Mixed Signal IC Design Notes set 7: Electrical device noise models.

Transcription

1 C145C /18C otes, M. owell, copyrighte 007 Mixe Sigal C Desig Notes set 7: lectrical evice oise moels. Mark owell Uiversity of Califoria, Sata Barbara rowell@ece.ucsb.eu , fax

2 Topics C145C /18C otes, M. owell, copyrighte 007 Math: istributios, raom variables, expectatios, pairs of V, joit istributios, mea, variace, covariace a correlatios. aom processes, escriptio, statioarity, ergoicity, correlatio fuctios, autocorrelatio fuctio, power spectral esity. Noise moels of evices: thermal a "shot" oise. Moels of resistors, ioes, trasistors, ateas. Circuit oise aalysis: etwork represetatio. Solutio. Total output oise. Total iput oise. geerator moel. / moel. Noise figure, oise temperature. Sigal / oise ratio.

3 C145C /18C otes, M. owell, copyrighte 007 Thermal Noise kt kt kt hf kt hf hf hf kt hf hf hf 4 4 these become For 1 ) / exp( 4 1 ) / exp( 4 << + + Available ower Frequecy hfkt kt

4 Available Thermal Noise ower C145C /18C otes, M. owell, copyrighte 007 Maximum power trasfer : loa matche to geerator. Withmatche loa, voltage across loa is Withmatche loa, curret through loa is N / N / Give that 4kT or 4kT loa kt loa is the maximum (the available) oise power, hece available, oise kt All resistors have equal available oise power. Ay compooet uer thermal equilibrium (o bias) follows thislaw.

5 C145C /18C otes, M. owell, copyrighte 007 ough Argumet for Thermal Noise xpressio ach egree of freeom i a system at thermal equilibrium with a reservoir must have expecte eergy kt /. Thermal equilibrium isobtaie via the resistor issipatio : circuit power heat N L C thermal oise : heat circuit power A filter of 1 Hz bawith, observe for 1seco, has two egrees of freeom (si(πf ) & cos(πf )), hece available power i this bawith must be kt f. o o the total

6 C145C /18C otes, M. owell, copyrighte 007 Noise from ay impeace uer thermal equilibrium For ay compoet or complex etwork uer thermal equilibrium ( o eergy supply) available, oise kt 4kT e( Z) or 4kT e( Y ) This follows from the law of thermoyamics. This allows quick oise calculatio of complex passive etworks This allows quick oise calculatio of ateas. Biase semicouctor evices are NOT i thermal equilibrium.

7 Noise from a Atea C145C /18C otes, M. owell, copyrighte 007 available, oise kt 4kT e( Z) The atea has both Ohmica raiatio resistaces. ra The Ohmicresistace has a oise voltage of spectral esity 4kT ambiet Ohmic, where T ambiet is the physical atea temperature,ra loss By the esity 4kT law, the raiatio resistace has a oise voltage of fiel ra, where T fiel is the average temperature of the regio from which the atea receives sigal power spectral,loss ter - galactic space is at 3.8 Kelvi...

8 C145C /18C otes, M. owell, copyrighte 007 Noise o a capacitor This also follows irectly from the Boltzma law. / ) (1/ So the mea store Capacitor eergy is We fi that 4 or 4 From kt C f C V V C f fc j fc j V V kt kt c c c c π π π π C Vc + -

9 Shot oise C145C /18C otes, M. owell, copyrighte 007 The proof (ot give) extes upo our earlier iscrete - time shot - oise calculatio. f, give a DC curret, the arrival iepeet of every other electro, of each electro is statistically the the curret has a oise power spectral q esity at lower frequecies of Most DC currets i circuits are ot a statistically iepeet flow of electros. The electro motioi a resistor geerates local fiels which ifluece all other electros. Classical resistors o ot exhibit shot oise the flow of

10 C145C /18C otes, M. owell, copyrighte 007 Shot Noise xample: Heavily Atteuate Light A optical fiber is illumiate by a oiseless source of optical power prouces a flux of photos per uit time of a the receive flux of photos is ph out out out out out out out F out with a shot oise of out i / hυ / hυ optical optical The fiber has atteuatio α, hece the receive optical power is through the fiber with probablity α, the process agai has shot oise with hυ This prouces o a photoetector with quatum efficiecyη a photocurret ( ηq / hυ) q F i i out a α. Becuase each photo passes i

11 C145C /18C otes, M. owell, copyrighte 007 Shot oise xample: everse Biase Schottky Dioe the metal, electros have a Fermi - Dirac eergy istributio. Some will have sufficiet eergy to cross over the barrier. This prouces reverse leakage curret. These evets are (almost) iepeet, curret has a oise spectral esity of hece the resultig leak leak q leak

12 Shot oise i N juctios C145C /18C otes, M. owell, copyrighte 007 The ioe curret is ioe s ( qv / kt e 1) s e qv / kt s forwar + reverse Both the forwar a reverse currets have shot oise, ioe ioe q forwar + q reverse q ( + ) ioe s hece Uer strog forwar bias, ioe ioe q ioe uer strog reverse bias, ioe ioe q s Uer zero bias, ioe ioe 4kT / r ioe, as require by the law. Va er Zeil erives oise i N juctios from the thermal oise of carrier iffusio. The oise curret spectral esity thus calculate isequal to that of shot oise.

13 C145C /18C otes, M. owell, copyrighte 007 Shot oise a N juctios: aother moel For a strogly forwar biase juctio or V hece ioe ioe ioe V ioe ioe q kt / ioe ktr ioe kt / r ioe where r ioe kt / q ioe A biase ioe has oise1/ that of a resistor of equal The factor of arises from oe - way curret flow. small - sigal impeace. Va er Zeil erives oise i N juctios from the thermal oise of carrier iffusio. The oise curret spectral esity thus calculate isequal to that of shot oise.

14 Bipolar Trasistor Moel---without Noise C145C /18C otes, M. owell, copyrighte 007 C cbx B bb C cbi c C be V be g m V be e -jωτ c C be,iff g m τ f C je ex

15 Bipolar Trasistor Moel---with Noise C145C /18C otes, M. owell, copyrighte 007 C cbx B bb Nb be C cbi Nc N,c c C N,bb V be C be,iff g m τ f C je g m V be e -jωτ c ex N,ex

16 Bipolar Noise Moel Collector shot oise cc qc kt Base shot oise b b There is a slight correlatio of whe πf ( τ q b b kt / r / r a + τ ) approaches 1. We will c e be ktg b m c (a cross - spectral esity) igore thissmall effect. C145C /18C otes, M. owell, copyrighte 007 The physical resistors ( bb, ex, c ) have thermal oise of spectral esity V 4kT be a r e The oise of 1/ g be m are ot physical a r e resistors. are the base a the collector shot oise geerators. Va er Zeil erives oise i N juctios from the thermal oise of carrier iffusio. The oise curret spectral esity thus calculate isequal to that of shot oise.

17 FT Small-Sigal Moel C145C /18C otes, M. owell, copyrighte 007 G g C g D i V gs s C gs g m V gs e -jωτ s S

18 FT Noise Moel C145C /18C otes, M. owell, copyrighte 007 G g N,i C g N N, D N,g Ng i V gs s C gs gmvgse -jωτ s S N,s

19 FT Noise moel C145C /18C otes, M. owell, copyrighte 007 G g N,i C g N N, D N,g Ng i g, s, are physical resistaces V 4kT V gs s C gs gmvgs e-jωτ is the thermal oise of the chael curret s 4kTΓg m N,s Γ / 3: graual - chael FT uer costat mobility Γ ~ 1 1.5: highly scale FT uer high - fiel coitios S i arises from the chael : N, i a ffect is egligible approximate as ucorrelate. have small correlatio g s N, i N, i 4kT i is the shot oise of the gate leakage curret : is ot a physical resistor - o associate oise geerator. g g q gate

20 Alterate FT Noise moel C145C /18C otes, M. owell, copyrighte 007 4kTg g Cg put oise term i Cgs 4kTGamma/gm Vgs gmvgs s 4kTs You will also see this i the literature. There is o ew physics here at We have just applie the formula that for a geeral impeace q gate + 4kT e( Y ) q gate...to get the iput i terms of a curret. + 4kT ( πfc ) gs i all.

21 Topics C145C /18C otes, M. owell, copyrighte 007 Math: istributios, raom variables, expectatios, pairs of V, joit istributios, mea, variace, covariace a correlatios. aom processes, escriptio, statioarity, ergoicity, correlatio fuctios, autocorrelatio fuctio, power spectral esity. Noise moels of evices: thermal a "shot" oise. Moels of resistors, ioes, trasistors, ateas. Circuit oise aalysis: etwork represetatio. Solutio. Total output oise. Total iput oise. geerator moel. / moel. Noise figure, oise temperature. Sigal / oise ratio.