ECE 145B / 218B, notes set 5: Two-port Noise Parameters
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1 class oes, M. odwell, copyrihed 01 C 145B 18B, oes se 5: Two-por Noise Parameers Mark odwell Uiersiy of Califoria, aa Barbara rodwell@ece.ucsb.edu , fax
2 efereces ad Ciaios: class oes, M. odwell, copyrihed 01 ources Ciaios: Kiel ad Kroemer : Thermal Physics a der iel : Noise i olid - ae Deices Papoulis : Probabiliy ad adom ariables hard, comprehesie Peyo.Peebles : Probabiliy,adom ariables, adom ial Priciples iroducory Wozecraf & Jacobs : Priciples of Commuica ios ieeri. M ochebaker : Low Noise lecroic Desi formaio heory lecure oes: Thomas Coer, aford, circa 198 Probabiliy lecure oes : M ari Hellma, aford, circa 198 Naioal emicoduc or Liear Applicaios Noes: Noise i circuis. uesed refereces for sudy. a der iel, Wozecraf & Jacobs, Peebles, Kiel ad Kroemer Papers by ukuideice oise, mih & Persoik opical receier Naioal emi. App.Noes! Coer ad Williams : lemes of formaio Theory desi
3 class oes, M. odwell, copyrihed 01 Our Noaio for pecral Desiies ad Correlaios cross specral desiy crosscorrelaio fucio specral desiy power auocorrelaio fucio,, frequecy fucio of ime fucio of Oucome adom Process * * f y x f y A Y f f A f f xy xy xy xy xy Y Y Y Y xy Y ad processes or saioary erodic * * y x xy Y. e weca simply wri, or i clear wheher coex makes Whe
4 Two-Por Noise Descripio class oes, M. odwell, copyrihed 01 As we haesee i heprior lecures, hrouh hemehodsof heieraloise eeraorsof ca be summed ad represeed by wo oise eeraors ad. circui aalysis, a circui The specral desiies of ad mus be calculaed ad specified. Thecross specraldesiy mus also be calculaed ad specified.
5 Calculai Toal Noise class oes, M. odwell, copyrihed 01 f heeeraor e N e 4, us has hermal oise, eprese he combiaio of amplifier olae ad curre oise by a sile source Toal N N e We ca ow calculae, oal, amplifier he specraldesiy of * e e e his oaloise : e
6 ial Noise aio of Geeraor class oes, M. odwell, copyrihed 01 sial,, oal ad, e are i series ad see he same load impedace. The raios of powersdeliered by hesewill o deped upo he load. Therefore cosider he aiable oise powers. The sial power aailable from he eeraor is P sial, aailable sial, M 4 e f we cosider a arrow badwidh bewee he he aailable oise power from N P [ ], f f oise, aailableeeraor,, e e is 4 f e sial f ad f sial f, The sialoi seraio of he eeraor is he N P P sial, aailable oise, aailableeeraor, sial, M, e f f 4 e 4 e sial, M f 4 e
7 ial Noise aio of Geeraor+Amplifier class oes, M. odwell, copyrihed 01 ial power aailable from he eeraor Noise power aailable from eeraor : Poise, a, : P 4 sial, aailable e sial, M f 4 Noise power aailable from amplifier : Poise, a, Amp, oal, amplifier e e f f 4 e ialoi seraio icludi amplifier oise: N P P oise, aail, e oal sial, M f sial, aailable 4 P 4 e oise, aail, amp e f oal f sial, M 4 e 4, e e f 4 e
8 class oes, M. odwell, copyrihed 01 Noise iure: ial Noise aio Deradaio Noise fiure sialoi se raio before addi amplifier sialoi se raio before addi amplifier ialoi seraio before addi amplifier : N sial, M f 4 e ialoi seraio afer addi amplifier : N oal sial, M f 4 4 e e f Noise fiure oal f 4 e f f Noise fiure 1 oal 4 e 1 amplifier aailable ipu oise power
9 Calculai Noise iure Noise fiure 1 oal 4 e class oes, M. odwell, copyrihed 01 We also kow ha : e *, oal We ca calculae from his a expressio for oise fiure : 1 s e 4 e * s
10 Miimum Noise iure class oes, M. odwell, copyrihed 01 Noise fiure aries as a fucio of e e e : 1 s e 4 e * s Afer some calculus, we ca fid a mimimum oise fiure ad a eeraor impedace which ies us his miimum : mi op 1 op 1 4 op m e m m Pois o remember : a which ies a miimum aries c. wih e, b hece here is a opimum e
11 Noise iure i Wae Noaio class oes, M. odwell, copyrihed 01 Wrie iseadi ermsof mi 4r 1 s s op 1 wae parameers, op These describe coous i he s plae of cosa oise fiure :" oise fiure circles", i.e. a descripio of wih source reflecio he ariaio of coefficie. oise fiure am o persuaded ha her e is aluei hererepeaihederiaioof hisexpressio
12 Low-Noise Amplifier Desi class oes, M. odwell, copyrihed 01 Desi seps are 1 i-bad sabilizaio: his is bes doe a oupu por o aoid deradi oise ipu ui for mi 3 oupu ui mach 4 ou-of-bad sabilizaio Noe ha ui for miimum oise fiure requires a *mismach* o he amplifier ipu; amplifier ai herefore mus lie below he rasisor MAGMG. Noe ha ui for miimum oise fiure implies ha amplifier ipu is mismached: ipu reflecio coefficie is herefore o zero! Discrepacy i ipu oise-mach & ai-mach ca be reduced by addi source iducace s s = o oise mach e
13 xample LNA Desi: 60 GHz, 130 m ige BJT class oes, M. odwell, copyrihed 01 ai & oise circles afer ipu machi oe compromise bewee ai & oise ui
14 Appedix class oes, M. odwell, copyrihed 01
15 class oes, M. odwell, copyrihed 01 Appedix: Deriaio of mi ad op 1 opimum eeraor reacace m 0 m e m m e 1 4 m e 1 4 m e e 1 4 e 1 4, op d dg G G
16 class oes, M. odwell, copyrihed 01 Appedix: Deriaio of mi ad op opimum eeraor resisace m 0 m e m e m m we hae foud for opimum eeraor reacace. Now subsiuei he expressio e m 1 4, op d dg G G G
17 class oes, M. odwell, copyrihed 01 Appedix: Deriaio of mi ad op! miimum oise fiure e m 1 e m 1 4 e m m m Now subsiuei he expressio for opimum eeraor resisace. 1 mi 1 mi mi mi G G
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