Acoustic ID-tags for Under Water Use

Acoustic ID-tags for Under Water Use

Acoustic ID-tags for Under Water Use

Arne Rønnekleiv

Norwegian University of Science and Technology

Trondheim, Norway

Abstract— Passive ID-tags that could be read remotely is

an area of growing commercial interest. Here we look at

a small tag in the low MHz range for under water use,

based on acoustic resonances. It could be used in sea

water, where RF-signals are heavily damped, and it

could easily be made small, as there is no need for bulky

antennas and hence will have an advantage over the

more common RF-ID-tags based on electromagnetic


The tag is intended for an as yet unspecified

laboratory use, where we may assume a moderate

distance between tag and detector system. As a design

example we look at a circular tag with diameter 300

micrometer, and resonances in the 1 to 4 MHz range.

The resonators are circular nitride membranes over an

evacuated cavity in the tag substrate. We review the

analysis of the resonators, which is based on coupling of

the acoustic vibration modes of the membranes and the

tag substrate through the fluid.

A detailed response of an ID-tag with on the order of

ten to twenty resonators may be found easily and fast

from predetermined data for resonators and substrate.

Both radiation losses and viscosity losses in water are

included. It is found that resonator Q’s are limited to

about 20 in water at 4 MHz, and further that the

viscosity leads to a small shift in the resonance

frequencies. The number of identities for a tag design as

discussed here could be in the range 50,000 to 100,000 or


Keywords-component; ID-tag; acoustic resonator; bulk



The concept of an ID-tag that can be used under water

and read remotely, based on resonators on the tag, was

introduced in [1] and also discussed in [2]. The tag

presented there was intended for identification of living fish,

primarily salmon in fish farms, and was introduced as a

means to link escaped fish to its fish farm origin. This early

work contains experiments with tags in the 200 kHz to 400

kHz range, and shows the feasibility of the concept.

Here we present a theoretical investigation of a smaller

tag, operating in the 1 to 4 MHz range, which could be

suitable for laboratory use in secure identification of fluid

samples in an automated laboratory test environment. The

tag is given the shape of a circular plate or substrate of

silicon, 300 µm in diameter and 60 µm thick. The resonators

are circular evacuated cavities in the substrate covered by a

57 nm thick membrane of silicon nitride. The structure

could be manufactured using bulk micromachining based on

fusion bonding of silicon nitride films to silicon [3]. A top

view of the tag is shown on Fig. 1 where possible positions

of resonator membranes are indicated by circles. The

membranes are placed close to the rim of the substrate, with

∆ in Fig. 1 equal to 5 µm.



ϕ n

ϕ 2

Fig. 1: Top view of tag. Substrate diameter is 300 µm.

Resonator membranes have diameters from 10 to 30 µm for

resonance frequencies in the range 4 to 1 MHz.

The analysis described in the following is based on a

lumped parameter description of the resonating membranes

and the substrate. Many of the parameters, as acoustic

radiation and coupling impedances are frequency dependent,

but change slowly with frequency, such that they may be

computed for a low number of frequencies, and then

interpolated to give the desired frequency resolution. Here

techniques based on convolution and Fourier transforms are

used to obtain the fields which are required for the lumped

parameters, but finite element methods could also be used.


The modeling is carried out in several steps. The

movement of the membranes is described through a limited

number of Eigen modes in the membrane without water load

and assuming that the substrate is fixed. In the same way

movement of the substrate is analyzed in terms of a limited

set of substrate modes without the membranes and loading

from the fluid. Then the acoustic coupling between the

different modes of the membranes and the substrate and to

the water is included to give the response of the complete

ID-tag. The coupling between the membrane and substrate

modes comes mainly through the fluid, but also through a

direct coupling between the two systems by reaction forces

between membrane and substrate.

We first consider the resonator membranes as sitting on a

substrate which is fixed in space. We assume that all


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deflections of the membranes are small, and perpendicular

to the membrane and substrate surface that both are in the x-

y plane. Hence the deflections will be in the z-direction.

Without any fluid present the modes of the membrane(s) are

orthogonal. We denote the membrane deflection for mode

number n by w n (x,y), taken to be positive for deflections in

the +z-direction, and with a normalization such that the peak

value of w n (x,y) is 1. As is discussed in more detail in [4],

we may then define an effective force F (me) n for membrane

mode number n due to an actual distributed force F z (x,y)

acting on the membrane in z-direction as

( me)

Fn Fz( x, y) wn( x, y)



= ∫

If we describe the deflection in mode n as W n w n (x,y)

where W n is independent of x and y, and refer to the v n =

iωW n as the membrane velocity in mode n, the required

effective force to accelerate the membrane in mode n is

F = M iωv where


m w dA

( me, acc)

n n n

( me) 2


= ∫ me n


Here m me is mass per unite area of the membrane, and M n is

the effective mass of the membrane for movement in this

mode. The stiffness of the membrane leads to an equivalent

spring force coefficient S (me) n for the nth mode given by

( me) ( me) 2

n m n



S = M ω


Here ω n is the angular resonance frequency of the nth mode

when the membrane is unloaded.

The dynamic pressure in the fluid outside the membrane

gives a force on the membranes that we describe through the

matrix, Z (me) m,n , the self and mutual acoustic impedance

matrix for the different Eigen modes of the membranes on

the fixed substrate. If we assume that the velocity

iωW (me) n w (me) n of the membrane leads to a tension t (me) zz,n (x,y)

acting in +z-direction on the membrane surface from the

water, we obtain the following expression for this matrix:

( me) 1

( me) ( me)


Zmn ,

= t

( me)

zzn ,





membrane m

The contribution to effective driving force for the mth mode

from the nth mode is then Z m,n (me) iωW n . Note that the mth

mode could be a mode of the same membrane or a mode in

a different membrane.

The substrate may move without deformation in three

different ways which we include here, uniformly in z-

direction, and with rotations about the x- and y-axis. In

addition the substrate may have movements which include

bending. They will be described through a number of modes

of the free substrate. Compressions of the substrate or inplane

translations are not included. Totally 19 substrate

modes are used in the calculations. For these orthogonal

modes with deflection patterns w k (sub) (x,y) that are

normalized to have a peak amplitude of 1 in +z-direction,

we may as for the membranes define an effective mass

M k (sub) , a spring force S k (sub) for mode k, and a set of acoustic

impedances Z kl (sub) giving the forces driving mode k due to

pressure in the water by movement in mode l, and losses

due to radiation. In analogy with what was done for the

membranes we define the displacement in z-direction of the

substrate as W (sub) k w (sub) k (x,y) where W (sub) k is independent of

x and y.

These two groups of modes are not orthogonal. Their

movements will be coupled through the water and the mass

of the membranes. We therefore define a set of cross

coupling masses between these modes, given as

( me, sub ) ( me) ( sub)

Mnk ,

= ∫ mmemwn wk

dA (5)


Here mode n is a membrane mode and mode k is a substrate

mode. The coupling through water between the modes may

be described by the matrix:


Z = ∫ t w dA

( sub, me) ( me) ( sub)

km zz,

m k

iωWm substrate

Here t (me) zz,m is the pressure due to the m th membrane mode.

Also for this impedance the coupling is reciprocal such that

multiplied by the velocity in m th membrane mode it gives

the force on the k th substrate mode, and vice versa.

To take into account the interaction with an exciting or

detecting transducer, we define a set of transfer impedances

from the velocity on a membrane mode, mode m, or a

substrate mode, mode k, to pressure on a transducer at a

distance r 0 from the centre of the tag, z (me,rad) m or z (sub,rad) k .

We assume that the transducer has an area A T that is focused

towards the tag, and well matched to the acoustic impedance

of the liquid. The phase of this transfer impedance will

depend on the position of the resonator on the substrate and

the direction to the transducer.

Only membrane modes which give non zero net volume

change at the membrane surface will couple strongly to the

far field. For membrane modes with zero volume change the

coupling to the far field is highly anisotropic and very weak,

and will be neglected here. None of the included substrate

modes give a finite volume change of the tag, and as

consequence they have zero coupling to uniform far field

radiation. The lower substrate modes will however have a

strong coupling to non uniform radiation, especially at

higher frequencies.

We get the following set of equations for the membrane

mode velocities v (me) (sub)

m and substrate mode velocities v k

for a velocity v tr on the transducer surface:

( me)

( me) Sm

( me) ( me) ( me)

( iωMm + ) vm + ∑ Zm,





( me, sub) ( me, sub) ( sub) ( me, rad )


( Z + iωM ) v = −z v


mk , mk , k m tr


( iωM ) v Z v


( sub)

( sub) k ( sub) ( sub) ( sub)




+ ∑ k,

l l



( me, sub) ( me, sub) ( me) ( sub, rad )

nk ,

+ ω

nk , n

= −

k tr

( Z i M ) v z v

In this equation indexes m and n refers to membrane modes,

and indexes k and l to substrate modes.

The field problem is solved in two steps. We first obtain

the acoustic field, mainly the pressure, due to the excited

mode assuming that the substrate surface is infinitely large

and rigid, i.e. without movement except for the mode in


question. We then make a correction of this field due to the

fact that the substrate has a finite size and thickness, but we

still assume that it is rigid, except for the investigated mode


Since the moving surface is fairly small, it is feasible to

calculate the field for the infinite substrate case using a

dense set of small pulsating volumes located at the surface

and radiating into the infinite half sphere of fluid above the

substrate. At the surface the particle velocity from the

sources will be parallel to the surface, and hence match the

boundary conditions at the rigid surface, assuming that the

viscosity of the fluid can be neglected. We easily obtain the

pressure p in the half space above a pulsating source of

volume ∆V at the angular frequency ω in a fluid with

density ρ L and plane wave velocity c L as [5]:



p =− exp( −ik0r)

where (8)



= ω / cL

Here r is the distance from the source to the field point.

Convolving this pressure with the source deflection for

mode n, w (me) n (x,y) , gives the desired pressure. The value in

the x-y-plane of this pressure we denote p p (x,y), where index

p means primary.

To find the correction to this pressure field, p c (x,y,z), due

to the fact that the substrate is finite, we consider the case

when the substrate has zero thickness, and is still rigid. We

may consider the primary pressure p p as the source for p c as

it encounters zero acoustic pressure where the substrate is

missing. The missing substrate will lead to additional

particle movements in the z-direction which will excite the

pressure field p c . This field must be anti symmetric about

the x-y-plane:

pc( xyz , , ) =−pc( xy , , − z)


For points outside the substrate at z = 0 the total pressure

must be continuous which means that

pc( x, y,0 + ) =− p p( x, y)/2 for ( x, y)

outside substrate (10)

On the substrate surface the correction pressure is so far

unknown, but we know that the substrate is rigid, and hence

that the particle velocity in z-direction for the correction

field on the substrate surface, v z,c (x,y,0+), must be zero.



( x, y,0 + ) = 0 for ( x, y)

on substrate (11)

If we use symbols in capital letters for spectral quantities,

we have for the correction fields at z=0 (Note F() and F -1 ()

are interchanged due to the r-dependence exp(-ikr)):

( )


Pc( kx, ky) = F pc( x, y,0 + )


c( kx, ky) = kz( kx, ky) Pc( kx, ky)/( ωρL) ( a)

( b)

v ( x, y,0 + ) = F V ( k , k ) ( c)

( )

zc , zc , x y

2 2 2

z 0 x y z

where k = k −k −k Im( k ) ≤0 ( d)


Based on these equations an iteration procedure is built

which allows us to find the wanted fields.

A finite viscosity in the water will add losses to the

system. The curl free part of the pressure, which is what we

so far have discussed, gives no significant losses close to the

tag. The important losses come from fields with curl, shear

waves, which are required to match water velocities parallel

to the tag surface to zero parallel velocity at the surface.

These waves have a penetration depth into the water of



= 2




The viscosity η = 10 -3 Ns/m 2 . The lost power due to these

shear waves is easily calculated, and should be incorporated

in the Z-parameters of (7) as an additional real part for the

diagonal terms. The shear viscosity will also reduce the

water movement close to the tag surface, and hence add an

essentially stagnant layer of water at the surface of the

vibrating structure. This essentially increases the effective

mass of the structure by a water thickness of half the

penetration depth of the shear wave. This is verified for a

resonator on an infinite planar surface using Fourier

transform based analysis.

The total radiated power from the resonators is given by:


( me) ( me) ( me)

Prtot ,

= ∑∑ Re( Zmn ,

vn vm

) (14)

2 n m

A similar expression gives the radiation from the

substrate modes. In these expressions the viscosity terms of

the real part of the diagonal elements in the impedance

matrices should be removed. The power absorbed by the

exciting transducer is easily found by summing the pressure

on it from all mode velocities.

Fig. 2 show contour plots of the total pressure on the

front and the back side of the substrate, and Fig. 3 shows the

importance of the correction pressure. Even though the

correction pressure magnitude is a small fraction of the total

pressure, it gives a large negative contribution to pressure in

phase with the membrane velocity, and hence significantly

reduces the radiated power.

y−pos. rel. resonator (µm)






−100 −50 0 50 100

x−pos. rel. resonator (µm)

y−pos. rel. resonator (µm)



−100 −50 0 50 100

x−pos. rel. resonator (µm)

Fig. 2: Contour plot of the pressure magnitude on the front

(left) and back (right) side of the substrate due to the

velocity of the lowest mode of a membrane with 20 µm

diameter close to the edge of the substrate at 2 MHz. 3dB

per contour. The periphery of the substrate shows up

through changes in the pressure at the edge.


The tag is excited from a transducer that has a numerical

aperture of 0.36 as seen from the tag, and the echoes from

the tag are detected by the same transducer. The transducer

is well into the far field of the tag, whereas the tag is in the




Relative pressure amplitude (lin)

In phase relative pressure (lin)


−100 −50 0 50 100

y−pos. rel. resonator (µm)

Fig. 3: Plot of pressure on the substrate surface along a

radius through the resonator. Left: amplitude of primary

pressure and correction pressure. Right: The pressure

component in phase with the membrane velocity for the

same quantities.

Response (dB)

Response (dB)







−100 −50 0 50 100

y−pos. rel. resonator (µm)

Fig. 4: Calculated tag responses. The top left figure shows

the effect of viscosity losses and added mass on a resonator.

The top right figure shows the response of two resonators

alone, and the response of the same two resonators when

they are 22.5 and 180 degrees apart (see Fig. 1).The bottom

figures show the response of a tag with 13 resonators

chosen among 16 possible frequencies, to the left with

resonators that are close in frequency far apart in space,

and to the right with the resonators positioned in frequency

sequence. * indicate nominal frequencies, 3 slots are empty.

Response (dB)


















Infinite substrate


No viscosity

With viscosity losses

With viscosity losses and mass

1.8 2 2.2 2.4

Frequency (MHz)

1 1.5 2 2.5 3 3.5 4

Frequency (MHz)

From resonators

From substrate

Fig. 5: Total radiated power from resonators and substrate

modes, relative to exciting signal.

near field of the transducer. The transducer is assumed to be

focused on the tag, and perfectly matched to water such that

no echoes from the tag are reflected back from the

transducer. All power levels in the figures 4 and 5 are

referred to the power in the signal transmitted from the

transducer. No propagation losses are included.




1 1.5 2 2.5 3 3.5 4

Frequency (MHz)

Response (dB)

Response (dB)












Infinite substrate

− Correction

Blue: Single resonators

Green: Angle = 180 degrees

Red: Angle = 22.5 degrees

1.6 1.8 2 2.2 2.4

Frequency (MHz)

1 1.5 2 2.5 3 3.5 4

Frequency (MHz)

Fig. 4 top shows the influence of water viscosity on a

resonator at 1.9 MHz with respect to Q and center

frequency, reducing the Q from 50 to 21 and shifting down

the center frequency by 1.2 %. Further it shows how two

resonators which are close in frequency influences each

other when they are close or far apart, as given by the angle

φ. Fig. 4 bottom shows how the positioning of the

resonators along the rim of the substrate influences the tag

response. The conclusion is that putting resonators that are

close in frequency, far apart on the substrate gives a better

tag response. Fig. 5 shows the total radiated power from the

resonators and from the substrate modes for the same tag as

the bottom left curve in Fig. 4. The latter power is seen to be

25 to 30 dB below the former. In all broadband responses

shown in Fig. 4 and 5 we se a response at about 3.85 MHz.

This is due to a higher order membrane mode in the lowest


If from 3 to 13 resonators are put on each tag with

frequencies chosen from a set of 16 possible slots, about

65,000 different tags could be obtained. If one of the

frequencies is present on all tags for reference purposes, the

number is reduced to about 32,000. The frequencies could

possibly be put closer, and the number of resonators on a tag

could possibly be increased, hence on the order of 50,000 to

100,000 or more tag identities could possibly be obtained.


Through analysis it has been shown that acoustic resonators

formed by bulk micromachining as thin membranes over an

evacuated cavity in a silicon substrate, may give

identification tags that could be detected acoustically under

water. In the frequency range 1 MHz to 4 MHz a tag with a

diameter of 300 µm could carry 13 or more different

resonators and give on the order of 50,000 to 100,000

different tag identities. Losses and frequency shifts due to

viscosity are included in the analysis, and the losses are

shown to limit the available Q of resonators in water to

about 20 at 4 MHz.


[1] A. Rønnekleiv et al.: “Design of Micromachined Resonators for Fish

Identification”, 2005 IEEE International Ultrasonics Symposium

Proceedings, pp 641-644.

[2] S. Holm et al.: “Acoustic passive integrated transponders for fish

tagging and identification”, Aquacultural Engineering


[3] K. Midtbø, A. Rønnekleiv, D. T. Wang, ”Fabrication and

Characterization of CMUTs realized by Wafer Bonding”, 2006 IEEE

Ultrasonics Symposium Proceedings, pp 934-937.

[4] A. Rønnekleiv, “CMUT Array Modeling Through Free Acoustic

CMUT Modes and Analysis of the Fluid CMUT Interface Through

Fourier Transform Methods”, IEEE Trans. on Ultrasonics,

Ferroelectrics, and Frequency Control, Vol. 52, No. 12, Dec. 2005,


[5] L. E. Kinsler and A. R. Frey, Fundamentals of acoustics, 2 nd ed. New

York: John Wiley & Sons, Inc. 1962.

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