### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Electromag Compatibility ECE 4391

GPA 3.64

### View Full Document

## 27

## 0

## Popular in Course

## Popular in ELECTRICAL AND COMPUTER ENGINEERING

This 0 page Class Notes was uploaded by Cassidy Effertz on Monday November 2, 2015. The Class Notes belongs to ECE 4391 at Georgia Institute of Technology - Main Campus taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/233915/ece-4391-georgia-institute-of-technology-main-campus in ELECTRICAL AND COMPUTER ENGINEERING at Georgia Institute of Technology - Main Campus.

## Reviews for Electromag Compatibility

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 11/02/15

Comparison of the JFET and the BJT An exact comparison of the BJT and the FET is impossible in general because the noise perfore mance of each is so dependent on device parameters and bias currents The JFET exhibits only Un noise whereas the BJT exhibits both Un and in noise For a low source resistance the BJT Un noise is its dominant noise In this case the BJT usually has a lower noise than the JFET For a high source resistance the BJT in noise can cause it to exhibit more noise than the FET This assumes that the BJT bias current remains xed as the source resistance is increased 1f the BJT is biased for minimum noise the collector bias current must be decreased as the source resistance is increased In this case the FET may not be the better choice device for the lowest noise To make an example comparison of the noise performance of the BJT and the JFET typical numerical values for device parameters must be assumed Although the conclusions may not be applicable to speci c devices such an example serves to illustrate the differences between the devices Because icker noise is so device dependent it will be neglected For the BJT we will assume that M 40 9 VA 00 and 5 500 For the JFET we will assume the parameters 5 5 X 10 4 AVg A 0 and VTO 72 V For these values the drainetoesource saturation current is IDSS ngo 2 mA Let the BJT be connected as a commoneemitter ampli er with its emitter connected to ac ground We calculate the noise both for a constant collector bias current and for the optimum collector bias current Copt Let the JFET be connected as a commonesource ampli er with its source connected to ac ground We calculate the noise for a constant drain bias current For the constant current cases we will assume that both the BJT and the JFET are biased at 1 mA so that the devices are compared at the same power dissipation This assumes the same bias voltage across each device Let R5 be the source resistance For C 1 mA the BJT spot noise voltage in VxE is 2 Uni 135 V 2 12 Af 4kTRsTm2qIBR5Tm22q10lt r 1 C 12 353 X 1044130 X 107 R5 40 500 R5 402 R5 130002 1 For C Copt it is U ygu 7 r 1 12 A f 7 4kTR1TmR2AfXW 132 X 1040413 40 2 For ID 1 mA the JFET spot noise voltage is U72 7 4kTR HM 12 7 1 29 X 1040413 471 3 A f 5 3m 39 5 Figure 1 shows the plots of HugiAf versus R5 for the three cases Curve a is a plot of Curve b is a plot of Curve c is a plot of For R5 small the two BJT cases give the lowest noise Although the curves almost coincide the noise is slightly lower for the BJT biased at Copt For R5 large the JFET and the BJT biased at Copt give the lowest noise Although the curves almost coincide the JFET noise is slightly lower than the BJT noise For R5 in the 3 to 4 k9 range the JFET and the BJT biased at C 1 mA give approximately the same noise while the BJT biased at Copt gives slightly lower noise 1 T iwiuu H STP Zonmh WonAhu 4r L Zenmn J YNE 5on2 w wPSburPu U YP ltOVSWDS Kayla 0 Nghpklxacrv S rmavoltr 41v Pv ox Syllor am D9cMFV u Y ltltrnri PSPltWU 314 A093 rlSsv 13 Fords focrw EX PIV rP3P Zoew h fa Ygtltsr renmh I31 rP3ltrnL To uvPsbsuLuhP NU o spwdwpd Am Yr mPfh ha I J nv oh fm w nltn H Erm L mnoiu nw u 497on AS w o 9T hj 553 H 323 2331 x Onifnpru it P krhssroVUSPMP 07 de pm 9 ltFuyruwmvox 15 9 L534 rC mpfocm zu cuT of lcul ho L YLv Verm rPVEF p1 m ou 13 wesx xnr frb As 9 V9 oh bErocrfp bv PF m H W m fh f 93 V2 VPTlnP x 97 P turf m d T IyP ltsgtu Faumcl S 7 95 lt u grlqamm aw w knr fvx ltoxzv ltSgtu 3392 F Woilusx rsx m noSmfIFv 14L rdw x3 u1A n KP us P FltPkltP WV 4 w H Scum N 1 SFan TPFOh Alpq Zo mP nouncPylccrw n72 07P7 Eb ha 4 u NJB F v CLOV 7 Arinrnvc H ywram FTFAIH TrXEuu 2 a Souvn ltowP Am You anA xPPvccmP ar ltPlt v 9 j V SoltygtuL 0va 3 Lu ferVPksxP IFx 0 Mt Pl mPPIy 0 79 roan w I Lwiow cK PXampTI fr roam OYPYuPM ru 050 u o an 11 PPltPp cltr 0705 hi 3 on Ami 0 00 m v my JIVCF JlfothSnS Fonw FPaLTJ at n ltFw4wolt av H 5 w 5133 SF In CmPL 9 chPSP wofro wolt a 755 mofwop 4Yr la Lfd L gtP oclt 4w wir Y ade AYN 4rmltrq5 Pn hcmk of h orfr y w Ask 9 Zoxyax Ou ocu 4 23 0cltlth Av wujtlf U KM raw H u W l IN 9 u 1394 lt2 Zokxvuos 04ltPcny V i m n gt nunwlfeax 4v rr or U vwm ZLr FPchrvUV ffupf 0 Wrin Fva 1Trrltvfnv So mf Dbrm0vqc w of ASPltP oltm Wo 50 ampRSPltTP ITYP SLukl 5o wh ltltP 09L vltolt ITrnm WU 005 orl warploi 33 or PPAPPCZV WPip o39x JPv Q 504 lto cSFPryy 1 HS NV PZT AmnTY a PmAmuwa Ermnr whfb u krm rF 7amh lti ATP 04ltncn A 9 l ozbin x in m wTJTw i 9wmc P MN Drip A nu n5 YPltSgtFF 021 anxncfy Tm 9 rp mavvrr 51 QFltanwcvxr 4f xxu0ltAvlt Lanxr nlb LIV Pnum Tv Tfh n9 PPoi Am mTSuS U my u W0 Altr Hntv lt lt 20 lt 2 n t3 2 n I n F HP ltlt WLI lt x wan TTQEmA I D I q w A III xi burl IV 0 mm lt 1 71153 T nxwi n p Iwzmn V H lt NRA wx Ta nvr H O 4rcm rr Swat4 P974Pltw fa most4 0 Trh no nllovf 4ruw 519 TYPy TYP rwllwo Lw rh 69un c Y nannelt LP10ltFltU m w Nqoh L Pfx v doin ufv Trr ltPwuv53 c Ynm w r OvrerV L hkuar Lw ltltP Orwmcga Tr 59 03 HS YPltP N c i X if 4 ffr quuy39o V 9350 WRXPINAIXP Q1 Iiwi cr roamP 4Y9 Moth ofnLLwnor CryPm b 0 uSPcPldlc 10ltltPltP ITYr 23an ltPmnmprnP 0 0L bch nwhip t pv PltltgtPJ ToAMP Mc cmf ltltr farx I ICLO CxPh Cnlz mwwm 99 hoSfAPxTPL a urXrZF En 9ampMcgp TVQIU 052 y Ynuirgtnr N ACD TKHCS IYP pnltptmyw 1W x 3 lt3 lt3 A17 o flt Lurinzvx w 1 N4 m V n Q U xNHnuu lt3 r xltL pr 1 Fl Z39IOB r Adan emu 739 gt V vh WW Kz R 9 Tha FuMAV A 1 V VL 77 x 0 R Ca oz alaafsz Lava Tngwal kwjfws Hmz SuLSmn rh And 2 Thu H auow 5 kg p HWYKTBR39LYh 91Ko Thu w NV 71 Pm Nol Jami r P Vn ovz K wou ol k LaLTWD U aw HM DA ALV WDU A ok o vj 9 9 2 kas Wou com x TwuL UmA 439th vmek HALVWJ E ulllbviuw AVQGOK NoL ow1 Thu ava aLh A o Power P T5 91 PthA 05 144 Maxqu Powev OML VLsiuv C0 lt42ka 0 avm uv 8 I1107 Le us Cows3e K 3 94 4 4 TH f AzHVLV5 wzv 41 K7 Ts K27 Pa f lngB 2IKL39L N s h Mo39 P Zo 72 125 Tag 3972 00 0V To waxiwiaf KL wx 31 A iAKL o A RR E aeaLzm RR Hsz W A 1 KER1 Tkgt 5 yvo I at z Lg R KL K Tkus P 5 SixLn kg 1 R PM 1 19T 5 may kT B WA H39j No ka kf 5 rw kezwktm a K wVHioU QPSP IfOKWL ZJJcnulf clt c V91 NW VP 9 nofrAPx 4 4FLPPP lTYQrIT r 9 wcsPnoS oh PJCrFPd 11 L1gtF ltltvurf Foawp ltoPwP VFSP nvL Fw OsPX TYP PSP awn mfllmv Am wltPf X 4 H TV4 m WP V L lt3 MXFSJm T 714 lt f H w lt 2F 093 OoLnLrwusP lt a LA SPUM nltw lt4 cf lt2an Lultawnof w Eb lt u lt n n lt III Ln A ltf n i ltEmh 4Y0 le ltPCh am 26 U lt ltw1 l0 51275 V L v v8 my forms walt gu Nggc HzTKB 1 may m 7 V C W H chY gzcaus MT VRVTLS wUrL gvgc uLwLD B was 94 vgvj 5w Ohngisz u hou WJSA M4143 va4 oviv 4d ban 3 ov L S cow Seu3rom VLJL So VL 1a m a I R 77 R I L 2 RRJYMC l ugc M Yj om 31134 L3 HM conjuso k 6 s o ALMA w LA39OV d 1 m3 7 H39IJU KL I39WBLJKC ltwg7 K t Riki wRCquot n 52710 Th1 M vvv v 51 vu H my 75 SVLV quotHtTRB k 1 WW JHL TE Humequot TLJS TS JFMJL Same OKMWLV 4L5 94 m 142 3JS ov470h WA 5 4 u MA A39QA39L WOCSA 39 VoH ajz FVDM 8 o 43 5324 as Punows fvsq 9 B au w 21v TM V h va re 1 g HTR quot9 w 101 Af LL Xza s RC Ga Ag AKZ W KC an I 2 7 g Ax gt V tvas 1C x1 Ah 5 quot a T j Tc fa U D T 1139 gt T 33 x 1 4a 1rlt c E u m S ow 1 V ltCx wy H W lt9 rub sgtm 4Y3 m bklrflr nTv erw 4olt sn says zllr 51 3 w mil 0 N 47 hoalrcor am PVP3 ltmPp LTo 0ncnrr Yn sgtmrxA lt TYanva haVb m Seamh Drnlto m 93B wrcsbn VCR Q nmvnf W V8274 H W nmff t rrb Txa v II mics gap m9 k Pkihhy 20 fvrnrv 0 P fwwu n s pnynl n a w Eu Ern 4v xi pruicf Txrn XSPhu lt2 vmh v yunrw rwmeINuXNn a I ltw I ulm urll clt 53w T w AlfP UteMth 4 Manlpk ht L9me HIM LPhMSPL 9M Trr sgtrFchnr San 313h olt 0Llt807 NPV CS2 FPFL2LIF gtr S le 076le ltr SP u Vuxs f TYP moi lg on 7 Sru 9 45 olt P fh 70VWP P MWFPF n PSwu fv bk chv 012 ltcdPMP m 4 4 mltf3 n Imlu r154 fb MNPOLVKP oh Tf ouMR 0CltPf m Hm r14 ymu MW AI Iml Ale hasw bv 5 3v lt5an lt1va 0 0ltltPiy S r forVPM Vac nikuPMltPm T F axn3 LwaLU oltrlt TrP VPVV 01 ITvK LIPrs LL Mva sl lt01 p t TxoTw 0L7 PPKWMTPM an irevanr Len r 3 xvicrsov Pallxvtf Am affix ofer Z t prv Hm Tr um sr wpfb rlf 90 xjcrivu rxrxrmf if Fair 45 rr rrrw hi 5 8 0 0109 ampw L 12 mF F arm 31 G A 5 3 vii face 1 o 53 3M mexs ltwrZanw a 5 onPHZomniv LL Kauwr 7PM rd L PhMFPr HP 9 1r viLP o I lx chL crnHu N 11f V4mv131rltVICS oioiu 0 marcmwmn 9V ltro 550 W w nfcl1Ho H 4v w celi d P AS Edam 03m At vltwzuv xix mxuhg uaww 4 4133 4 M33 31er 514141 3 vniuwh 4 oSSJU 424 JAum JJL IXjM 4gtJgt n 45 P4 Ja x Jddkr I we onv 454 Ad 4633461 In akwdldnwl mJCU N tr ncLZKW n AVA ZVm q 13 3 3231 f f 2 PWAELVV u gtVgtva u dldgt 334 n JQs m a gt12 444 DTTASQ 4i nigtgtl rT mriow ampP lthlhultf 0 L HSN A Whlnr f u NXD PPWF P 79 Wltltrv WP ITKP wgr 47 P OhITL ob Lllsxr 110 7 hk buPLw f lt5 M lu wnltPi rU quot EXT 227klt i Ark mojaiufm Tmr w quv ML Dr F I lt5L19m S L is Tr b 7 v kltx3 owq Ni 930 PW 033 m 0009N r 099915 33 WJCNltPX Coum WYLzaP Afr PJCQPFC 7019 vaLithl LAM 9 WATTF m wrh ah Kr LPOIP wF wVVMMNM W9ltShr SAM Sanwgt n Trh hn CLYPSPV 77P dSWL S 63403 oisq TS mL L l ow vass fH Lv quotC l Amm Va 1 MW Iam FH hv EquaA Ann 5 K c F n 06 Afis EMU 3amp1 oi gt 8 1ngan AS Exawa a 39 e R V W 1 m I huoow u Iwzlnl u I q n I J ENA CL 041 9 ma Ni u V 3 F u g 3 13 3 11 I know Du we wx 9 W m Lx a o a o waMv e x 21 III IPI wn Tgxl var gt7va am 5 m 37 N 55 w 75 4 3 m 7 4 mtiow gtv 5 Sn ltthnm W NWShanv Am 3101 an leN w 3w Tut EHL TF ob Tf Pxnltr h frlt m Vulwm upy 0lt lt 333 lt0 ob H m N mix i t 9 mszl v H MxPn97wu ultV lt Wwv LI HZ 9 gt9 WI La 6 3 man 9 33603 mo aarj39 1 4 Cow OL sk w L 4 A L k m wuw 5 a 5W 5 azk L Mo7e guw w 3r r 1 1 E L Q EMWVIL Cl RL Vzo VO quot 1 VD RlCL K 4 4 IRP 4 tcik nlt0 H ft lt TT gt I if gtE I K v 862 LI LI L J II EN FTM MV r E i 1 FAr k 7 5 r i 5 I U IT I QED Cr ET Dlt QI S oh w EH 31 LLBH PA Zen N41 a a M M 3 mgi wiolow wrok 19th 33 FE V Pmuoal w 1 Oclt yy fa 9Pltouw 0a 1 PJHP rPs plt MQPr oJm P a uwcrvkmoSH Av av 70 LL JDGltL 0 Lawrz ryyr P7Pltwnu Err 59 3 f Tolruv Oz RcAF anUP Pclt rvr 41 Slt rr a anr ri 07rltw 4 csn ff u fry CPNV errorL Trr DCxP JF xx 417p InnPlayCovyuNoS wRX VKrb pv or 0cltgtr7 Scum DoryPD Mrs foan Mrs fkob 2PM mawpojl ny a5 ltncc3 crhv HS Twinw mfroi NU W ultP W rww Ihnvaurt We f rcwol n olt if gw wrap 79ng nc PF H nu UWltP7 u Hm II DA HLAW Pst w ssw Sffltnl H P7P 9 0 mh H fr x z 3 O u I JTWTw H U WP AVC hgi 59 1uq m u in vviryi p r133 4 4P0y1 Pun7m 4v waltp7 J HM b My u m 5 3 wr 0an Am wPSP PVqPV VS mci ylox 10va ovib W44 m4 LLV for DOVPix feta adwa PPCMP TYnF mm 50 quart mr WYKltCPlt 0P ffncf frh cltltflw 04uf v 32 gtlt9L0LgtPrv Zo mp 7ltonrlt narr roan aw Mnfnnf Ara mfgk Fodwp H 90053 S d x P40 L m FL 05 LVka 92 F warb 1 7 ltn rLoZi KPU any Ivaincrlt 09vu7rrb Foaml xu Svch dltPPv TYS metal Foam but YL 3 701 63 50sM IAC CovJ39ocJ No L CHAWL MTL Ts CavSLJ b3 6 uc uc fuj VasigXLwca AUL 41 fmgwF9 comLL5 LL4WL LL 4 wc Mk X39 WOSu 1 Occu v5 rm sw x 4 91 awacs vaa3 Couhck was Tovgt 1 70 15 ETTA 045 I 0 Lr Maorsz uw Cow cAr w s 1 c v Hitknv WOTSL 5 noise a ow X Lc utwcj mo T5 2 TM igwsr L J o y wa u Vbocsk TS jva m ISMH 5 thVL k S39L39kav Ma39xsl Coa f 7 u V14 S7K rv max gtkfow1m hTI 4olow Ho PX P mu lt3an 5 qum r m 3 ll uf V hex Pxn mm Spawn 1 quphm WA x ux NIL mAgtQ n od on 103 gt7 PYZFL 53 Sela H 95 9r he 5 almanpwfj a wacxmm i m 95 39759 49635 91 Mara Scamp moltSw s rn h if P Pnfwiocxw n ltu ru Sa w 9403 S01 w nozzm rU sgt9xcb nltltnyu VLF H 0023 as 33 2 fluke a Erurv ltPltv hi Silo Mp ofmw Irv MPPoxnww JIrP ltPr v chWos 9 w ltltPM his mkltgtS isv rb cubuu mhlt mhhofp 0 rum ufrPr DSLP wcmr mhlt sis7T 4r cw Sltawrm 93 armydnnPZU 019 rltSPM IEP xxx 13 To w 417 Mrr rz wPFwan STE or m EYPJxP Sump H xm av OLltltPS Sada v up 3 S if s rqmr 962 mu qorow gtWP1LD 0b 193 lta 3me rr 51 07V APTC r kin Snip a Zxovwsw 3216 n euth Tduri v Vs auric Zr 52 Sb ltP73 ltn gtP lenv ivCr Tf vrv ltPltP ltr IV leLr vSM asp P 7 lt s u TMi 49 tw u awch p 55 691 sari N lull F lt5 G lt9 AP kT ltr Hun 5 w ArrW Cf TWV OrVP mL meunw yrw DD Ti wbrbhik Trks Ahr qurqv I c H 2 M 0 ltu u ltM 5w m mis t H 5 Mai ofmnwx rP ltoylrwsv of PofleH ynw H frwv Fw lt12 arrhvir fmk no lth Fylwos fth b vah rf JN Pm xviaim 4975 4350 lt9ltr u 573 576 I d ltvltr Hr ATV 00L u as um whC39S v lt92 r 4 ltM P14 ltPltr lt0 l F7 Ir wroivr I I MioxlA anuf hw exiiuxr rtc 14 4 A313 753 UV 4n 4 I lo Tu 60 H lt Pamc cuokuu ltN mnsrLH 499 4amp3 l lt lte nomi xaw ltlt FIJIJI meNEw NV vgaw Ho V m HS wnISPlntix Yhlt S sumn QIVV wafak Svmwo deXPlryv W Ly l rc39lv WPr APPw Qr xp ASDFAP Spyvlntu W 9224 I MPEPV wuwnIc v 4 IIINI r e9 93 5b a l 5 a M a2 66 5 S w 4 u u frank pick 5 21er m l 39I o3 7 V Hammae Pavag 2assov3 WV kl1 rm UNA mz M 4m metr amp gt w 1 ampTE R l T17 1201 NH mm 7 VW V Mnmwmfs u iiow Eo wh KSMCltP rMm 79 S Ev mcl b P 112 027 Dh or p d uhlt H P9 P ltnxL n nnw yra LLAL ar4lt U awn pnfm U f ir 9 7Alpz 0L gtL 41 NP ltPN 2c lthsgtn7yw AP 0 5qu Sp mci rm ltokltmxvnlt T Hf fek up 0 Ivscf ltltSv 5an H 12 f o 35 brim 9W 3 olt MKPF V w AVG viii mfg Ln Pr gnvmv ru hw 7 79 pr Lift 50 ii OQPC r53 forwcfrwx MOEQ oy gavryub v ltPMQ97L A J r 9ltPltPwn P7 ab L Pnuvanpn lt0 yvnenx PxfrnV Ifzwpv I rx lt 6JV Equivalent Noise Input Voltage Figure 1 shows the ampli er noise model with a Th venin input source where V5 is the source voltage Z5 R5 sz is the source impedance Vts is the thermal noise voltage generated by the source and Vn and In are the noise sources representing the noise generated by the ampli er The output voltage is given by Z L AZi ZL V0 AV V V V Z 1 ZoZL Z5ZiZoZL ST T 7LT n 5 where A is the voltage gain and Z5 is the input impedance The equivalent noise input voltage Vm is de ned as the voltage in series with V that generates the same noise voltage at the output as all noise sources in the circuit It consists of the terms in parenthesis in Eq 1 and is given by Note that this is independent of both A and Z5 It is simply the noise voltage across Z5 considering Z to be an open circuit ZL V0 Z8 Vs Vn Amplifier 20 was Figure 1 Dy 7 in ampli er model with Thev nin source The meanesquare value of Vm is solved for as follows VnV 2Re MM 2 125 szg 4mm 25 Ar M Re W 3 where 39y 7 j39yi is the correlation coe icient between Vn and In and it is assumed that V25 is independent of both Vn and In The correlation coef cient is given by V 1 7 4 072 2 Effect of a Series Impedance at the Input Figure 2 shows the input circuit of an ampli er with an impedance Z1 added in series with a Th venin source The noise source th models the thermal noise generated by Z1 As is shown above the equivalent noise voltage in series with the source can be solved for by rst solving for the openecircuit input voltage ie the input voltage considering Z to be an open circuit It is given by v10 V5V25V21Vn1nzszl V5Vm 5 where Vni is the equivalent noise voltage in series with the source It is given by Vni VtsVt1 Vn1nZsZ1 W V Luz 6 where VnS and InS are the new values of Vn and In on the source side of Z1 It follows from this equation that Vns ltl Vn Inzl InS In 8 Note that VnS consists of all terms which are not multiplied by Z and InS consists of the coefficient of Z in the term that is multiplied by Z5 Figure 2 Ampli er input circuit with Thevenin source and series impedance added at input It follows that the addition of a series impedance at the input of an ampli er increases the Vn noise but does not change the In noise If Z1 is not to increase the noise7 lle should be as small as possible If Z1 is lossless7 it generates no noise itself so that V 0 The meanisquare values and the correlation coefficient for VnS and InS are given by 4M Re 21 Ar a Rewz W 9 27m E 10 1 E 2 2 7221 1ng ZELS The meanisquare equivalent noise input voltage is given by 73 4kTReZ5 Z1Af E 2xT xEReMZ ZI Elzszmg 12 Effect of a Shunt Impedance at the Input Figure 3 shows the input circuit of an ampli er with an impedance Z2 added in parallel with the source The noise source Itg models the thermal noise generated by Z2 The openicircuit input voltage is given by V2100 Vs W5 Vn B2 In ZsllZ2 A Z5Z2 i V V39 Z2 13 5 mZZg where Vni is the equivalent noise voltage in series with the source It is given by Vni z Vt Vn 1 12 17 Z 2 Vt Vm IMZS 14 where VnS and InS are the new values of Vn and In on the source side of Z2 It follows from this equation that Vns Vn V Ins It2 l 7 l In 2 Note that VnS consists of the term which is not multiplied by Z and InS consists of the sum of the coef cients of Z in the terms that are multiplied by Z5 Z8 Vts V11 I e Zi Figure 3 Ampli er input circuit with Thevenin source and shunt impedance added at input s It follows that the addition of a parallel impedance at the input of an ampli er increases the In noise but does not change the Vn noise If Z2 is not to increase the noise7 lZQl should be as large as possible If Z2 is lossless7 it generates no noise itself so that Im 0 The meanisquare values and the correlation coef cient for VnS and InS are given by I n 17 T 1 0 5 2 7 Y 7 2m4kTRe 72 AfW2 Un ane 72 2 18 2 2 vxvU Z Z2 75 r 1ng ZELS The meanisquare equivalent noise input voltage is given by 19 lZsl2 A 2 Z 6 2 vgRe 7 1 ZS 2 lZSlg 20 Dc bias networks and rf matching networks usually consist of series and parallel elements at the input to an ampli er One method of analyzing the effect of these elements on the ampli er noise is by transforming the Vn and In sources from the ampli er input back to the source by use of the above relations This is illustrated in the following example 4kTRe 25 Z52 1 Z2 Example 1 Figure 4shows the input circuit of an ampli er It is given that R 75 9 R1 1 k9 C 10 nF R2 100 Q a 2 nV HE 15 12A 7 02j01 The noise speci cations are for a frequency f 100th and a bandwidth Af 1 Hz Calculate 11 in series with the source by transforming Vn and In back to the source with Eqs 9 through 11 and 1 7 through 19 Vts C V71 AAA ll 39quot l l lt 1 Vs R1I1t1 R2It2ll lln Vi Zi Figure 4 Ampli er input circuit xEav n nv 4kTAf 472 v T2Eg2xugReltfg 23 2 vxUg R2 7aT xviaxiia The capacitor impedance is Z0 1j27TfC 7j159 9 To the left of C 12 quib via 24ng igm Re yazg 2 ZCF 43 nV ME 4 24pA 02 iTZC 7b l mem 0394 710335 V ibv ii iu Ew 1U ib 43 nV 12 4 112 4kTA f V 2 Rig R1 if 263 pA 2 2 U g 4 n In Unb an E Yc 2 2 V Unc V ch Solution To the left of R2 12 24 pA 47 lmi 0347 1626 X 103 To the left of R1 0523 710807 The equivalent noise voltage in series with the source is 12 569 nV The following example illustrates the calculation of HI 2 for the circuit of Fig 4 by rst calcui lating the openicircuit input voltage due to all sources in the circuit factoring out the coe icient of V and assigning all remaining noise terms to Vm Example 2 For the circuit of Erample I calculate Hui by calculating the openicircuit input voltage factoring out the coe icient of V5 and assigning all remaining noise terms to Vm Solution The equivalent source impedance seen by the ampli er is given by 1 Z R R 6867 294 sq R2HltWC 1H J The thermal noise voltage generated by R5 R1 and R2 has a meanisquare value of 4hT Re Zeq Denote the phasor value of this voltage by Vteq The openicircuit input voltage is given by V V 1 L we SR1 3 R2R1lle11WC 0292 10273 V mm Vn 12eel we Vi 172 0292 10273 Weq Vn InZeq 0292j0273 V5 It follows that the equivalent noise input voltage is given by 12 U2 7 4kT Ream 03 21uRe39yzeq 22 zeql m 292 10273 2 569 nV This is the same as that found in Example 1 Note that the method used in this example is more straightforward because it is necessary to transform only one source through the network That source is the signal source V5 Noise Factor and Noise Figure The noise factor F of an ampli er is de ned as the ratio of its actual SNR and the SNR if the ampli er is noiseless where the temperature is taken to be the standard temperature To When it is expressed in dB it is called noise gure and is given by NF 1010g Consider the ampli er model in Fig 1 If the ampli er is noiseless the signalitonoise ratio given by SNR U gUtgs where 11 is the meanisquare source voltage and 11 55 is the meanisquare thermal noise voltage generated by the source i aedance When the ampli er noise is included the signalitoinoise ratio is given by SNR Thus the noise factor is given by viv5 r2 712 2 U1Re v22 st 7 21 1 21 U 4kT0R5Af It follows from this expression that a noiseless ampli er has the noise factor F 1 A useful relation which follows from the de nition of F is EFXEFx4kTOReZs 22 This relation is used below in the method for measuring F Example 3 Calculate F and NF for the ampli er in Eacample 1 for which R5 75 Q and 569 nV Assume Af 1 Hz and T To 290 K Solution The meanisquare thermal noise voltage of the source is 11725 AUCTRS 120 X 10 18 V2 Thus the noise factor and noise gure are 569 X 1092 F 12 X 10 18 270 NF 10log 270 143 dB When Af 1 Hz7 as in this example7 F is called the spotinoise factor and NF is called the spotinoise gure Measuring the Noise Factor This method is the most general one because it does not require knowledge of either the ampli er gain or its noise bandwidth Consider the noise model of an ampli er given in Fig 5 Consider the source to be a white noise source having the spectral density 5v VSV Af The total noise voltage at the output can be written V0 A 9 tsvn InZsllZi AZr ZS V Vt V7 InZ 23 Z2 Z5 Z5 The meanisquare value is given by Z Z5 HMVEM v29 1242 i AZi 2 57 f Bn 4hT0 Re Z5Bn 11 2 2 Z5Zi ls fBquot ml Z5 Z5 2 lSv f B F X 4kT0 Re Z5 Bu where Bn is the ampli er noise bandwidth and Eq 22 has been used to relate to the thermal noise vo ge of the source Let 1131 be the value of U with the noise source at the input set to zero7 ie 5v 0 Now7 let S7 be increased until the rms output voltage increases by a factor 7 ie 11 3 THU 21 It follows by taking the ratio of the two meanisquare voltages that r2 1 F X 4kT Re Z5Bn F X 4kT0 Re Z5

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I made $350 in just two days after posting my first study guide."

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.