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Sensors and Actuators

PHYSICAL

A 67 ( 1!)98) CO-64

Design of SAW delay lines for sensors Waldemar Soluch *

Abstract Transversal filter and circuit models are used for a SAW delay-line transfer-function derivation.Thedesign procedureof SAW sensor delay linesis described.Calculation and measurement results of a SAW delay line for a centre frequency of about 70 MHz on a 128’ YX LiNbO, 0 199s substrate are presented. Very good agreement is obtainedbetweentheoreticalandexperimental parameters of the delayline. ElsevierScienceS.A. All rightsreserved. Keywords:

Surface acoustic waves; Delay lines; Sensors

1. Introduction

Acoustic Absorber /

Surface acoustic wave (SAW) delay lines are frequently

AClk Layer /

used as piezoelectric elementsin sensors.Such a deIay line consists of a piezoelectric substrateand two bidirectional

interdigital transducers( IDTs) (Fig. 1). The ends of the piezoelectric substrateare angledandan acousticabsorberis applied to reduce SAW reflections. In the caseof chemical sensors,an active layer is usually locatedin the areabetween the lDTs. There are two main structuresof the delay line. In the casewhen the phaseor amplitudeof the output signal is measuredby meansof a vector meter, the delay line may have broad bandwidth. If it is usedin an oscillator circuit, the bandwidth should be narrow enoughto eliminate undesired modes.In both cases,for correct sensoroperation the delay line shouldbe properly designed.

Fig. 1. SAW delay line with double-electrode

IDTs.

2. Transfer function In the case of double-electrode IDTs [ 1] (Fig. 1) , the voltage transfer function of the delay line, q/E (Fig. 2), can be written as [ 1,2] u2 -= E

548 22 34 90 03; E-mail:

0924-4247/98/$19,00 0 PII 50924-4247(97)01737-S

system.

However, we usually measurethe ratio

1’1J’12 Y:~-(YI+YII)(Y~+)‘~~)

(11

whereyI andy2 are the sourceand load admittances,y, I and yZ2are the input admittancesof IDTl andIDT2; respectively, andY,~ is the transfer admittance. * Fax:

Fig. 2. SAW deIay line as a two-port

[email protected]

1998 Elsevier

Science

S.A. .4H rights reserved.

wher’: idaJis the output voltage for the casewhen sourceand load are directly connected.In this case

UT) A-=y1 E

Yl+Yz

(3)

W. Soluch /Sensors

and Actuators

A 67 (1998)

6064

61

Then from Eqs. ( 1) and ( 3) we obtain bkfY,)Y,* YlY-(Y1+Yl1)(Y*fY22)

A12=

0

x2

a

(4)

Eq. (4) can be written in the form A12=IA121exp(j @)

(5)

where IAl is the ratio of amplitudes and Q, is the phase angle. The insertion loss IL ( in dB ) and group time delay Q-are defined as IL=-20

log IAL

(6)

[email protected]/do

(7)

The variations of the group time delay are a measure of the non-linearity of the phase response @. The term JJ,~’ in the denominator of Eq. (4) represents a so-called triple transit signal (TTS). The ratio of the TTS voltage to that of the main signal can be calculated from the expression [ 21

y,** ~Yl+Yll)(Y*+Y22)

A,*=

(8)

and the suppression S,, (in dB) of the ITS can be calculated as St,=-20

log IA,,]

(9)

The suppression should be high enough to eliminate distortions of the transfer function of the delay line.

3. Calculation

of admittances

To calculate the above responses we have to know y , , , yZ2 and yi2 (y, and y1 are known from the measuring system). It should be noticed that )I,, and yZZcan be calculated from the general expressions given in Refs. [ 3,4]. To derive an expression for the transfer admittance y,*, we assume that we have two different double-electrode IDTs (Fig. 3) of the same aperture W (one of them can be apodised). The double electrodes were chosen to eliminate reflections from the periodic electrodes [ 21. Using the results of Ref. [ 41, and the same procedure as DeVries [ 21, the following expression for the transfer admittance y,2 was obtained: yi2=2YOA,A2

exp(-jkrd)

(10)

where A =

y12y13-y23(yo+y~1)

1 [

A

=

(y”+yll)2-~y12)2

yl2y13-y23(yo+y11)

2 (yo+~,1)2-(~,2)2

1 1

(11)

,

(12)

*

Yeis an equivalent characteristic SAW admittance, A, and A,

Fig. 3. Structure

of a SAW delay line with ordinary

IDTs.

are the transfer admittance elements of IDTl and IDT2, respectively, Y,i, YIZ, Y13and YZ3are the admittance matrix components of the IDTs, and d is the internal distance between the IDTs (Fig. 3). After substitution of proper expressions (derived in Ref. [4]) for Y,, YII, Y12, Y,, and Y,, in Eqs. (IO)-( 12), we obtain (13)

Y,z=GoH(w)

where Go is a conductance given by expression (20) in Ref. [4] and H(w)=H;F(w)H,(w)

exp{-j[k,(l,+1,)/2+k,dl}

(14)

lq(w)=

% aIn exp(jk,xd ?I=1

(15)

H*(W)=

2 azn exp(-jk,x2,) II=,

(16)

Here M,, M, are the numbers of gaps, a,, and uZn are the transversal filter coefficients [ 5 ] , and xlrl and xZn are the gap positions along the xi and x2 axes of IDTl and IDT2, respectively. kf=m/uf, kt=wlv,, where vf is the SAW velocity in the area between the IDTs, and v, is that in the area of the IDTs. The velocity vt can be calculated from an expression given in Ref. [ 61.

4. Simplified

expressions

We assume that the IDTs have constant period p, and that the widths of gaps and of electrodes are equal to a (n =p/2) (Fig. 3). The expression for the conductance Go can be written as [41 Go=2.443fo

W(Q+EJK~

(17)

wheref, is the centre frequency, W is the aperture (Fig. 3)) e0 is the dielectric constant of the vacuum, eP is an effective dielectric constant of the piezoelectric substrate and K’ is the square of the effective electromechanical coupling coefficient of the SAW. The static capacitance Cs of a single full-aperture overlap can be calculated from the expression cs=o.707

W(EO+Ep)

(18)

W. Soluch /Sensors

62

and Actuators

The velocity L’, in the area of the IDTs is given by [ 61

(19) where L+ and U, are the SAW velocities for the free and metallized surface, respectively. In this expression, the influence of the mass of the electrodes is not taken into account. Then, the expression for the centre frequency& can be written as fo=~At4p)

(20)

For simple IDTs (Fig. 3), we obtain the following expressions for the admittances y, ,, yZZand y12: C-21)

~J1l=G+j(Bl+~Col) with 2

(22)

(2X,)-2X11/(2X:)

(23)

Co, =N,Cs

(24)

y22=G2+.i(B2+wCo2)

(25)

(36)

A,,=.Y:~/YIY~

From, Eqs. (35) and (36)) at the centre frequencyfe we obtain (37)

This expression can be used for estimation of W, N, and N2. The expression for Go can be written as G,=G,

W/h,

G2=G0Nz(sinX2/X2)

2

WI

(2X,)-2X,1/(2X:)

(27)

C,,z=NzC,

(28)

yt2=GONIN2sinX,lX,

sinX,/Xz

exp(-jwrO)

(29)

where x,=~N,WfoWh

(30)

Xz=rJJz(f-hY3-6 d r,=-f-(l,+-ld Uf 24

(31)

yl,(~d=GoN~+j~,Col

(33)

y22(wd=GON~+j~OC02

(34)

Y~~~)=G~N~N~

(35)

exp(-joovJ

5. Design procedure

To obtain the amplitude and phase responses without undesired ripples, the levels of the spurious signals should be sufficiently low [2]. The main sources of these signals

(39)

is the wavelength in the area of the IDTs, and G,=‘.443r;,(~~+q,)K~

(40)

Then,, Eq. (37) can be written as Q’WdW=~

(41i

The minimum value of the acoustic aperture W is limited by diffraction effects, therefore usually W/h, 2 20. In the case of two identical IDTs, N, = N2 = N, and from Eq. (41) we obtain (42)

(32)

N, and N2 are the number of gaps with non-zero overlap (gaps for which the nearest electrodes are connected to the opposite bus bars). For example, in Fig. 3, N, = 6 and NZ= 4. r0 is the time delay between the centres of the IDTs. Fort=&, from Eqs. (21)-(32), we obtain the following expressions:

(38)

where &=4-p

with

B,=GONz[sin

are acouseic reflections of the SAW from the edges of the piezoelectric substrate, feedthrough and the TTS. The acoustic reflections of SAWS can be eliminated by angled ends of the piezoelectric substrate and by an acoustic absorber (Fig. 1) . Feedthrough can be reduced by proper shielding and by making the distance d (Fig. 3) large enough. In the case of ordinary bidirectional IDTs, the TTS can be lowered by making the TTS suppression S,, high enough. Since for high S,, the insertion loss IL is also high, which means that the input and output IDTs are strongly unmatched, we may omit the input admittances yl, and yZ2in preliminary calculation ofA,, from expression (8). We obtain

GJW,=~

G,=G,,N:(sinX,/X,) B,=GoN:[sin

A 67 (I 99816064

For the preliminary Wand N, we calculate the input admittances of the IDTs, and the accurate values of Ai2 and A, from Eqs. (4) and (8)) respectively. Then, an eventual correctio:n can be done,

6. Examples 6.1. Example 1

A delay line, with two identical IDTs, should be designed on a 128” YX LiNb03 substrate for a centre frequency& = 70 MHz, for operation in a 50 R phase-measuring system. The amplitude of phase ripples [email protected] should be less then 1”. Since the output voltage of a delay line is the sum of voltages of the main signal and that of the ITS, IA,, I can be estimated from the expression IA,,l

(43)

W. Soluch

Fig. 4. Structure

of a SAW delay line with ladder-type

/ Sensors

and Actuators

A 67 (1998)

63

60-64

IDTl.

We obtain lAttI <0.017. If we assume that IA,,1 =O.Ol (which is equivalent to S,, = 40 dB), then [email protected]= 0.6”. For the 128” I’X LiNbO, substrate we have vr= 3978 -I L’, = 3865 m s-’ (measured in our laboratory), KOi55. e&)=55 [7]. From Eq. (19) we obtain rl,=3882 m s-‘, and from Eq. (40) G,=0.26 pS. Since At=~+/fO, then h,=55.46 pm, p = 13.86 p.m and a = 6.93 km. Then, the aperture IV= 1.5 mm can be chosen (it is greater then 20h,). Since in this case y,=y2=0.02 S, from Eq. (42) we obtain N= 17. Finally, after exact calculations, N= 18 was chosen (38 electrodes). For a given distance d (Fig. 3), the time delay r0 can be calculated from Eq. ( 32). It was found from Eqs. (5) and (6) that IL(&) = 15 db.

(4

start

68.60

MHz

stop

72 -88 MHz

6.2. Example 2 A delay line on a 128” YX LiNbO, substrate should be designed for operation as a feedback coupling element in a 50 R oscillator circuit. The centre frequency should be about 70 MHz, IL(&) =: 15 db, d=4 mm (Fig. 4), and the suppression of two nearby longitudinal modes should be more then 7 dB (to prevent jumps of the generated frequency). One long and one short IDT were chosen for this delay line. The long IDT should give a proper bandwidth to suppress the unwanted modes. The structure of the delay line is shown in Fig. 4. To keep IL&) = 15 dB, the number of overlaps N, should be lowered. Therefore the IDTl is a ladder type. In this case eight segments of the ladder were chosen (only one segment is shown in Fig. 4). Then N, = 18 (two overlaps per segment plus one at the beginning and one at the end). IDT2 can be the same as that designed in Example 1 (IV= 1.5 mm, N2= 18). If the time delay 7, between the centres of tapes ( non-zero overlap area of the IDTl ) is equal to the time delay T* along the IDT2 (Fig. 4), then the additional passbands of IDTl are eliminated by the zeros of IDT2. Then the number of electrodes of IDTl will be equal to 294 (36 electrodes per segment plus three at the beginning and three at the end).

7. Calculations

and measurements

The SAW delay line designed in Example 2 was fabricated and measured. The period of the electrodes was chosen as p=13.8 p,m (a=6.9 pm j . Aluminium was used as a metal

7

B (b) STP.i?T

i 68.600

000

MHz

Fig. 5. Amplitude responses for a narrow (b) measurements.

STOP

frequency

72

0130

000

MHz

range: (a) calculations;

for fabrication of the IDT electrodes (thickness about 0.25 p,m). The delay line was mounted in a metal package and measured.Fig. 5(a) showsthe calculated and Fig. 5(b) the measuredinsertion lossIL (HP Network Analyzer 8752A) in a narrow frequency range. The above calculations were done by using Eq. (13) for Y,~ and a general algorithm for the calculation of the input admittances [4]. In a narrow frequency range, it can also be done by using simplified expressions.However, for the IDTl, we shoulduseNI = 2N, in Eq. (30)) where N,Vis the number of wavelengths along IDTl (in our caseN, =73). The measuredIL(&) = 15 dB, asexpected. Markers 2 and 3 in Fig. 5 (b) correspondto the frequenciesat which the phaseshift comparedto the centre frequency (marker 1) differs by 2~ (the nearby modes). The insertion lossat thesefrequenciesis about 9 dB higher than that at the centre frequency. Fig. 6 showsthe calculated and measuredresponsesat a broad frequency range. Some differencesexist near the zerosof the transfer function of IDT2,

W. Sobtch /Sensors

64

I 10$/d

and Acmators

I I I I I I I I

iiu

A 67 (1998) 60-64

To decreasethe influence of the triple transit signals, the minimum insertion loss of the delay line should be about 1.5dB.

Acknowledgements This work was supportedby the State Committee for Scientific Research(KBN) under grant no. 8 TIOC 013 11.

References

start TRN *

50.00 log

stop

MHz

NAG

LB dB/

REF

-15.03

(

dB

90.80 l-15.029 29 0en 70

MHZ dB MHz

G.L. Matthaei, D.Y. Wong, B.P. O’Shaughnessy, Simplification for the analysis of interdigital surface-wave devices, IEEE Trans. Sonics Ultrasonics X7-22 ( 1975) 105. [21 A.J. De Vries, Surface wave bandpass filters, in: H. Matthews (Ed.), Surface Wave Filters, John Wiley, New York, 1977, p. 263. transducers, IEEE~ [31 H. Engan, Surface acoustic wave multielectrode Trans. Sonics Ultrasonics SU-22 (6) ( 1975) 395-401. [41 Vi’. Soluch, Admittance matrix of a surface acoustic wave interdigital transducer, IEEE Trans. Ultrasonics Ferroelectrics Freq. Control 40 (;993)828. I51 R.H. Tancrell, M.G. Holland, Acoustic surface wave filters, Prcc. IEEE 59 (1971) 393. 161K. Blotekjer, K.A. Ingebrigtsen, H. Skeie, Acoustic surface waves in piezoelectric materials with periodic metal strip on the surface, IEEE Trans. Electron Devices ED-20 ( 1973) 1139. S. Jen, M.A. Domalewski, J. Andle, Improved accu[71 C.S. Hartmann, racy for determining SAW transducer capacitance and K*, IEEE Ultrasonics Symp., 1987, p. 161.

Biography

(b) STRRT

50

QQQ

000

MHZ

STOP

Fig. 6. Amplitude responses for a broad frequency (b) measurements.

98.000

range:

000

MHZ

(a) calculations;

but they will have hasno influence on the delay-line operation in an oscillator circuit. The suppressionof the T’IS wasalso measured,and S,,= 40 dB wasobtained.The feedthroughand reflections were suppressedby more than 50 dB.

8. Conclusions It was shownthat transversalfilter and circuit modelscan be applied for the accurate design of SAW delay lines for sensors.Double electrodesshouldbe usedto eliminatereflections from periodic electrodesof the interdigital transducers.

Waldermr Sohrchreceived his MS. degreein electrical engineeringfrom the Warsaw University of Technology in 1961, and his Ph.D. degree from the Military Academy of Technology in 1967.From 1961to 1967he worked as a research assistantand from 1967 to 1973 as a laboratory head at the Military Academy of Technology. He was engaged in research on acousto-electric interactions in piezoelectric semiconductors, acousto-optic interactions and surface acousticwaves incrystals. From 1974to 1975he worked as a managerof the Crystal PhysicsDepartmentat the Research Centre for Crystals. From 1976to 1992he was a managerof the Piezoelectric Filter Department at the Tele and Radio ResearchInstitute, andsince 1993he hasbeenprofessor and a managerof the PiezoelectronicsDepartmentat the Institute of Electronic Materials Technology, Warsaw, Poland. His current researchinvolves measurements of new piezoelectric crystals, and surface acoustic wave filters, resonators and sensors.He is a seniormemberof the IEEE.

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