Design, fabrication and performance characteristics of a 50kHz tonpilz type transducer with a half-wavelength diameter

Design, fabrication and performance characteristics of a 50kHz tonpilz type transducer with a half-wavelength diameter

Dae-Jae L EE * and Won-Sub L EE

¹

Division of Marine Production System Management, Pukyong National University, Busan 608-737, Korea

1

Dept. of Harbor and Marine Products, Gangseo District Office, Busan Metropolitan, Busan 618-701, Korea

In a split beam echo sounder, the transducer design needs to have minimal side lobes because the angular position and level of the side lobes establishes the usable signal level and phase angle limits for determining target strength. In order to suppress effectively the generation of unwanted side lobes in the directivity pattern of split beam transducer, the spacing and size of the transducer elements need to be controlled less than half of a wavelength. With this purpose, a 50 kHz tonpilz type transducer with a half-wavelength diameter in relation to the development of a split beam transducer was designed using the equivalent circuit model, and the underwater performance characteristics were measured and analyzed. From the in-air and in- water impedance responses, the measured value of the electro-acoustic conversion efficiency for the designed transducer was 51.6%. A maximum transmitting voltage response (TVR) value of 172.25dB re 1 μPa/V at 1m was achieved at 52.92kHz with a specially designed matching network and the quality factor was 10.3 with the transmitting bandwidth of 5.14kHz. A maximum receiving sensitivity (SRT) of 183.57dB re 1V/ μPa was measured at 51.45kHz and the receiving bandwidth at 3dB was 1.71kHz. These results suggest that the designed tonpilz type transducer can be effectively used in the development of a split beam transducer for a 50kHz fish sizing echo sounder.

Keywords: 50kHz tonpilz type transducer, Half-wavelength diameter, TVR, SRT

* Corresponding author: [email protected], Tel: 82-51-629-5889, Fax: 82-51-629-5885

,

,

, split beam echo sounder

. split beam echo sounder ,

, ,

. ,

28, 50, 75, 200kHz

,

(Simmonds et al., 1995).

. ,

,

70kHz split beam echo sounder

(MacLennan and Simmonds, 1992).

4 ,

side lobe

. , 4

,

. ,

side lobe .

,

side lobe , 4

split beam echo sounder

, , ,

,

(Dziedzic et al., 1995, Zakharia, 1995).

50kHz

4

, tonpilz

, ,

, .

Tonpilz

Fig. 1 ,

tonpilz , .

Fig. 1 ,

Z 1b , Z 2b , Z 1p , Z 2p , Z 1h , Z 2h

tail mass, , head mass 4

Z 1b jZ

b

tan (k 1 1 1 /2) , Z 2b Z b /[j sin (k 1 1 1 /2)]

Z 1p jZ

p

tan (k e 1/2), Z 2p Z p /[j sin (k e 1/2)]

Z ^1h jZ ^h tan (k ² 1 ² /2), Z ^2h Z ^h /[j sin (k ² 1 ² /2)] (1) Fig. 1. Equivalent circuit for the longitudinal mode of a 50kHz tonpilz type transducer.

Tail mass

Z

bL

Z

1b

Z

1b

Z

1h

Z

1h

Z

2h

Z

2P

Z

hi

1:N Z

bi

C

o

Z

1p

Z

1p

Z

2b

Z

hL

Head mass

Piezoelectric ceramic

stack

. , Z b , Z p , Z h tail mass, , head mass , k 1 , k e , k 2

, l 1 , 1, l 2 . , C o (clamped capacitance), N

( ) .

Z bL , Z hL tail mass head mass ,

(Hughes et al., 1969).

,

(prestress bolt), (silver electrode), (bonding layer)

. Fig. 1 tonpilz

Z i

Z m

Z i ____________ (2)

N

²

j ωC

^o

Z

m

, , ω 2πf f , Z

m

, tail mass

head mass Z

bi

, Z

hi

, Z

m

(Z

1p

Z

hi

) (Z

1p

Z

bi

) Z

m

Z

2p

_________________

2Z

1p

Z

hi

Z

bi

(2)

, Z

bi

, Z

hi

Z

2h

(Z

1h

Z

hL

) Z

hi

Z

1h

_____________

Z

1h

Z

2h

Z

hL

(4)

Z

2b

(Z

1b

Z

bL

)

Z

bi

Z

1b

_____________ (5)

Z

1b

Z

2b

Z

bL

(Rosenbaum, 1988; Wilson, 1991; Stansfield, 1991; Shuyu and Tien, 2008).

50kHz tonpilz (2)

50kHz tonpilz

, Fig. 2 .

Fig. 2 split beam

50kHz

, , 15mm 12mm ,

. split beam assembly

, , ,

, tonpilz

, ,

(copper shim) head mass O-ring

, .

Fig. 2 50kHz tonpilz PZT4 6.0mm, 11.8mm, 15.6mm

, head mass brass ,

12mm, 12.8mm, , tail

mass 8mm, 3mm steel

prestress nut . Fig. 2

,

tail mass 0.5mm steel

plate .

Fig. 2. Structure and schematic diagram of a 50 kHz tonpilz type transducer developed in this study.

φ11.8

16.0

12.8 copper shim

copper shim

O-ring O-ring head mass

(unit : mm) prestress bolt tail mass (prestress nut)

piezoceramic tube

φ12.0

(matching network)

Fig. 2 tonpilz

,

matching network

, Fig. 3 .

Fig. 3 matching network terminal Z S Z S R S jX S ,

,

reactance X S X S 0 ,

(resistance) R S , Z S R S

. , , resistance,

reactance Z L , R L , X L , Z L

Z L R L jX L (6)

, , Z S

1

¹

Z S jX ( ^{jB ____} _{Z L} ) ⁽⁷⁾

. Fig. 3

R S R L

matching network , , R L

R S , Fig. 3 lumped

element matching network B X R L

X L ___ R L

²

X L

²

Z S R L

Z S

B ___________________________ (8) R L

²

X L

²

BZ S R L X L

X ____________ (9)

1 BX L

, B ωC, X ωL matching

C

L (Tse, 2003).

( ),

, 50kHz tonpilz

( ) LCR

meter (Model 7600, QuadTech)

. (transmitting

voltage response, TVR .)

(L B D, 5 6 5 m) ,

Fig. 4 PC

pulse LFM (linear

frequency modulation) , , chirp RS232C interface (Model 33120A, HP) memory

,

. up-chirp S (t)

S (t) A rect ( ^___ 1 _T ) ^{sin (2 πf s t παt}

²

^{) (10)}

LFM , , A

chirp , f s chirp

(start frequency) , f s f 0 ___ Δf (f 0 : 2

, Δf : chirp ) .

, α chirp sweep rate , chirp

T , α ____ Δf . 0 t

T

T , rect ( ____ t ) 1 , t 0 or t T , T

rect ( ___ t ) 0 . T

Fig. 3. An example of lowpass L matching network used in this study to achieve the maximum power transfer from the signal source to the load. The inputs to the design procedure are the load (Z

L

) and source impedances (R

S

). The outputs are the reactances X and B.

R

S

ω Z

S

jB Z

L

jX

Matching circuit

up-chirp T 1.25ms, f s 25kHz, Δf 40kHz, , 1V,

25 65 kHz chirp

(Model 2713, B&K) ,

matching network

.

(Model 8105, B&K C304, Cetacean research technology)

, charge amplifier (Model 2635, B&K) measuring amplifier (Model 2610, B&K)

digital storage oscilloscope (Model 475, Gould) FFT analyzer (Model 3525, AND)

. FFT analyzer

,

, ,

(Harris et al, 2004).

, (receiving sensitivity, SRT .)

, , chirp

(projector) .

, 30kHz

60kHz

(Model R209,

Airmar) .

, chirp

,

digital storage oscilloscope

FFT analyzer ,

, ,

, .

Fig. 2 50kHz tonpilz ,

(PZT4, 11.8mm,

Fig. 4. Schematic diagram of the experimental setup for measuring the underwater performance characteristics of a developed 50kHz tonpilz type transducer. (a):

diagram of time and frequency, (b): transmitted chirp pulse, (c): received chirp response, (d): distance between projector and receiver.

Power amplifier

Rotator

PC AFG

MN

PA T1 T2

(a)

d projector receiver

(b) (c) Digital OSC FFT analyzer

Fig. 5. Measured electrical impedance magnitude (a) and phase (b) characteristics for the PZT4 ceramic tube used in designing the a 50kHz tonpilz type transducer.

1.0E+07 1.0E+06 1.0E+05 1.0E+04 1.0E+03 1.0E+02 100 80 60 40 20 0 -20 -40 -60 -80 -100

70 80 90 100 110 120 130

PZT element

Impedance magnitude (ohm) Impedance phase (deg)

(a)

PZT element (b)

Frequency (Hz)

6.0mm, 15.6mm)

Fig. 5 .

Fig. 5 (a) , (b)

.

split beam ,

, sidelobe

(15mm) ,

11.8mm . Fig. 5

, 85.6 kHz, 115.6 kHz ,

174.0k Ω, 16.6 5.87M Ω, 37.6 .

Tonpilz

, Fig. 5 PZT4

Fig. 2

50kHz tonpilz ,

head mass, tail mass ,

.

,

Fig. 6 . Fig. 6 (a) , (b)

, ,

.

, 50kHz tonpilz

,

51.05 kHz, 54.66 kHz ,

662 Ω, 4.67 352.6k Ω, 3.73 . ,

51.43 kHz, 54.66 kHz ,

17 Ω, 37.56 1484.62k Ω, 69.41

. ,

. , 0.38kHz ,

.

50kHz tonpilz Scotchcast 2130 rubber (3M)

,

Fig. 7

. Fig. 7 50kHz tonpilz

50.80 kHz, 50.56 kHz , Fig. 6. Comparison of calculated and measured electrical

impedance magnitude (a) and phase angle (b) char- acteristics for a 50kHz tonpilz type transducer in air.

400 350 300 250 200 150 100 50 0 100 80 60 40 20 0 -20 -40 -60 -80 -100

40.0 45.0 50.0 55.0 60.0 65.0

50kHz tonpilz element _ _ Measured ____ Calculated

50kHz tonpilz element _ _ Measured ____ Calculated

Frequency (kHz)

Impedance magnitude (ohm) Impedance phase (deg)

(a)

(b)

54.53 kHz, 54.26

kHz .

, Fig. 7

resistance reactance

Fig. 8 .

Fig. 8 reactance ( Ω) ,

resistance ( Ω) .

vector diagram ,

vector diagram . Fig. 8 circle

(f s ) f s 54.40

kHz , f 1 f 2 f 1

53.74 kHz, f 2 55.06 kHz

Q Q f s /(f 2 f 1 ) 41.2 . , Fig. 5

(f s ) f s 54.13 kHz , f 1

f 2 f 1 52.83 kHz, f 2 55.74 kHz Q Q f s /(f 2

f 1 ) 18.6 . , tonpilz η

D w D w

η ____ (1 ____ ) (11)

R m D a

, , R m

loop resistance , D w

(motional impedance) circle , D a

circle . (11)

tonpilz

51.4 .

Tonpilz

50kHz tonpilz Fig. 4 LC (coil-condenser) lumped element matching network ,

, tonpilz Fig. 9 . Fig. 9

(a) conductance ( μs)

, (b) susceptance ( μs)

. Fig. 9 (a) (b) , ,

conductance susceptance .

Fig. 4 B X B

ωC 2292.64 10

⁶

X ωL 423.79 , Fig. 7. Comparison of measured electrical impedance

magnitude curves for a 50kHz tonpilz type transducer in air (solid line) and in water (circle).

120 100 80 60 40 20 0

40.0 45.0 50.0 55.0 60.0 65.0

Frequency (kHz)

Impedance magnitude (kohm)

50kHz tonpilz element _ _ Measured (water) ____ Measured (air)

Fig. 8. Comparison of impedance loops for a 50kHz tonpilz type transducer in air (circle) and in water (diamond).

60 40 20 0 -20 -40 -60 -80

0 20 40 60 80 100 120

Resistance (kohm)

Reactance (kohm)

50kHz tonpilz element

_ _ Measured (water)

____ Measured (air)

matching C

L ,

C 7.297nF, L 1.349 mH ,

50 Ω . Fig. 9

,

conductance peak mode

, peak

51.427kHz 50.187kHz

. Fig. 9 1 peak ,

conductance, susceptance 50.31kHz,

48.50 μs, 6.15μs , 2 peak ,

conductance, susceptance 52.70kHz,

48.46 μs, 6.90μs peak

2.39kHz .

Tonpilz

50kHz tonpilz

chirp

Fig. 10 . Fig. 10 (A)

1.25ms, 25kHz,

40kHz chirp matching network

, chirp

(E T (f)) , (B) chirp

R

(E R (f)) .

TVR (dB re 1 μPa/1V at 1m) E R (f)

TVR (f) 20 log ( ^_______ _E ) ^{M R (f) 20 log (R)}

T (f)

(12) (Hughes, 1998),

Fig. 11 . , M R (f)

(dB re 1V/ μPa) , f .

Fig. 10

(dB) , (kHz) . Fig. 10

(a) chirp

25 65 kHz

, 50 60kHz

,

. ,

, Fig.

10 (b) . Fig. 10 (a) Fig. 9. Comparison of conductance (a) and susceptance

(b) curves versus the frequency for a 50kHz tonpilz type transducer without (circle) and with matching network (solid line).

300 250 200 150 100 50 0 500 400 300 200 100 0 -100

40.0 45.0 50.0 55.0 60.0 65.0

Frequency (kHz) (a)

(b)

Conductance Susceptance

50kHz tonpilz element _ _ without matching ( μs) ____ with matching ( 0.25ms)

50kHz tonpilz element

_ _ without matching ( μs)

____ with matching (ms)

chirp

,

peak mode, , 1 2 peak

49.74 kHz 52.68 kHz ,

51.70kHz drop

. Fig. 9

conductance

1 2 peak 50.31kHz,

52.70kHz , peak

51.43kHz conductance drop

.

, Fig. 10 (a) E T (f) Fig.

10 (b) E R (f)

TVR (dB re 1 μPa/1V at 1m)

Fig. 11 . Fig. 11

(dB) , (kHz) .

Fig. 11

, Fig. 10 (b) 1 2 peak

, 52.92kHz 172.25dB , Fig. 11 1 peak 50.17kHz 170.88dB

, peak 51.45kHz

drop 166.66dB

. , peak

3dB (f 1 49.25kHz, f 2

54.39kHz) Δf 5.14kHz 50kHz tonpilz

(quality factor) Q Q 10.3 .

Tonpilz 50kHz tonpilz

(R209,

Airmar) chirp ,

50kHz tonpilz

Fig. 12 . Fig. 12 (a)

1.25ms, 25kHz, 40kHz

Fig. 10. Measured frequency spectrums of input chirp signal at matching network terminal (a), transmitting chirp signal received by hydrophone (b) for a developed 50kHz tonpilz type transducer.

0 -10 -20 -30 -40 -50 -60 -70 0 -10 -20 -30 -40 -50 -60 -70

Relative spectrum level (dB)

20 30 40 50 60 70

Frequency (kHz)

(a)

(b) Frequency spectrum of chirp pulse signal at electric terminal of developed transducer with matching circuit

Frequency spectrum of chirp pulse signal received by C304 hydrophone

Fig. 11. Measured transmitting voltage response (TVR) for a developed 50kHz tonpilz type transducer.

190 180 170 160 150 140 130 120

20 30 40 50 60 70

Frequency (kHz)

TVR (dB re 1 μ Pa/1V)

Transmitting voltage response of developed transducer

_ _ with matching circuit

chirp R209

, 1m

chirp (H R (f)) , (b)

chirp (H T (f)) .

SRT (dB re 1V/ μPa) H T (f)

SRT (f) M ^R (f) 20 log ( ^_______ _{H R (f)} ) ⁽¹³⁾

(Hughes, 1998), ,

M R (f) (dB re

1V/ μPa) , f .

Fig. 12

(dB) , (kHz) . Fig. 12

(a) chirp

30 60 kHz

. , chirp

Fig. 12 (b) . Fig. 12 (b) 50kHz tonpilz

51.45kHz

. , Fig. 12 (a)

H R (f) Fig. 12 (b) H T (f)

SRT (dB re 1V/ μPa) Fig. 13

. Fig. 13 (dB) ,

(kHz) . Fig. 13

, Fig. 12 (b)

peak ,

51.45kHz

183.57dB . , 3dB

(f 1 50.72kHz, f 2 52.43kHz) Δf

1.71kHz 50kHz tonpilz

(quality factor) Q

Q 30.09 .

split beam echo sounder Fig. 12. Measured frequency spectrums of chirp signal

transmitted from broadband transducer (a), chirp signal received by the developed transducer (b) for a developed 50kHz tonpilz type transducer.

Fig. 13. Measured receiving sensitivity (SRT) for a devel- oped 50kHz tonpilz type transducer.

0 -10 -20 -30 -40 -50 -60 -70 0 -10 -20 -30 -40 -50 -60 -70

Relative spectrum level (dB)

20 30 40 50 60 70

Frequency (kHz)

(a)

(b) Transmitting frequency spectrum of R204 projector

Receiving frequency spectrum of developed transducer

-170

-180

-190

-200

-210

SRT (dB re 1V/ μ Pa)

20.0 30.0 40.0 50.0 60.0 70.0

Frequency (kHz)

Receiving sensitivity of developed transducer

_ _ with matching circuit

4 , side lobe

4

.

50kHz tonpilz ,

, ,

. 50kHz tonpilz

, 51.4 . ,

chirp

TVR (dB re

1 μPa/1V at 1m) , TVR

52.92kHz 172.25dB ,

3dB (f 1 49.25kHz, f 2

54.39kHz) Δf 5.14kHz 50kHz tonpilz

(quality factor) 10.3 . , 20 70kHz chirp ,

50kHz tonpilz

SRT (dB re 1V/ μPa)

, SRT 51.45kHz

183.57dB , 3dB

(f 1 50.72kHz, f 2 52.43kHz) Δf

1.71kHz 30.09 .

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( 2009 0071881).

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Encyclopedia of applied physics, 22, 67 84.

Hughes, W.J. and M.J. Zipparo. 1969. Computer modeling of ultrasonic piezoelectric transducers.

Technical report No. TR 96 007, Applied Research Lab., The Pennsylvania State Univ., pp. 116.

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Shuyu, L. and H. Tian. 2008. Study on the sandwich piezoelectric ceramic ultrasonic transducer in thickness vibration. Smart Mater. Struct., 17, 1 9.

Simmonds, E.J., F. Armstrong and P.J. Copland. 1995.

Species identification using wideband backscatter with neural network and discriminant analysis. ICES Int. Symp. on Fish. and Plank. Acoustics, Aberdeen, Scotland, 1 14.

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196 266.

Tse, M. 2003. Impedance matching. Technical note for high frequency circuit design elective, pp. 53.

Wilson, O.B. 1991. Introduction to Theory and Design of Sonar Transducers. Peninsula Publishing, California, pp. 11 108.

Zakharia, M.E., F. Magand, F. Hetroit and N. Diner.

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