F3 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. Tasiso cofiguaios: Thee ae hee mai ways o place a FT/BJT i a achiecue: BJT FT : ommo mie : ommo ouce B: ommo Base G: ommo Gae : ommo olleco D: ommo Dai / has he lages powe amplificaio. /D is used o achieve high ipu impedace ad low oupu impedace. G/B is used by achieve low ipu impedace ad high oupu impedace.
Whe he i is calculaed fo he gae/bias i is almos equal fo all cofiguaios. Hece he i, ad calculaed fo / ca also be used i /D ad B/G cofiguaios. This assumes ha he fequecy is so low ha he ieal colleco-base feedback capaciace ca be igoed. NB! Alhough he ipu oise is he same his does o apply o he oupu oise.
0- ommo-mie The figue 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 mall sigal equivale schemaic fo he cicui is show o he ex page.
The schemaic shows a hybid- model ogehe wih passive bias elemes. The volage gai : Z i L Z Z i Z i D D 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 Z Z The ipu esisace Zi cosiss also of he esisace you ca see hough he base o emie. (+=/B). L 0 i The load esisace cosiss of boh he colleco bias esisace, he asiso ieal esisace ad he ipu esisace of he ex sage: i. Z jx. The emie impedace cosiss of a eal pa ad a imagiay pa (a esisace ad a capaciace i paallel). Z jx The souce impedace is a esisace i seies wih a capacio. f we assume igoable loss i biasig, couplig ad feedback we ca simplify he expessio fo o: L Z Z x
f Zs << ad Z << e he expessio is simplified o: L m e L g We simplify ad igoe he exeal load ad simplifies L so ha: L fo ' We will he have he followig expessio fo he equivale ipu oise: ' D D D s i jx 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:
' j Back o he expessio fo i: ' D D D s i jx Fom he expessio we fid ha o have low oise: D should be lage elaive o. should be gea. s should be small. should be small (less ha ). should be high. should be lage. should be lage. f he A-couplig is o eeded is emove D ad. has he geaes powe amplificaio ad oise fom sages followig he amplifie ca pobably be igoed. The ipu esisace vaies wih.
hoice of capaciace value. has a high pass effec wih 3dB limi equal o he sum of he souce esisace ad esisace o he amplifie (icludig bias). 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 emie A-wise o goud. The impedace of should be small i elaio o he ieal esisace i he emie: e. Basically oise i has he same weigh as he oise i he souce. Howeve, will educe he coibuio fom. he expessio below is he oise coibuio fom i he umeao.
ommo-emie wih oe volage supply. Hee a poi A is esablished supplyig a sable D poeial fo he base ad ha A-wise is sho cicuied o goud hough B.
The oise schemaic is as follows: quivale ipu oise ca be expessed as: ' D D B B B B A A D D s i jx 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 /D aio. The D-volage a he base is deemied by he elaioship bewee A ad B as follows: 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 chose B so lage ha he oise i he eleva fequecy age saisfies he iequaliy: A xa B xb D A B B B Noise i he amplifie is give i he followig able: 0Hz 0kHz 4.5V 4.5V 0.3pA 0.pA 0 0k 45 NF@0 0.68dB 0.35dB 80 i 780
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... i o 3 3 s o 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.
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 as say LTspice, o measue he sysem afe ealisaio. Ticks fo simulaio (ad measueme): f oe is usue of he impac of oise fom a souce: simulae oly wih his souce ad measue esuls o he ed.
ombied achiecues: ommo-ouce --- ommo-mie couple povides high ipu impedace ad high volage gai. he example is a JFT bu he cosideaios applies o MOFTs also.
The oise figues fo his cicui ae as follows: 0Hz 0kHz 8V 4V 7fA 7fA 0.M 570k NF@0 0.03dB 0.05dB The volage amplificaio fo he -sage is: g ml gm Z L ad Z is give by: L D d i ad L D d i The oal volage gai is: g ml c g mz x Whe >> D ad >> o we have ha: g md c e
To educe he -oise coibuio fom he FT we icease D. Bu his assumes a smalle D which meas less oal gai. The expessio fo he equivale ipu oise fo his cicui is: c D D G G G G s i jx G mus be lage compaed o G mus be lage compaed o mus be sufficiely lage should be lage ad c should be gea.
ommo-colleco --- ommo-emie couple - 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: x L x L c Z whee x L Z The expessio fo c ca be simplified whe L>>(+x+) ad >>x+z: e c
quivale ipu oise is: ' ' c s i is he gai i he fis sage wih as load. ' e x ad D should he emie esisace be lage.
ommo-mie --- ommo base couple -B has low ipu capaciace ad high oupu impedace. Due 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 (ie 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: B x x L B x x L c Z Z Z Z whee e B x L Z Whe =0 ad >>/ we ca simplify c o: e c The equivale ipu oise is: c B B B A B A B L s i Z
egaed BJT cascade amplifie Hee Q acs as a -sage ad Q as a B-sage. Q3 is load. The oal volage gai is: 3 e o c The equivale ipu oise is: 3 c o B e s i Z Hee is =e/e. ice he colleco cues ae equal so will =. ZB is he impedace o VBB (should be low). ice e also is small he coibuio fom should also be igoable.
The oise volage fom Q3 is: 3 3 3 o The gai i Q3 is: c e o 3 3 Wih hese simplificaios he expessio fo he equivale ipu oise is educed o: 3 3 3 s s i
Diffeeial amplifie The wo ipu sigals V ad V ca be defied elaive o a commo value (commo-mode) V, ad a diffeece value VD. V V V, ad V D V V We will he have: V V D V, ad V V D V The oise schemaic looks as follows: The equivale ipu oise is: i s s
Diffeeial coecio: We assume ha he posiive ad egaive ipu has he same oise chaaceisics ad adds ogehe he ad -values fo he amplifie. T T Whe we pu ogehe wih he souce esisace, we obai he equivale ipu oise: s i
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 g m Hee is gm=/e fo each of he asisos. Assumig ideical asisos ad ==, == ad ==. Fo he ypical cases whee =0 ad << we ca simplify dm o: dm e
b) Gai fo he commo volage sigal: m s s o o cm g V V V V Whe is lage we ge: cm c) Diffeeial volage gai bewee oupus wih commo ipu sigal: m m m m o o dc g g g g V V V deally if he ipus wee compleely symmeical dc should be 0. Whe his is o he case oe ca educe dc say by iceasig.
i: dc V V dm i Hee is V ad V oise o he volage supplies.
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 will be lile. This is exploied by basig desigs moe o he symmey bewee he elemes ha o hei acual values. O iegaed cicuis he commo-mode oise ejecio is impoved. O he ohe had, o iegaed cicuis equies compomises ha may give moe oise ha whe opimizig a pocess fo a sigle isolaed compoe. xamples of hese compomises ae: log isulaio diffuse sessios, acive loads, ad powe souces.
The figue shows he iegaed vesio of he diffeeial amplifie we sudied peviously. quivale ipu oise: e dc V V s s s s i 5 4 3 ice commo-mode ejecio is high ad all acive cicuis have appoximaely he same geomey ad oise mechaisms, i will be educed o: 4 i
Paallel amplifie sages Wha whe seveal amplifies ae placed i paallel? chemaically, we ca daw oise souces as follows: We have: N ' ad ' N A ew opimal souce esisace ca be defied as: ' o ' ' o N Gai is give by: A' v NA v 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.