shut-down of amplifier

Figure 31 presents this characteristic after a shut-down of amplifier supply. Shapes of characteristics in delay line operation band are similar in both figures. It suggests that signal source at the sensor output is situated behind SAW delay line. This signal strength is –35dB below the sensor frequency characteristic signal. Beyond the operation band the signal strength equals –40dB. Conducted measurements make use of the time trace of stationary signals. The lack of information about the delay of these signals does not allow to determine their source. IDTs are selectively matched to the impedance of 50Ω. It can be a signal going At sensor input a signal in form of wave packet at frequency of 74MHz has been delivered. The length of the packet is smaller than line delay. In this way a temporary separation of the direct and useful signals has been ensured.

**Figure 33.** Time run of signals in SAW delay line.

Figure 33 presents timing of signals at the output of SAW vibration sensor. There are five signals at the sensor output. The first signal is going directly from sensor output to its input. The second one is a useful signal. Next three signals are reflected from the plate edge. Reflected signals will be attenuated by a damping paste. The amplitude of direct signal is – 35dB below the useful signal. It leads to conclusion that the signal shown in Figure 31 is a signal going directly between SAW delay line IDTs. When the electronic system is properly made, the elimination of this signal is the most fundamental problem in SAW vibration sensor design.

## **4. Measurements of vibration sensor parameters**

SAW-based vibration sensors with SAW were made as described in Section 3. Delaying lines of a 74MHz middle frequency and various delay quantities of 4.2μs, 6.2μs, 8.2μs were worked out. These delaying lines were made on ST-cut quartz plates of different lengths. These plates were 5.7 mm wide and 0.5 mm thick.

Seismic Vibration Sensor with Acoustic Surface Wave 467

**Figure 35.** System to measure responses from SAW-based vibration sensor pulse plates.

response was approximately 5s and its frequency was 92Hz.

programme – (a) and oscilloscope – (b)

component.

Figure 36 presents a pulse response of a sensor where a delaying line with a 65 mm long plate was used. The sensor plate was not loaded with a seismic mass. The length of the pulse

**Figure 36.** Pulse response of sensor with 65 mm long plate without seismic mass recorded with VEE

The spectrum of a pulse response (a Fourier transform) was calculated with the help the Agilent VEE Pro programme, but it can be achieved also directly on an oscilloscope. Figure 37 presents the amplitude of this spectrum. Its shape corresponds to the amplitude of the frequency characteristics of a tested sensor. The resonance frequency equals theoretical values calculated with the relationships presented in Section 2. The frequency characteristics shows a harmonic at a 400Hz frequency. Its level is –26dB below the level of the sensor characteristics for the resonance frequency. This level is higher than its theoretical estimate presented in Section 2. It is difficult to determine the reason for this difference. It can be the inaccuracy of the model. However, it can be also due to a differing effectiveness of incitation of the resonance frequency component and harmonic frequency

The signal passing thru a sensor is continuous one. In a sensor every parasite signal adds up to a useful signal and causes the amplitude of a useful signal to modulate. This causes the sensor sensitivity to decrease; therefore parasitic signals must be removed. An essential problem is the reduction of a signal passing directly from the delay line inlet to the delay line outlet. The magnitude of this signal for sensors with lines of different delays is shown in Figure 34. The larger the line delay the lower the direct signal level. This level depends on the outlay of electric inlets to the delaying line converters. This is illustrated in Figures 35 (oscilloscope signals A and C). In order to lower the direct signal level additional screening of interdigital transducers or a symmetric supply of one of the converters was used [34]. For executed sensors a direct signal at a level of –36dB was obtained.

**Figure 34.** Direct and useful signal in delaying lines of different delays: A – 4,2μs, B – 6,2μs, C – 4,2μs, D – 8,2μs.

To basic parameters of vibration sensors belong their frequency characteristic curves and the static sensitivity. We will present the way they are measured. Determined experimental characteristics will be compared to the theoretical one. This will enable to estimate the model precision and to what extent it can help to model the parameters of SAW-based vibration sensors. The sensor frequency characteristics were determined in two stages. At the first stage the sensor pulse response was registered. At the second stage the spectrum of this pulse response was determined. Its shape corresponds with the sensor frequency characteristics. Pulse responses of sensors were measured and recorded as well as the spectrum of pulse responses from sensors were calculated with the aid of the system shown in Figure 35. Sensors were agitated for vibrations by an impact. Pulse responses were recorded with the help of the Agilent VEE Pro programme.

**Figure 35.** System to measure responses from SAW-based vibration sensor pulse plates.

466 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

executed sensors a direct signal at a level of –36dB was obtained.

recorded with the help of the Agilent VEE Pro programme.

These plates were 5.7 mm wide and 0.5 mm thick.

D – 8,2μs.

worked out. These delaying lines were made on ST-cut quartz plates of different lengths.

The signal passing thru a sensor is continuous one. In a sensor every parasite signal adds up to a useful signal and causes the amplitude of a useful signal to modulate. This causes the sensor sensitivity to decrease; therefore parasitic signals must be removed. An essential problem is the reduction of a signal passing directly from the delay line inlet to the delay line outlet. The magnitude of this signal for sensors with lines of different delays is shown in Figure 34. The larger the line delay the lower the direct signal level. This level depends on the outlay of electric inlets to the delaying line converters. This is illustrated in Figures 35 (oscilloscope signals A and C). In order to lower the direct signal level additional screening of interdigital transducers or a symmetric supply of one of the converters was used [34]. For

**Figure 34.** Direct and useful signal in delaying lines of different delays: A – 4,2μs, B – 6,2μs, C – 4,2μs,

To basic parameters of vibration sensors belong their frequency characteristic curves and the static sensitivity. We will present the way they are measured. Determined experimental characteristics will be compared to the theoretical one. This will enable to estimate the model precision and to what extent it can help to model the parameters of SAW-based vibration sensors. The sensor frequency characteristics were determined in two stages. At the first stage the sensor pulse response was registered. At the second stage the spectrum of this pulse response was determined. Its shape corresponds with the sensor frequency characteristics. Pulse responses of sensors were measured and recorded as well as the spectrum of pulse responses from sensors were calculated with the aid of the system shown in Figure 35. Sensors were agitated for vibrations by an impact. Pulse responses were Figure 36 presents a pulse response of a sensor where a delaying line with a 65 mm long plate was used. The sensor plate was not loaded with a seismic mass. The length of the pulse response was approximately 5s and its frequency was 92Hz.

**Figure 36.** Pulse response of sensor with 65 mm long plate without seismic mass recorded with VEE programme – (a) and oscilloscope – (b)

The spectrum of a pulse response (a Fourier transform) was calculated with the help the Agilent VEE Pro programme, but it can be achieved also directly on an oscilloscope. Figure 37 presents the amplitude of this spectrum. Its shape corresponds to the amplitude of the frequency characteristics of a tested sensor. The resonance frequency equals theoretical values calculated with the relationships presented in Section 2. The frequency characteristics shows a harmonic at a 400Hz frequency. Its level is –26dB below the level of the sensor characteristics for the resonance frequency. This level is higher than its theoretical estimate presented in Section 2. It is difficult to determine the reason for this difference. It can be the inaccuracy of the model. However, it can be also due to a differing effectiveness of incitation of the resonance frequency component and harmonic frequency component.

Seismic Vibration Sensor with Acoustic Surface Wave 469

more than 2 times. These changes are obvious and their quantities determine explicit relationships describing the sensor model. The only difference between the results of experimental tests against the theoretical model is a higher level of the harmonic resonance frequency. To explain this difference classical measurements of the sensor resonance characteristics must be conducted. To conduct these measurements an exciter of stable mechanical vibrations of the sensor housing of an adjusted amplitude and frequency is

**Figure 39.** Pulse response of sensor with 65 mm long plate with a 1.07g seismic mass recorded with

The test results demonstrated a good compatibility between the theoretical parameters of the sensor pulse response (resonance frequency and the decay time) and their experimental realization. The model presented in Section 2 was used to elaborate SAW-based sensors, which featured required parameters of the pulse response. Figure 42 shows a block diagram

required. It was not possible for the authors to carry out these tests.

VEE programme – (a) and oscilloscope – (b)

**Figure 40.** Spectrum of a 65mm long sensor with 1.07 g seismic mass

of an electronic warning system with SAW-based vibration sensors.

**Figure 37.** Spectrum of sensor with 65 mm long plate without seismic mass

Figure 38 presents the measurement of the statistical sensitivity of a sensor. It was conducted by recording the sensor output signal during its rotation by 180 degrees. This rotation causes the constant acceleration affecting a sensor to change by a value of two gravitational accelerations – i.e. 2 "g". An estimated static sensitivity of a sensor is 40mV/("g").

**Figure 38.** Method of determining static sensitivity of sensor

A 1.07g (r=2,27) seismic mass was placed on a sensor. This caused its resonance frequency to drop to 29Hz, and then for this sensor the above-presented tests were repeated. Fig. 39 shows the pulse response of a sensor with a 65mm long plate with a 1.07 g seismic mass. The pulse response is longer than 10s, with its frequency being 29Hz.

Figure 40 shows the frequency characteristics of the tested sensor. The value of the resonance characteristics equals the theoretical value. The characteristics shows a harmonic at 58Hz. Its level is –4dB below the sensor characteristic value for the resonance frequency, and being low, practically has no impact on the sensor function. Figure 41 shows the measurement result of the sensor static sensitivity as 100mV/("g"). Against a sensor without a concentrated mass this value rose 2 ½ times. The length of the pulse response increased more than 2 times. These changes are obvious and their quantities determine explicit relationships describing the sensor model. The only difference between the results of experimental tests against the theoretical model is a higher level of the harmonic resonance frequency. To explain this difference classical measurements of the sensor resonance characteristics must be conducted. To conduct these measurements an exciter of stable mechanical vibrations of the sensor housing of an adjusted amplitude and frequency is required. It was not possible for the authors to carry out these tests.

468 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**Figure 37.** Spectrum of sensor with 65 mm long plate without seismic mass

**Figure 38.** Method of determining static sensitivity of sensor

The pulse response is longer than 10s, with its frequency being 29Hz.

40mV/("g").

Figure 38 presents the measurement of the statistical sensitivity of a sensor. It was conducted by recording the sensor output signal during its rotation by 180 degrees. This rotation causes the constant acceleration affecting a sensor to change by a value of two gravitational accelerations – i.e. 2 "g". An estimated static sensitivity of a sensor is

A 1.07g (r=2,27) seismic mass was placed on a sensor. This caused its resonance frequency to drop to 29Hz, and then for this sensor the above-presented tests were repeated. Fig. 39 shows the pulse response of a sensor with a 65mm long plate with a 1.07 g seismic mass.

Figure 40 shows the frequency characteristics of the tested sensor. The value of the resonance characteristics equals the theoretical value. The characteristics shows a harmonic at 58Hz. Its level is –4dB below the sensor characteristic value for the resonance frequency, and being low, practically has no impact on the sensor function. Figure 41 shows the measurement result of the sensor static sensitivity as 100mV/("g"). Against a sensor without a concentrated mass this value rose 2 ½ times. The length of the pulse response increased

**Figure 39.** Pulse response of sensor with 65 mm long plate with a 1.07g seismic mass recorded with VEE programme – (a) and oscilloscope – (b)

**Figure 40.** Spectrum of a 65mm long sensor with 1.07 g seismic mass

The test results demonstrated a good compatibility between the theoretical parameters of the sensor pulse response (resonance frequency and the decay time) and their experimental realization. The model presented in Section 2 was used to elaborate SAW-based sensors, which featured required parameters of the pulse response. Figure 42 shows a block diagram of an electronic warning system with SAW-based vibration sensors.

Seismic Vibration Sensor with Acoustic Surface Wave 471

**Figure 43.** Frequency characteristics of sensors of resonance frequency of 41Hz, 56Hz, 73Hz, 159Hz.

sensor mass taking into account its moment of inertia [37] was developed.

**Figure 44.** SAW-comprising vibration sensors attached to steel ropes

These five SAW-based vibration sensors fabricated and used in an electronic warning system proved the efficiency of the presented modeling method. The system was tested on a stand shown in Figure 44. The sensors were attached to steel ropes tensioned as required. In order to describe the movement of sensors and ropes a model of a string loaded with a

Vibrations of sensors were stimulated by deflecting them out of the state of equilibrium. The string vibration time was several times as long as that of the decay time of a senor plate

**Figure 41.** Method of determination the sensor static sensitivity

**Figure 42.** Block diagram of electronic warning system with SAW-comprising vibration sensors.

During operation of the system vibratons of the sensor plate change the phase of the measuring signal. The frequency of these changes equals the plate resonance frequency. Thus the signal from every sensor passing thru a set of filters at the phase detector inlet can be separated. The system operation is discussed further in the following works [35][36]. The said system required SAW-based vibration sensors having parameters given in the Table 2; the authors prepared these sensors.


**Table 2.** Parameters of SAW-VS sensors made for electronic warning system

By selection of a seismic mass required resonance frequencies of sensors were achieved. In case of sensors No. 1 and 2 as well as No. 3 and 4 plates of similar lengths were used. Figure 43 presents characteristics of four assembled sensors.

**Figure 41.** Method of determination the sensor static sensitivity

the authors prepared these sensors.

Divide

SAW

**Figure 42.** Block diagram of electronic warning system with SAW-comprising vibration sensors.

Guarded object

SAW-VS SAW-VS SAW-VS

Data Acquisition System

SAW-VS SAW-VS

Phase

Phase

Filter

Phase

During operation of the system vibratons of the sensor plate change the phase of the measuring signal. The frequency of these changes equals the plate resonance frequency. Thus the signal from every sensor passing thru a set of filters at the phase detector inlet can be separated. The system operation is discussed further in the following works [35][36]. The said system required SAW-based vibration sensors having parameters given in the Table 2;

Sensor No. 1 2 3 4 5 Resonance frequency [Hz] 41 56 73 90 159 Plate length [mm] 86 85 66 68 26 Seismic mass - r 0.22 0 0.14 0 1 Line delay [μs] 6.2 4.2 8.2 4.2 4.2

By selection of a seismic mass required resonance frequencies of sensors were achieved. In case of sensors No. 1 and 2 as well as No. 3 and 4 plates of similar lengths were used. Figure

**Table 2.** Parameters of SAW-VS sensors made for electronic warning system

43 presents characteristics of four assembled sensors.

**Figure 43.** Frequency characteristics of sensors of resonance frequency of 41Hz, 56Hz, 73Hz, 159Hz.

These five SAW-based vibration sensors fabricated and used in an electronic warning system proved the efficiency of the presented modeling method. The system was tested on a stand shown in Figure 44. The sensors were attached to steel ropes tensioned as required. In order to describe the movement of sensors and ropes a model of a string loaded with a sensor mass taking into account its moment of inertia [37] was developed.

**Figure 44.** SAW-comprising vibration sensors attached to steel ropes

Vibrations of sensors were stimulated by deflecting them out of the state of equilibrium. The string vibration time was several times as long as that of the decay time of a senor plate

pulse response. The movement of a sensor was a sum of the fading with time of the pulse response and vibrations enforced by a cyclic movement of the sensors housing. The frequency of the housing movements was that of the rope vibration frequency, which was selected so that it was lower than the resonance frequency of sensors. Thus it was possible to analyze every component of the sensor movement. For experimental testing a string vibration frequency of some 6 Hz was chosen. For every sensor the output signal from the phase detector (Fig. 42) was recorded and processed with the VEE program. Figure 45 and 46 show the course of signals of vibrating sensor of various resonance frequencies and their spectra.

Seismic Vibration Sensor with Acoustic Surface Wave 473

Pulse responses of sensors of an 91Hz (Fig. 45) or a 41Hz (Fig. 46) frequency can be easily discerned form signals derived from a string movement of a 6.7 Hz frequency, especially within the signal spectrum. Relations between their amplitudes are visible. After decay of pulse responses sensors measure the rope vibrations; they work then like classical vibration

In case of a sensor plate without the seismic mass (Fig. 45) the harmonic amplitude occurs at the – 34dB level below the resonance frequency amplitude. With the plate loaded with a small seismic mass (r=0,22, Fig. 46) the level is lower than -40dB. Harmonic vibrations had

Depending on the use of a sensor by selection of its resonance frequency we can change its sensitivity and linearity. The practically prepared electronic warning system with SAWbased vibration sensors has fully proven the usefulness of the model presented in Section 2.

The work presents development, execution and parameters of SAW seismic vibration sensors. A sensor is a two-terminal pair network consisting of a delaying line with SAW and an amplifier compensating losses introduced by a ST-cut quartz. The delay line is fabricated

A simple vibration model of an anisotropic plate was used to develop sensors. By way of successive simplifications of the description of vibrations of a viscous-elastic sensor plate a model of one degree of freedom was obtained. An explicit description of the movement parameters of the sensor plate was achieved. A material damping of the plate practically causes it to vibrate at only one resonance frequency, thus enabling to design SAW seismic vibration sensors. The results of experiments proved the effectiveness of using this model to

Basic parameters of realised vibration sensors (resonance characteristics, pulse responses,

The range of resonance frequencies of plates made of ST-cut quartz, which were feasible, was determined. The plate length restricts the lower range of resonance frequencies. This range was determined on the basis of an available length of 100mm of a CT-cut quartz. The upper range of resonance frequencies is restricted by the speed of decay of a pulse response of a sensor plate. However, this restriction applies only to a sensor operating on its pulse responses. For the determination of this range the magnitude of stresses occurring in the plate was not taken into account. This magnitude must be smaller than the size of critical stresses presented in Table 1. In the subject work this element was not analysed. The magnitude of dynamic, critical stresses for a ST-cut quartz was determined in works [22] [23]. These values do not conform to standards and they apply to a series of plates cut out with a wire saw. In the course of that determination it turned out that the technology of plates production has a great impact on the value of dynamic critical stresses. The work [18] demonstrated that their value for a given design of a sensor does not restrict the determined

no impact on the operation of a system presented in Figure 43.

sensors.

**5. Conclusions** 

on the CT-cut quartz surface.

design SAW-comprising seismic vibration sensors.

static sensitivity) are presented and analysed.

range of the plate resonance frequencies.

**Figure 45.** Part of output signal from sensor of plate resonance frequency of 91 Hz and string vibration frequency of 6.7 Hz and its spectrum

**Figure 46.** Part of output signal from sensor of plate resonance frequency of 41 Hz and string vibration frequency of 6.7 Hz and its spectrum

Pulse responses of sensors of an 91Hz (Fig. 45) or a 41Hz (Fig. 46) frequency can be easily discerned form signals derived from a string movement of a 6.7 Hz frequency, especially within the signal spectrum. Relations between their amplitudes are visible. After decay of pulse responses sensors measure the rope vibrations; they work then like classical vibration sensors.

In case of a sensor plate without the seismic mass (Fig. 45) the harmonic amplitude occurs at the – 34dB level below the resonance frequency amplitude. With the plate loaded with a small seismic mass (r=0,22, Fig. 46) the level is lower than -40dB. Harmonic vibrations had no impact on the operation of a system presented in Figure 43.

Depending on the use of a sensor by selection of its resonance frequency we can change its sensitivity and linearity. The practically prepared electronic warning system with SAWbased vibration sensors has fully proven the usefulness of the model presented in Section 2.

## **5. Conclusions**

472 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

spectra.

frequency of 6.7 Hz and its spectrum

frequency of 6.7 Hz and its spectrum

pulse response. The movement of a sensor was a sum of the fading with time of the pulse response and vibrations enforced by a cyclic movement of the sensors housing. The frequency of the housing movements was that of the rope vibration frequency, which was selected so that it was lower than the resonance frequency of sensors. Thus it was possible to analyze every component of the sensor movement. For experimental testing a string vibration frequency of some 6 Hz was chosen. For every sensor the output signal from the phase detector (Fig. 42) was recorded and processed with the VEE program. Figure 45 and 46 show the course of signals of vibrating sensor of various resonance frequencies and their

**Figure 45.** Part of output signal from sensor of plate resonance frequency of 91 Hz and string vibration

**Figure 46.** Part of output signal from sensor of plate resonance frequency of 41 Hz and string vibration

The work presents development, execution and parameters of SAW seismic vibration sensors. A sensor is a two-terminal pair network consisting of a delaying line with SAW and an amplifier compensating losses introduced by a ST-cut quartz. The delay line is fabricated on the CT-cut quartz surface.

A simple vibration model of an anisotropic plate was used to develop sensors. By way of successive simplifications of the description of vibrations of a viscous-elastic sensor plate a model of one degree of freedom was obtained. An explicit description of the movement parameters of the sensor plate was achieved. A material damping of the plate practically causes it to vibrate at only one resonance frequency, thus enabling to design SAW seismic vibration sensors. The results of experiments proved the effectiveness of using this model to design SAW-comprising seismic vibration sensors.

Basic parameters of realised vibration sensors (resonance characteristics, pulse responses, static sensitivity) are presented and analysed.

The range of resonance frequencies of plates made of ST-cut quartz, which were feasible, was determined. The plate length restricts the lower range of resonance frequencies. This range was determined on the basis of an available length of 100mm of a CT-cut quartz. The upper range of resonance frequencies is restricted by the speed of decay of a pulse response of a sensor plate. However, this restriction applies only to a sensor operating on its pulse responses. For the determination of this range the magnitude of stresses occurring in the plate was not taken into account. This magnitude must be smaller than the size of critical stresses presented in Table 1. In the subject work this element was not analysed. The magnitude of dynamic, critical stresses for a ST-cut quartz was determined in works [22] [23]. These values do not conform to standards and they apply to a series of plates cut out with a wire saw. In the course of that determination it turned out that the technology of plates production has a great impact on the value of dynamic critical stresses. The work [18] demonstrated that their value for a given design of a sensor does not restrict the determined range of the plate resonance frequencies.

As the plate resonance decreases the sensor sensitivity increases. Therefore high sensitivity sensors can be designed. Increasing its length can lower the resonance frequency of a plate. This is the most effective way to reduce the plate resonance frequency. It is possible to develop high-sensitivity vibration sensors of resonance frequencies in the order of a few Hz. To design such sensors one can use directly the presented model. Lets compare the SAW (SAW-VS) vibration sensor presented in the work to three kinds of sensors used at present. Resonance frequencies and basic applications of these sensors are presented in the introduction to this work.

Seismic Vibration Sensor with Acoustic Surface Wave 475

sensitivity for the resonance frequency of the sensor plate or some other frequency. For

An example: for a SAW-VS with a plate 57.5 mm long and 0.5 mm thick, loaded with a seismic mass equal to 4 times the plate mass, a static sensitivity of 0.5V/"g" was achieved. The sensitivity of SAW-sensors for changing accelerations can be a couple of times greater than that for constant accelerations. The sensitivity degree is determined by the resonance curve of a sensor plate. The sensitivity of vibration sensors with SAW-VS can be increased by decreasing the length of the surface wave, or changing the sensor design (i.e. reduction of the plate thickness), by increasing the concentrated mass or by increasing the delay of the

SAW vibration sensors can be cascaded which offers many system designs what in turn offers an increase in the sensitivity and a reduction of the cross sensitivity of sensors. This is not possible with a MEMS sensor and a piezoelectric sensor. The high measuring frequency

In terms of the design and the method of measuring MEMS and SAW-VS acceleration sensors have a lot in common. In a MEMS sensor a vibrating plate of silicon changes the capacity of a capacitor. Mechanical properties of silicon (density 2.330kg/m-3, and an equivalent Young's modulus of 106 Gpa) are similar to mechanical properties of quartz. Therefore the parameters of MEMS and SAW-VS must be similar. In our opinion SAW-VS

This work presents an example of using SAW-sensors in an electronic warning system. Vibration sensors placed at selected points record vibrations within areas they cover. An alert central station registers signals from a vibration sensor. This is a typical system to be

All sensors included in a system can be placed within one area; then this system will perform the role of an analyzer of vibrations within this area. This is a second prospective application of the system under discussion. The possibility of preparing high-sensitivity vibration sensors of resonance frequencies in the order of a few Hz is a prospective area of application for monitoring vibrations of bridges and buildings, where the frequency of free vibrations is in the order of fractions of Hz up to a dozen or so Hz. The presented application examples apply to working on the pulse response of an SAW-sensor. This kind of a sensor can be used to measure one component of the acceleration vector. Then, the pulse response means for a measurement of acceleration a parasitic signal, and should be eliminated. Therefore thru the use of sensor plates, where the decay of a pulse response is fast, acceleration sensors can be developed. The movement of a plate shows then a character of acceleration changes in time. Works [38] [39] show development of this kind of sensors.

*Institute of Electronic and Control Systems, Technical University of Czestochowa, Częstochowa,* 

comparison's sake we can assume the sensitivity for a constant acceleration.

of SAW-comprising sensors allows designing wireless sensor versions.

sensors have their place in the measuring technology.

applied for perimeter protection systems.

SAW-delaying line.

**Author details** 

*Poland* 

Jerzy Filipiak and Grzegorz Steczko

The first kind of these sensors is geophones, where the sensor pulse response is utilized, which explains their low resonance frequency (several Hz) and a high sensitivity.

The two remaining kinds of vibration sensors are micro-mechanical silicone acceleration sensors (Micro Electro Mechanical Systems accelerometers - MEMS accelerometers) and piezoelectric acceleration sensors. Lets compare the basic parameters of these sensors: sensitivity, range of measured values and the frequency of acceleration changes, their structure (resonance frequency (natural frequency), weight and the manner of measuring the acceleration. We don't compare acceleration sensors reacting to impacts. They are very light and feature a very broad measuring range. Piezoelectric acceleration sensors work within a range between fractions of Hz thru a dozen or so kHz. The lower and upper range of the measurement dynamics is from 1 "mg" up to 100.000 "g". ("g" is a unit of acceleration equal to the gravitational acceleration at sea level, i.e. 9.81m/s-2 ). Depending on the design the sensor sensitivity is 0.2mV/g - 0.7V/g. The natural (resonance) frequency ranges from a few Hz to a few dozen of Hz. These sensors weigh from 3g to 500 g. The structure of these sensors is relatively simple, however, the measuring system is complicated (measuring of charge changes in the order of pC). MEMS accelerometers are characterized by small dimensions (an integrated circuit) and a low price. With these devices constant and variable acceleration up to a frequency of a few hundred Hz can be measured.

The lower and upper range of the measurement dynamics is from fractional "g" to 10 000 "g". Depending on the design the device sensitivity ranges from 0.2mV/g up to 10V/g (this applies to seismology sensors).

The device resonance frequency (natural frequency) is high: several Hz. These devices weigh from a few g up to 2 500 "g" (in case of seismology sensors). The sensor design is relatively simple; as well its measuring system is simple. (Measuring of changes in the charge in the order of aF's.)

The measuring system of a MEMS sensor is similar to a measuring system of an SAWvibration sensor presented in the work (Figure 35). It consists of a measuring generator of a 1MHz frequency, two measuring paths and a phase detector.

The mechanical frequency of SAW-comprising vibration sensors can be changed within a range from several to a few hundred Hz. This is a significant difference between these both kinds of sensors. The sensitivity of an SAW vibration sensor depends on the resonance characteristics of the sensor plate, the length of the surface wave utilized in a sensor and on the sensor design. One can define here the sensitivity for a constant acceleration and the sensitivity for the resonance frequency of the sensor plate or some other frequency. For comparison's sake we can assume the sensitivity for a constant acceleration.

An example: for a SAW-VS with a plate 57.5 mm long and 0.5 mm thick, loaded with a seismic mass equal to 4 times the plate mass, a static sensitivity of 0.5V/"g" was achieved. The sensitivity of SAW-sensors for changing accelerations can be a couple of times greater than that for constant accelerations. The sensitivity degree is determined by the resonance curve of a sensor plate. The sensitivity of vibration sensors with SAW-VS can be increased by decreasing the length of the surface wave, or changing the sensor design (i.e. reduction of the plate thickness), by increasing the concentrated mass or by increasing the delay of the SAW-delaying line.

SAW vibration sensors can be cascaded which offers many system designs what in turn offers an increase in the sensitivity and a reduction of the cross sensitivity of sensors. This is not possible with a MEMS sensor and a piezoelectric sensor. The high measuring frequency of SAW-comprising sensors allows designing wireless sensor versions.

In terms of the design and the method of measuring MEMS and SAW-VS acceleration sensors have a lot in common. In a MEMS sensor a vibrating plate of silicon changes the capacity of a capacitor. Mechanical properties of silicon (density 2.330kg/m-3, and an equivalent Young's modulus of 106 Gpa) are similar to mechanical properties of quartz. Therefore the parameters of MEMS and SAW-VS must be similar. In our opinion SAW-VS sensors have their place in the measuring technology.

This work presents an example of using SAW-sensors in an electronic warning system. Vibration sensors placed at selected points record vibrations within areas they cover. An alert central station registers signals from a vibration sensor. This is a typical system to be applied for perimeter protection systems.

All sensors included in a system can be placed within one area; then this system will perform the role of an analyzer of vibrations within this area. This is a second prospective application of the system under discussion. The possibility of preparing high-sensitivity vibration sensors of resonance frequencies in the order of a few Hz is a prospective area of application for monitoring vibrations of bridges and buildings, where the frequency of free vibrations is in the order of fractions of Hz up to a dozen or so Hz. The presented application examples apply to working on the pulse response of an SAW-sensor. This kind of a sensor can be used to measure one component of the acceleration vector. Then, the pulse response means for a measurement of acceleration a parasitic signal, and should be eliminated. Therefore thru the use of sensor plates, where the decay of a pulse response is fast, acceleration sensors can be developed. The movement of a plate shows then a character of acceleration changes in time. Works [38] [39] show development of this kind of sensors.

## **Author details**

474 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

introduction to this work.

applies to seismology sensors).

charge in the order of aF's.)

As the plate resonance decreases the sensor sensitivity increases. Therefore high sensitivity sensors can be designed. Increasing its length can lower the resonance frequency of a plate. This is the most effective way to reduce the plate resonance frequency. It is possible to develop high-sensitivity vibration sensors of resonance frequencies in the order of a few Hz. To design such sensors one can use directly the presented model. Lets compare the SAW (SAW-VS) vibration sensor presented in the work to three kinds of sensors used at present. Resonance frequencies and basic applications of these sensors are presented in the

The first kind of these sensors is geophones, where the sensor pulse response is utilized,

The two remaining kinds of vibration sensors are micro-mechanical silicone acceleration sensors (Micro Electro Mechanical Systems accelerometers - MEMS accelerometers) and piezoelectric acceleration sensors. Lets compare the basic parameters of these sensors: sensitivity, range of measured values and the frequency of acceleration changes, their structure (resonance frequency (natural frequency), weight and the manner of measuring the acceleration. We don't compare acceleration sensors reacting to impacts. They are very light and feature a very broad measuring range. Piezoelectric acceleration sensors work within a range between fractions of Hz thru a dozen or so kHz. The lower and upper range of the measurement dynamics is from 1 "mg" up to 100.000 "g". ("g" is a unit of acceleration equal to the gravitational acceleration at sea level, i.e. 9.81m/s-2 ). Depending on the design the sensor sensitivity is 0.2mV/g - 0.7V/g. The natural (resonance) frequency ranges from a few Hz to a few dozen of Hz. These sensors weigh from 3g to 500 g. The structure of these sensors is relatively simple, however, the measuring system is complicated (measuring of charge changes in the order of pC). MEMS accelerometers are characterized by small dimensions (an integrated circuit) and a low price. With these devices constant and variable

The lower and upper range of the measurement dynamics is from fractional "g" to 10 000 "g". Depending on the design the device sensitivity ranges from 0.2mV/g up to 10V/g (this

The device resonance frequency (natural frequency) is high: several Hz. These devices weigh from a few g up to 2 500 "g" (in case of seismology sensors). The sensor design is relatively simple; as well its measuring system is simple. (Measuring of changes in the

The measuring system of a MEMS sensor is similar to a measuring system of an SAWvibration sensor presented in the work (Figure 35). It consists of a measuring generator of a

The mechanical frequency of SAW-comprising vibration sensors can be changed within a range from several to a few hundred Hz. This is a significant difference between these both kinds of sensors. The sensitivity of an SAW vibration sensor depends on the resonance characteristics of the sensor plate, the length of the surface wave utilized in a sensor and on the sensor design. One can define here the sensitivity for a constant acceleration and the

which explains their low resonance frequency (several Hz) and a high sensitivity.

acceleration up to a frequency of a few hundred Hz can be measured.

1MHz frequency, two measuring paths and a phase detector.

Jerzy Filipiak and Grzegorz Steczko *Institute of Electronic and Control Systems, Technical University of Czestochowa, Częstochowa, Poland* 

## **Acknowledgement**

This work was supported by the Polish Ministry of Science and Higher Education as a project "Vibration Warning System with SAW Vibration Sensors" included in the scientific budget of 2009–2011.

Seismic Vibration Sensor with Acoustic Surface Wave 477

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**Acknowledgement** 

budget of 2009–2011.

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**Chapter 20** 

© 2013 Pirk et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2013 Pirk et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Acoustics and Vibro-Acoustics** 

Gustavo Paulinelli Guimarães and Luiz Carlos Sandoval Góes

During flight, Expandable Launch Vehicles (ELV) are excited by severe acoustic loads in three phases of flight: lift off, transonic flight and maximum dynamic pressure instant [1]. As such, principles to make onboard equipment compatible with the mission environments must be adopted. At lift off, the highly intense acoustic loads occur; and these levels are usually adopted to qualify payloads and equipments. However, during the transonic flight and maximum dynamic pressure phase, acoustic excitation is also present and such characteristics are also significant for performance evaluation as well as for specific system dynamic qualification/acceptance programs. In this way, noise control treatments (NCT) shall be adopted to alleviate internal vibro-acoustic environments, in view of decreasing

The hostile in-flight environments can damage sensors/conditioners as well as make measurements unreliable. In this way, installation adapters must be designed to protect the sensors. The acoustics of such protective cavities influence the measured sound pressure level (SPL) As such, the cavities must be analyzed and their amplitude-frequency characteristics evaluated. Finally, the measurement corrections, necessary to obtain the

Concerning the internal environment found during flights, important launcher subsystems as payload fairing (PLF) and equipment bays shall be investigated and vibro-acoustic analysis can be done, as pointed by [2], [3] and [4]. The PLF is the structural compartment of a launcher where the payload is placed during the flight mission. PLF inner acoustics and its attenuation designs, using virtual prototypes are analyzed using deterministic and statistic techniques. However, when in-flight loading are not characterized, the accounted external air-borne excitation can be those described in [5]. In a similar way, SPL along the launcher structure at

and reproduction in any medium, provided the original work is properly cited.

**Applied in Space Industry** 

Rogério Pirk, Carlos d´Andrade Souto,

http://dx.doi.org/10.5772/49966

**1. Introduction** 

costs and developments.

actual external SPL, are determined.

Additional information is available at the end of the chapter

**Chapter 20** 
