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Design and Fabrication of a 2D Array Ultrasonic Transducer

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(1)

5G#⇮⮲㯓#㋆ⴊ㣊#㡶ᵚ⡢᩾⛚ⴖ#⛢ኂ#⇍#ⷚⵏ

‡•‹‰ƒ† ƒ„”‹…ƒ–‹‘‘ˆƒʹ””ƒ›Ž–”ƒ•‘‹…”ƒ•†—…‡”

ąҚʂॡİşćėॡę

ۿսێۙțښێս܁ێۙțښێ޽࢘ێۙțښێ

ొ ߧ: ҆ȦЛقԴə48×64 ޽ȇͿۋΘرݕؓۻɳĀ܁2D ѕَ঍ߣڼ͔ࣷ࣡֟˕ԴۆԺć, ܃ۚфथÀε

ॠٕɰ. ۻşۺٍĀۋڌۋॢथϸѕَĵܓεԸ܁ॢ঳, ŔقϑóĵՁՙۙε܃ۚॠٕɰ. ڮॢڅՙ३Եںࣀॠي

͔࣡֟˕ԴۆՃҙĵܓεԺćॠٕɰ. ͔࣡֟˕ԴۆՁɠںॳԜ֨ࢅşڦ३࠘फۆȃҼٮۦΒεܓۼॠيՙۙÂ

Ԝ঒ÂԾں۹ÇॠČ, ؓۻɳĀ܁ф܁०ࠗۆ߯ۺ˃ƍεԺćॠيЀशܳࣷսʂًफںĵইॠٕɰ. Ժćق˰͆

͔࣡֟˕Դۆ֨ۚुں܃ۚॠČŔ࣢Ձںࠑ܁ॢ঳, ࠑ܁ʽĀęεڮॢڅՙ३ԵĀęٮҼİॠيÒьʽ͔࣡֟

˕ԴۆՁɠںथÀॠٕɰ.

ෑਕ૳ઘ:ߣڼ͔ࣷ࣡֟˕Դ, 2޲ڙѕَ঍͔࣡֟˕Դ, ؓۻɳĀ܁

ABSTRACT: In this paper, a 48×64 channel 2D array ultrasonic transducer with piezoelectric single crystals was designed, fabricated, and evaluated. Structure of the transducer was chosen to facilitate the electric connection on the planar array, and then components were fabricated in accordance with the structure. Detailed structure of the transducer was designed through finite element analyses. In order to improve the performance of the transducer, the crosstalk between adjacent elements was reduced through the control of kerf width and material, and the target frequency bandwidth was achieved through optimal design of the thickness of the single crystal and matching layers. After fabricating a prototype of the transducer according to the design and measuring its characteristics, the results were compared with those of finite element analyses to evaluate the performance of the developed transducer.

Keywords: Ultrasonic transducer, 2D array transducer, Piezoelectric single crystal PACS numbers: 43.38. Fx

School of Mechanical Engineering, Kyungpook National University, 1370 Sankyukdong, Bukgu, Daegu 702-701, Republic of Korea

(Tel: 82-53-950-6828; Fax: 82-53-943-8716)

*Դ΁

ইۦۆΒڌٖԜݕɳۤ࠘ۍCT(Computed Tomo- graphy), MRI(Magnetic Resonance Imaging) фPET (Positron Emission Tomography)əۓߕٖԜں܃ėॢ

ɰ. ॠݓχইۦȇνԐڌʼČەəʂҙқۆߣڼ

ٖࣷԜۤ࠘əɳϸٖԜχ܃ėॠəʚ, ۋɳϸٖԜ

ڹʫςՙۙÀԸ঍ڷͿѕَʽ1D ߣڼ͔ࣷ࣡֟

˕Դεࣀ३ন˛ʽɰ. 1D ߣڼ͔ࣷ࣡֟˕Դۆą ڍߣ۾äνÀێ܁ॠيٖԜۆĵÂق܃ॢۋە ڷ϶, ɰδѓॳۆɳϸٖԜںصşڦ३Դə͔࣡

֟˕Դۆڦ࠘εѺąॠيآॢɰ. ۋ͠ॢЛ܃ε

३ĀॠيۓߕٖԜںন˛ॠşڦॢߣڼ͔ࣷ࣡֟

˕Դقəࡾó˃ÀݓܛΪÀەɰ. Ϥ۹1޲ڙڷͿ

ѕَʽʫςՙۙεşćۺڷͿڦ࠘܃رॠيন˛

ॢيࠗ͠ۆɳϸٖԜںۓߕٖԜڷͿ०Ձॠəş ćۺ3޲ڙߣڼ͔ࣷ࣡֟˕ԴÀەɰ.[1-3]ɰڼڷͿ

(2)

əʫςՙۙε2޲ڙڷͿѕَॢ঳Áՙۙεۻş ۺڷͿÒѻĵʴॠيۓߕٖԜںন˛ॠə2D ѕ

َ঍(2D array) ߣڼ͔ࣷ࣡֟˕ԴÀەɰ.[4-8]şćۺ

3޲ڙߣڼ͔ࣷ࣡֟˕Դۆąڍ1D ͔࣡֟˕Դε

şćۺڷͿধۻ֨ࢅş˺ЛقۓߕٖԜন˛՚ʪ ق܃ॢۋەڷ϶, ١͔şÂԐڌॠóʼϸşćۺ

ҙुق՜ԜۋьԦॠČٖԜۆݗۋ̆رݓóʽ ɰ. ъϸق2D ѕَ঍ߣڼ͔ࣷ࣡֟˕Դəʫςՙ

ۙ˞ۋथϸѕَʽĵܓۋ϶, Áʫςՙۙ˞ںۻ şۺڷͿ܃رॠيʴۺݚ՚(dynamic focusing)ęӁ

࣯֟رτ(beam steering)ۋÀɠॢĵܓۋɰ. ˰͆Դ

2D ѕَ঍͔࣡֟˕Դəۋʴػۋʪي͠ڦ࠘ق ԴۆɳϸٖԜӼχ؉ɦ͆ۓߕٖԜۆ܃ėۋÀɠ ॠɰ. ̚ॢ֪঒ߌνşցۆॳԜقۆ३֬֨Âۓ ߕٖԜۆন˛ۋÀɠ३ܐɰ. ॠݓχψڹսۆʫ ςՙۙ˞ۋێ܁ॢϸۺǴقܕۦॠş˺Лقՙۙ

ÂԜ঒ÂԾ(crosstalk)ۋࡾ϶, Ԝ঒ÂԾقۆ३Á

ʫςՙۙۆʂًफфս֪ÇʪÀҝŒێॠČǰڷ

϶ѓԐःࢤۋٷčʼş֖ɰ.[9]̚ॢʫςՙۙۆࡾ

şÀۚ؉Դۓͳےक़ʏ֟Àȭş˺Лقڼॳҙٮ

ۻۙধͿÂۆ܁०ۋرͷČ, ͔࣡֟˕Դۆս֪Ç ʪÀǰڹЛ܃۾ۋەɰ. ŔνČÁՙۙۆÒѻۺ

ĵʴںڦॠيՙۙ˞ںşćۺڷͿқν֨ࢇ঳ۻ

ۙধͿٮٍĀॠيآॠəʚ, ՙۙۆսÀψ؉Դ

ٍĀۋϔڍرͷɰəЛ܃Àەɰ. ˰͆ԴÁʫς ՙۙٮۻۙধͿÂۆۻşۺٍĀۋÀɠॠ϶, ՙۙ

ÂԜ঒ÂԾںܶيॳԜʽڼॳ࣢ՁںÀݓ϶Ͽ˜

޽ȇۆڼॳ࣢ՁۋŒێॢ͔࣡֟˕ԴۆÒьۋज़ څॠɰ.

2D ѕَ঍ߣڼ͔ࣷ࣡֟˕Դۆąڍ͔࣡֟˕Դ ۆţۋ(azimuth) ѓॳęÏۋɰսۆʫςՙۙÀफ (elevation) ѓॳڷͿʪѕَʽĵܓۍʚ, ۋقؘԴ

फѓॳڷͿѕَʽʫςՙۙۆսÀ8ÒͿۺڹ

1.75D ѕَ঍ߣڼ͔ࣷ࣡֟˕ԴεԸॱٍĵॠٕ

ɰ.[10] 2D ѕَ঍ߣڼ͔ࣷ࣡֟˕Դۆ޽ȇս҃ɰ

ۺݓχɰսۆ޽ȇۋܙڹϸۺقܕۦॠə1.75D ѕَ঍ߣڼ͔ࣷ࣡֟˕Դεڮॢڅՙ३Եںࣀ३

ՙۙÂԜ঒ÂԾں۹Çॠي͔࣡֟˕Դۆڼॳ࣢

ՁںॳԜ֨ࡎɰ. ٍ҆ĵقԴəRef. [10]ںц࢖ڷ Ϳ޽ȇսÀښˣ০ψڹ2޲ڙѕَ঍͔࣡֟˕Դ

قԴڼॳ࣢Ձقٖॳںй࠘əۍۙεқԵфܓ ۼॠي͔࣡֟˕Դۆۻߕ޽ȇۋŒێॠČॳԜʽ

ڼॳ࣢ՁںÀݗսەə2D ѕَ঍ߣڼ͔ࣷ࣡֟

˕ԴۆĵܓԺćεݕॱॠٕɰ.

ٍ҆ĵقԴəफѓॳڷͿ48Òфţۋѓॳڷ Ϳ64Òۆʫς޽ȇںÀݓ϶, ۋ˞ߪ3,072Òۆ޽

ȇقèߝŒێॢڼॳ࣢ՁںÀݓəؓۻɳĀ܁঍

2D ѕَ঍ߣڼ͔ࣷ࣡֟˕ԴεԺćф܃ۚॠٕ

ɰ. Ϥ۹Ͽ˜ՙۙ˞ۆÒѻۺۻşٍĀۋÀɠॠ ʪ΀͔࣡֟˕ԴۆĵܓεԸ܁ॠٕɰ. Ը܁ʽĵܓ قϑóĵՁՙۙε܃ۚॢɰڼ, Ԝڌ३Եʪĵۍ

PZFlex(Weidlinger Associates, NY)εۋڌॢڮॢڅ ՙ३Եںࣀॠي͔࣡֟˕ԴۆՃҙĵܓεԺćॠ

ٕɰ. ͔࣡֟˕ԴۆԺćЀशə-6 dB ܼ֮ܳࣷսÀ

3.5 MHz ± 7.5 %ۋ϶, -6 dB Ҽʂًफ(fractional bandwidth)ۋ60 %ۋԜۋ϶, Ͽ˜޽ȇۆս֪Çʪ

शܵठ޲À1 dBۋॠÀʼʪ΀Ժ܁ॠٕɰ. ̚ॢ2D ѕَ঍͔࣡֟˕ԴۻߕقèߝŒێॢ࣢Ձںĵই ॠşڦॢĵܓεʪ߻ॠٕɰ. ǣ؉ÀԺćقϑó

͔࣡֟˕Դۆ֨ۚुں܃ۚॠČڼॳ࣢Ձںࠑ܁

ॢĀęٮڮॢڅՙ३ԵĀęεҼİॠي, Òьʽ

2D ѕَ঍ߣڼ͔ࣷ࣡֟˕ԴۆՁɠںथÀॠٕɰ.

**%ѕَ঍ߣڼ͔ࣷ࣡֟˕ԴۆԺć

2D ѕَ঍ߣڼ͔ࣷ࣡֟˕ԴقəێъۺڷͿҼ İۺܙڹϸۺǴقɰսۆʫςՙۙ˞ۋܕۦॠي

ݚۺʪÀȭڷ϶ۻşۺÂԾۋȭ؉ۻşۺٍĀۋ

رͷɰ. ۋ͠ॢڌʪۆۻşۺٍĀںڦॢşցق əɰࠗ঍ڮٍۍթধͿşࣺ(FPCB: Flexible Printed Circuit Board)ںԐڌॠəѓѪęۻʪՁ঳ϸࠗ

(conductive backer)ںۋڌॠəѓѪ˞ۋەɰ.[11-12]

ɰࠗ঍ڮٍۍթধͿşࣺڹÁ֪঒Ըۆۻşۺ

ÂԾۋۺڷ϶Òѻ޽ȇۆۻşۺ࣢ՁۋŒێॠɰ əۤ۾ۋەş˺Лق, ٍ҆ĵقԴəۋFPCBεۋ ڌॢĀԸѓѪںԐڌॠٕɰ. ɰࠗ঍ڮٍۍթধͿ

şࣺںۋڌॠيFig. 1ęÏۋ8×64Òۆ޽ȇͿĵ ՁʽϿ˗ںĵՁॢ঳, Ͽ˗6Òεѕَॠي48×64 Òۆ޽ȇںÀݓʪ΀2D ѕَ঍͔࣡֟˕Դۆĵܓ εԸ܁ॠٕɰ. Ϥ۹Ͽ˗ڹؓۻɳĀ܁PMN-PTε

(3)

Ilj1#41#Vfkhpdwlf#vwuxfwxuh#ri#wkh#5G#duud|#xowudvrqlf wudqvgxfhu1

Wdeoh#41#Surshuwlhv#ri#wkh#dfrxvwlf#pdwhuldov#iru#wkh#

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Material Impedance [Mrayl]

Density [kg/m3]

Longitudinal velocity

[m/s]

Backer 5.5 3,230 1,710

1st matching layer 7.4 2,430 3,020 2nd matching layer 2.0 1,030 1,960

Kerf 1.3 1,430 960

Wdeoh#51#Ghvljq#shuirupdqfh#ri#wkh#prgxoh1

Description Value

center frequency [MHz] 3.7 fractional bandwidth [%] 80.2

Sensitivity [dB] -62.6

crosstalk level [dB] -30.6 acceptance angle [°] 40.9

ɠʴՙۙͿԐڌॠٕڷ϶, սʴՙۙə঳ϸࠗ(backer),

܁०ࠗ(matching layer) ф࠘फ(kerf)ڷͿĵՁʽɰ.

PZFlexεۋڌॠي࠘फۆНՁęȃҼÀՙۙÂԜ

঒ÂԾقй࠘əٖॳںқԵॢ঳, ؓۻɳĀ܁ę

܁०ࠗۆ˃ƍق˰δܼ֮ܳࣷսٮҼʂًफۆڼ ॳ࣢ՁںқԵॠČԺćѺսق˰δڼॳ࣢Ձں॥

սজॠيڮۻ؎ČνݏںۋڌॠيҼʂًफۋ߯

ʂÀʼʪ΀߯ۺԺćεॠٕɰ. ۋ˺Ԑڌʽսʴ ՙۙۆНՁڹTable 1ęÏڷ϶ԺćʽϿ˗ۆڼॳ

࣢Ձڹ3.7 MHzۆܼ֮ܳࣷսεÀݓ϶Ҽʂًफڹ

80.2 %, ս֪Çʪə-62.6 dB, Ԝ঒ÂԾڹ-30.6 dB, ս ġÁ(acceptance angle)ڹ40.9°ͿTable 2ٮÏɰ.[10]Ͽ

˗ۆĵߕۺۍԺćф܃ۚۼ޲əRef.[10]قۙՃ ০ǣࢍǣەɰ.

ۋ˞Ͽ˗˞ںѕَॠي2D ѕَ঍͔࣡֟˕Դ

ĵܓεĵՁॠəٍ҆ĵقԴəϿ˗Ǵՙۙ˞ۆۻ şۺٍĀںڦॢGRS(GRound Sheet)ٮڮٍۍթধ ͿşࣺۋؓۻɳĀ܁ۆڬϸę؉͘ϸقڦ࠘ॠə ʚ, ۋڮٍşࣺ˞ڹÁϿ˗ۆफѓॳتޅڷͿǣ ٮԴ঳ϸࠗхڷͿӇ܋ǣ٣ɰ. ݌, 6ÒۆϿ˗ۋ

Ā०ʽ2D ͔࣡֟˕Դۻߕۆ3,072Òۆ֪঒Ը˞

ڹÁϿ˗˞ۋۿॠəϸԐۋͿӇ܋ǣٮ͔࣡֟

˕Դ঳ϸࠗ˓ɳقܕۦॠəĵʴڌۻşধͿٮٍ

Āʼəĵܓۋɰ. ÁϿ˗˞ۆफѓॳąćϸقڦ

࠘ॢՙۙ˞ڹϿ˗ۆܼ֮قەəՙۙ˞قҼ३

ąćܓæۋɰβČۍۿॢϿ˗ۆٖॳںыş˺Л ق, ϿԴνՙۙ˞ڹϿ˗ÂÂüقࢀٖॳںыə ɰ. ˰͆Դۋ˞Ͽ˗˞ںѕَॠيŒێॢڼॳ࣢

ՁںÀݓə2D ѕَ঍ߣڼ͔ࣷ࣡֟˕Դεχ˞

şڦॠي, Ͽ˗ÂÂü(gap)ق˰δӁःࢤ, ս֪Ç ʪ, ܼ֮ܳࣷսфҼʂًफۆѺজεқԵॠي2D ѕَ঍ߣڼ͔ࣷ࣡֟˕Դۆۻߕ޽ȇۋŒێॢڼ ॳ࣢ՁںÀݓə߯ۺϿ˗ÂÂüںĀ܁ॠٕɰ.

Ͽ˗ÂÂüق˰δڼॳ࣢ՁںқԵॠşڦॠي

Fig. 1قǣࢍǶϿʝںԐڌॠي३Եںսॱॠٕ

ɰ. Fig. 1ۆϿʝقԴڼॳͬ݋ٮНڹϿ˗ۆۻߕ εʙČەəĵܓۍʚ, ͔࣡֟˕Դۆĵܓقʂॢ

ۋ३εʲşڦॠيڼॳͬ݋фНࠗںţۋѓॳ ڷͿъχ঍Ձ֨ࡈǣࢍǴؽɰ. ڼॳͬ݋əϿ˗˞

ںÇֳԴٽҙۆ߿üقʂ३Ͽ˗˞ں҃঒ॣս

ەəşćۺÌՁںÀ܋آॢɰ. ڼॳͬ݋قۆॢ

ڼॳقȃݓۆÇկÀݓǣ࠘óࡾݓ؍ČϿ˗ۋر ɗ܁ʪۆşćۺÌՁںÀݗսەʪ΀ڼॳͬ݋

ۆ˃ƍεࣀԜۺڷͿȇνۋڌʼə1 mmͿ܁ॠ

ٕɰ. ڮॢڅՙϿʝںĵՁ॥قەرԴ३Ե֨Âں

ܶۋşڦॠي঳ϸࠗۆ˃ƍε1 mmͿČ܁ॠČ

(4)

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঳ϸࠗۆцɱϸقড়սąćܓæں˃رъԐࣷۆ

ٖॳں܃äॠٕڷ϶, 1Òۆʂࠡϸںफѓॳęս थॢѓॳڷͿ˃رڮॢڅՙϿʝۆࡾşεٕܶ

ɰ. Ͽ˗˞Ԑۋقəڼॳͬ݋ٮÏڹۦΒÀ޽ڗ

܋ەəĵܓۋ϶, ڼॳͬ݋ٮ࠘फۆۦΒəÏɰ.

2D ѕَ঍ߣڼ͔ࣷ࣡֟˕Դۆąڍţۋѓॳ ęʴێॠóफѓॳڷͿʪӁपу(beam forming)ں

ॠيآॠəʚ, ي͠Òۆՙۙ˞ۋʴۚॠيÁՙ

ۙقۆ३঍ՁʽӁڹFig. 2ٮÏۋݓॳՁںÀݓ óʽɰ. ˰͆ԴTable 2قԴϿ˗Àڏʚڦ࠘ॢՙ

ۙ1Òεʴۚ֨ࡈьԦʽӁःࢤۆսġÁ҃ɰफ

ѓॳڷͿ48Òεĵʴ֨ࡈьԦʽӁःࢤۆսġÁ ۋۚɰ. يşԴϿ˗ÂÂüق˰δӁःࢤںқԵ ॠşڦॠي, फѓॳڷͿ48Òۆՙۙقʴێॢے ऑ֟঍ࢗۆۻؓںʴ֨قۍÀॠيŪۋ(depth) ѓ ॳقԴफѓॳڷͿÁʪľق˰δӁःࢤںFig. 2 ٮÏۋĵॠٕɰ. ۋεڦॢęʪ३ԵقԴؓۻɳ Ā܁قےऑ֟঍ࢗۆۻؓںۍÀॠيڼࣷεьԦ

֨ࢇ঳, Нࠗقڦ࠘ॢȤ˚˞قڼࣷÀۻࣷʼϸ

ÁȤ˚˞قۓͳʽڼؓۆ܁҃εۋڌॠيٽԙѪ (extrapolation)ڷͿɳĀ܁ڷͿҙࢢێ܁ॢäνق ԴۆӁःࢤںĵॠٕɰ.[13] Fig. 2əϿ˗ÂÂüۋ

300 쩋mێ˺ۆӁःࢤںǣࢍǶìۋɰ. ǣ؉ÀϿ

˗ÂÂüں100 ~ 500 쩋mۆѩڦقԴ100 쩋mÂüڷ ͿѺąॢĀę, Ͽ˗ÂÂüق˰δӁःࢤڹࢀ޲

ۋε҃ۋݓ؍ؕɰ. ӁःࢤۆْܳڹӸܔॠ϶Ͽ

˗ÂüقԜěػۋڮԐॢϿتںÀݓČەؽڷ

϶, ҙْ˞ۆڼؓͪѲۋϿ˃-15 dB ۋॠͿϿ˗Â

ÂüڹӁःࢤقࢀٖॳںй࠘ݓ؍əìڷͿǣ

ࢍǮɰ.

Fig. 2ٮÏڹĀęͿҙࢢϿ˗ÂÂüق˰δս ġÁۆѺজąॳںFig. 3قǣࢍǴؽəʚ, Ͽ˗Â

ÂüۋݒÀॣս΀սġÁۋйՃॠݓχۚ؉ݓə

ĀęÀǣࢍǮɰ. ۋìڹÂüۋݒÀॣս΀ѓԐʼ əڼڙۆڮমţۋÀţر܋ݓॳՁۋݒÀॠş˺

Лۋɰ. ॠݓχϿ˗ÂÂüۆѺজѩڦǴقԴս ġÁۆѺজ܁ʪÀϔڍۚş˺ЛقϿ˗ÂÂüڹ

Ӂःࢤقй࠘əٖॳۋۺɰČࣺɳॣսەɰ. ˰

͆ԴϿ˗ÂÂüں܁ॠşڦॢ͔࣡֟˕Դۆڼॳ

࣢ՁقԴӁःࢤڹČͲॠݓ؍şͿॠٕڷ϶, Ͽ

˗ÂÂüق˰δ͔࣡֟˕ԴۆՙۙÂս֪Çʪ,

ܼ֮ܳࣷսфҼʂًफχČͲॠٕɰ.

2D ѕَ঍ߣڼ͔ࣷ࣡֟˕ԴεĵՁॠəϿ˗ۆ

ϿԴνݓ۾ęܼ֮ݓ۾قڦ࠘ॢʫςՙۙ˞ڹą ćܓæۆٖॳںы؉йՃॠݓχڼॳ࣢ՁقԴ޲

ۋεÀݕɰ. Œێॢڼॳ࣢ՁںÀݓə͔࣡֟˕Դ ۆԺćεڦॠيϿ˗ۆܼ֮قڦ࠘ॢʫςՙۙٮ

Ͽ˗ۆϿԴνݓ۾قڦ࠘ॢʫςՙۙۆڼॳ࣢Ձ ںҼİқԵॠٕɰ. Ϥ۹Ͽ˗ÂÂüق˰͆ՙۙ

ÂԜ঒ÂԾ, Ͽ˗ܼ֮ݓ۾ۆՙۙٮϿԴνݓ۾ۆ

ՙۙÂۆܼ֮ܳࣷս޲ۋ, Ҽʂًफ޲ۋ, ս֪Ç ʪ޲ۋεڮॢڅՙ३Եںࣀ३қԵॠٕɰ. ۋ˺

३Եڹęʪ३ԵڷͿսॱʼؽڷ϶, Ӂःࢤ३Եę

ʴێॢѓѪڷͿٽԙѪںۋڌॠيڙäνڼۤق

ڦ࠘ॢÀԜۆъԐߕقԴъԐʼرʮ؉٣ڼؓں

НࠗۆȤ˚˞قۍÀॢ঳, ÁȤ˚˞ͿҙࢢьԦ ʽڼࣷε͔࣡֟˕ԴقԴۻş֪঒ͿѺঞॠيऑ

(5)

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Ilj1#71#Dfrxvwlf#shuirupdqfh#yduldwlrq#dffruglqj#wr#

wkh#jds#ehwzhhq#prgxohv1

֟ъԐ֪঒εĵॠٕɰ.[13]Ϥ۹Fig. 1ۆÀڏʚڦ

࠘ॢϿ˗ۆܼ֮قەəՙۙقχۻؓںۍÀॠي

ܼ֮ՙۙقۓͳʼəऑ֟ъԐ֪঒ۆս֪Çʪ, ܼ

֮ܳࣷս, Ҽʂًफںĵॠٕɰ. ս֪Çʪə֩(1)ę

Ïۋĵॠٕڷ϶,¯ƁƃƌƒƃƐ àƇƌƎƓƒڹբ֪ܼ֮֨ՙۙ

قۍÀʼəĵʴۻؓۋ϶,¯ƁƃƌƒƃƐ àƍƓƒƎƓƒəս֪֨

ܼ֮ՙۙقԴьԦʼə߻ͳۻؓۋɰ. ֨Âًٖۆ

ऑ֟ъԐ֪঒εऻνقѺঞںࣀ३֟घ࣡ͤںĵ

ॢ঳ܼ֮ܳࣷսٮҼʂًफںĵॠٕɰ.

¬ƃƌƑƇƒƇƔƇƒƗ á Ï× _ “–ŽÎ×Þ ć¯ƁƃƌƒƃƐ àƇƌƎƓƒ

¯ƁƃƌƒƃƐ àƍƓƎƓƒß. (1)

ɰڼڷͿFig. 1ۆÀڏʚڦ࠘ॢϿ˗ۆϿԴν (edge)قەəՙۙۆڼॳ࣢Ձںܼ֮ՙۙٮʴ ێॢѓѪڷͿĵॠٕɰ. ۋ˺ϿԴνՙۙۆऑ

֟ъԐ֪঒ۆս֪Çʪə֩(2)ٮÏۋĵॠٕČ,

¯ƃƂƅƃ àƇƌƎƓƒəբ֪֨ϿԴνՙۙقۓͳʼəĵʴ

ۻؓۋȝƃƂƅƃ àƍƓƒƎƓƒəս֪֨ϿԴνՙۙۆ߻

ͳۻؓۋɰ. ̚ॢϿ˗ÂÂüق˰δՙۙÂԜ঒

ÂԾʪ(crosstalk level)ε֩(3)ęÏۋĵॠٕəʚ,

¯ƍƎƎƍƑƇƒƃ àƍƓƒƎƓƒəբ֪֨ۍۿॢϿ˗ۆϿԴνقڦ

࠘ॢՙۙ(opposite)ۆ߻ͳۻؓۋɰ.

¬ƃƌƑƇƒƇƔƇƒƗ á Ï× _ “–ŽÎ×Þ ć¯ƃƂƅƃ àƇƌƎƓƒ

¯ƃƂƅƃ àƍƓƎƓƒß, (2)

œƐƍƑƑƒſƊƉ ƊƃƔƃƊ á Ï×_“–ŽÎ×Þć¯ƃƂƅƃ à ƇƌƎƓ ƒ

¯ƍƎƎƍƑƇƒƃ à ƍƓƒƎƓƒß. (3)

Ͽ˗ÂÂüں100 ~ 500 쩋mۆѩڦقԴ100 쩋mɳ ڦͿѺąॠي३Եॠٕڷ϶, Ͽ˗ÂÂüق˰δ

ՙۙÂԜ঒ÂԾʪٮܼ֮ՙۙٮϿԴνՙۙÂۆ

ս֪Çʪ޲ۋ, ܼ֮ܳࣷս޲ۋфҼʂًफ޲ۋ ε֩(4)-(6)εࣀॠيĵॠٕɰ. ֩(4)قԴ¬ƁƃƌƒƃƐə

Ͽ˗ۆܼ֮قەəՙۙۆս֪ÇʪۋȬƃƂƅƃəϿ

˗ۆϿԴνقەəՙۙۆս֪Çʪۋɰ. ֩(5)ق

ԴƄƁƃƌƒƃƐəϿ˗ۆܼ֮قڦ࠘ॢՙۙۆܼ֮ܳࣷ

սۋČƄƃƂƅƃəϿ˗ۆϿԴνقەəՙۙۆܼ֮ܳ

ࣷսۋ϶, ֩(6)قԴŸ›°ƁƃƌƒƃƐəϿ˗ۆܼ֮قە

əՙۙۆҼʂًफ,Ÿ›°ƃƂƅƃəϿ˗ۆϿԴνقە əՙۙۆҼʂًफۋɰ.

ƇƄƄƃƐƃƌƁƃ ƍƄ ƑƃƌƑƇƒƇƔƇƒƗ áç¬ƁƃƌƒƃƐà ¬ƃƂƅƃç, (4)

ƇƄƄƃƐƃƌƁƃƍƄƁƃƌƒƃƐ ƄƐƃƏƓƃƌƁƗ áçƄƁƃƌƒƃƐàƄƃƂƅƃç, (5)

ƇƄƄƃƐƃƌƁƃ ƍƄ ƄƐſƁƒƇƍƌſƊƀſƌƂƕƇƂƒƆ á矛°Ɓ ƃƌ ƒƃƐàŸ›°ƃƂƅƃç. (6)

Fig. 4ٮÏۋϿ˗ÂÂüۋɚرǨս΀ՙۙÂ

Ԝ঒ÂԾʪÀܶر˞ČϿ˗ۆܼ֮ݓ۾قەəՙ

ۙٮϿԴνݓ۾قەəՙۙÂۆڼॳ࣢Ձ޲ۋÀ

ܶر˜ɰ. ݌, Ͽ˗ÂäνÀϥرݗս΀ՙۙÂԜ

঒ÂԾۋܶر˞ş˺Лق, Ԝ঒ÂԾۆٖॳۋÇՙ ʼرϿ˗ܼ֮ݓ۾ۆՙۙٮϿԴνݓ۾ۆՙۙÂ

(6)

FPCB

Nose piece

Acoustic lens

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ڼॳ࣢Ձۆ޲ۋÀۚ؉ݕɰ. ۋԜۆĀęͿҙࢢϿ

˗ÂÂüں͔࣡֟˕ԴÀŒێॢڼॳ࣢ՁںÀݓ ə߯ՙÂüۍ300 쩋mͿ܁ॠٕɰ.

Ͽ˗ÂÂԾʪəϿ˗ÂÂü߿ݕۦΒۆНՁق ʪٖॳںыş˺Лق, ߿ݕۦͿԜ঒ÂԾں۹Ç

֨࢈սەəۦΒεԸ܁ॠيآॢɰ. Ըॱٍĵۍ

Ref. [10]ق˰͆Ͽ˗Ǵ࠘फۆ߿ݕۦΒͿԐڌʽ

ČқۙۦΒεϿ˗Â߿ݕۦΒͿԸ܁ॠٕɰ. ǣ؉

Àۋ߿ݕۦΒə2D ѕَ঍͔࣡֟˕Դۆڼॳͬ

݋ͿʪԐڌʼؽɰ. χأϿ˗ÂÂü߿ݕۦΒٮ

ڼॳͬ݋ۆۦΒÀɰεąڍ͔࣡֟˕Դۆ܃ۚۋ

ϔڍرͲڗݓ϶, ԸॱٍĵۍRef. [10]قԴڼॳͬ

݋εϿ˗ۆ࠘फۦΒٮʴێॠóԐڌॠيʪڼॳ

࣢ՁقЛ܃Àػəìںঝۍॠٕş˺ЛقϿ˗Â

߿ݕۦΒٮʴێॠóԸ܁ॠٕɰ.

फѓॳڷͿČ܁ʽӁःࢤںÀݓə1D ѕَ঍

ߣڼ͔ࣷ࣡֟˕Դۆąڍڼॳͬ݋ۆčέںܓۼ ॠيӁपуںॠş˺Лقڼॳͬ݋ۆϿتںԺ ćॠيآॢɰ. ॠݓχ2D ѕَ঍ߣڼ͔ࣷ࣡֟˕

ԴۆąڍफѓॳڷͿѕَʽՙۙ˞ںʴۚ֨ࡈ

Ӂपуںॠş˺Лقڼॳͬ݋ۆϿتڹथϸڷͿ

܁ॠٕɰ.

***%ѕَ঍ߣڼ͔ࣷ࣡֟˕Դۆ

܃ۚфՁɠथÀ

IIۤقԺϼॢԺćĵܓٮʴێॠó2D ѕَ঍ߣ ڼ͔ࣷ࣡֟˕Դۆ֨ۚुں܃ۚॠيFig. 5قǣࢍ

Ǵؽɰ. ֨ۚुڹ6ÒۆڼॳϿ˗, ڼॳͬ݋, ҃঒ڌ

ʙÒ(nose piece) фɰࠗ঍ڮٍۍթধͿşࣺ˞Ϳ

ĵՁʼرەɰ. Ͽ˗ۆफѓॳتޅڷͿÁ256Òۆ

֪঒Ը˞ۋप॥ʽɰࠗ঍ڮٍۍթধͿşࣺ12ۤ

ۋÁϿ˗ۆԐۋεࣀ३঳ϸࠗˏठڷͿӇ܋ǣ ٮߪ3,072Òۆ޽ȇۋۻşধͿٮٍĀۋʽɰ. 2D ѕَ঍ߣڼ͔ࣷ࣡֟˕Դۆ܃ۚė܁ڹϿ˗܃ۚ

ęϿ˗Ā०ė܁ڷͿǣɀرݕɰ. Ϥ۹Ͽ˗ۆ܃

ۚė܁ڹՙۙ܃ۚфۿ޳, ܁нۼԑ, ࠘फ߿ݕڷ ͿۋΘر܋ەڷ϶, Ͽ˗܃ۚقԐڌʽՙۙۆН ՁڹTable 1ęÏɰ. ɰڼڷͿԸॱٍĵۍRef. [10]

ق˰͆܃ۚॢϿ˗˞ںĀ०ॠəė܁ڹϿ˗ѕ

َ, Ͽ˗ÂÂü߿ݕфڼॳͬ݋ܳܓͿۋΘرݕ ɰ. 2D ѕَںۋΘəϿ˜Ͽ˗˞ڹÂüфȭۋÀ

ŒێॠيآॠČϿ˗ԐۋقǛڗ܋ەəɰࠗ঍

ڮٍۍթধͿşࣺۆ՜ԜۋػرآॠдͿ, ÁϿ

˗˞ۆڦ࠘ε܁нॠó܃رॣսەəࠄĵٮȭ ڹѕڱۆইйąںۋڌॠيϿ˗ںѕَॠٕɰ.

Ͽ˗ۆѕَۋٰΒʽ঳Ͽ˗ÂÂüقϿ˗ۆ࠘

फęʴێॢۦΒε߿ݕॠٕɰ. ߿ݕė܁ڹϿ˗

˞ۆѕَÂüۋцljݓ؍ʪ΀ࠄĵεۋڌॠي

Ͽ˗ęڮٍşࣺ˞ںČ܁ॢ঳߿ݕۦεԙۓॠə ʚ, ߿ݕę܁قԴÂüǴقşपÀьԦॠݓ؍ʪ

΀ݕė࢐पė܁ںʴ֨قսॱॠٕɰ. ɰڼڷͿ

ڼॳͬ݋ܳܓė܁ڹ܁०ࠗڦقŒێॢ˃ƍε

Àݓ϶şपф߿ݕۋʼݓ؍ڹҙқۋػəڼॳ

ͬ݋ࠗں঍ՁॠəìڷͿ, ѕَфÂü߿ݕۋٰ

ΒʽϿ˗˞ں࠘ĵεۋڌॠيČ܁ॢ঳, ڼॳͬ

݋ۦΒε܁०ࠗԜҙقʪपॠČ࢐पॠϸԴąজ

֨ࡈڼॳͬ݋ࠗں঍Ձॠٕɰ. ۋ˺Ͽ˗Â߿ݕ

ۦΒٮڼॳͬ݋ۦΒÀʴێॠş˺Лق, ۋ˞Ԑ ۋقąćϸۋԦՁʼݓ؍؉͔࣡֟˕ԴۆǴҙĵ ܓÀŒݗॠó঍Ձʾսەؽɰ.

ࠑ܁ʽ2D ѕَ঍͔࣡֟˕ԴۆÁ޽ȇѻڼॳ

࣢ՁںFig. 6ęÏۋऑ֟ъԐ֪঒ۆࠑ܁ںࣀ३

ঝۍॠٕɰ. ߪ3,072Ò޽ȇۆऑ֟ъԐ֪঒εÒ

(7)

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Ilj1# :1# Dfrxvwlf# vhqvlwlylw|# glvwulexwlrq# ryhu# wkh#

wudqvgxfhu#fkdqqhov1

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Ilj1#;1#Frpsdulvrq#ehwzhhq#phdvxuhg#dqg#fdofxodwhg#

sxovh0hfkr#uhvsrqvhv1

ѻۺڷͿࠑ܁ॠşڦ३঳ϸࠗۆˏޅڷͿǣٮە ə256Òۆ֪঒ԸۋٍĀʽɰࠗ঍ڮٍۍթধͿ

şࣺ12ۤںտ޲ۺڷͿMUX(National instruments PXI-2575)قٍĀॠٕɰ. ۋ˺MUXə256Òۆ޽ȇ ںÀݓČەڷ϶, pulser-receiver(Olympus 5800PR)ٮ

١֬Ϳ֟ࡑ॒(Agilent DSO6012A)قٍĀॠٕɰ.

ࠑ܁ʽऑ֟ъԐ֪঒ۆ޽ȇѻս֪Çʪқपə

Fig. 7ęÏɰ. थŒս֪Çʪə-88.6 dBۋČशܵठ

޲ə0.8 dB ۋ϶, थŒս֪ÇʪقԴ±2.5 dBεѫر ǣə޽ȇۆսÀ13 ÒͿۻߕ޽ȇսʂҼ1 %ۋॠ ۍìڷͿࠑ܁ʼؽɰ. ۋ˺޽ȇѻս֪Çʪə֩

(1)ęÏۋĵॠٕڷ϶, थŒս֪Çʪəۻߕ޽ȇ ۆս֪ÇʪۆथŒۋɰ. ҝ͟޽ȇڹ܃ۚ١޲قۆ ३ьԦॢìڷͿԴ, ÁՙۙۆࡾşÀϔڍۚş˺

Лقҝ͟޽ȇۆێҙқقԴəGRSٮؓۻɳĀ܁

Âۿ޳ࠗۆ˃ƍܓۼۋ܃ʂͿۋΘرݓݓ؍؉

ս֪ÇʪÀ̆رݕìڷͿঝۍʼؽɰ. ̚ɰδҙ

қقԴə঳ϸࠗںĵՁॠəࢫ֟ࢮۓۙÀʗرν

঍ࢗͿУߝݕҙқۋьԦॠٕəʚ, ࢫ֟ࢮڹۻʪ ՁۋەرԴۓۙʗرνÀڮٍۍթধͿşࣺę

ۿߤʾąڍق޽ȇÂۆ०Ըںێڷࢅş˺Лقۋ

ҙқقԴÇʪÀȭóǣࢍşʪॠٕɰ. ॠݓχ҆

ٍĵقԴÒьʽ2D ѕَ঍ߣڼ͔ࣷ࣡֟˕Դə

ࣀԜۆߣڼ͔ࣷ࣡֟˕Դۆս֪ÇʪŒێʪεࣺ

ɳॠəşܵۍशܵठ޲À1.0 dBۋॠۋČҝ͟޽

ȇҼڱۋ1 %ۋॠيآॠɰəܓæںχܔ֨ࡎڷ дͿ܃ۚʽ2D ѕَ঍ߣڼ͔ࣷ࣡֟˕ԴəŒێ

ॢڼॳ࣢ՁںÀݓəìڷͿࣺɳॣսەɰ.

Á޽ȇۆ࣢ՁںFig. 8قǣࢍǴؽəʚ, ऑ֟ъ Ԑ֪঒ۆܼ֮ܳࣷսə3.7 MHzۋČҼʂًफڹ

76.4 %ڷͿࠑ܁ʼؽɰ. ۋəЀशԐتۍ3.5 MHz ± 7.5 % ф60 % ۋԜںÁÁχܔ֨ࢅəÉۋɰ. ۋ˺

ऑ֟ъԐ֪঒ۆ३ԵĀęəIIۼقԴFig. 1ۆ३Ե

ϿʝقԴܼ֮قڦ࠘ॢϿ˗ۆÀڏʚەəՙۙق

(8)

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Wdeoh#61#Uhvxow#ri#wkh#5G#duud|#wudqvgxfhu#ghvljq#dqg#

phdvxuhphqw1

Description Designed Measured center frequency [MHz] 3.7 3.7 fractional bandwidth [%] 80.2 76.4

focal depth [mm] 60 62

ےऑ֟ۻؓںۍÀॠيٽԙѪںࣀॠيĵॢìۋ ɰ. ֨Âًٖۆऑ֟ъԐ֪঒ۆڮॢڅՙ३ԵĀ ęÀ֬ॹĀęقҼ३أÂţóǣࢍǦìڹٽԙ Ѫںۋڌॠيڙäνڼۤقڦ࠘ॢÀԜۆъԐߕ قъԐʼر˞ر٣ڼؓںĵॣ˺Нقۆॢڼؓ

ۆÇկÀ܁ঝ০ČͲʼݓ؍ؕş˺Лۋɰ. Ҽʂ

ًफۋՙۙÂԜ঒ÂԾڷͿۍ३ڮॢڅՙ३ԵĀ ę҃ɰأÂۚóǣࢍǮݓχ, ऑ֟ъԐ֪঒ۆࣷ

঍ęܳࣷս֟घ࣡ͤڹҼİۺ۞ێ࠘ॠəìڷͿ

ǣࢍǮɰ.

ɰڼڷͿFig. 6ۆۤ࠘قԴԸ঍ъԐߕۆڦ࠘ق

ॠۋ˚Ϳब(ONDA HNR-0500)ںۤ޳ॠي͔࣡֟

˕ԴۆѓԐӁःࢤںࠑ܁ॠٕɰ. ͔࣡֟˕Դۆ

फѓॳڷͿ28Ò޽ȇقےऑ֪֟঒εʴ֨قۍ ÀॠيߣڼࣷεьԦ֨ࢅϸԴ, Ŕق˰͆ьԦॢ

ڼۤںॠۋ˚Ϳबں1 mmÂüڷͿۋʴ֨ࢅ϶ࠑ

܁ॠٕɰ. ڼڙşܵڷͿफѓॳۆܼ֮قԴݚ՚

Ūۋ(focal depth)εFig. 9قǣࢍǴؽəʚ, ڮॢڅՙ

३ԵĀęۆݚ՚Ūۋə60 mmۋČ, ࠑ܁ʽݚ՚Ū ۋə62 mmͿǣࢍǮɰ. ۋ˺Fig. 9قԴӁःࢤۆ

ڮॢڅՙ३ԵĀęəڼؓۆ঍ࢗͿĵॣսەݓ χ, ֬܃ࠑ܁قԴəڼؓۆࡾşÀ߻ͳۻؓۆ঍

ࢗͿǣࢍǣəॠۋ˚Ϳबںۋڌॠٕş˺Лقࠑ

܁ĀęۆŔ॒͒قԴՃͿ߹ڹ߻ͳۻؓڷͿǣࢍ

Ǵؽɰ. ŪۋۋԜęÏۋࠑ܁ʽ֨ۚुۆ࣢Ձ˞ں

Table 3ق܁νॠيԺćʽ͔࣡֟˕Դ࣢Ձ˞ęҼ İॠٕəʚ, ܃ۚʽ͔࣡֟˕ԴəԺćĀęٮڼॳ

࣢ՁۋҼİۺ۞ێ࠘ॠČ, Fig. 7قǣࢍǦцٮÏ ۋŒێॢ࣢ՁںÀݓəìڷͿঝۍʼؽɰ.

*7Ā΁

҆ȦЛقԴəؓۻɳĀ܁ڷͿĵՁʽ48×64 ޽ ȇۆ2D ѕَ঍ߣڼ͔ࣷ࣡֟˕ԴεԺćф܃ۚ

ॠČ, ܃ۚʽ֨ۚुۆ࣢ՁںथÀॠٕɰ. 8×64 ޽ ȇۆϿ˗6ÒεĀ०ॠي48×64 ޽ȇںÀݓəĵ ܓεԸ܁ॠٕəʚ, ԸॱٍĵقԴÒьʽϿ˗ںۋ ڌॠيϿ˗ÂÂüق˰δڼॳ࣢ՁںқԵॠي࣡

͔֟˕Դۆۻߕ޽ȇۋŒێॢڼॳ࣢ՁںÀݓə

ĵܓεԺ܁ॠٕɰ. Ŕ঳Ժćʽĵܓق˰͔͆࣡

֟˕Դۆ֨ۚुں܃ۚॠيՁɠںࠑ܁ॠٕČ, ࠑ

܁ʽĀęٮڮॢڅՙ३ԵĀęεҼİॠيٍ҆

ĵقԴÒьॢ͔࣡֟˕ԴۆՁɠںथÀॠٕɰ. ऑ

֟ъԐ֪঒εࠑ܁ॢĀęߪ3,072Ò޽ȇۆथŒ

ս֪Çʪə-88.6 dBۋČशܵठ޲ə0.8 dBͿŒێ ॠٕڷ϶, ܼ֮ܳࣷսٮҼʂًफڹÁÁ3.7 MHz ٮ76.4 %Ϳڮॢڅՙ३ԵĀęٮҼİۺ۞ێ࠘ॠ

϶ЀशԐتںχܔ֨ࡎɰ. ̚ॢफѓॳڷͿ28Ò ۆ޽ȇںʴ֨قĵʴ֨ࡈࠑ܁ॢݚ՚ʪʪ३ԵĀ

(9)

ęٮ۞ێ࠘ॢìڷͿǣࢍǣ, ܃ۚʽ2D ѕَ঍ߣ ڼ͔ࣷ࣡֟˕Դ֨ۚुڹԺćĀęε۞ъٖॢ

ìڷͿঝۍʼؽɰ.

ÇԐۆŘ

ٍ҆ĵəݓ֩ą܃ҙԓغڙߎşցÒьԐغ (No. 10035282)ęĶѓęॡٍĵՙ(No. UD130007DD) ۆݓڙڷͿսॱʼؽڷ϶, ۋقʂ३ŪۋÇԐε

˚ςɦɰ.

3FGFSFODFT

1. A. Nguyen-Dinh, P. Mauchap, N. Felx, R. Dufait, P.

Auclair, and A. Flesch, “Integrated mechanism based multiplaned/3D ultrasonic imaging probes,” in Proc.

IEEE Ultrason. Symp., 1147-1150 (2001).

2. R. Canals, G. Lamarque, and P. Chatain, “Volumetric ultrasound system for left ventricle motion imaging,” IEEE Trans. Ultrason, Ferroelect., Freq. Contr. 46, 1527-1538 (1999).

3. H. Eun, S. Lee, and Y. Roh, “Design and fabrication of a 3-dimensional diagnostic ultrasonic probe” (in Korean), J.

Acous. Soc. Kr. 21, 766-771 (2002).

4. S. W. Smith, G. E. Trahey, and O. T. von Ramm, “Two- dimensional arrays for medical ultrasound,” in Proc. IEEE Ultrason. Symp. 628-628 (1991).

5. R. L. Goldberg and S. W. Smith, “Multilayer piezoelectric ceramics for two-dimensional array transducers,” IEEE Trans. Ultrason,, Ferroelect., Freq. Contr. 41, 761-771 (1994).

6. S. S. Brunke and G. R. Lockwood, “Braod-bandwidth radiation pattern of sparse two-dimensional vernier arrays,”

IEEE Trans. Ultrason,, Ferroelect., Freq. Contr. 44, 1101- 1109 (1997).

7. P. K. Weber, R. M. Schmitt, B. D. Tylkowksi, and J. Steck,

“Optimization of random sparse 2-D transducer arrays for 3-D electronic beam steering and focusing,” in Proc. IEEE Ultrason. Symp. 1503-1506 (1994).

8. D. F. Lemmerhirt, X. Cheng, R. D. White, C. A. Rich, M.

Zhang, J. B. Fowlkes, and O. D. Kripfgans, “A 32 X 32 capacitive micromachined ultrasonic transducer arrays manufactured in standard CMOS,” IEEE Trans. Ultrason, Ferroelect., Freq. Contr. 59, 1266-1271 (2012).

9. W. Lee and Y. Roh, “New design of the kerfs of an ultrasonic two-dimensional array transducer to minimize cross-talk,” Jpn. J. Appl. Phys. 49, 07HD06, 2010.

10. W. Lee and Y. Roh, “Design and fabrication of a 1.75D ultrasonic transducer” (in Korean), J. Acoust. Soc. Kr. 32, 199-207 (2013).

11. R. E. Davidsen and S. W. Smith, “Two-dimensional arrays for medical ultrasound using multilayer flexible circuit interconnection,” IEEE Trans. Ultrason,, Ferroelect., Freq.

Contr. 45, 338-348 (1998).

12. L. Daane and M. Greenstein, “A demountable interconnect system for a 50 X 50 ultrasonic imaging transducer array,”

IEEE Trans. Ultrason,, Ferroelect., Freq. Contr. 44, 978-982 (1997).

13. N. N. Abboud, G. L. Wojcik, D. K. Vaughan, J. Mould, D. J.

Powell, and L. Nikodym, “Finite element modeling for ultrasonic transducers,” in Proc. SPIE Int. Symp. Medical Imaging, (1998).

۹ۙأͳ

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ʴ३Ե

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