ECE 145B / 218B, notes set 3: Electrical device noise models.

Transcription

1 class otes, M. owell, copyrighte 2012 C 145B / 218B, otes set 3: lectrical evice oise moels. Mark owell Uiversity of Califoria, Sata Barbara rowell@ece.ucsb.eu , fax

2 class otes, M. owell, copyrighte 2012 Thermal Noise hf hf hf hf hf hf hf 4 4 these become For 1 ) / exp( ) / exp( 2 4 Available ower Frequecy hf=

3 Available Thermal Noise ower class otes, M. owell, copyrighte 2012 Maximum power trasfer : loa matche to geerator With matche loa, voltage across loa is / 2 With matche loa, curret through loa is N N / 2. Give that 4 or 4 loa loa is the maximum (the available) availableoise, oise power,hece All resistors have equal available oise power. Ay compooet uer thermal equilibriu m (o bias) follows this law.

4 class otes, M. owell, copyrighte 2012 ough Argumet for Thermal Noise xpressio ach egree of freeom i a systemat thermal equilibriu m with a reservoir must have expecte eergy / 2. Thermal equilibriu m is obtaie 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(2πf ) & cos(2πf )), hece available power i this bawith must be f. o o the total

5 class otes, M. owell, copyrighte 2012 Noise from ay impeace uer thermal equilibrium For ay compoet or complex etwork uer thermal equilibriu m ( o eergy supply) availableoise, 4 e( Z) or 4 e( Y ) This follows from the 2 law of thermoyamics. This allows quick oise calculatio of complex passiveetworks This allows quick oise calculatio of ateas. Biase semicouctor evices are NOTi thermal equilibriu m.

6 Noise from a Atea class otes, M. owell, copyrighte 2012 availableoise, 4 e( Z) The atea has both Ohmic a raiatio resistaces. ra The Ohmic resistace has a oise voltage of spectral esity 4 ambiet Ohmic, where T ambiet is the physicalatea temperature,ra loss By the2 esity 4 law, the raiatio resistace has a oise voltage of fiel ra, where T fiel is the average temperature of the regio from which theatea receives sigal power spectral,loss ter - galactic space is at 3.8 Kelvi...

7 Noise o a capacitor class otes, M. owell, copyrighte 2012 From We fi 4 that or 4 C + Vc - V V c c 1 1 j2fc 1 1 j2fc f C So the mea store Capacitor eergy is (1/ 2) C V V c c f 2 2 C 2 / 2 This also follows irectly from the Boltzma law.

8 Shot oise class otes, M. owell, copyrighte 2012 The proof (ot give) extes upoour 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 esity 2q at lower frequecie s of M ost DCcurrets i circuits are ot a statistically iepeet flow of electros. The electro motio i a resistor geerates local fiels which ifluece all other electros. Classical resistors o ot exhibit shot oise theflow of

9 Shot Noise xample: Heavily Atteuate Light class otes, M. owell, copyrighte 2012 A optical fiber is illumiate by a oiseless source of optical power prouces a flux of a ph the receive ( q / h) flux of photos The fiber has atteuatio, hece per uit time of photosis F with a shot oise of i the receive / h / h optical optical through thefiber with probablity, the process agai 2h optical power is. Becuase This prouces o a photoetector withquatum efficiecy a photocurret 2q F i each i has shot oise with a i photopasses

10 class otes, M. owell, copyrighte 2012 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, hece curret has a oise spectral esity of the resultig leak leak 2q leak

11 Shot oise i N juctios class otes, M. owell, copyrighte 2012 The ioe curret is ioe s e qv / 1 s e qv / s forwar reverse Both the forwar a reverse currets have shot oise, ioe ioe 2q forwar 2q reverse 2q ioe 2 s hece Uer strogforwar bias, ioe ioe 2q ioe uer strog reverse bias, ioe ioe 2q s Uer zero bias, ioe ioe 4 / r ioe, as require by the2 law. Va er Zeil erives oise i N juctios from the thermal oise of carrier iffusio. The oise curret spectral esity thus calculate is equal to that of shot oise.

12 Shot oise a N juctios: aother moel class otes, M. owell, copyrighte 2012 For a strogly forwar biase juctio or ioe ioe 2q ioe 2 / r ioe where r ioe / q ioe V ioe hece V ioe 2r ioe ioe / 2 A biase ioe has oise1/2 that of a resistor of equal small - sigal impeace. The factor of 2 arises from oe - way curret flow. Va er Zeil erives oise i N juctios from the thermal oise of carrier iffusio. The oise curret spectral esity thus calculate is equal tothat of shot oise.

13 Bipolar Trasistor Moel---with Noise class otes, M. owell, copyrighte 2012 C cbx B bb C cbi c C be V be g m V be e -j c C be,iff =g m f C je ex

14 Bipolar Trasistor Moel---with Noise class otes, M. owell, copyrighte 2012 C cbx B bb Nb be C cbi Nc N,c c C N,bb V be C be,iff =g m f C je g m V be e -j c ex N,ex

15 Bipolar Noise Moel Collector shot oise cc 2qc 2 Base shot oise b b There is a slight correlatio of whe 2f ( 2q b b 2 / r / r a ) approaches1. We c e be 2g b m c will (a cross - spectral esity) igore this small effect. class otes, M. owell, copyrighte 2012 The physicalresistors( bb, ex, c ) have thermal oise of spectral esity V 2 4 be a r e The oise of 1/ g be m are a r ot physicalresistors. e 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 is equal tothat of shot oise.

16 FT Small-Sigal Moel class otes, M. owell, copyrighte 2012 G g C g D i V gs s C gs g m V gs e -j s S

17 FT Noise Moel class otes, M. owell, copyrighte 2012 G g N,i C g N N, D N,g Ng i V gs s C gs gmvgse -j s S N,s

18 FT Noise moel class otes, M. owell, copyrighte 2012 G g N,i C g N N, D N,g Ng i g, s, are physicalresistaces V 2 4 V gs s C gs gmvgse -j is the thermal oise of the chael curret s 4g m N,s 2 / 3: graual - chael ~ 11.5: highly scale FT uer costat mobility FT uer high - fiel coitios S i arises from the chael : N, i a ffect is egligible approximate as ucorrelat e. have small correlatio g s N, i N, i 4 i is theshot oise of the gate leakage curret : is ot a physicalresistor - o associate oise geerator. g g 2q gate

19 Alterate FT Noise moel class otes, M. owell, copyrighte g g Cg put oise term i Cgs 4Gamma/gm Vgs gmvgs s 4s You will also see this i the literature. There is o ew physicshere at We have just applie the formula that for a geeral impeace 2q gate 4 e( Y ) 2q gate...toget the iput i terms of a curret. 4 2fC gs 2 i all.