Transducer design for a correlation log

Transducer design for a correlation log B. W o o d w a r d , S.K. Hole and W. Forsythe Department of Electronic and Electrical Engineering, Loughborough University of Technology, Leicestershire LE11 3TU, UK Received 31 March 1992; accepted 25 June 1992 A correlation log is a specialized sonar system for measuring the velocity of a vessel at sea. Here, the parameters for designing a transducer array comprising a projector and two or more hydrophones are discussed; these parameters include the choice of ceramic, frequency of operation, beam pattern directivity, projector power, projector matching circuit and housing construction. Also, the effect of differently-sized combinations of projector and hydrophones on their combined directional response and beamwidth is discussed. The research is primarily concerned with high-frequency piezoelectric transducers, with a low-impedance backing and a thin acoustic window.

Keywords: transducers; correlation; navigation

Even in an age of satellite navigation, seafarers still need an accurate method of dead reckoning as a back-up 1. Although the N a v y Navigation Satellite System (NNSS) and the Navstar Global Positioning System (GPS) are capable of accuracies of better than 50 m, most navigators would prefer to have an additional stand-alone system in case of loss of contact, so it is important to be able to determine the velocity of a ship using only instruments sited on board. In the case of an a u t o n o m o u s underwater vehicle, which cannot use satellite navigation directly, a back-up system for its inertial navigation system is even more important. There are a number of navigation systems that use speed measuring logs; these include mechanical types such as the propeller-driven rotometer and the pressure tube log, and electronic types such as the electromagnetic, Doppler, and correlation logs. In this paper, we concentrate on the correlation log 1 -9, whose mode of operation is to project an acoustic signal vertically downwards and to pick up the reflected signal using two or more on-board hydrophones separated by a few centimetres. The projector and hydrophones are placed on a line parallel to the fore-and-aft axis of the ship and the separation (in time or distance) between the received signals gives a measure of the ship's forward velocity. Hydrophones placed at right angles to this axis will give the athwartships velocity. A correlation log has a transducer geometry and beamwidth similar to a conventional echo sounder. It works on the principle of waveform invariance, with two or more hydrophones receiving echoes at different times and places. There are two types of correlation log according to the depth requirement. These are categorized as Type 1 : bottom-tracking on the continental shelf or water-tracking off the continental shelf; and Type 2: bottom-tracking on or off the continental shelf. A typical Type 1 log has a m a x i m u m bottom-tracking depth capability of about 250 m, beyond which it resorts 0041-624X/93/010021 13 © 1993 Butterworth-Heinemann Ltd

to water-tracking. It uses transducers operating at about 150 kHz, with a compact transducer array that fits inside a gate valve or is mounted inside a streamlined housing attached to the hull. A Type 2 log is larger and always works in the bottom-tracking mode. The advantage is that certain types of error introduced by water-tracking no longer exist, but the array required is larger because a lower frequency is used, typically less than 2 5 k H z for low acoustic absorption and penetration to greater depths. Correlation logs may also be classified as spatial or temporal, each of which can operate in either a pulsed or a continuous mode 2. The simplest configuration, which we shall use in this paper as a basic model, is a temporal log comprising a projector P and two hydrophones H 1 and H2; two possible arrangements are shown in Figure 1. The criteria for selection of suitable parameters such as frequency, transducer material, beamwidth and housing construction (and their interdependence) applies to any type of correlation log and is fundamental to the design of an efficient system.

C h o i c e of p r o j e c t o r f r e q u e n c y To bottom-track satisfactorily, the sea-bed echoes must be detected against a background of noise and reverberation. In deep water the dominant source of transmission loss is absorption. This can be reduced by lowering the operating frequency, although below about 100 k H z the background ambient noise and the vessel's self-noise levels increase. The signal-to-noise ratio can also be improved by increasing the transmitted acoustic power, but there are limitations on this. The projector operates into the water through a thin acoustic window and has a half-wavelength thickness ceramic element. The element operates at resonance in the thickness vibration mode and the resonant frequency

Ultrasonics 1993 Vol 31 No 1

21

Transducer design for a correlation log." B. Woodward et al. is given by

larger square plate 20 x 20 mm. Alternatively, slots can be cut in the back of the ceramic element to decouple the interacting resonances.

(1)

,lo =

where N3t is the frequency constant of a thin plate and lp is its thickness (Table 1). The m a x i m u m thickness of a P Z T ceramic plate or disc commercially available is about 16 mm. Assuming the frequency constant N3t of the ceramic is 2000 Hz m, then the resonant frequency of the plate is 125 kHz. This is the lowest possible operating frequency of a simple projector, i.e. one made from the thickest available piece of ceramic. Operation at lower frequencies requires the use of 'sandwich' transducers comprising a number of elements bolted together. As the sonar operating frequency increases, attenuation due to absorption increases as the square of frequency. Above about 200 kHz the background ambient noise is exceeded by the thermal noise of the sea. The frequency range from 50 2 0 0 k H z is the noise window in the deep-sea ambient-noise spectrum where the minimum noise level occurs (and therefore the maximum signalto-noise ratio) as shown in Figure 2. Since any active sonar on board a moving vessel has to overcome the vessel's self-noise, which is dominant at lower frequencies, it is necessary to operate at as high a frequency as possible but without losing significant power through absorption. Thus, the frequency range for a correlation log bottomtracking on the continental shelf to a maximum depth of 250 m should be in the range 125 200 kHz. The thickness-mode resonance is only dominant when the transducer is a 'true' plate, i.e. when its thickness is much less than any other dimension. When the projector's width or diameter is of the same order of magnitude as the thickness, spurious resonances can occur close to the main resonance. To suppress any spurious resonance, the transducer can be constructed from a number of smaller ceramic elements, e.g. four plates of l0 x 10ram to construct a

C h o i c e of t r a n s d u c e r m a t e r i a l Lead zirconate titanate ( P Z T ) ceramics have largely replaced naturally occurring piezoelectric crystals, such as quartz, and other electrostrictive ceramics, such as barium titanate, for the majority of sonar transducer applications. They are available in a variety of shapes and sizes and with different electrical characteristics, which makes it possible to choose the most suitable type for any particular application. These ceramics are stable with temperature and time, and their high efficiency and high sensitivity, when used as the element in 'simple' transducers, make them ideal for use in a correlation log. A correlation log uses a separate projector and hydrophones, so the appropriate types of ceramic can be selected. For example, materials such as PZT-4 and PZT-8 with high dynamic strength, high mechanical quality factor and low dielectric heating are suitable for projectors, while PZT-5A and P Z T - 5 H are suitable for hydrophones. Ceramic plates and discs are the most suitable shapes for a correlation log operating at resonance in the thickness vibration mode (Table 1). A simple ceramic plate at resonance radiating directly into water has a Q of approximately 30, which is suitable for a projector operating at a single frequency. For good receiver sensitivity, it is important that the frequency response of the projector and hydrophone are very similar and preferably the same.

120 10o 8o

H~

H2

[eve[ ~

Beauforf

6o z

z+C 2o

Hi

~

H~

10-- -

100

l~k

--

~ 1Ok

---J lOOk

1H

Frequency (Hz)

Figure1

Transducer configurations for a temporal correlation log

Table 1

Properties of PZT ceramics (Vernitron Ltd)

~:t3/ ~:o

g~3/EO tan &

d33 g33 QM N3t k33 Tm~× h p

22

Figure 2

Deep water ambient noise spectra

PZT-4

PZT-5A

PZT- 5 H

PZT-8

1300 635 0.004 289 26.1 500 2000 0.70 200 2.1 7500

1700 830 0.020 374 24.8 75 1890 0.70 250 1.5 7750

3400 1470 0.020 593 19.7 65 2000 0.75 110 1.5 7500

1020 582 0.004 225 24.9 > 1000 2067 0.64 175 2.1 7600

Ultrasonics 1993 Vol 31 No 1

xl0 xl0

12my 1 3VmN 1

kHzmm °C Wm kgm

1K 3

1

Transducer design for a correlation log: B. Woodward et al.

Projector A projector converts electrical power into acoustic power. Ideally, this should be a lossless operation, but in reality there are certain loss mechanisms, principally due to heating within the ceramic. For high electroacoustic efficiency, a high mechanical quality factor Q, high transmitting constant g33 and low dissipation factor t a n 6 are needed (Table 1). There is little to choose between PZT-4 and PZT-8, but PZT-8 has a greater tolerance to high voltages and greater mechanical strength. A simple P T Z ceramic projector operating directly into water usually has an electro-acoustic efficiency of 80 90% but at high power levels the internal losses in the ceramic can become significant. The temperature of the ceramic should therefore be limited to a value below its maximum operating temperature to prevent depolarization. PZT-4 is better than PZT-8 in this respect.

Hydrophone A hydrophone converts acoustic power incident on its face into an electrical signal. A high sensitivity hydrophone requires a ceramic with a high receiving constant d33 and a high electromechanical coupling coefficient k33. PZT-5H is the most suitable material, but PZT-5A is also acceptable ( Table 1). If the projector and hydrophones are operated at resonance and are made from ceramic elements of the same type and size, then ideally the elements should be from the same batch so that they are closely matched in impedance. In this case PZT-4 or PZT-8 is preferable, because maximizing the projector power has priority over hydrophone sensitivity. Limitations on projector power A correlation log needs to transmit the maximum acoustic power possible to maximize the sea-bed echo level and maintain a high signal-to-noise ratio for reliable echo detection. The main limitations on power output are the dynamic strength of the projector's ceramic element, acoustic cavitation in the water and heat generation in the projector. There are five limitations to the maximum power handling capability of electrostrictive ceramics 1°, which depend on the ceramic only. These are (i) (ii) (iii) (iv) (v)

dynamic strength of the ceramic; depolarization of the ceramic by a temperature rise; depolarization of the ceramic by high electriclosses; decrease in efficiency due to internal dielectric losses; decrease in efficiency due to internal mechanical losses;

For a simple half-wavelength resonant plate projector made of PZT-4 or PZT-8, we can neglect (iii) as the voltage levels required to achieve this would, in any case, cause stresses that would exceed the dynamic strength of the ceramic. We can also neglect (iv) and (v) because at the high power levels at which these effects occur, losses are masked by the effects of temperature rise. So, for a simple projector, the main factors which limit the power are (i), particularly for pulsed operation, and (ii), which is applicable to continuous wave (cw) and gated cw operation.

Ceramic dynamic strength The maximum power from a thickness-mode resonant ceramic plate with no compressive bias is limited by its peak dynamic strength areax. Driving the plate beyond its rated strength may fracture it and thus cause permanent damage. The maximum acoustic intensity for an airbacked electrostrictive plate at resonance can be written as I 1 /max -- (PC)F( O'max ~2 X 10 .4.

4 \(pc)p/

[ W c m - 2]

(2)

where (pc)F is the characteristic impedance of water, which loads the front face of the ceramic, and (pc)p is the characteristic impedance of the plate. The minimum rated dynamic tensile strengths for PZT-4 and PZT-8 are typically 24 and 34 MPa respectively, although the exact value will depend on each material's composition and its freedom from manufacturing defects. The maximum acoustic power for a projector is simply AI . . . . where A is the surface area of the radiating face. For an air-backed electrostrictive plate transducer operating at resonance directly into water, we obtain the maximum intensities for PZT-4 and PZT-8 of 18.1 and 35.5 W cm - 2 respectively. These values must be taken as the upper limits of intensity realizable, and ideally should be derated by a factor of two for working values, i.e. 9 W c m -z for PZT-4 and 1 8 W c m -1 for PZT-8. This will ensure reliable long-term operation at these drive levels. If the ceramic element has a supportive backing, the maximum intensity is increased over that of an air-backed element.

Acoustic cavitation Acoustic cavitation is a phenomenon whereby voids are produced in the water on the negative pressure cycle of an acoustic wave; this sets a limit on the acoustic intensity the water itself can sustain. When an acoustic wave is propagated, cavitation can occur at the projector's interface with the water. If the acoustic intensity exceeds the cavitation threshold, bubbles start to form and the acoustic output from the projector starts to fall. There are a number of detrimental effects caused by acoustic cavitation, including 12: (i) (ii) (iii) (iv)

erosion, or pitting, of the projector's face by the cavitation bubbles; loss of acoustic power owing to an increase in absorption and scattering by the cavitation bubbles; deterioration in the projector's beam pattern caused by scattering from the cavitation bubbles; reduction in the acoustic impedance of the water in front of the projector.

The cavitation threshold for water is raised by decreasing the pulse length, increasing the frequency or increasing the hydrostatic pressure; thus, cavitation is less likely for a projector mounted on a deep-hulled vessel than for one on a shallow-hulled vessel. The cavitation threshold can be written empirically as 12

Pc= 1 + 7 . 2 × 10 4fz

[atm]

(3)

where the frequency f is in kHz. This formula is suitable for a cw signal in fresh water at atmospheric pressure over a freqency range of 60 300 kHz, but it is only an estimate because the cavitation threshold is dependent on the gaseous condition of the water. The water could

Ultrasonics 1993 Vol 31 No 1

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Transducer design for a correlation log: B. Woodward et al. be air-saturated or degassed; the former would lower the cavitation threshold while the latter would increase it. The cavitation threshold as a function of depth z for a typical long-pulse correlation sonar can be expressed a s 12

I c = 0.15 Pc + 1~0

[Wcm

2]

pattern is the far-field two-dimensional directional pressure response of the transducer. If the transducer is reciprocal, the radiation pattern is valid when the transducer acts as either a projector or a hydrophone. The radiation pattern for a circular piston transducer, radius a, is given by

(4) D(~) -

On substituting Equation (3) into Equation (4) we obtain the cavitation threshold as a function of frequency and depth, i.e. I c = 0.15 1 + 7.2 x 10-4f 2 + 10.0

2Jl(ka sin ~)

(6)

ka sin ~k

where J1 is the first-order Bessel function and k is the wave-number (2~/2), while that for a rectangular piston transducer, width Wand height H, is given by

[Wcm-2](5) sin(~sin

As an example, the cavitation threshold for a Type 1 correlation sonar projector at a depth of 3 m and operating at a frequency of 150 kHz is 44.38 W cm -2 which is a much higher intensity than would be expected for a practical log. The corresponding threshold for a Type 2 log operating at the same depth at 25 kHz is 0.46 W cm - 2. For a typical practical situation of a hull-mounted correlation sonar on a vessel under way in a high sea state there is the additional problem of aeration at the hull/water interface. This is in the form of bubbles drawn under the hull at the bow by the vessel's forward motion. These bubbles reside in a turbulent layer below the boundary layer of the hull's surface. Since the bubbles are randomly distributed in the turbulent layer, the projector's beam pattern will be subjected to localized short-term effects, with the creation of additional sidelobes and nulls. Considerable power can be propagated in these sidelobes, causing surface or wake reverberation, or echoes from parts of the hull; these are received with the bottom echo and cause a decrease in the signal-tonoise ratio so that there may be difficulty in detecting the bottom echo.

qS)sin(7

sin Z )

D(¢o,Z) =

(7)

Similarly, the radiation pattern for a square piston transducer, where Wand H are equal, is /kW ', /kW sin~ sin qS) sin~ ~ - sin Z ) z) =

(8)

(7)2

sin q5 sin Z

Acoustic intensity is proportional to the mean square pressure so we can define the far-field directional response

Infinite baffle

J Axis

Transducer beam patterns Narrow beamwidths provide discrimination against unwanted reverberation and noise, whilst wide beamwidths ensure a tolerance to pitching and rolling of the ship. Here we consider the radiation patterns, beamwidth and directivity index of a transducer and the equivalent beamwidth of a projector/hydrophone combination. The three main combinations of ceramic plates and discs for use as projectors and hydrophones in the transducer array of a correlation log are as follows. (i) (ii) (iii)

Ultrasonics 1993 Vol 31 No 1

d

a

Infinite b a ' "

A circular piston projector and circular hydrophones. A square piston projector and square hydrophones. A square or rectangular piston projector and rectangular hydrophones 6.

For a simple one- or two-axis temporal correlation log array, any of these combinations could be used, depending on the construction of the array. If a small hydrophone separation is required to satisfy the velocity depth limitation that exists in certain circumstances 2's, the hydrophones can be smaller than the projector. This has the effect of broadening the equivalent projector/ hydrophone beamwidth. It is now appropriate to define the radiation pattern or Directivity Function for the circular and rectangular piston transducers shown in Figure 3. The radiation

24

"

J Axis

b F i g u r e 3 Transducer geometry for circular and rectangular piston transducers

Transducer 1.o

for a correlation

log:

B. Woodward

et al.

These three equations enable the combined projector/ hydrophone response to be modelled as a function of transducer size. They are used to determine the beamwidth of the main lobe downwards towards the sea bed and that of any side lobe.

0.0 -5.0

0.9

design

-10.0 0.8 -15.0

0.7

N

Transducer

-20.0

3 3 0.6 _; p! II 0.5 s

-25.0 5 "0 -30.0 2 -35.0

"a 0.4

9

-40.0 0.3 -45.0 0.2

-50.0

0.1

plane-angle

beamwidths

It is now appropriate to define the plane-angle beamwidth @ for a piston transducer, obtained from its directional response D2. The -3 dB plane-angle beamwidth Ksde of a transducer is defined as twice the angle at which the intensity drops to one-half of the axial intensity. Similarly, the - 6 dB beamwidth @ _ 6dRis defined as twice the angle at which the intensity drops to one-quarter of the axial intensity. The - 3 dB and - 6 dB beamwidths of a circular piston transducer are defined in terms of the wave-number k and radius a as follows

-55.0

0.0 _ -10

-8

-6

-4

-2

0

2

4

6

8

-60.0 10

m-3dB =

2 arcsin

E (

(13) )

x = ka sin $

Q- 6dB = 2 arcsin Figure

4

Directional

response

for a circular

piston

transducer

2$ (

(14) )

The transducer diameter d as a function of its - 3 dB beamwidth and - 6 dB beamwidth respectively is therefore given by (power response) for a transducer as D2. This function is shown for a circular piston and a square piston respectively in Figures 4 and 5. For two different transducers the directional response of a projector/ hydrophone combination is 0;”

= (D;D;)“.”

= 1D,D,I

(9)

but the validity of this formula assumes the projector and hydrophones are (i) mounted in individual infinite baffles; (ii) lie close to each other; and (iii) have effectively the same propagation axis. We can now derive the directional responses for the three possible projector/hydrophone combinations for a correlation log. The directional response for a circular projector and hydrophone, obtained from Equation (6), is 2J,(ka,

%(1cI)

=

sin II/) ZJ,(ka,

ka, sin $

(15)

k sin(@-,,,/2) 4.44

d=

(16)

k sin(@-,,,/2)

The - 3 dB and -6 dB beamwidths of a rectangular piston transducer are defined in terms of the wave-number k and transducer width W(i.e. smallest dimension) as @- 3dB = 2 arcsin

2J$ (

(17) >

1.o

0.0 .--5.0

sin rl/) (10)

ka, sin II/

The directional response for a square projector hydrophone, obtained from Equation (8), is

The directional response for a square rectangular hydrophone is obtained Equations (7) and (8), which gives

3.24

d=

0.9 -

and

projector and by combining -55.0

D&A& X) =

L

0.1 O.OLwdTx -10 -8

-6

-4

I1III -2 0 x = (kW/Z)

Figure

5

Directional

response

2

II 4

6

8

10

sin @

for a square

Ultrasonics

*Ni-60,0i

1993

piston

transducer

Vol 31 No 1

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Transducer design for a correlation log." B. Woodward et al. below the vessel would then vary by up to one-half of the peak value for any given depth. This can be taken as a basis for calculating the equivalent projector/hydrophone beamwidth. One purely empirical formula is

hydro

es

(1)PH_3d B = Cl(0eitch,Roll -~- C 2 )

Main lobe - Rolling/pitching angle

Figure 6 and roll

Variation of combined directional response with pitch

(ID_ 6 d B =

2 arcsin(~-W9 )

(18)

It follows that the transducer width as a function of its - 3 dB beamwidth and - 6 dB beamwidth respectively is given by W=

2.78

(19)

k sin(O 3riB/2) W=

3.79

(20)

k sin(@_6aB/2 )

Projector / hydrophone equivalent beamwidth Since a correlation log consists of a projector/hydrophone combination, it is of interest to consider the equivalent beamwidth of the combination, particularly in relation to the maximum pitch and roll angles of a vessel. Three circular projector/hydrophone combinations are analysed for their equivalent beamwidth. From the preceding theory it is evident that the directional responses corresponding to the - 3 d B and - 6 dB beamwidths a r e D2H((I)pH 3dB/2) = 0.5 and DZH(~PH_6dB/2)=0.25. TO obtain the equivalent projector/hydrophone beamwidth OpH it is necessary to evaluate these expressions in the required plane in small angle increments until the required half-angle beamwidth is found. For circular transducers this requires the calculation of the first-order Bessel function, which can be evaluated as the sum of a series expansion. To obtain a suitable practical value for the equivalent projector/hydrophone beamwidths for a correlation log, we need to consider the pitching and rolling of the vessel (for forward and athwartships velocity measurement respectively). The combined directional response at its - 3 dB beamwidth has a value of 0.5 (by definition), which means that the intensity is one-half the axial intensity. If the projector/hydrophone array is mounted horizontally in the hull of a vessel, the array can tolerate a total pitching or rolling angle less than its equivalent half-power beamwidth, as shown by Figure 6. The equivalent acoustic intensity on the sea-bed directly

26

Ultrasonics 1993 Vol 31 No 1

[degrees]

(21)

where C1 = 1.25 ° and C z = t5 ° are constants whose values were chosen intuitively. For example, if the maximum pitching and rolling of the vessel is + 5 ° from the horizontal, then from Equation (21) we obtain OPH--3dB = 1.25 (10 + 15) = 31.25 °. This is a suitable value for the equivalent projector/hydrophone beamwidth in the vessel's forward and athwartships direction. Once the equivalent projector/hydrophone beamwidth has been determined, it is necessary to consider the projector and hydrophone dimensions to achieve this beamwidth. If we consider circular transducers with diameters d H and dp, then there are three projector/ hydrophone combinations of interest. (1)

dH = d p

The projector and hydrophone have the same diameter, so the combined directional response is the same as that of either the projector or hydrophone, i.e. Dp2n(0) = D2(~O)= D2(~), from which the - 3 d B and - 6 dB beamwidths are obtained, i.e. OP_3d B = OH-3aB = (I)eH_3d B and (I)p_6d B = (I)H_6d B = (I)pH_6d B (2)

d H << dp

If the hydrophone has a much smaller diameter than that of the projector, the beamwidth of the hydrophone becomes broad, approaching that of a point source mounted in an infinite baffle. The directional response is approximately D2(O).~ 1 for - n / 2 < t~ < + n/2. Therefore, the combined directional response is D2H0p) = IDp(~)l 2 and the equivalent projector/hydrophone beamwidth is ~PH-3dB = CI)p--6dB- In this case, the equivalent projector/hydrophone beamwidth is equal to the 6 dB beamwidth of the projector. (3)

dp = 1.22)~ or 2.232

In these two special cases the first and second null of the projector's directional response are perpendicular to the propagation axis. This corresponds to nulls in the horizontal plate when the propagation axis is vertically downwards. There is, therefore, reduced insonification of parts of the hull, propellers, steering gear, the sea surface and the wake, which suppresses unwanted echoes and leads to an improved signal-to-noise ratio. Under these conditions the two projector beamwidths are given by (i) (ii)

~p 3dB ~-- 5 0 ° a n d ( I ) p - 6 d B = 70.8° forde = 1.222 ~ P _ 3 d B = 2 6 . 7 c' and Op 6dB=36.9 ° for d e = 2.23)~

A similar result can be achieved for a square projector, although strictly the nulls would only lie in the horizontal in the q ~ = 0 and Z = 0 planes (Figure 3b), as the directional response is not symmetrical about the propagation axis. When dp ~> d u the following criterion relates the projector beamwidth to the equivalent projector/hydrophone beamwidth: qbp 3dB ~ (IDpH--3dB ~ (I)p--6dB" This expression also relates the projector beamwidth to the equivalent projector/hydrophone beamwidth for square transducers, when Wp > WH.

Transducer design for a correlation log. B. Woodward et al. a

angles when the transducer has narrow plane-angle beamwidths, usually with the assumption that d and W are much greater than a wavelength. The solid angle for a circular transducer is given by

Direction of :> propagation

Sphere r = 1.0 m

b

W = 2~(1 - COS(O_3dB/2))

Direction of propagation

Sphere r = 1.0 m Figure 7 Solid angle for circular and rectagular piston transducers

It is evident from the above theory that the equivalent projector/hydrophone beamwidth is primarily determined by the projector dimensions, provided they are greater than or equal to those of the hydrophone. Assuming the vessel pitches and rolls a total of 10 °, then a suitable equivalent projector/hydrophone beamwidth is 31.3 °, as shown by Equation (21). Our calculations show that the second null then occurs in the horizontal when the - 3 dB projector beamwidth is 26.7 ° and the - 6 dB beamwidth is 36.9 °. The equivalent projector/hydrophone beamwidth of 31.3 ° lies between these two angles, which implies that the projector satisfies the equivalent beamwidth requirement. Transducer sofid angle The plane-angle beamwidths are useful in interpreting the physical geometry of the transducer beam patterns, but the corresponding solid angle is also useful because it can be substituted directly in standard sonar equations to determine the target strength for bottom and volume reverberation. So far, we have described beamwidths in only two dimensions. For a circular piston transducer, the solid angle can be conveniently defined by a cone that is symmetrical about the propagation axis, with its vertex at the centre of a sphere of unit radius (Figure 7a). Similarly, for a rectangular piston transducer, this definition also applies to a pyramid with its vertex at the centre of a unit sphere (Figure 7b). In this case, the pyramid originates from the two perpendicular planeangle beamwidths of a rectangular piston transducer. The wide plane-angle beamwidths for a correlation log signify that accurate formulae are required to calculate the solid angle. Some formulae only give accurate solid

(22)

This formula for the solid angle of a circular transducer is accurate for plane-angle beamwidths (I)_3d B < radians. For a circular projector/hydrophone combination the plane-angle beamwidth O--3aB in Equation (22) is replaced by the equivalent projector/hydrophone planeangle beamwidth OPH--3aB. The solid angle for the rectangular transducer shown in Figure 7b is given approximately by 13 ud -

J

[Steradians]

17.4 (k2HW)

[Steradians]

(23)

for kH >> 1 and kW>> 1. The two conditions, on transducer height and width, can be replaced by a condition on the maximum value for the plane-angle beamwidth in each plane, so that (I)_3dB < ~/3 radians. A correlation log will usually satisfy this condition. When a rectangular projector/hydrophone combination is used, the height and width in Equation (23) are replaced by the height and width of an equivalent transducer, whose beamwidths are equal to those of the combination. Directivity index Conventionally, a projector's directivity index is the decibel ratio of the acoustic intensity at a point on its axis of propagation to that of an omnidirectional projector transmitting the same acoustic power from the same point. Similarly, a hydrophone's directivity index is the decibel ratio of the acoustic power received from a distant isotropic source to that received by an omnidirectional hydrophone from the same source. A directional hydrophone can therefore discriminate against isotropic noise. The transmitting and receiving directivity indices can be defined in terms of the solid angle as follows 14. DIp ~ 10 loglo

[dB]

(24)

DI H ~ 101Ogao(4~-~ ~

[dB]

(25)

These can be used directly in the sonar equations.

02 Terminals /,jj/,~xz

~

i " ~"!i:iii:i ~

Housing Acoustic window

::iiiiiiiiiiiiii~ ~

PZT ceramic plate

:::::::::~:.~i:::.:i:::::.i::~!~i~i::::i::iii]

O°

YJ2YY Syntactic foam Figure 8 Piezoelectric projector for the heat flow model

Ultrasonics 1993 Vol 31 No 1

27

Transducer design for a correlation log: B. Woodward et al. 500 /

M a x i m u m projector p o w e r Once a suitable projector beamwidth has been determined, it is possible to determine the m a x i m u m acoustic power, subject to these limitations, as a function of frequency. This is achieved by performing a discrete frequency sweep between an upper and lower frequency limit and calculating the projector's diameter or width from Equations (15) and (19) respectively to obtain its radiating surface area. F r o m Equation (5), the surface

&

1000 950 900 850 800 750 700 650 600

tatior

PZT-4

550

~o

500 450 4O0 350 300 250 20O 150 100 ~50 0 I I I [ I I l I I I I I I 0 20 40 60 80 100120140160180200220240260280 Frequency (kHz)

Figure 9 Maximum acoustic power limited by acoustic cavitation and the dynamic strength of the ceramic element; circular projector, 1 5 ~ beamwidth

950

[-

900 [-

850 r 800 [750 F

7oor 650 ~600

o

I-

550 [-

"~ 500 r 450 r

300 250 200 150 100

PZT-4

F [~r r

0 0

,,,oI i,t coust,ccvity 375 [-

~ 325 o 300 275 "~ 250 ~ 225 200

-

1O0 75 50 25 0

0

20 40 60 80 100120140160180200220240260280 Frequency (kHz)

Figure 11 Maximum acoustic power limited by acoustic cavitation and the dynamic strength of the ceramic element; circular projector, 30 ° beamwidth

area is used to calculate the maximum acoustic power for the onset of cavitation in the water in front of the projector. F r o m Equation (4) it is also used to calculate the m a x i m u m acoustic power so as not to exceed the peak dynamic strength of the ceramic. These maximum powers can be found for projectors made of either PZT-4 or PZT-8 ceramic. We can perform a frequency sweep of 50-250 kHz in 1 0 k H z steps for beamwidths of 15 °, 20 °, 30 ° and 40 ° for a circular projector. If we solve for the above equations, we obtain the m a x i m u m acoustic power as a function of frequency, as shown in Figures 9-12. These results for circular projectors approximate to those from square projectors of the same beamwidth, with only marginal differences. These graphs show that the maximum acoustic power is available in the frequency range 8 0 - 1 6 0 k H z . This coincides with the lowest operating frequency for a simple half-wavelength resonant transducer, which was shown to be 125 kHz. The cavitation threshold of water depends on its gaseous condition and there is an uncertainty in its predicted value. In view of this, it is advisable to make the power limitation dependent on the dynamic strength of the ceramic, rather than on the cavitation threshold. This is achieved by opting for a slightly higher operating frequency. For example, a 150kHz projector made of PZT-8 with a 30 ° beamwidth can propagate an acoustic power of 60 W (Figure 11).

Projector heat f l o w I I I I 1 I I I [ I I • [ 20 40 60 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 Frequency (kHz)

Figure 10 Maximum acoustic power limited by acoustic cavitation and the dynamic strength of the ceramic element; circular projector, 20' beamwidth

28

400 ~-

175 150 125

._

1000

475 F 450 1425 1-

Ultrasonics 1993 Vol 31 No 1

In a recent paper is a heat-flow model is developed for a high-frequency directional sonar projector, which is applicable to cw or quasi-cw transmissions. The projector is a ceramic plate mounted in a syntactic-foam backing, with a thin epoxy resin acoustic window, as shown in Figure 8. The aim here is to apply the results to obtain

Transducer design for a correlation log: B. Woodward et al.

oo.

250 240 230 220 210 200 190 180 170 160 150 140 130 120 110 100 9O 8O 70 i 6O

If 0 2 is set to the maximum operating temperature for the ceramic, we obtain the maximum electrical input power limited by temperature rise. If we limit this maximum temperature to 150 °C to allow a safety margin we get the maximum permissible electrical input power. As an example, we consider a 150 kHz projector made of a ceramic plate mounted in a syntactic foam backing with a polyurethane resin acoustic window, and apply the following specifications: d = 30.0 mm; A = 706.9 mm2; lp = 13.3 mm; lw =2.0 mm; Ko = 2.100Wm-1 K - l ; Kw = 0.268 W m - 1 K - l ; , = 0.7.

PZT-4

5O

30

20 10 0 0 210

1 40

1 60

I 80

I I I 100 120140

l I I I I I 160 180 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0

Frequency (kHz)

Figure 12 Maximum acoustic power limited by acoustic cavitation and the dynamic strength of the ceramic element; circular projector, 40 ° beamwidth

maximum power levels subject to the heat dispersion properties of the projector. It is necessary to make the following assumptions. (i) (ii) (iii) (iv) (v)

The projector operates at resonance in the steadystate condition. Heat loss from the back and sides of the plate is negligible. The acoustic window is thin with uniform thickness. There is uniform heating within the plate. There is sufficient water flowing past the acoustic window to dissipate the heat.

With reference to Figure 8, we can identify the temperatures at the acoustic window/water interface, ceramic plate/acoustic window interface and the syntactic foam/ceramic plate interface as ®o, O1, ®2 respectively. The thicknesses of the ceramic plate and acoustic window are Ip and lw, and their thermal conductivities are Kp and Kw respectively. The power dissipated in the ceramic, which accounts for temperature rise, depends on the electroacoustic efficiency , of the projector. When an electrical input power PE is applied to the projector, the peak temperature rise Oz at the syntactic foam/ceramic interface given by 02=0o+PE(1--,)

( lw

Kw +

IP~/A 2KpJ/

[K]

(26)

It is important that the maximum temperature for the ceramic is not exceeded in order to prevent depolarization; the approximate maximum operating temperature for PZT-4 and PZT-8 is 200°C and 175 °C respectively. Alternatively, we can express Equation (26) in terms of the electrical input power required for a given temperature at the syntactic foam/ceramic interface as PE =

A ( O 2 -- 0 0 )

(1-.)

( tw

tp

gw

2~p

[W]

(27)

If 0 o = 10 °C and 02 = 150 °C, then the maximum input power using the above values in Equation (27) is 31 W. This corresponds to an acoustic intensity of 3.1 W cm- 2 (0.031 W m m -2) on the radiating face. By changing the acoustic window to one which is more conductive, it is possible to increase the acoustic power output of the projector when operated near its maximum temperature. For example, using a thermally conductive epoxy resin with a thermal conductivity of 1.256 W m - 1 K-1, which is four times more conductive than normal epoxy resins, the maximum input power under the same conditions becomes 69.3W. This corresponds to an acoustic intensity of 6.9 W cm- 2 (0.069 W m m - 2) on the radiating face. This example shows the importance of considering the heat dissipation properties for a high-frequency sonar projector transmitting a cw signal and the important role that the acoustic window plays in conducting heat away.

T r a n s d u c e r e q u i v a l e n t circuit The equivalent circuits of the projector and hydrophones are important when considering: (i) matching the power amplifier to the projector; (ii) matching the input pre-amplifier to the hydrophones; (iii) the effect of backing and matching layers on performance, particularly with regard to bandwidth and electro-acoustic efficiency. Several models for a transducer have been proposed, including one that incorporates the effects of backing and matching layers on the bandwidth and efficiency of water-loaded ceramics16'1 v and another for high frequency operation as. Variations between batches of ceramic and interaction effects within the ceramic can cause the measured values of the transducer equivalent circuit to vary considerably from the predicted values. For a simple air-backed half-wavelength resonant plate transducer operating near resonance, the equivalent circuit can be approximated as shown in Figure 13. The parallel capacitance and resistance are known as the clamped capacitance and static resistance respectively; the power dissipated in the static resistance accounts for dielectric losses in the transducer. Theoretical values for these can be calculated from Co -

Ro -

~3

A

(28)

Ip 1

(29)

mCo tan 6

where e~3 is the dielectric constant measured when the transducer is 'clamped' and tan 6 is the dielectric loss factor.

Ultrasonics 1993 Vol 31 No 1

29

Transducer design for a correlation log: B. Woodward et al. C

L

input impedance bf 9

o

Ro

Figure13

RR

where l,. is the length of the cable (assumed lossless) and 7 =Jco(LC) 1/2 is the cable propagation constant and Z o = (L/C)I/2; here C is the cable capacitance per metre (F m - 1) and L is the cable inductance per metre (H m - ~). If the cable is terminated by a complex impedance, then the termination impedance is given by

[l

Static resistance Static (unclamped) capacitance Motional capacitance Motional inductance Mechanical resistance Radiation resistance

1 + ( Z t / Z o ) t a n h 71~

ZT = RT + jXT

Equivalent circuit of a transducer plate near resonance

The series C and L represent the 'motional' capacitance and inductance of the ceramic near resonance in the thickness vibration mode. This is damped by the series resistance, which is in two parts. The first is the radiation resistance RR, which represents the water load; power dissipated in this 'resistance' is transferred to the water as acoustic power. The second resistance RM is the resistance associated with mechanical losses within the ceramic; power dissipated by it is the power lost within the ceramic and to the backing material. If we neglect the dielectric losses in R 0, which for PZT-4 and PZT-8 are small for low electrical drive levels, then the electro-acoustic efficiency for a projector may be defined as GA -- Gw

RR -

R R 4- R M

(30)

GA

where G A and Gw are the conductances of the transducer at resonance, measured in air and water respectively. These can be obtained from an admittance plot of the transducer near resonance. Since the acoustic impedance of air is very small, an air-backed transducer has a high efficiency because negligible power is dissipated in the air, owing to the impedance mismatch between the air and the ceramic. Typical air-backed transducers have a narrow bandwidth and a (2 of approximately 30. Those which are not air-backed have additional losses, which result in a lower efficiency and wider bandwidth (lower Q). When a projector is driven by a low-impedance power amplifier, it should 'appear' resistive for m a x i m u m power transfer. The approximate equivalent circuit of an electrostrictive transducer at resonance is given by the clamped capacitance Co in parallel with a resistance Rp, i.e. the combined static, mechanical and radiation resistances. When a projector terminates a coaxial cable, the load seen by the amplifier is the input impedance of the cable. This can also be represented by a parallel capacitance and resistance, and the capacitance can be 'tuned out' by an external inductor connected in parallel, as shown in Figure 14. Transmission line theory can be used to calculate the input impedance of the coaxial cable. If the coaxial cable has a characteristic impedance Zo and is terminated by an arbitrary impedance ZT, the

30

U l t r a s o n i c s 1 9 9 3 V o l 31 N o 1

(32)

where R T is the resistance and X T is the reactance. By solving Equation (31) for the input impedance and using Equation (32) together with the relationship t a n h j x = j tan x, we obtain the input impedance of the mismatched cable as Re(Zln ) =

-

(31)

ZIn =

o

= = = = = =

Z T + Z o tanh 71c

RM Co

Ro Co C L RM Ra

gin of this mismatched cable is given

lm(Z~.) =

RT(1 -- X T T / Z o ) + (XT + Z o T ) ( R T / Z o ) 2

2

2

(1 -- X T T / Z o ) 2 4- R x T / Z o (1

XTT/Zo)(XT

+ goT) 2

-

R2T/Zo

2

(1 - X T T / Z o ) 2 + RTT / Z 20

(33) (34)

where T = tan ¢01o (LC) ~/2. The input impedance of the cable is represented by a parallel resistance and capacitance, denoted by Ri. and Cin respectively, where Re(Z~.) 2 + Im(Z~n) 2 Rln =

C~n =

(35)

Re(Zln) -Im(Zl,)

(36)

c o [ R e ( g , n ) 2 + I m ( Z l n ) 2]

These equations were solved by computer to calculate the input impedance and the equivalent parallel resistance and capacitance when the cable was terminated by a resonant projector. For the model to be valid, the projector's termination resistance must be greater than or equal to the characteristic impedance of the cable. It was found necessary to use the exact formulae, i.e. Equations (35) and (36), under the following conditions: (i)

when the cable length is over 10m or the carrier frequency is over 5 0 0 k H z (i.e. well above the frequencies of operation considered here);

Coaxial cable

Projector at resonance

Zln ~

T

F i g u r e 14 Equivalent circuit of a coaxial cable terminated by a resonant projector

Transducer design for a correlation log. B. Woodward et al. Table 2

Acoustic impedances of selected materials

Sea water PZT-4 Polyurethane resin Syntactic foam Lexan Air Perspex Epoxy resins Natural rubber Silicone rubber

~ 1.5 34.5 ~ 1.7 ~ 1.5 (typ.) 2.62 ~ 400 3.4 ~ 3.0 ~ 1.5 ~ 1.1

MRayl MRayl MRayl MRayl M Rayl Rayl M Rayl M Rayl MRayl MRayl

would therefore protrude into the water and its connecting lead would pass through the hull. This type of housing is in the form of a 'shoe' whose back is contoured to the shape of the hull and bolted to it. The housing can be made from Nylatron and streamlined for minimum drag. Considerable forces are exerted on the hull of a vessel and consequently a hull-mounted transducer array must be durable. This leads to two possible construction techniques: (A)

(ii)

when the projector's parallel input resistance R T is less than 10 Z 0.

When these two conditions do not exist, the parallel input resistance and capacitance of the cable are given approximately as Rp and (Co + Clc) respectively. The parallel inductance to 'tune out' the capacitance is simply 1/(~o2C~,); this inductance is also the secondary winding inductance of a transformer for matching the parallel resistance to the power amplifier. An inductor can also be used with a hydrophone to 'tune out' the parallel capacitance which would otherwise attenuate the signal. If the projector and hydrophone are identical, then L o is a suitable inductor value. The addition of the inductor also forms a bandpass filter centred on the carrier frequency, which gives the sonar receiver some signal pre-selection.

Choice of housing material/construction A sonar array consists of five main parts, the housing, the acoustic element support and backing, the acoustic elements, the acoustic window and the connecting leads. The array must be firmly attached to the hull, where considerable forces are imposed on it. The housing is usually made from a rigid metal or plastic, its purpose being to support the array and provide environmental protection. It must be inert to water and be capable of withstanding static and shock loads. Inside the housing, the acoustic elements are normally supported by a passive acoustic material 2°. Its presence can affect the transducer's characteristics, in particular by lowering its electro-acoustic efficiency. The material must have high acoustic attenuation, low acoustic impedance, be electrically insulating and resistant to compressive loads. The acoustic window couples the acoustic power into the water. Suitable materials must have a low acoustic attenuation and an acoustic impedance similar to that of water (or an intermediate value between that of water and the element). They must also be capable of withstanding mechanical shock, and must be electrically insulating, chemically inert and non-absorbent. Table 2 shows the properties of some common acoustic materials. The projector/hydrophone array must be mounted on the hull so that acoustic waves can be propagated downwards. One mounting arrangement is to lower the array through a gate valve in the hull. The advantage is that it can be removed for maintenance but it imposes severe constraints on the array dimensions. The housing material would normally be made of brass or bronze and custom-made to fit the gate valve and accommodate the transducers. The array may protrude slightly into the water but should cause minimal turbulence. Alternatively, the array can be fixed onto the hull; it

Air-backed elements on a rigid acoustic window, e.g. Lexan, a clear, strong plastic material, as shown in Figure 15a. There are certain advantages and disadvantages of this arrangement.

Advantages (i) The transducers have a high electro-acoustic efficiency, as the elements are air-backed. (ii) The array can usually be dismantled from its housing. Disadvantages (i) It may be difficult to obtain the window thinner than ()~/4) to make it appear transparent to the acoustic waves. (ii) There is a slight mismatch between the acoustic impedance of the window and that of sea water. (iii) The window may flex when under pressure if it is not sufficiently thick or if the array is large; this imposes limitations on the size of the array. (B)

Elements mounted in a low density syntactic foam for support and sealed with a polyurethane epoxy resin which also acts as the acoustic window, as shown in Figure 15b. The advantages and disadvantages of this arrangement are as follows.

Advantages (i) The polyurethane resin can be mixed so its acoustic impedance is nearly identical to that of sea water. Consequently, it will not load the elements and appears transparent to the acoustic waves. (ii) The syntactic foam has considerable compressive strength (up to 2 × 1013 Pa, equivalent to a water depth of 2000m) and provides the elements with

Lexon -111--

ocouslic window

Air b a c k i n g PZT element

7•.•...............:.:.:.:.:.:.: --'-'--'- ~ Synfaclic f o a m hocking

Polyurethane acoustic window

- -

PZT element

b

Figure 1 5 Cross-section of a transducer with an air-backed and syntactic foam-backed element

Ultrasonics 1993 Vol 31 No 1

31

Transducer design for a correlation log: B. Woodward et al.

(iii) (iv)

(v)

a rigid backing; the mix ratio can be altered to change the foam's properties to suit the application. The loading on the elements' rear face broadens the bandwidth. The elements can be positioned accurately within the foam, by milling out the required shape to accept them. The acoustic window may have barnacle growth after a long immersion in the sea. If the array can be removed, it is possible to grind partially away the acoustic window and barnacles, and then re-cast the window to its original thickness.

Disadvantages (i) The syntactic foam may load the back face of the elements in an unpredictable manner. (ii) The electro-acoustic efficiency of a projector is reduced due to the effect of loading on its rear face, although this is small. (iii) The liquid polyurethane resin can have entrapped bubbles or dissolved air in it and can remain there while it sets. If these minute bubbles are present in the acoustic window they have a detrimental effect on the beam pattern. Summarizing, the main disadvantage of a rigid acoustic window, particularly for large arrays, is that it cannot be made sufficiently thick to prevent flexure under pressure and to match the water load at the same time; ideally the thickness of the acoustic window should be less than 2/4. Considerable forces can be exerted on the array during a shock load and a rigid acoustic window could shatter. A syntactic foam-backed array is therefore preferable for large arrays, although this would not have such high efficiency as an air-backed array. A specially mixed polyurethane resin with an acoustic impedance close to that of sea water can be used; this allows a thick window to be used, provided its attenuation is not excessive.

power and an increase in unwanted surface and wake reverberation for pulsed transmissions. This reduces the depth capability of a correlation log when bottomtracking. The equivalent p r o j e c t o r / h y d r o p h o n e beamwidth determines the bandwidth of the echo signal. A vessel which pitches and rolls in the sea must have a broad beamwidth to ensure that adequate power is incident on the sea-bed beneath the vessel. Using this analogy, a formula for the equivalent beamwidth has been proposed; this makes it possible to convert the plane-angle beamwidth into the solid-angle beamwidth, which can be used directly in the sonar equation. When a circular or square plate piston projector is used, it is possible to design for a null of the directional response to be in the horizontal plane. This has the beneficial effect of reducing reflections from the hull and other parts of the ship and reducing surface and wake reverberation. A simple equivalent circuit has been shown for a transducer at resonance and formulae are available for calculating the component values, but they can give misleading results and should only be used as a first approximation. When a projector's face dimensions lie between 1.5 and 3.0 wavelengths in water, it becomes an inefficient radiator due to interaction effects. The most appropriate transducer array for a small vessel is in the form of a 'shoe' which is attached onto the hull. Larger vessels with a fiat steel hull may use a gate valve, but this is expensive and limits the size of the array. An air-backed array mounted on Lexan will flex when subjected to static and shock loads, which limits the size of this type of array. A syntactic foam backing is better for supporting the elements and a polyurethane resin acoustic window provides a better impedance match to sea water than Lexan. This type of transducer will not have such a high efficiency as an air-backed one, although it will have a wider bandwidth.

Acknowledgements Conclusions For a correlation log, the most suitable P Z T ceramic materials for the projector and hydrophones are PZT-8 and PZT-5H respectively. The P Z T ceramics considered have fairly similar responses, but it is important to maximize projector power and this requires a low-loss ceramic with good power handling capability. A good compromise for both the projector and hydrophones is PZT-4. For simple thickness-mode resonant plate transducers, the lowest operating frequency is limited by the maximum available thickness of the ceramic, which sets the lower frequency limit to approximately 125kHz. The upper frequency range, which is limited by increasing absorption, ambient noise and thermal noise, is chosen as 200 kHz. The frequency range where maximum power can be propagated is approximately 8 0 - 1 6 0 k H z for PZT-8, peaking at approximately 120 kHz (Fiyures 9-12). Since sea water close to the surface is highly gassed, its cavitation threshold will be lower than its predicted value. An allowance must be made for this and consequently the optimum operating frequency for maximum power propagation is increased to approximately 150 kHz. Aeration at the hull/water interface has an adverse effect on transducer beam patterns, resulting in a loss of

32

Ultrasonics 1993 Vol 31 No 1

The authors acknowledge the financial support of the U K Science and Engineering Research Council (SERC) and our industrial sponsors S. G. Brown Ltd, Welwyn Garden City, whose Technical Director, Mr D Brooks, was particularly helpful during the research project.

References 1 2 3 4 5 6 7 8

Tetley, L. and Calcutt, D. Electronic Aids to Navigation Edward Arnold, London (1986) Dickey, F.R. Jr and Edward, J.A. Velocity measurement using correlation sonar IEEE Conf on Position Location and Navigation San Diego, California, USA (1978) 6 9 November Denbigh, P.N. A design study for a correlation log to measure speed at sea J Navigation (1982) 35 160-184 Denbigh, P.N. Ship velocity determination by Doppler and correlation techniques l E E Proc (1982) 131 315-326 Atkins, P. and McQueen, P.D. Acoustic correlation logs lEE Colloquium on Underwater Navigation London, England (1984) 24 May Atkins, P. and Smith, B.V. A high accuracy two-axis velocity measuring device Proc IERE Con,[" on Electronics Jbr Ocean Technology Edinburgh, Scotland (1987) 24 26 March Atkins, P. and Smith, B.V. The optimal extraction of velocity information from a sonar correlation log Microprocessing and Microprogramming (1987) 21 161 169 Atkins, P. and Smith, B.V. The predicted performance of an underwater navigation system based on a correlation log Proc lnst Acoust Conf on Underwater Communication and Position

Transducer design for a correlation log. B. Woodward et al.

9

10 11 12 13

Fixing (University of East Anglia, Norwich, England (1987) 17-18 December Hole, S.K., Forsythe, W. and Woodward, B. An experimental acoustic temporal correlation log for ship navigation Proc lost Acoust Conf on Underwater Communication and Position Fixing University of East Anglia, Norwich, England (1987) 17-18 December Berlincourt, D.A. Power limitations of piezoelectric ceramics in radiating transducers Technical paper TP-225 Piezoelectric Division, Clevite Corporation (1962) Seto, W.W. Acoustics McGraw-Hill, Schaum's Outline Series, New York, USA (1971) Urick, R.J. Principles of Underwater Sound McGraw-Hill, New York, USA (1975) Clay, C.S. and Medwin, H. Acoustical Oceanography Wiley, London (1977)

14 15 16 17 18 19 20

Kinsler, L.E., Frey, A.R., Coppens, A.B. and Sanders, J.V. Fundamentals of Acoustics Wiley, London (1982) 3rd edition Hole, S.K., Forsythe, W. and Woodward, B. Heat flow model for a high-frequency sonar projector Acoust Lett (1989) 13 39-41 Mason, W.P. An electromechanical representation of a piezoelectric crystal used as a transducer Proc IERE (1935) 23 1252-1263 Kossof, G. The effects of backing and matching on the performance of piezoelectric ceramic transducers IEEE Trans (1966) SU-13 20-30 Smith, B.V. and Gazey, B.K. High-frequency sonar transducers: a review of current practice IEE Proc (1984) 131 285 297 Chipman, R.A. Transmission Lines McGraw-Hill, Schaum's Outline Series, New York, USA (1968) Pelmore, J.M. Ultrasonic properties of passive materials for transducer use Proc Inst Acoust Conf on Transducers University of Birmingham (1976) 15 December

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