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Sensors and Actuators A 207 (2014) 1 9

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical

jo ur nal homepage: www.elsev ier .com/ locate /sna

ew approach for the QCM sensors characterization

.L. Casteleiro-Roca, J.L. Calvo-Rolle , M.C. Meizoso-Lopez, A. Pinn-Pazos,.A. Rodrguez-Gmez

epartamento de Ingeniera Industrial, University of A Coruna, A Coruna, Spain

r t i c l e i n f o

rticle history:eceived 23 October 2013eceived in revised form6 November 2013ccepted 2 December 2013vailable online 18 December 2013

a b s t r a c t

The present work shows a novel approach for the QCM characterization. The method is based on the reso-nance principle of passive components. With the proposal, the QCM equivalent circuit parameters basedon BVD (Butterworth-Van Dyke) model are obtained. The results achieved with this new technique arecompared with specific commercial equipment usually employed for this purpose. The best advantagesof the proposed method are its intuitivity and the possibility to obtain it with basic electronic equipment,usually present in any electronic laboratory.

eywords:io-sensorVDlectronics interfacempedance measurementharacterization

2013 Elsevier B.V. All rights reserved.

CM sensor

. Introduction

The quartz crystal microbalance (QCM) is a versatile classf physical, chemical, and biological sensors known to be cost-ffective, high-resolution, mass sensing devices [1]. As an onlineensor, one of its working principles is based on changes in theirrequency of oscillation in proportion to changes in mass depositedn its surface. One of the main advantages of this device is thatt can be easily adapted for detecting a wide range of analyses bypplying different coatings, which make this sensor type extremelyersatile [2].

The QCM has found a wide range of applications in areasf food [3], environmental and clinical analysis since its discov-ry, due to its inherent ability to monitor analyses in real timeimmunosensors, DNA biosensors, drug analysis, etc.) [4]. Theyave been used, too, in adverse environments: monitoring dif-

erent degradation processes (automotive lubricants, composter)58] or monitoring the state of charge in lead acid batteries [9].

ast years the efforts have been focused on decreasing the limitf detection in assays and improving selectivity with difficult sub-trates [2]. One disadvantage of these sensors is the need of an

Corresponding author. Tel.: +34 981 337400; fax: +34 981 337401.E-mail addresses: jose.luis.casteleiro@udc.es (J.L. Casteleiro-Roca),

lcalvo@udc.es, jlcalvo@cdf.udc.es (J.L. Calvo-Rolle), mmeizoso@udc.esM.C. Meizoso-Lopez), andres.pinon@udc.es (A. Pinn-Pazos), benigno@udc.esB.A. Rodrguez-Gmez).

924-4247/$ see front matter 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.sna.2013.12.002

appropriate characterization of the sensor in relation to the specificapplication [1014].

For this purpose many different systems have been developed inthe last years (network or impedance analysis, impulse excitationor decay methods, oscillators and lock-in techniques) see [10] for acomprehensive review of them.

In the case of impedance analysis based systems, the impedancesensor is studied over a range of frequencies near resonance, andthen, the parameters are obtained by fitting the model to theimpedance data measured. Ref. [15] is a classic reference of thesesystems where the well established electric model Butterworth-Van Dyke (BVD) [10,12] is extended to include the effects of themass layer and contact liquid. In [16], a voltage divider with thesensor and a capacitor of known value is used to obtain the real andimaginary components of the quartz crystal BVD equivalent circuit.These systems offer a complete characterization of the sensor asrequired for biosensors operating in liquid media [17].

Impulse excitation or decay methods measure the response ofthe sensor to an excitation signal of the desired harmonic. Thedamping of the sensors oscillation is registered at regular intervalsto measure the properties of the mass deposited over the sensorsurface. These methods provide an accurate characterization beingQCM-D system its major representative [18]. Ref. [19] analyzes theexcitation method with application to liquid media.

On the other hand, several advances of the biosensors based onQCM have been implemented. For instance, in [20] a new methodof improving frequency pullability uses inductance to compen-sate for quartz stray capacitances. In [21] the oscillator can switch

dx.doi.org/10.1016/j.sna.2013.12.002http://www.sciencedirect.com/science/journal/09244247http://www.elsevier.com/locate/snahttp://crossmark.crossref.org/dialog/?doi=10.1016/j.sna.2013.12.002&domain=pdfmailto:jose.luis.casteleiro@udc.esmailto:jlcalvo@udc.esmailto:jlcalvo@cdf.udc.esmailto:mmeizoso@udc.esmailto:andres.pinon@udc.esmailto:benigno@udc.esdx.doi.org/10.1016/j.sna.2013.12.002

2 nsors and Actuators A 207 (2014) 1 9

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scillation between two resonance frequencies switching betweenwo impedance loads obtaining a good accuracy. With the proposalxposed in [22] the compensation of any influence on the crystals possible such as the compensation of the non-linear tempera-ure characteristics and the ageing of both the crystal and otherscillating circuit elements, as well as the reduction of the out-ut frequency measurement errors with the help of an additionaleference frequency.

Many researchers develop their own circuits seeking to over-ome some drawbacks of commercial equipment, such as the highost of better performance systems, or some of the limitations of theheapest (less accuracy [10], slow operation [23], manual compen-ation of parasitic capacities [24,25]). Oscillators and phase lockedoop based (PLL) techniques [26,27] would be in this category. Aomemade quartz crystal oscillator circuit was developed in [12]o overcome the reduced functionality of QCM in a damping media.

cost-effective design is presented in [23] using low cost hardwareor fast monitoring the impedance of the QCM for electrochemicalpplications.

Our proposal is based on a voltage divider similar to that pre-ented in [16], however our circuit uses a basic principle of theehavior of the passive elements to determine the parameters ofhe sensor that make it intuitive. Other goal is trying to use basic lab-ratory equipment in the implementation, due to the fact that theommon techniques require very expensive equipment. For exam-le, both oscillators and PLLs need a careful calibration to maintainhe accuracy of the measurements under damping conditions, andhis calibration may require expensive instruments such as Vectoretwork Analyzers [17].

This paper is organized as follows: It starts with a brief descrip-ion of the novel approach, where the equivalent circuit used for theCM is explained, and the way to characterize the sensor through

he proposal. The experimental section is then presented, it intro-uces the necessary equipment and the topology implemented toest the proposal. Next section gives the results achieved, and at theast section, conclusions reached are shown.

. Novel approach

In this section the novel approach for the QCM characteriza-ion is described. The proposal is based on the commonly usedutterworth-Van Dyke (BVD) equivalent circuit [15,28]. In its sim-le topology the model has the appearance shown in Fig. 1. As itan be seen, the scheme has two parallel branches. The first oneas the C0 capacitor and the other one has a series RLC branch with1 resistor, L1 inductor and C1 capacitor. Several alternatives tohe simple topology of BVD used in this research, like [29,30], haveeen developed with the aim to allow a better approach, above all,o make approximations to specific cases of QCM uses. But due tohe good results achieved with the simple form, this option haseen chosen.

The C0 capacitor is due to the static capacitance and dependsn the QCM geometry [31]. The series RLC branch does not have

specific electric meaning; it models the mechanical phenomenahat describe its performance [31]. The changes on QCM componentan be added as additional passive components in the RLC brancho the model shown in Fig. 1.

.1. Obtaining parameters

For the characterization task, this work is based on the theoryxposed in [15]. In it, the expressions are deducted to obtain thearameters of the electric model of the QCM. Different cases areontemplated on the model described: unperturbed QCM, liquid

Fig. 1. Butterworth-Van Dyke (BVD) equivalent circuit.

loading and mass loading. Fig. 1 only shows the unperturbed QCM,and the expressions for it are Eqs. (1)(4).

C0 = 22Ah

(1)

C1 = 8K20 C0

(N)2(2)

L1 = 12s C1

(3)

R1 = qc66C1

(

s

)2(4)

where 22 is the quartz permittivity, A is the electrode surface area,h is the quartz thickness, K0 is the electromechanical coupling con-stant for quartz, N is the overtone or harmonic number = 1, 3, 5, . . .,s is the angular series resonant frequency for the unperturbedQCM = 2fs, fs is the series resonant frequency in hertz, is theangular excitation frequency = 2f, q is the effective quartz vis-cosity, c66 is the quartz elastic constant.

The expression (1) is function of the physical characteristics(material properties and dimensions) of the QCM, and expressions(2)(4) are function of the physical characteristics of the QCM andof the values obtained for the other components. Therefore, withthe physical features of the QCM, first it is necessary to obtainC0 parameter. When QCM is used, it is usually based on AT-cutquartz. Taking this fact into account, the parameters correspondingof material properties of the expressions (1)(4) can be consideredas constants. As it can be seen in equations, with C0 it is possible to

obtain C1, and with it, L1 and R1 values are obtained. Then, to getthe model, it would only be necessary to obtain the QCM dimensionparameters.

J.L. Casteleiro-Roca et al. / Sensors and Actuators A 207 (2014) 1 9 3

2

booQtgQa

rBfsW(ia

sf

Fig. 2. Circuit approach.

.2. Proposed method

As seen in the previous subsection, the characterization startsy obtaining C0 parameter, and then, with its value, it is possible tobtain the series RLC branch. C0 is the only parameter that dependsn the dimensions of the QCM. Obtaining the dimensions of theCM could be a difficult task due to different reasons [10]. That is

he reason why, in this research, a novel approach is described toet C0 parameter without the need of obtaining dimensions of theCM. The new method is based on the circuit shown in Fig. 2, wheren inductor is added in series with the QCM.

The proposal is based on the operation principle when the seriesesonance phenomenon occurs between the C0 capacitance of theVD model of the QCM and the added inductor at their resonant

requency (r in radians). Then, it is necessary to feed the circuithown in Fig. 2 with an AC source and perform a frequency sweep.

hen the source frequency is the same as the resonant frequencyr), then the impedance (C0 in series with L) is zero. If the addednductor is known, then it is possible to obtain the C0 capacitances described in Eq. (5).

XL = jL

XC0 =1

jC0

jrL +

1jrC0

= 0 C0 = 12r L

(5)

Commonly, the frequency of the laboratory equipment is pre-

ented in hertz (fr), and then it is only necessary to convert therequency r with the expression (6).

r = 2fr (6)

Fig. 3. Practical circuit.

If the frequency is obtained in hertz, the capacitance C0 isobtained through Eq. (7), as a result of replacing Eq. (6) in (5).

C0 = 1L(2fr)

2(7)

In a practical view, it is necessary to implement the circuitshown in Fig. 3, where a resistor has been added. The reason isthat when resonance occurs, the impedance (C0 in series with L) iszero, then the source would be in short-circuit, and it is not usuallya desired state.

With the aim to obtain a very satisfactory result of the C0 capac-itance value, it is necessary to make the tests far from the resonantfrequency of the QCM. In [10], it is recommended to choose at leastthe double of the QCM resonant frequency value. Other consider-ation is to use elements with a good precision and accuracy, aboveall, the inductor L. The R resistor is not as important, because itsmain aim is to protect the source from a short-circuit. But, the cho-sen resistor must have a very precise value, too (small tolerance)to solve the following subsections satisfactorily.

2.3. Inductor calibration

As mentioned before, it is very important to have a very precisevalue of the inductor L to obtain C0 capacitance value. Due to the factthe inductor tolerances are usually very high, then, it is necessary toget its real value for a good performance of the method. To measurethe real values of the inductors, in this research the circuit shownin Fig. 4 is used.

Like in the above subsection, to solve the problem, the series res-onance phenomenon between passive elements is used. The circuitwill have a source with the possibility to make a frequency sweep.In this case, the capacitor Ccal is known and, it must have a veryprecise value (small tolerance). Then, by knowing the capacitance(Ccal), it is possible to obtain the exact value of the L inductor (Eq.(8)).

XL = jL

XCcal =1

jCcal

jrL +

1jrCcal

= 0 Ccal = 12r L

(8)

Also in this case, it has been necessary to add a resistor (Rcal)with the aim to avoid the short circuit possibility of the source.Here, the exact value of the resistor need not be known.

4 J.L. Casteleiro-Roca et al. / Sensors and Actuators A 207 (2014) 1 9

alibra

2

t(amwwtu

sofRcvb

V

Fig. 4. Circuit to c

.4. The special case of the resistor model value

In several works like [15,29], it is shown as a possible methodo obtain the R1 value of the BVD model (Fig. 1) through Eq.4). Nonetheless, other studies like [10,12], prove that the resultchieved in this way is wrong, even [15] obtains R1 value with otherethod despite showing the above equation too. For this reason,ith the goal to obtain the real value of the resistance, a similaray like in the above subsections is proposed. It is only necessary

o remove the L inductor of the circuit shown in Fig. 3. For a goodnderstanding of the proposal, Fig. 5 is shown.

Like in the above cases, it is necessary to apply a frequencyweep to the source and pay special attention when the series res-nance phenomenon occurs on the QCM. Just at series resonantrequency, the series RLC branch of the BVD model only has the1 resistance, because L1 and C1 impedances are cancelled. In thisondition, the circuit is a voltage divider. Since Rcal and the appliedoltage to the circuit are known, it is possible to obtain the R1 valuey measuring the voltage drop on the QCM as shown in Eq. (9).

QCM =R1

R1 + Rcal Vin R1 =Rcal VQCMVin VQCM

(9)

Fig. 5. Circuit to obtain R1 value of BVD model.

te the L inductor.

3. Experimental

In this section the experiments carried out to validate the pro-posal are described. First of all, in the first subsection, all necessarythings to obtain the real values of the QCM parameters are pre-sented. Then, the experiment carried out to implement the proposalwith basic equipment frequently used in any electronic laboratoryis described. In this section, the methods carried out to obtain theQCM parameters following the proposed method, as well as the realvalues of the components necessary in it, are shown.

3.1. Obtaining QCM parameters with the novel approach

The general scheme to test the novel approach is illustrated inFig. 6.

As it can be seen in the figure, basic equipment present in anyelectronic laboratory is used to make the characterization of theQCM:

Function/Arbitrary Waveform Generator, mod. 33220A, 20 MHz. Oscilloscope, mod. DSO3062A, 60 MHz. GPIB/Ethernet converter, NI GPIB-ENET/100. PC-Windows with LabView software.

The first two items are essential, however the last two areoptional. The main advantages of the configuration with the allequipment are:

It is possible to achieve more accuracy. It is possible to automate the measurement operation.

Fig. 7 shows the assembly of the proposal. On the bottom-right ofthe figure, the physical implementation of the circuit correspondingwith Fig. 3 is shown too.

The QCM is allowed in a crystal holder ready to introduce thesensor in a liquid media. The QCM used is the standard sensor of theQCM200 system [25]. It consists of a thin disk (1 in. in diameter) of5 MHz, AT-cut, -quartz with circular gold electrodes patterned onboth sides. The elements used to connect the circuit with the equip-ment have a very low attenuation and a very good performance forthis purpose. The circuit used in the proposal has been designed tominimize disturbance.

Also, to create good test conditions, the own holder has beenintroduced into a methacrylate box. Into it, with the help of anincandescent lamp and a temperature controller, temperature isfixed to 25 C during the experiments. Even, to depressurize insidethe box there is a fan on the top of the box. With this fact, a low

level of humidity (between 20% and 30%) is achieved. The fre-quency sweep could be made manual, but in this case, with thehelp of the GPIB to Ethernet converter is automated with a pro-gram made under LabView software. Then it is possible to achieve

J.L. Casteleiro-Roca et al. / Sensors and Actuators A 207 (2014) 1 9 5

to te

ma

3p

a

Fig. 6. General scheme

ore accuracy and the operation is automated (up to 101 Hz). Theppearance of the developed application is shown in Fig. 8.

.2. Obtaining the real values of the components used in the

roposal

So, to obtain the real value of the inductor used in the approach,s to obtain the real value of the resistor R1 of the QCM model, with

Fig. 7. Equipment used for

st the novel approach.

the circuits explained in previous subsections, it is only necessaryto make modifications in the circuit shown in Fig. 7. For the firstcase, the QCM is replaced by a NPO type capacitor that has verylow tolerance (0.5%). For the second case, compared with the first

circuit, a short-circuit is placed instead of the inductance. Also, inthis case, the frequency sweep could be made manually, but like inthe above case, it is made with the help of the application devel-oped. The operation can be made automatically due to the iterative

the novel approach.

6 J.L. Casteleiro-Roca et al. / Sensors and Actuators A 207 (2014) 1 9

Fig. 8. Application developed under LabView software.

Table 1Commercial values of the used inductors (H).

Inductor index L1 L2 L3 L4 L5 L6 L7 L8

silao

4

aiam

4

iAtov

ot

Table 2Values of the precision capacitors (NPO type, pF).

Inductor index C1 C2 C3 C4

Value 10 15 20 22

Table 3Tests to calibrate L4 inductor with C2.

C2 = 15 pF; L4 = 56 H

Test index Capacitancevalue (pF)

Resonancefrequency (Hz)

Inductor value(H)

1 15 5408362.5 57.7321082 15 5408362.7 57.7321043 15 5408362.8 57.732102

.

.

.28 15 5408362.9 57.73210029 15 5408362.7 57.73210430 15 5408362.7 57.732104

Value 2.2 20 40 56 100 100 220 330

earch of the lowest amplitude of the signal made with the virtualnstrument implemented in LabView software. When this value isocalized approximately, then it is possible to narrow the searchrea. Consequently, a better accuracy is obtained, which dependsn the precision of the equipment.

. Results

This section shows the test results obtained to check the novelpproach. To characterize the QCM, the experiments are describedn detail. For the proposal, it is only necessary to have the equipmentnd software described in the above section. Another equipmententioned in this section, is only used to validate the method.

.1. Obtaining the real inductor values

The main component, which allows carrying out the approach,s the inductor to measure the capacitance C0 of the QCM model.s it is commented in the above sections, it is necessary to obtain

he real value of this inductor to achieve a good accuracy. Amongthers, because the L1 and C1 model parameters are function of C0alue.

Table 1 shows the commercial values of the used inductors. Allf them have a tolerance of 5%, which it is the typical tolerance ofhe precision inductors.

Average 15 5408362.72 57.732104

All the used inductors are without core type, except the L6inductor, which is an iron core type. Table 2 shows the capaci-tor values employed to obtain the inductor real value according toSection 2.3. The capacitors have a tolerance of 0.5% and they areNPO type. This characteristic ensures the less value variance for alltemperatures ranges.

Then, to obtain the inductor real values, each inductor in Table 1was tested with all capacitors in Table 2. For each combination

(each inductor with each capacitor) a representative number ofmeasurements with the aim to obtain a reliable result have beenmade. Table 3 shows six of the thirty measurements made for the

J.L. Casteleiro-Roca et al. / Sensors and Actuators A 207 (2014) 1 9 7

Table 4Inductors real values.

Inductor index Commercial value (H) Tolerance (%) Real value (H)

L1 2.2 5 2.214L2 20 5 20.2L3 40 5 40.72L4 56 5 57.73L5 100 5 104.3L6 100 5 101.3L7 220 5 210.5L8 330 5 316.7

Table 5Test to obtain C0 with L6 inductor.

L6 = 100H

Test index Inductor value(H)

Resonancefrequency (Hz)

Capacitancevalue (pF)

1 101.3 3537963.1 19.9767222 101.3 3537479.0 19.9821293 101.3 3536872.3 19.989046

.

.

.28 101.3 3538056.5 19.97566729 101.3 3535738.6 20.001866

cta

wmta

4

t

tpfe

ttd

Atii

Table 7Values of the precision resistors ().

TC

30 101.3 3535094.7 20.009153

Average 101.3 3537317.33 19.984027

ombination between L4 (56 H) with C2 (15 pF). At the end ofhe same table, the real value of L4 inductor is shown, where theverage has been made with all the values.

Since four capacitors have been considered for the test, thereill be four inductor values. Then, with these values the average isade again, whose value is considered the real value of the induc-

or. Table 4 is obtained as a result of the measurements. In it, thechieved real values of the inductors are shown.

.2. Obtaining QCM parameters

Once completed the previous step with the aim to characterizehe QCM, it is necessary to work with the circuit showed in Fig. 3.

Here, with the method described in Section 2.2, the objective iso obtain the C0 capacitance with the inductors calibrated in therevious subsection. In this case, thirty measurements were madeor each of the eight inductors and the average was obtained forach one (Table 5 shows the test for L6 inductor).

The present test has more variance in frequency than the one inhe previous case. Due to it, during this test, it has been necessaryo pay special attention to insulate the QCM site to avoid externalisturbances like humidity, airstream, and so on.

In Table 6 the C0 values obtained for each inductor are shown.

lso, L1 and C1 values that were calculated with the equa-

ions described in Section 2.1 are presented. Another parameter,ncluded in this table, is the resonance frequency between thenductor and the C0 capacitance. This parameter is very important,

able 60, C1 and L1 values obtained with all inductors.

Inductor index Value (H) Frequency (MHz)

L1 2.2 23.923 L2 20 7.929 L3 40 5.552 L4 56 4.7055 L5 100 3.497 L6 100 3.538 L7 220 2.221 L8 330 1.997

Resistor index Rcal 1 Rcal 2 Rcal 3 Rcal 4 Rcal 5

Value 7.50 8.25 9.31 10.0 12.0

attending to the work [10]. In it, it is recommended to choose theparameter values, when the frequency values are at least twice thenatural resonance frequency of the QCM. By following these rec-ommendations, the correct values are measured with L1, obtainedfrom a frequency nearly 5 times the QCM frequency (5 MHz). Stat-ing that, as it can be seen in Table 6, all the values calculated arevery similar.

The last parameter of the QCM model is R1. To calculate it, themethod described in Section 2.4 is followed, then, in this case, theused circuit is the one shown in Fig. 5. Now, the tests are made witha set of precision resistors with a tolerance of 0.1% (Table 7).

As in the above cases, thirty measurements were made for eachof the five resistors and the average was obtained for each one(Table 8 shows the test to obtain R1 value with Rcal 3).

Different tests were made using all the Rcal; the averages cal-culated of R1 are presented in Table 9. Then, with these values, theaverage is made again and it is considered the R1 real value.

4.3. Novel approach validation

With the aim to validate the novel approach, in this subsectionthe equipment used to obtain the real values of the QCM param-eters in a common way is presented. Then, with these values, theproposal will be validated. Also, the real values of the componentsused in the proposal are measured to check the procedure describedabove. Both are the dispositive to characterize the QCM and tomeasure the real values of the used components. The first one isRohde & Schwarz ZVL303 Vector Network Analyzer with a range offrequency between 9 KHz and 3 GHz. The second one is a generalpurpose dispositive that can function as Vector Network Analyzer,and in this mode the range of frequency goes from 1 Hz to 40 MHz.Attending to the features, the first is medium and the second is lowrange. Equally they are very precise for these applications and givevery good results. The calibration in both cases is made once a year.

A representative number of measurements have been made andin all cases, the values obtained only differ in less than 1% comparedto the results of the new method.

4.4. The liquid media and load case

The great majority of the applications based on QCM sensors arecarried out in liquid media. In fact, the sensor was characterized in acrystal holder ready to introduce it in liquid media. Under this con-dition the BVD equivalent circuit includes two new elements: an

additional inductance (L2) and a resistance (R2) in the series branchrepresenting the liquid load. So in this case, the new resonant fre-quency is fs = 1/(2

LC1), where the inductance L = L1 + L2 and C1

has the same value as in air media. Then it is possible to determine

C0 value (pF) C1 value (fF) L1 value (mH)

19.99 125.41 8.1219.95 125.16 8.1320.18 126.60 8.0419.82 124.34 8.1819.86 124.59 8.1719.98 125.35 8.1220.20 126.73 8.0320.06 125.85 8.09

8 J.L. Casteleiro-Roca et al. / Sensors and Actuators A 207 (2014) 1 9

Table 8Calculating R1 with Rcal 3.

Rcal 3 =9.31

Test index Rcal value () Resonance frequency (Hz) Voltage measure (V) R1 calculated ()

1 9.31 5005725.2 0.5020 9.3866642 9.31 5005729.0 0.5020 9.8472133 9.31 5005722.5 0.5020 9.068463

.

.

.28 9.31 5005720.4 0.5020 9.55000129 9.31 5005722.9 0.5020 9.25505530 9.31 5005723.5 0.5020 9.701506

Average 9.31 5005722.32 0.5020 9.507207

Table 9R1 values obtained.

Resistor index Rcal value () Resonance frequency (MHz) QCM voltage (mV) R1 calculated ()

Rcal 1 7.50 5.006 557 9.44Rcal 2 8.25 5.006 537 9.56Rcal 3 9.31 5.006 505 9.51Rcal 4 10.0 5.006 487 9.51Rcal 5 12.0 5.006 447 9.69

R1 average 9.54

equiva

ti

cBF

u

5

ttpca

masra

ppf

t

[

[

Fig. 9. BVD

he value of L1 first, and with the same procedure and the sensormmersed in the solution, the new value of L.

When the QCM has a load, in liquid media or not, the same pro-edure can be carried out to achieve the model parameters. TheVD model for the QCM in liquid media and with load is shown inig. 9.

In this case, the BVD circuit is not as accurate as that for thenperturbed situation but it is still valid [10].

. Conclusions

A new method to characterize QCM sensors has been shown inhis work. The achieved model is based on the simple topology ofhe BVD equivalent circuit. As it can be seen in this research, theroposed method is based on the traditional properties of passiveomponents, like resonance principle, and it makes it very intuitivend easy to understand.

Two are the main advantages achieved with the novel proposedethod. The first one is that the proposed method itself is an

lternative to the existing techniques to characterize QCM basedensors. With it, it is possible to obtain the QCM parameters rep-esented as BVD model. As it can be seen in Section 4, the methodllows reaching a good accuracy and precision.

With basic laboratory equipment, it is possible to carry out theroposed method. This is the second reliable advantage of the pro-

osal, because it is only necessary to have an oscilloscope and aunction waveform generator to get satisfactory results.

In previous works, it is advised to obtain the C0 value far fromhe oscillation frequency of the quartz crystal. However, as it can

[

lent circuit.

be checked in Section 4, it is not necessary to move away from it somuch.

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[4] C.K. Sullivan, G.G. OGuilbault, Commercial quartz crystal microbalances the-ory and applications, Biosensors & Bioelectronics 14 (1999) 663670.

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iographies

.L. Casteleiro-Roca was born in A Coruna, Spain, in 1981. He received the B.S. fromniversity of Coruna in 2003, the M.S. in Industrial Engineering from the University

f Leon in 2012, and now he is a Ph.D. student in the University of Coruna. He is aechnical Engineer in Spanish Navy, and he has been working in Ferrols Missilesorkshop since 2004. His main research interests have been centered in applying

xpert system technologies to the diagnosis and control systems and in intelligentystems for control engineering and optimization.

nd Actuators A 207 (2014) 1 9 9

J.L. Calvo-Rolle was born in A Coruna, Spain, in 1974. He received the M.S. and Ph.D.degrees in Industrial Engineering from the University of Leon, Leon, Spain, in 2004,and 2007, respectively. He is a Associate Professor of Automatic Control and thehead of Industrial Engineering Department, Faculty of Engineering, University of ACoruna, Spain. His main research interests have been centered in applying expertsystem technology to the diagnosis and control systems and in intelligent trainingsystems for control engineering, optimization and education.

M.C. Meizoso-Lopez was born in A Coruna, Spain, in 1967. She received the M.S.degree in Telecommunications Engineering from the University of Vigo, Pontevedra,Spain, in 1994 and the Ph.D. degree in Industrial Engineering from the Universityof A Coruna, Spain in 2012. She joined the Industrial Engineering Department atUniversity of A Coruna, Spain as Associate Professor in 1994. She has led and partici-pated in several research projects. Her main research interests include solar energy,temporal series of solar radiation.

A. Pinn-Pazos was born in A Coruna, Spain, in 1969. He received the M.S. degreesin Industrial Engineering from the University of Coruna, Coruna, Spain, in 1998. Heis Associate Professor in the Systems Engineering and Automatic Control area ofIndustrial Engineering Department, Faculty of Engineering, University of A Coruna,Spain. His main research is centered on sensors, electronic instrumentation andfieldbus sensors.

B.A. Rodrguez-Gmez received his B.S. in Science (Physics) from the University

tal) from the University of A Coruna, Spain in 2010. He is a Associate Professor ofInstrumentation and Control Systems at the Faculty of Nautical Science and NavalMachinery, University of A Coruna, Spain. His current specific interests includeassessment of natural resources and systems modeling.

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approach for the QCM sensors characterization1 Introduction2 Novel approach2.1 Obtaining parameters2.2 Proposed method2.3 Inductor calibration2.4 The special case of the resistor model value3 Experimental3.1 Obtaining QCM parameters with the novel approach3.2 Obtaining the real values of the components used in the proposal4 Results4.1 Obtaining the real inductor values4.2 Obtaining QCM parameters4.3 Novel approach validation4.4 The liquid media and load case5 ConclusionsReferencesBiographies