NF 5460 lecoic oise simaes ad couemeasues Lecue 3 (Mo 0) Amplifie Achiecues
Whe a asiso is used i a amplifie, oscillao, file, seso, ec. i will also be a eed fo passive elemes like esisos, capacios ad coils o povide biasig so ha he asiso has he coec wokig poi. These passive elemes will ifluece o he oise. he followig we will look a some achiecues ad how hey affec he equivale ipu oise.
Mille capaciace Befoe we look a he asiso cofiguaios we eed a fas epeiio of he Mille effec. Whe a capacio is coeced bewee a sigal lie ad a sable poeial he sigal lie will expeiece a capaciace accodig o he sadad fomula (=A/). f he poeial o he ohe side ae i phase a smalle capaciace will be expeieced. f he sigal is exacly equal he capaciace will "disappea". f he sigal is i opposie phase he expeieced capaciace will be lage. f i is i opposie phase ad exacly equal he capaciace will be double. 3
Tasiso cofiguaios: Thee ae maily hee aleaives fo placig a FT/BJT i a achiecue: / has boh volage ad cue amplificaio esulig i he highes gai. Bu i has also he highes ipu capaciace (due o he Mille effec) / has a high cue gai bu a volage gai close o oe. has a low ipu capaciace (fom he Mille effec) esulig i a high ipu impedace. also has low oupu impedace. G/B is used o achieve low ipu impedace ad high oupu impedace. FT : ommo ouce : ommo ai G: ommo Gae BJT : ommo mie : ommo olleco B: ommo Base 4
0- ommo mie The schemaic shows a asiso ha is biased fo low oise opeaio bewee 0Hz ad 0kHz. The oise values ae as follows: 0Hz 0kHz V V pa 0.3pA 0 000 6700 NF@0.8dB 0.3dB The oise schemaic shows a hybid- model ogehe wih passive bias elemes. Noe ha whe V ad V ae sable -souces ha ae meged ogehe wih goud duig oise aalysis. 5
The volage gai : Zi is he volage gai fom Vs o Vo. The fis paehesis is he volage gai wihi he asiso ( is /B) while he secod paehesis is he ewok i fo of he base. i x The ipu esisace Zi icludes he esisace you ca see hough he base owads emie. The load esisace cosiss of he colleco bias esisace, he asiso ieal esisace ad he ipu esisace of he ex sage: i. The emie impedace cosiss of a eal pa ad a imagiay pa (a esisace ad a capaciace i paallel). L Z Zi Z Z Z L 0 i jx i Z 6
The souce impedace is a esisace i seies wih a capacio. jx Z x L Z Z L m e L g L fo ' f we assume igoable loss i biasig, couplig ad feedback we ca simplify he expessio fo o: f Zs ad Z e he expessio is simplified o: f we simplify ad igoe he exeal load we have: 7
We will he have he followig expessio fo he equivale ipu oise: he expessio, we ecogise he fis lie (say fom secio. 7.3). Las em is also kow. The secod las em, howeve, eed some commes. The volage ove will o be fo highe fequecies, because will "aemp o sho-cicui" his. We choose o model he hemal oise i as a cue oise of size =/. The oise cue ove ad will be: ' s i jx ' j 8
Back o he expessio fo i: Fom he expessio we fid ha o have low oise: should be lage elaive o. should be lage. s should be small. should be small if is o lage should be lage. should be lage. f he A-couplig is o eeded, we ca emove ad. (ommo mie) has he geaes powe amplificaio. Thus oise fom sages followig he amplifie ca pobably be igoed. ' s i jx 9
hoice of capaciace values is a high pass file ogehe wih he esisaces a he asiso gae (.e. bias esisace i paallel wih he asiso ipu esisace). Wih egad o oise, /() should be much less ha a he lowes eleva fequecy. This is because hese ae added ad deemies he coibuio of : (+j/()). Obviously he las em should be ied made small (</00) elaive o. NB! Hece due o oise mus o be used ieioally fo file fucios! should sho-cicui he emie A-wise o goud. The impedace of should be small elaive o he ieal esisace i he emie: e. Basically oise i has he same weigh as he oise i he souce (gai=), howeve will educe he coibuio fom. 0
ommo-emie wih oe volage supply Hee a poi A is esablished supplyig a sable poeial fo he base. The poi A is A-wise sho cicuied o goud hough B. 0Hz 0kHz 4.5V 4.5V 0.3pA 0.pA 0 0k 45k NF@0 0.68dB 0.35dB 80 i 780
The equivale ipu oise ca be expessed as: addiio o he kow ems, we have ow a ew em i squae paehesis due o he base bias ewok. The paehesis is weighed wih he / aio. The -volage a he base is deemied by he elaioship bewee A ad B as follows: ' B B B B A A s i jx B A B A V V
The coibuig oise fom he esisos A ad B should be elaively small. A good saig poi is o choose B so lage ha he oise i he eleva fequecy age saisfies he iequaliy: A B AB BB 3
Noise i cascaded sages We have peviously sudied he oise figue fo cascaded amplifies. We will ow look a he equivale ipu oise: The expessio fo equivale ipu oise ca be expessed as follows Hee o is he oupu esisace of sage. imilaly fo o, o3 ec. i is as ealie he volage gai. As peviously if he gai is lage eough i he fis sage, oise fom subseque sages ca be igoed. 3 3 o o s i 4
Thee ae hee mehods oe ca use fo oise aalysis of moe complex sysems such as cascaded ewok: Maual ewok aalysis (had calculaios), use a simulao (like LTspice), o measue he sysem afe ealisaio. Tick fo simulaio (ad measueme): f you ae usue of he impac of oise fom a souce - simulae wih his souce oly ad ispec he simulaio esuls a he oupu. 5
ommo-souce --- commo-emie couple povides high ipu impedace ad high volage gai. The example uses a JFT bu he cosideaios does also apply o MOFTs. 0Hz 0kHz 8V 4V 7fA 7fA 0.M 570k NF@0 0.03dB 0.05dB 6
The volage amplificaio fo he -sage is: L ad Z ae give by: ad The oal volage gai is: Whe ad o we have ha: m L m Z g g i d L jx Z Z g g x m L m c e m c g 7
To educe he -oise coibuio fom he FT we may coside iceasig. Bu his equies a smalle which meas less oal gai. The expessio fo he equivale ipu oise fo his cicui is: G mus be lage compaed o mus be lage compaed o mus be sufficie lage should be lage ad c should be lage. c G G G G s i jx 8
ommo-colleco --- ommo-emie - has oly a lile lage ha a pue sage bu ca offe highe ipu esisace ad lowe ipu capaciace. Fis sage has a gai of appox.. The oal gai is: Whee The expessio fo c ca be simplified whe L (+x+) ad x+z: x L x L c Z x L Z e c 9
quivale ipu oise is: is he gai i he fis sage wih as load. ad should he emie/souce esisace be lage. ' ' c s i ' e x 0
ommo-mie --- ommo-base -B has low ipu capaciace ad high oupu impedace. ue o he low ipu esisace of he secod sage he volage gai of he fis sage will be low. This educes he high fequecy feedback (Mille effec) hough as discussed befoe. The ipu capaciace is hus much less ha fo a egula sep. Q povides powe amplificaio bu o volage gai (i.e. Q povides a cue gai.) Q povides a lage volage gai. is used o povide exa colleco cue o Q whe hee is a eed fo lage gai-badwidh.
The oal powe gai ca be expessed as: Whee Whe =0 ad / we ca simplify c o: The equivale ipu oise is: B x x L B x x L c Z Z Z Z e B x L Z e c c B B B A B A B L s i Z
-3pow -pow - - -B 0Hz 0kHz 0Hz 0kHz 0Hz 0kHz 0Hz 0kHz 0Hz 0kHz V V 4.5V 4.5V 8V 4V 6V 5.8V.6V.4V pa 0.3pA 0.3pA 0.pA 7fA 7fA 0.3pA 0.pA 0pA.5pA 0 k 6.7k 0k 45k.M 570k 0k 58k 80 930 NF@0.8dB 0.3dB 0.68dB 0.35dB 0.9dB 0.3dB 7dB db 3
egaed BJT cascade amplifie Hee Q acs as a -sage ad Q as a Bsage. Q3 is load. The oal volage gai is: o 3 c The equivale ipu oise is: i s Hee is =e/e. ice he colleco cues ae equal is =. ZB is he impedace o VBB (should be low). ice e also is small he coibuio fom should also be igoable. e o3 e Z B c 4
The oise volage fom Q3 is: The gai i Q3 is: Wih hese simplificaios ad assumig all asisos ae equal he expessio fo he equivale ipu oise is educed o: 3 3 3 o c e o 3 3 3 3 3 s s i 5
iffeeial amplifies wo souces The wo ipu sigals V ad V ca be defied elaive o a commo value (commo-mode) V, ad a diffeece value V. V V V ad We will he have: V V V ad V V V The figue shows he oise schemaic. V The equivale ipu oise is: i s s V V 6
iffeeial coecio oe souce We assume ha he posiive ad egaive ipu has he same oise chaaceisics ad adds ogehe he ad values fo he amplifie. Whe we add ogehe wih he oise fom he souce esisace, we obai he equivale ipu oise: T T s i 7
Noise model fo he diffeeial amplifie xample of diffeeial sage: a) Volage gai of diffeeial sigal: dm V V o s V V o s Hee is gm=/e fo each of he asisos. g m Assumig ideical asisos ad ==, == ==. Fo he ypical cases whee =0 ad we ca simplify dm o: dm e ad 8
m s s o o cm g V V V V cm m m m m o o dc g g g g V V V b) Gai fo he commo volage sigal: Whe is lage we ge: c) iffeeial volage gai bewee oupus wih commo ipu sigal: deally if he ipus wee compleely symmeical dc should be 0. Whe his is o he case oe ca educe dc say by iceasig. 9
i: Hee is V ad V oise o he volage supplies. dc V V dm i 30
egaed BJT diffeeial amplifie ca be elaively lage vaiaio i pocess paamees fo iegaed cicuis fom poducio o poducio. Howeve bewee he elemes o he same cicui he vaiaio ca be made vey small. This is exploied by usig desig saegies based moe o he symmey bewee he elemes ha o hei acual values. iegaed cicuis he commo-mode oise ejecio is impoved. O he ohe had, iegaed cicuis equie compomises ha may give moe oise ha whe opimizig a pocess fo a sigle isolaed compoe. xamples of hese compomises ae: log diffusio isulaios, acive loads, ad powe souces. 3
The figue shows he iegaed vesio of he diffeeial amplifie we sudied peviously. quivale ipu oise: ice commo-mode ejecio is high ad all acive cicuis have appoximaely he same geomey ad oise mechaisms, i will be educed o: 5 4 3 dc V V s s s s i 4 i 3
Paallel amplifie sages Wha whe seveal amplifies ae placed i paallel? chemaically, we ca daw oise souces as i he figue. We have: ' ad A ew opimal souce esisace ca be defied as: ' o ' ' o N N Gai is give by: ' A' v NA v N A sigifica coibuio o he -oise i a BJT is he base esisace x. The base esisace ca be educed by placig he base coacs all he way aoud he emie ad he closes possible o he emie. FTs i is deemied by he chael esisaces, ad by gm. Low esisace ad high gm ca be achieved by havig a lage W/L aio. By paallelisig boh he ad he Mille effec is iceased. 33