MODELLING OF SAW BIOSENSORS

Marija Hribšek, Slavica Ristić, Zdravko Živković

Goša Institute, Milana Rakića 35, Belgrade, Serbia

Dejan Tošić

Faculty of Electrical Engineering, Bulevar kralja Aleksandra 73, Belgrade, Serbia

Keywords: SAW devices, SAW filters, biosensors.

Abstract: New approach in surface acoustic wave (SAW) biosensor’s modelling is presented. Biosensor is modelled

as a three port network. The model is general and can be used also in the case of transponder type of sensor.

The closed form solutions for transfer function and input admittance at the electrical port of SAW devices

with uniform transducers based on complex equivalent circuit are presented. Transfer function and input

admittance in two different cases are calculated and compared with the experimental results showing very

close agreement.

1 INTRODUCTION

Surface acoustic waves (SAW) were discovered in

1885 by Lord Rayleigh, and are often named after

him: Rayleigh waves. A surface acoustic wave is a

type of mechanical wave motion which travels along

the surface of a solid material. Rayleigh showed that

SAWs could explain one component of the seismic

signal due to an earthquake, a phenomenon not

previously understood. The velocity of acoustic

waves is typically 3000 m/s, whish is much lower

than the velocity of the electromagnetic waves. A

basic SAW device consists of two interdigital

transducers (IDTs) on a piezoelectric substrate such

as quartz. The IDTs consist of interleaved metal

electrodes which are used to launch and receive the

waves, so that an electrical signal is converted to an

acoustic wave and then back to an electrical signal

(Morgan,1985)

The basic application of the SAW device is as

delay line. Central frequency and the bandwidth are

determined by the IDT`s geometry and the substrate

type. The IDT geometry is capable of almost endless

variation, leading to a wide variety of devices.

Starting around 1970, SAW devices were developed

for pulse compression radar, oscillators, and

bandpass filters for domestic TV and professional

radio. In the 1980s the rise of mobile radio,

particularly for cellular telephones, caused a

dramatic increase in demand for filters. New high-

performance SAW filters emerged and vast numbers

are now produced, around 3 billion annually. In the

last two decades SAW devices have found numerous

different applications outside their conventional

fields of application: communications and signal

processing. In the last decade considerable work has

been done in the development of SAW sensors of

different types of high quality. SAW filters are used

as temperature, pressure and stress sensors as well as

chemical and biosensors (Seifert, 1994, Pohl, 2000).

At Imperial College in London are working on

implantable and wearable SAW devices for long

term clinical monitoring. Saw sensors are also used

for wireless monitoring in harsh environment. There

are two different types of SAW sensors: transversal

and resonant. In liquids usually SH SAW type of

sensors are used. In the references only analyses in

time domain of the sensors exist. In the frequency

domain only resonant type of SAW sensors are

modelled (Campbell, 1989).

In this paper modelling of transversal SAW

sensors is presented. It is well known that the exact

analysis of SAW devices using surface wave theory

is very complex (Matthews, 1977). Because of that

approximate methods of analysis are developed. The

simplest method of analysis is using delta function

model. It gives the approximate results relatively

376

Hribšek M., Risti

c S., Živkovi

c Z. and Toši

c D. (2009).

MODELLING OF SAW BIOSENSORS.

In Proceedings of the International Conference on Biomedical Electronics and Devices, pages 376-379

DOI: 10.5220/0001544203760379

 SciTePress

fast, but its use is limited to small loads and

substrates with lower coupling constants.

The better approximate methods use equivalent

models for IDTs, where the analysis tools known in

electrical engineering can be applied. In these

methods the accuracy depends on the complexity of

the model. The closed form solutions for transfer

functions and input admittances mostly only for

simple models are given (Matthews, 1977, Morgan,

1985, Smith 1, 1969, Smith 2, 1969, Debnath, 1983,

Hribšek, 1983). In this new algorithm SAW

biosensor is modelled as three port network. The

IDT`s equivalent circuit based on Milsom`s and

Redwood`s equivalent model (Milsom and

Redwood, 1971) is most complex. Using the

symbolic analysis method (Hribšek, 2007) the closed

form solutions for transfer function and input

admittance of the SAW biosensor are derived. The

algorithm is valid for both types of sensors: direct

and transponder types (Pohl, 2000). The algorithm is

verified by two examples: insertion loss and input

admittance are computed and compared with

experimental results. It is also shown that in the case

of the transponder straightforward dependence of the

loss and measured value is obtained.

2 THE MODEL

The transversal SAW biosensor can be

schematically presented as in Figure 1: between the

interdigital transducers (IDT) on the top of the

piezoelectric substrate the chemical or bio sensitive

layer is placed.

Figure1: The basic configuration of SAW biosensor.

The surface wave is induced by electrical signal

applied to the input IDT. The output signal (voltage)

is taken from the second IDT. The interdigital

transducers are wideband with uniformly spaced

electrodes. The configuration presented in Figure 1

can be modelled by equivalent electrical scheme

given in Figure 2 where IDT`s are three port

networks and the middle sensing part is a two port

network.

Figure 2: Equivalent electrical model of a saw sensor.

The characteristic acoustic impedance of the

unloaded substrate is Z

, and the electrical

impedances of the generator and load, are Z

and Z

respectively. Each part is defined by its

corresponding admittance matrix Y

(1)

, Y

(2)

and Y

(3)

These matrices are calculated following the

procedure presented in (Hribšek, Tošić). In general

case matricies Y

(1)

and Y

(3)

are different, but usually

in sensors they are equal with small number of

electrodes, thus simplifying the calculations. Since

the circuit is passive for all matrices the passivity

condition: Y

,= Y

, for i

≠

j, is valid. F

`s and v

denote the electrical equivalents of mechanical

forces and velocities. The elements of Y

(2)

of the

sensing part is given by:

cot

)2(

(1)

ecj

cos

)2(

(2)

where

ff /

f is the central frequency,

Z is the acoustic impedance of the sensing part,

and f is the frequency of the input signal.

Now the whole sensor can be represented as an

equivalent two port where one port is the electrical

input of the input IDT and the second port is the

electrical port of the output transducer. The transfer

function of the two port defined as:

T =

(3)

can be expressed in the following form:

MODELLING OF SAW BIOSENSORS

377

ZYYZY

21121122

)1)(

( −++

−

(4)

where Y

are the admittance parameters of the

equivalent two port. Therefore, for the transfer

function determination y parameters should be

found. They are found in several steps. In each step

one partial Y matrix is derived. In the first step

matrix Y`, which connects input voltage and current

with force F

and velocity v

, is found. Than the

matrix Y`` which gives the relationship between the

input signals and the F

and v

is determined.

Finally, the Y matrix is derived in terms of

parameters of the matrices Y

(1)

, Y

(2)

and Y

(3)

. The

expressions are in closed form, but very bulky and

that is the reason why they are omitted in this text.

The symbolic circuit analysis method is used. The

obtained relations are general. In the case of SAW

sensors they can be less complex if input and output

transducers are equal. Also if the simpler models of

IDTs are used, the calculation will be easier, but in

any case computer must be used.

For matching purposes, the input admittance

must be determined. It can be expressed in terms of

the y parameters of the input transducer as follows:

121111

1112

1333

))((

yYyYy

YYyy

yyY

−++

+++

−=

(5)

Using the algorithm presented, the computer

program which calculates frequency dependence of

input conductance and susceptance and insertion

loss of SAW device with two uniform transducers

was made. The program was verified by two

examples taken from (Smith et al.1., Smith et al.2).

In these cases the substrate between transducers was

unloaded, e.g.

ZZ = . The computed results are

presented in Figures 3. and 4., solid lines. To allow

comparison between the computed and measured

data, the experimental results are also presented in

the same figures, dotted lines.

From Figures 3 and 4 is obvious that

experimental and calculated data are in excellent

agreement, even better than in (Smith et al.1., Smith

et al.2).

Figure 3: Real (G

) and imaginary (B

) part of the input

admittance.

Figure 4: Calculated and measured insertion loss.

Since the algorithm and computer programs are

verified than can be successfully used in the analysis

or prediction in any particular case in SAW

biosensors. In that case due to the loading of the

sensitive film the acoustic impedance will change

accordingly, and therefore Y

and T have to be

changed.

The algorithm is general. It can be also very

efficiently used in the frequency domain analysis of

SAW transponders (Pohl, 2000). SAW transponders

are SAW devices which do not have sensing film

between the transducers. They get the signal

obtained from the actual physical sensor on the

impedance Z

. In that case from relation (4) is

obvious that for one device all admittances are

constants and the only variable is Z

. Than, since

ZZ = ,

, and

RZ = , transfer

function can be expressed as:

TZT

∝=

)()(

(6)

where

)(

∝

T denotes the transfer function when Z

is infinite. Now two cases can be discussed: when Z

is real and when it is of capacitive or inductive type.

BIODEVICES 2009 - International Conference on Biomedical Electronics and Devices

378

is real e.g.

PPP

GRZ /1=

, ratio of

)(

ZT and )(∝T can be represented as in Figure

If the loading is purely inductive or capacitive ratio

)(

and )(∝T can be expressed as follows:

RjB

TBT

∝=

)()(

(7)

1 2 3 4 5 6

0.2

0.4

0.6

0.8

1.0

Figure 5: Relative amplitude versus resistive load.

In that case relative insertion loss can be represented

as in Figure 6.

1 2 3 4 5 6

inf

Figure 6: Relative insertion loss versus load susceptance.

3 CONCLUSIONS

The new developed algorithm is general. It can be

used in frequency analysis of SAW based

biosensors, as well as of SAW transponders. The

efficiency of the presented algorithm is

demonstrated with calculations of frequency

dependence of input conductance and susceptance

and insertion loss of SAW devices with uniform

transducers. The results are compared with

corresponding experimental data showing very close

agreement.

ACKNOWLEDGEMENTS

The authors thank the Ministry of Science and

Technological Development of Serbia for financial

support under the project number 11026.

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