( ) Thermal noise ktb (T is absolute temperature in kelvin, B is bandwidth, k is Boltzamann s constant) Shot noise

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1 OISE

2 Thermal oe ktb (T abolute temperature kelv, B badwdth, k Boltzama cotat) 3 k.38 0 joule / kelv ( joule /ecod watt) ( ) v ( freq) 4kTB Thermal oe refer to the ketc eergy of a body of partcle a a reult of t fte temperature, vbrato ketc eergy may be coupled electrcally to aother devce Shot oe ( freq) ei ( A Hz) 0 9 e.6 0 coulom, I O average curret Domat cotrbuto to flcker oe through modulato, whe frequecy of carrer gal get hgher, o hot oe, make F MI hgher. (hgher frequecy, wore F, maller ga cotrbute too) Shot oe oy curret flow through a load retace. Shot oe caued by the quatzed ad radom ature of curret flow (curret ot cotuou), the varato of curret radom type. Oe example the geerato ad recombato of hole/electro par (G- oe) emcoductor

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4 The Joho oe of a retor gve by the mea quare voltage V 4kTB The maxmum avalable oe power P A from a retor ktb V 4kTB P A kbt F gal receved from atea at 5 o C ha oe power level Load dbm/hz Thermal oe whte oe type 4

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6 Electro drft velocty oe Spectrum ( FET) characterzed by the oe at low frequecy f -- f oe caued by the geerato-combato cycle owg to the trap the depleto layer below the gate electrode. characterzed by the thermal ad dffuo oe -- Dffuo oe reulted from hgh electrc feld codto (hgh dra-ource bag), the electro drft velocty wll fluctuate aturato velocty (A type of Shot oe). Shot oe of FET le tha BJT, whch mea the F MI of FET maller compared at the ame frequecy. mot from kee frequecy hot oe f Dffuo oe get hgher at hgh electrc fled rego mot from thermal oe (oe floor) Electro Feld The carrer drft velocty of GaA hgher tha Slco reulted hgher kee oe frequecy. 6

7 F S S o o GS S ( a G ) a G G > (where G the ga of the ytem) Sce thermal oe expreed a ktb (T abolute temperature, B badwdth) oe Factor ca be rewrtte a F kto BG kt BG a o Iput Power Output Power oe Fgure F F 0 log0( F ) Frequecy Frequecy 7

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16 F kto BG kt BG a o Output oe Power GkBT Slope GkB a a Iput oe Temperature T (Kelv, ) 6

17 Obta a * Avalache Dode uually ued a ource for meauremet. * It geerate two dfferet oe power T C ad T H whe tur o or clod. * Slope derved by makg two meauremet correpodg to T C ad T H Output oe Power Slope GkB a T C T H Source oe Temperature T (Kelv, ) 7

18 F F F F 3 F 4 L F F F G F3 G G F4 G G G 3 L Where G the ga of each amplfer Whe mxer the meaured ytem, oe put power wll be dtrbuted Ito lower ad upper de bad of f LO. If total put oe power ued for F calculato whle a meaured from oly oe gle de bad, t referred a the DSB oe fgure meauremet. If gle de bad oe put power ued the t SSB oe fgure. SSB uually 3 db hgher tha DSB for t baed o equal de bad dtrbuto of covero. 8

19 9 Derve for two tage a G G F EF : F F F G G ) ( F KTG G G F a ) ( F KTG a et ad et are 50 OHM match for both put ad output. KT for both et. ) ( G F KTG G a a a a a G G G G G G G G G G G G G G F G F F G G G G G F a a

20 oe Parameter jx F, m g opt, X opt All four parameter are fucto of frequecy. F F ( ) ( X X ) m g ( opt opt ) a G G a / G > oe fgure F acheve mmum value whe X It called the oe match X opt opt 0

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22 The trc oe ource of a FET ca be decrbed by two correlated whte-oe: g, d g d : epreet the oe duced o the gate electrode by charge fluctuato aocated wth the fluctuato. : epreet the oe geerated alog the Dra-to-Source chael due to curret fluctuato. g, d are partally correlated, the correlato coeffcet C jc E( ( E( * g g d ) ) E( d )) 0

23 I oy Two-Port V V _ Z,Y _ parameter I oe-free V Two-Port V _ Y parameter _ I oe-free Two-Port _ e Z parameter e _ V V I I I I e I * oe-free _ V * Two-Port, Z parameter _ V V I V * * I V e () V V * Z Z From () ad () we have V V V V Z Z Z Z ( I ( I I I Z Z e ) Z ) Z I I I e e I e Z e e I I * * e Z Z Z Z I I I () oe ource ca be rearraged 3

24 & e partally correlated e e u Z c where eu fully ucorrelated wth ad Z c c jx c I eu Zc oe-free _ Two-Port, V V Z parameter I 4

25 I eu Zc _ oe-free V Two-Port, V _ Z parameter _ I jx e jx e u Z c _ jx e _ oe-free Two-Port, Z parameter Z L jx 5

26 F a / G > e jx e u Z c jx a / G real ( real ( jx jx e ( jx )( e u ( jx )( jx ) jx jx ) jx jx jx ) * ) * real ( ( Zc Z)( Z jx jx c Z )( * ) ( jx jx ) jx ) * See dervato ext page for the ecod term of a/g!!! 6

27 jx real ( _ Z Z where c Z c ( Zc Z)( Z jx jx Z Z, c Z )( jx jx Z jx Z Zc ( ) Z Z Z Z Zc Z ( ) The power to Z Z Z Why ue g equato? See explaato ***!!! * ) ( jx c jx ) *** The queto whether actg a ehacg or cacelg role to whch would decde the polarty of voltage ource Z c Z c Z ot mpedace but correlato coeffcet, the real part of Z c may be ether potve or egatve. Aume cacelg effect ext (due to certa Z ad actually t doe ext) ad force real part of Z c to be potve, the polarty of hould be aged a Z c how. * jx ), c 7

28 F Let a / G e u e ( Z e 4kTB e 4kTB e e u 4kTB ue c Z ) e u () ( Z e c Z )( Z c Z ad ubttute to () the we have ) * F ( Zc Z) ue F ca be rewrtte a u u F ( ) ( X X ) F The famou equato!!! m g ( c c ) 8

29 F m Th aroud 5 to 0% I d / I d 9

30 oe fgure F acheve mmum value whe X It called the oe match C C, S X S 30