Application of transformer for improvement of noise performance of ultrasonic preamplifier

Transcription

1 ISSN 39- ULTRAGARSAS, Nr(57) 005 Applicatio of trasformer for improvemet of oise performace of ultrasoic preamplifier V Dumbrava, L Svilaiis Sigal processig departmet, Kauas Uiversity of Techology, Studetu str 50, LT-538 Kauas, Lithuaia, tel , vytautasdumbrava@ktult Itroductio Whe a ultrasoic applicatio requires additio of a preamplifier i order to provide the additioal gai ad sigal-to-oise ehacemet, trasducer receptio sesitivity is defied as thigal-to-oise ratio (SNR) achieved by the combied trasducer ad preamplifier oise performace The trasducer oise figure is idepedet of the receiver load impedace ad depeds critically o dissipative losses The preamplifier oise figure performace requires oise matchig [] The gai badwidth of moder operatioal amplifiers is reachig GHz, which makes it attractive choice for a preamplifier desig i ultrasoics [-] Itroductio of a trasformer betwee the trasducer ad the preamplifier iput ca help to reduce this stage oise Sources [5-7] preset justificatio of this idea It is aalyzed how oise performace improvemet ca be achieved for a kow source impedace The limitatio of the methods metioed is a assumptio of a ideal trasformer I this paper we are tryig to get mathematical equatios for complete iput system, icorporatig a trasducer, a lossy trasformer ad a oisy operatioal amplifier, icludig the oise of the rest of electroics We will try to evaluate ifluece of trasformer parameters o a oise performace ad to compare various optimum value computatio methods Trasformer model For a most commo case, whe icrease of thigal source impedace R ge is givig rise for as U s ~ R ge (which is usually the case with trasformer couplig), R ge matchig to R opt (see below) allows to expect the better sigal to oise ratio I geeral, trasformer applicatio ca be justified by three reasos: oise improvemet thaks to ability to modify thource impedace, isolatio ad optimum power trasfer thaks to impedace matchig We add the fourth oe effective operatioal amplifier direct curret (DC) biasig is possible exploitig the trasformer widig iductace The last reaso could be the exploitatio of primary widig iductace for elimiatio of the trasducer parasitic capacitace C 0 The complete trasformer model is preseted i Fig [5] L Lp C C r L r Tr Ls R c Fig Complete trasformer model L m C Resistaces r ad r are presetig the losses i the primary ad secodary widigs, respectively These resistaces are icreasig with a frequecy because of the ski effect of the wire itself Sice wide-bad trasformers usig ferromagetic cores have fairly short wire legths, this cotributio is small ad if source ad load impedaces are small, ca be omitted The core losses are ecoutered through thhut resistace R c Those losses are maily hysteresis ad eddy curret losses caused by the ferromagetic material, which icreases with the operatig frequecy as f or eve f 3, ad arigificat i the trasformers that are operated ear the resoace of the core material Therefore, proper cosideratio must be give to thelectio of the core material The widigs couplig factor defies the level of leakage iductaces L Lp ad L Ls These iductaces armall i compariso to the magetizig iductace L m This iductace represets the effects, associated with a fial core permeability ad together with thource impedace determies the lowest operatioal frequecy Oce operatig withi the trasformer passbad, this iductace ca be omitted, sice thource ad the load impedaces are prevailig The cumped capacitaces C, C ad C are presetig the distributed capacitaces resultig from iterwidig couplig I the trasformers havig a sigificat amout of wire, the iterwidig capacitace ca iteract with the trasformer iductaces ad create a trasmissio zero Keepig i mid the frequecies of ultrasoic sigals, this capacitace ifluece ca be omitted I further aalysis wimplify the trasformer model ad split it depedig o the case of thource impedace I the case of a low trasducer impedace oly r ad r are used sice the core losses ca be eglected I the case of a high trasducer impedace, thhut resistace R c represets the major problem, so it should be take ito accout

2 ISSN 39- ULTRAGARSAS, Nr(57) 005 System oise model It is assumed that trasmissio of a ultrasoic trasducer oise ad sigal are modeled usig BVD (Butterworth-Va Dyke) model [8] This model is simple, but coveiet for iterpretatio of the behavior i the ear resoace frequecy rage The operatioal amplifier is usig AC coupled feedback with DC gai of uity (refer to Fig) The trasformer havig the trasformatio coefficiet : is placed betwee a trasducer ad a o-ivertig operatioal amplifier iput The operatioal amplifier oise is prevailig over ext stages, if the gai is large eough (>0) The operatioal amplifier iput usually is a differetial stage for voltage feedback amplifiers Therefore the expected oise is higher tha i the case of a sigle trasistor preamplifier [7] Rs Ls Cs Tr C 0 R Fig System circuit diagram The operatioal amplifier itrisic oise ca be modeled usig voltage ad curret oisources at the iput The operatioal amplifiers data sheets provide the values for oispectral desities of thosources i / Hz, i / Hz, e / Hz The optimal source resistace R opt exists, which miimizes the amplifier oise figure It is defied as [, 7, 9]: R C U e R opt () i Table gives the oise parameters of low oise represetatives of FET (OPA57) ad BJT (LMH) operatioal amplifiers Table Low oise operatioal amplifiers parameters Parameter LMH OPA57 e, V / Hz 09 8 i, fa/ Hz BW, MHz R opt, kω 0 39 C i, pf 09 5 Table is used to preset the two most specific ultrasoic trasducer cases Oe [0] is the air coupled low impedace composite trasducer The aother is also a air coupled trasducer where the matchig is obtaied usig a special layer This trasducer is exhibitig a high electric impedace Table Trasducer parameters Trasducer R s, Ω C s,pf L s, uh C 0, pf Low impedace High impedace Widig losses model If a ultrasoic trasducer exhibits a low output impedace, oly r ad r are used ad the trasformer core losses ca be eglected The preamplifier oise model, icorporatig the trasformer : ad it s widig losses is preseted i Fig3 The operatioal amplifier itrisic oise is modeled usig the voltagource e ad the curret oise sources i ad i - The ultrasoics trasducer has a slightly modified schematic it is preseted by the voltagource, followed by the complex impedace Z s The trasformer, except the primary ad secodary widig losses r ad r, is ideal Z s r Tr : r Fig 3 Preamplifier oise model accoutig for widig losses Thchematic above ca be trasformed ito the equivalet circuit, preseted i Fig r e r e r r / e / i Z s i Fig Preamplifier oise model equivalet circuit The oispectral desity at the operatioal amplifier iput is give by e i - i - R e R - e - R R e e 3

3 ISSN 39- ULTRAGARSAS, Nr(57) 005 r e Re( ) i kt Z s r r i Z s r e where k [J/C] is the Boltsma costat, T is the absolute ambiet temperature i Kelvi I order to miimize the oise oe eeds to a fid optimal trasformatio coefficiet This ca be obtaied by differetiatig ( Eq by ad settig the derivative equal ) d e zero i r 0 Usually Z s >> ad this compoet ca d be omitted After simplificatio: r R opt r r e i r i opt (3) i Z s r Z s r It ca bee that the optimal trasformatio coefficiet opt is defied by widig losses r, ad r Usually coditio r <<e >> i r is satisfied, therefore r ca be omitted: Ropt Ropt opt () Z r Z r s s Eq allows calculatio of the optimal trasformatio coefficiet whe widig losses should be take ito accout Assumig that ultrasoic trasducer impedace ca ot be modified it makes sese to use the oise figure istead of thigal-to-oise ratio for the preamplifier oise performace aalysis The oise factor is give by []: () (S/ N) i No Si F, (5) (S/ N) o Ni So where (S/N) i ad (S/N) o sigal to oise ratio at the iput ad the output correspodigly; N i ad N o the oise power at the iput ad the output likewise; S i ad S o thigal power at the iput ad the output respectively I order to calculate thigal-to-oise ratio let us get the expressio for thigal level at the iput: U s Si, () Z s r where U s is thigal amplitude at the trasformer iput which is a fuctio of frequecy The exact evaluatio of this voltage is ot ecessary sice it will be divided by the output sigal power: ( U s G) So, (7) R where G is the amplifier gai, is the amplifier R load impedace For the oise figure thigal power ratio may be obtaied by dividig Eq by Eq7: Si So U s Z s r (8) ( U G) G Z s r s I order to calculate the oise power ratio, the iput oise power desity ca be used: ( Re( Z ) r ) U i s Ni, (9) Z s r Z s r where U i is the iput oise amplitude, which is the fuctio of the real part or Z s ad r The output oise power desity: e ( Re( ) ) kt Z s r i Zs r G No ( G ) e e i R (0) Eq0 cotais additioal oise compoets, which are caused by the exteral resistaces R, R, (refer to Fig) The criteria for selectio of the resistaces R, R i order to miimize their oise cotributio ad resultig oise aalysis are preseted i [3] Whe the gai is large eough (G>>) ad thelectio criteria are obeyed, these additioal compoets ca be removed from equatio The resultig oise ratio is e G Z s r ( Rs r) i Z s r N0 Ni ( Re( Z s ) r) () Isertig Eq8 ad to Eq5 after somimplificatio we obtai: e i Z s r F () ( Re( Z ) r ) ( Re( Z ) r) s s The oise figure: NF 0lg F 0lg e i Z s r ( Re( Z ) r ) ( Re( Z ) r) s s (3) After isertig Eq ito Eq ad Eq3 we get the miimal oise factor ad the oise figure: e i Z s r Fmi s ( Re( Z ) r ) e mi 0lg i Z s r NF s ( Re( Z ) r ) () (5)

4 ISSN 39- ULTRAGARSAS, Nr(57) 005 Core losses model If a ultrasoic trasducer has a high output impedace, thhut resistace R c represets the major problem, so it should be take ito accout The widig losses r ad r ca be eglected i such case Fig5 idicates the preamplifier equivalet circuit for modelig of oise performace whe trasformer core losses are icluded Usig the circuit preseted above we calculate the oise spectral desity at the preamplifier iput: Z s r R C r / e / e r e r i i - R - R e The oise figure is give by e ( ) Z s Rc Z s NF 0 lg i () Re Z s R C Lossless model It should be oted that both cases aalyzed above are usig the amplifier oise parameters the voltagource e ad the curret oisources i ad i - I the case whe FET amplifier is used, thources i ad i - disappear for a covetioal ultrasoic trasducer Oe would be iterested to calculate a optimal trasformer turs ratio, omittig trasformer losses Solutio for such case is give i literature [] A equivalet circuit diagram is preseted i Fig Zs Tr : e Fig 5 Core losses icorporatig preamplifier oise model e Ci ei Re Re r s r ( Z ) r Z s r R c e i r Z s r R c Rc r Z s r R c () I order to simplify the equatio, it is assumed that both r ad r / are much smaller tha Z s, the from Eq: Rc e Z s Rc ei Re( Z s) i Z s Rc Z s Rc (7) I thame way as for Eq3 we fid the optimal trasformatio coefficiet whe the core losses are take ito accout: Z s Rc opt Ropt (8) Z s Rc Thimilar method ca be used for the oise factor: e Z s Rc Z s F i Re( Z ) Re( Z ) (9) s Rc s Isertig Eq8 ito Eq9 we get the miimal oise factor: e Zs Rc Z s Fmi i (0) Re ( Zs) R C Fig Lossless trasformer preamplifier oise model Applicatio of a oiseless trasmissio circuit with the gai K allows improvemet of the oise factor Ramp F, () K Req where R amp is the amplifier oise modelig resistace, R eq is the ultrasoic trasducer equivalet oise resistace The trasformer load is accouted as the amplifier iput capacitace C i The trasmissio coefficiet of such a circuit is maximized whe (3) ωc i Z s The the oise factor ca be calculated: Ramp Fmi ωci Z s () Req Model applicatio results The optimal turs ratio opt ca be determied usig Eq3 ad Eq for a low impedace trasducer (refer a Table ) For this purpose the trasformer parameters eed to be evaluated Measuremet results of :3 trasformers dedicated for a high source impedace, low frequecy (high L m is eeded) ad low source impedace, high frequecy, are preseted i Table 3 ad core loss behavior versus frequecy measuremet results arhow i Fig7 5

5 ISSN 39- ULTRAGARSAS, Nr(57) 005 Table 3 Trasformer parameters Parameter L m r r L LP L LS For low Z s 095mH 03 Ω 7 Ω 0uH 08uH For high Z s 0mH 5 Ω 8 Ω uh 7uH 7 5 r 53Ω r 03Ω The operatioal amplifiers usig FET iput exhibit a extremely low curret oise i ad i - Therefore R opt is a megaohms rage (refer to Table ) Thource [9] recommeds usig those whe thource impedace is high If Eq is used for a low impedace trasducer (refer to Table ) the turs ratio opt becomes very high (~00) The realizatio of such a trasformer will get too complicated The amplifiers usig BJT exhibit a lower voltage oise e, but much higher curret oises i ad i - Therefore R opt is i a hudreds ohms rage Applicatio of a step-up trasformer i such case icrease the ultrasoic trasducer impedace by The turs ratio opt have reasoable values, which ca be achieved i practice 000k opt k 00k 500k 00k 700k Fig 8 Low impedace trasducer opt whe widig losses accouted NF, db Rc, ohm 500k 000k 500k opt (f) 0 300k 00k 500k 00k 700k Fig 9 Noise figure for a low impedace trasducer Fig 7 Measured core losses R c f, MHz Therefore for a low impedace trasducer we use oly BJT amplifier Fig8 is idicatig the ratio opt chage versus frequecy for two trasformer widig resistaces (refer to Table 3) As ca bee from Fig8, opt is chagig i a wide rage I practicuch trasformer is ot realizable Therefore oly oe value of opt should be used Let us examie how oise performace will degrade i such a case Fig9 is idicatig the oise figure for a theoretical case whe the ratio opt is maitaied over a whole frequecy rage (tholid curve) The other curves idicate the various alteratives, whe the trasformatio ratio is fixed The case (dot-dash curve) is whe o trasformer is used The trasducers uder aalysis are usig theries a trasformer resoace frequecy rage, therefore applicatio of turs to be useful here The oise figure versus frequecy ad the trasformatio coefficiet cotour plots are useful for choosig the right turs ratio i a desired frequecy rage (refer to Fig0) I thame way oise reductio of a high impedace trasducer with a trasformer applicatio may be aalyzed db db db 3dB 05dB 0dB 300k 50k 700k Fig 0 Noise figure cotour plots for a low impedace trasducer Here the operatioal amplifiers usig FET iput are mai cadidates, sice they exhibit a extremely low curret oise, which i tur will allow lowerig the oise compoet due to i /Z s / The R c losses should be accouted hero opt is calculated usig Eq8 The opt shape is similar to Fig7 with turs the ratio value equal at the ultrasoic

6 ISSN 39- ULTRAGARSAS, Nr(57) 005 trasducer series resoace ad 8 at the parallel resoace Such ratios are ot practical Agai, opt is varyig with frequecy, thereforuch a trasformer ca ot be realized Ivestigatio of a oise performace with fixed revealed that degradatio at the lower tha optimum trasformatio coefficiet is ot sigificat The oise figure chage versus frequecy ad the trasformatio coefficiet cotour plots are preseted i Fig (OPA57 amplifier) ad Fig (LMH) It should be oted here that the trasformatio coefficiet for BJT amplifier is lower tha, eg thtepdow trasformer should be used 5 3 0dB 05dB db db 3dB db 00k 00k 00k Fig 0 NF for high impedace trasducer ad FET amplifier db 3dB db db 05dB 0dB 00k 00k 00k Fig NF for high impedace trasducer ad BJT amplifier If FET amplifier is used, Eq3 ca be used for calculatio of opt The calculatio results idicate the turs ratio value equal 9 at the ultrasoic trasducer series resoace ad 55 at the parallel resoace Coclusios Applicatio of a trasformer ca be justified by five reasos: oise improvemet by modificatio of thource impedace, isolatio, optimum power trasfer, trasformer widig iductace exploitig for amplifier DC biasig ad elimiatio of the trasducer capacitace C 0 Ufortuately, the trasformatio coefficiet ca ot be varied over the frequecy, therefore degradatio of the oise figure is expected due to the o-optimal The high turs ratio will degrade the badwidth ad losses performace Therefore a low turs ratios should be cosidered Aalysis has show that the degradatio is ot sigificat eve usig lower tha the required values Theoretical aalysis idicates that i the case of a high impedace ultrasoic trasducer matchig to BJT (low R opt ) applicatio of a step-dow trasformer is ecessary This idea requires examiatio of thigal-to-oise ratio for further proof Further oise improvemet aalysis usig a trasformer should be prove by experimetal ivestigatios Refereces Rhye T L Characterizig ultrasoic trasducers usig radiatio efficiecy ad receptio oise figure IEEE Trasactios of ultrasoics, ferroelectrics ad frequecy cotrol 998 Vol 5 P Yaez Y, Garcia Heradez M J, Salazar J, Turo A, Chavez JA Desigig amplifiers with very low output oise for high impedace piezoelectric trasducers NDT&E Iteratioal 005 Vol38 P Svilaiis L, Dumbrava V Desig of a low oise preamplifier for ultrasoic trasducer Kauas: Techologija ISSN 39- Ultragarsas Nr(55) 005 P8-3 Svilaiis L, Dumbrava V Ivestigatio of a preamplifier oise i a pulse-echo mode Kauas: Techologija ISSN 39- Ultragarsas Nr3(5) 005 P-9 5 Trask Ch Desigig wide-bad trasformers for HF ad VHF power amplifiers QEX/Commuicatios Quarterly P3-5 Motchebacher C D, Coelly J A Low oise electroic system desig Joh Willey & Sos Ic 993 P 7 Leach W M Noise aalysis of trasformer-coupled preamlifiers J Audio Eg Soc 99 Vol 0 No/ P3-8 Sherrity S, Wiedericky H D, Mukherjeey B K ad Sayerza M Accurate equivalet circuit for the uloaded piezoelectric vibrator i the thickess mode J Phys D: Appl Phys 997Vol30 P Jiasheg Xu, Yisog Dai, ad Derek Abbott A complete operatioal amplifier oise model: aalysis ad measuremet of correlatio coefficiet IEEE trasactios o circuits ad systems 000 No 3(7) P0-0 Žukauskas E, Cicėas V, Kažys R Applicatio of air coupled ultrasoic techique for sizig of delamiatio type defect i multilayered materials Kauas: Techologija ISSN 39- Ultragarsas, No(5) 005 P7- Domarkas V, Kažys R-J Piezoelectric trasducers for measurig devices Vilius: Mitis 975 P 55 V Dumbrava, L Svilaiis Trasformatorių audojimas ultragarsiio trakto pradiio stiprituvo triukšmo charakteristikoms pageriti Reziumė Nagriėjama, kaip trasformatoriai galėtų pageriti stiprituvo triukšmies charakteristikas pradiiame jo laipsyje Trasformatorių uostoliai modelyje buvo įvertiti apvijų uostolių varžomis esat mažiems ultragarsiio keitiklio išėjimo impedasams Esat dideliems ultragarsiio keitiklio išėjimo impedasams, šerdies uostoliai modelyje vertiami 7

7 ISSN 39- ULTRAGARSAS, Nr(57) 005 uostolių varža R C Nesat galimybės keisti ultragarsiio keitiklio vidiio impedaso, triukšmiei aalizei prasmiga audoti triukšmo koeficietą, o igalo ir triukšmo satykį Gautos išraiškos trasformatorių su uostoliais triukšmo koeficietui apskaičiuoti audojat skirtigus elektroiės dalies modelius Remiatis šiomis išraiškomis sudarytos formulės trasformatorių su uostoliais optimaliems trasformacijos koeficietams apskaičiuoti Pateikti kokrečių ultragarsiių keitiklių ir operaciių stiprituvų optimalaus trasformacijos koeficieto ir triukšmo koeficieto skaičiavimų rezultatai Pateikta spaudai