and No, the noise figure of the amplifier is defined as (Fig.L8.1):

Transcription

1 ECE 504, Sprin 03 Speil Tpi: tive Mirwve Ciruit nd MMIC Zy Ppvi, Univerity f Clrd, Bulder LECTURE 8 LOW-OISE MPLIFIERS; MPLIFIER OISE PRMETERS L8 OISE FIGURE D OISE TEMPERTURE REVIEW The nie fiure f n mplifier r mixer ive infrmtin ut the nie tht the mplifier dd t inl while mplifyin it, r the nie tht the mixer dd t the inl while perfrmin the frequeny nverin If the input t n mplifier i inl S i with nie level i preent, nd t the utput the inl nd nie re S nd, the nie fiure f the mplifier i defined (FiL8): F Si S / / i Thi quntity derie the derdtin f the inl-t-nie rti frm input t utput nd i uully defined with the input nie ein white nie with petrl pwer denity f 0 90K perfet mplifier wuld hve nie fiure f, r 0dB nie ftr f (3dB) men tht the SR h een redued y ftr f tw typil lw-nie mplifier (L) yu will mke in the l will hve nie fiure rund db By inludin the in f the mplifier frm FiL8, the fllwin n e written: S GS nd G, i i where i the nie dded y the mplifier meured t the utput f the mplifier The nie fiure n nw e written / G F i i, where i the nie dded y the mplifier referred t the input S i G S i, T FiL8 ie fiure nd temperture f n mplifier

2 In rditrnmy nd tellite reeiver, the enertr nie i nwhere ner the tndrd t rm temperture, eue the nie me frm n ntenn tht i lkin int the ky with very lw effetive temperture f nly 3K In uh e, it de nt mke ene t tlk ut nie fiure ed n rm temperture reitr nie, ut rther ut mplifier nie temperture T iven y T kg k w the nie fiure n e relted t the nie temperture f the mplifier T F T The nie temperture f -db nie fiure L i 70K, nd the et rditrnmy reeiver hve nie temperture f K 8 ie f Cded mplifier Cnider de f mplifier with repetive in G, G,, G, in FiL8 Wht i the equivlent nie fiure f thi de? With ll the mplifier nie referred t the input f the individul mplifier, the fllwin fllw frm the definitin f nie fiure: Thi i uully written in the fllwin frm 3 F i G GG GG G F F F F3 F G G G G G G In the previu frmul, the G i re ville pwer in f the individul mplifier Therefre, the firt mplifier in the hin h the mt effet n the verll nie fiure, nd the de dein huld minimize the firt mplifier nie fiure nd mximize it in Uully tility i n iue with uh de nd limit the in If the hin i nneted t reeivin ntenn, the ve frmul tell u tht the firt L huld e le t the ntenn feed pint pile ny lenth f ly le will hve netive in (l) nd it reitne will e ure f nie, the nie fiure f the de will e verned y the le rdin t the de equtin

3 S i G S G G S i F F F FiL8 ie fiure nd temperture f n mplifier de L83 ie Wve frm Pive Multiprt etwrk Bm Therem nie wve n e defined fr ne-prt, FiL83, fllw The mplitude f nie wve i rndm quntity with zer vere vlue, nd the expeted vlue i nie pwer, meurle quntity When the nie ure impedne i equl t the nrmlizin impedne, the nie pwer i equl t the pwer delivered y the ure, When the ure impedne i nt the me the nrmlizin impedne, the refletin effiient f the ure i nt zer, nd in thi e the nie wve pwer per Hz ndwidth i equl t Thi fllw frm therml equilirium When the ure nd ld re t the me temperture, if they re mthed, the pwer flw n the line need t e lned If they re nt mthed, it till need t remin lned, therwie mre pwer wuld flw in ne diretin, viltin therml equilirium FiL83 ie wve f ne-prt nie ure The S prmeter f the ne-prt i nrmlized t the impedne f the ld The ve diuin fr ne-prt netwrk n e enerlized t multiprt netwrk fllw In the ne-prt in FiL83, ne n write the fllwin exprein fr the nie wve in term f the ne-prt tterin prmeter: 3

4 The ltter i true eue the inident wve emnte frm the termintin nd i unrrelted with the nie wve Sine therml equilirium require, it fllw tht Fr tw-prt netwrk, FiL84, ne n write the me in mtrix frm:, nd the rrepndin rreltin mtrix f the nie wve i defined C S S () S () FiL84 ie wve f tw-prt pive netwrk () nd the me tw-prt with the prt mined in diretinl upler () The upler i initilly umed t e 80 nd then 90 3-dB upler Sine the nie frm the tw termintin re nt rrelted, nd the tw-prt i in therml equilirium, the fllwin n e written: nd 0, The nly quntity tht remin unknwn i the rreltin f the ttered (ut-in) wve, The fundmentl prpertie f nie wve llw methd y whih it n e determined, utlined elw In rder t lulte thi rreltin, we mix the tw utin wve y ddin diretinl upler t the utput f the tw-prt, FiL84 The primed quntitie in the fiure re the ne tht ptentilly hned frm FiL84 y the dditin f the lle diretinl upler w the tw nie wve re iven y nd, 4

5 5 ine the hyrid in thi e i 3-dB 0 /80 diretinl upler The nie pwer f the dditin f tw rndm vrile n e lulted p where the tw lt term re mplex njute f eh ther nd their um i therefre rel, we tin j w the ve exprein n e mpred in rder t tin the rreltin f the utput wve fllw Fr the input wve t the tw-prt, imilr exprein n e written: j nd ine the nie wve emntin frm the tw termintin re unrrelted nd their petrl pwer denitie re, it fllw tht j j Thi men tht the diretinl upler did nt ffet the nie wve input t the pive tw prt, nd therefre in therml equilirium, i till vlid Therefre, the ttered wve t the utput f the upler re

6 Sine the pwer f nie wve fr therml equilirium h t e, then 0 w the 0-80 hyrid n e repled y 0-90 hyrid, nd the reult i hwn t e imilr, ut fr the iminry prt f the rreltin: 0 Therefre, ine th rel nd iminry prt re zer, it fllw tht 0 Thi diuin n e enerlized t multiprt netwrk, where mplex njute eme Hermetin vetr (mplex njute trnpe) S, fr n n-prt netwrk, we n write: I with the in menin Hermetin vetr, nd I ein the identity mtrix The diretinl upler experiment n nw e pplied t ny tw prt i nd j t time, nd eh time the fllwin i true: nd 0 i j i j Therefre, in mtrix frm, I Thi i urpriin reult! Input nie wve t the input (the ) prdue ttered wve whih re nw rrelted (the ij i ), ut the net rreltin vnihe! Thi men tht the pive tw-prt prdue nie wve (the ) tht nel the rreltin It n e prven (ee pper y Wede nd Rutlede) tht thi reult i nitent with Bm therem fr the fundmentl prperty f the nie rreltin mtrix The nluin f thi therem i tht the nie wve ntriuted y the netwrk re imply the neery t nel the effet f rreltin preent in the ttered wve S in rder t mintin the lk f rreltin in utput wve nd the hieve lne f pwer flw Bth f thee nditin re required fr thermdynmi equilirium L84 ie Fiure nd ie Wve f MESFET mplifier Given trnitr, hw de ne dein lw-nie mplifier ptimized t hve the lwet pile nie fiure nd lret pile in? The peifitin iven y the mnufturer ive three nie prmeter, uully fr numer f frequenie: the minimum nie fiure ( F min ), the ptimum input refetin effiient (uully written pt ) nd the nie reitne ( R n ) Thee re meured uin ure-pull tuner (t the input) nd nie-fiure meter, nd 6

7 the ptiml input impedne i fund when the nie fiure i meured t e miniml Then the input f the L n e deined y deinin mthin iruit fr tht impedne, while njute-mthin the utput t mximize in Thee prmeter, hwever, d nt ive u ny iniht int the ure f nie in the trnitr, r why there i n ptiml input impedne Furthermre, fr very lw nie mplifier, the ure-pull methd i diffiult, ine the tuner hve t e very tle nd lirted refully ll the time The nie emntin frm trnitr n e deried lterntively y input nd utput nie wve quntitie nd their rreltin, we will ee elw S S () () FiL84 Equivlent tw-prt nie wve fr n mplifier () nd the me nie wve referred t the enertr ide () In the e f n mplifier preented tw-prt netwrk (uully, mmn ure), the nie equivlent iruit i iven in FiL84 The trnitr i prduin nie wve t th input nd utput, nd The enertr t the input i hwn ne-prt with refletin effiient The nie wve n th e referred t the enertr in uh wy tht the ttl nie t the utput f the mplifier remin the me The new mined nie wve i equl t T find the mplifier nie temperture nd nie fiure, we lve T k Frm the reltinhip etween nie fiure nd nie temperture, the mplifier nie fiure i iven y F 0 7

8 The nie fiure n e written me minimum hievle nie fiure, fr n ptiml input nie mth, plu me dditinl term tht depend n the enertr refletin effiient nd n ptimum refletin effiient f the enertr ( ): 0 f F min If nd, well their rreltin, re nrmlized t 0, thi ftr dipper in the denmintr f the lefthnd ide, nd the previu equtin n e written ( F ) f f f min If thi i t hld fr ny enertr refletin effiient, the effiient f ll the pwer f mut e equl, reultin in the fllwin three equtin: F f min ( F ) f Thee equtin n nw e lved t find f min f ( pt ) f F min f f i fund y lvin qudrti equtin, nd ne rt f the equtin i hen The riterin fr hin the rt with the plu in i tht the ptimum refletin effiient need t e mller thn unity In the pre f thi derivtin, we ue the ft tht the expeted vlue f the nie pwer whih i um f tw nie wve i p The firt tw term re f the nie wve nd the lt tw term re rreltin term Thee tw term re mplex njute f eh ther, their um i rel The rreltin term re zer if 8

9 the tw nie wve me frm phyilly different nie ure, uh tw reitr If the nie re rrelted, uh in MESFET, ne trie t he the refletin effiient f the enertr t nel muh f the nie pile t the utput If the tw nie wve me frm the me ure, they re prprtinl t eh ther nd they re id t e mpletely rrelted In thi e, the r-rreltin eme By ervin the exprein fr the ptiml refletin effiient, it i een tht it i prprtinl t the rreltin f the tw nie wve If the tw nie ure re unrrelted, then 0, ut in MESFET uully the mnitude f the ptimum enertr tterin effiient i le t unity, nd thi indite tht the tw nie ure re lely rrelted nd tht they phyilly me frm ne ure inide the trnitr In trnitr peifitin heet, uully minimum nie fiure nd ptiml tterin prmeter re iven fr numer f frequenie Inted f f, relted prmeter referred t the nrmlized nie reitne i iven: f 4Rn k 90K Z 0 Wht re the ure f nie in MESFET? With referene t very implified unilterl mde, FiL85, the reitne etween the te nd ure prdue nie vlte tht eme prt f the input vlte, nd i upled t the utput thruh the trnndutne It n e hwn (ee the pper y Wede nd Rutlede) tht the input nd utput nie pwer petrl denitie nd the input nd utput nie wve rreltin fr trnitr (MESFET r HEMT) n e writin in term f the devie -prmeter nd the effetive nie temperture f the te nd drin whih derived frm Bm therem Sine the trnitr i nt pive, therml equilirium n e hieved nly if the d input i mdeled y n effetive inree in nie temperture In prtie, the drin effetive nie temperture i the min effet L84 ie Meurement Fr MESFET r HEMT, mentined, minimum nie fiure nd rrepndin ptiml input refletin effiient re uully iven Thee re meured uin tuner t the input f the devie (referred t ure tuner ), while imultneuly meurin the nie fiure Hw i the nie fiure meured? There re everl methd fr determinin the nie fiure f n mplifier methd ey t undertnd, ut nt ey t implement urtely in prtie, i the Y-prmeter meurement, r ht-nd-ld meurement, FiL85 Firt reitr R nneted the nie ure t the input f n mplifier i heted t temperture T H nd then led t temperture T C The reultin meured nie pwer denitie in ndwidth f t the utput f the mplifier re PH GHf Gf P G f G f C C 9

10 () () () FiL85 () Ht nd ld (Y-ftr) nie fiure meurement, () petrum nlyzer nie fiure meurement nd () utmted nie fiure meter lk dirm The Y-ftr i defined the rti f thee tw nie pwer nd n e written T Y T T T H C, TH YTC tht T Y By meurin the Y ftr, the nie temperture f the mplifier, nd therefre the nie fiure, re determined The ury f the meurement depend n the tw temperture ein fr prt pile, nd require tht the refletin effiient f the ld reitr R de nt vry with temperture Sine we trt with tw equtin with tw unknwn (the in i l unknwn), the in f the mplifier n l e determined Sine the in n e meured independently with netwrk nlyzer, thi n help the ury f the meurement 0

11 nther wy t meure nie fiure i diretly with petrum nlyzer, FiL85 The methd i nt very urte fr nie fiure elw 3dB knwn pre-mplifier, with in G pre-mp nd utput nie petrl pwer denity pre-mp i ued in ne rnh f the ytem Fr limited frequeny ndwidth, the petrum nlyzer IF ndwidth i et t B, nd the reulted meured DUT nie fiure i F G pre-mp pre-mp G B, where G i the unknwn mplifier (DUT ) in The nie pwer meured y the petrum nlyzer interted ver the IF ndwidth will hve rretin ntnt f C=-dB whih inlude different detetin effet, fr exmple the vide filter ued fr the pt-detetin diply, whih i uully et t ne hundredth f the IF ndwidth In db, the nie fiure n e written in term f the meured pwer y the petrum nlyzer: F( db) P G G 0lB74 C n pre-mp (Where de the 74 numer me frm?) In the utmti nie fiure meter, nie ure i ued t prvide different level f nie Thi i uully pn dide ied in revere vlnhe rekdwn, nd the ville nie pwer i inverely prprtinl t the dide urrent implified lk dirm f ilent nie fiure meter i hwn in FiL85 ie fiure n l e meured indiretly y meurin nie wve Thi i epeilly ueful fr hrterizin trnitr fr the ptiml input nie mth The meurement de nt require ure tuner, nd eliminte errr due t tuner limited rne nd tuner lirtin Cnider the ytem in FiL86 The nie wve emntin frm the devie re nd They re dded t nie wve enerted y tw nie ure tht n eh e t tw equivlent temperture, T nd T The reultin wve pwer petrl denitie t the input f the withed fur-prt re d d d d Thee re meurle quntitie, nd in rder t tin frm them the unknwn, nd, firt thru i inerted in the ple f the withed fur-prt In thi e, d e nd d e, nie pwer meurement i perfrmed t eh temperture f the nie ure, reultin in fur nie pwer meurement T meure the rreltin, firt 0-80 deree 3-dB upler, nd then 0-90 deree upler re inerted in the ple f the fur-prt The firt et f meurement t the tw temperture f the nie ure ive the rel prt f

12 the rreltin, nd the end et ive the iminry prt Fr exmple, fr the 0-80 deree hyrid e, the fllwin n e written: d d e e d d e d d e The reultin numer f meurement prvide n verdetermined ytem f equtin, nd in dditin t tinin the -prmeter f the devie, me ttitil nlyi f thee meurement n e perfrmed FiL86 ie wve meurement ytem lk dirm (frm Wede nd Rutlede)