High Speed Mixed Signal IC Design notes set 8. Noise in Electrical Circuits: circuit noise analysis

Transcription

1 C145C /18C otes, M. odwell, copyrihted 007 Hih peed Mixed ial C Desi otes set 8 Noise i lectrical Circuits: circuit oise aalysis Mark odwell Uiversity of Califoria, ata Barbara rodwell@ece.ucsb.edu , fax

2 Noise i electrical circuits: topics C145C /18C otes, M. odwell, copyrihted 007 Math: distributios, rado variables, expectatios, pairs of, joit distributios, ea, variace, covariace ad correlatios. ado processes, descriptio, statioarity, erodicity, correlatio fuctios, autocorrelatio fuctio, power spectral desity. Noise odels of devices: theral ad "shot" oise. Models of resistors, diodes, trasitors, ateas. Circuit oise aalysis: etwork represetatio. olutio. Total output oise. Total iput oise. eerator odel. / odel. Noise fiure, oise teperature. ial / oise ratio.

3 Noise i electrical circuits: tratey C145C /18C otes, M. odwell, copyrihted 007 Aai, our tie here is liited. Work thesiplest possible eaiful proble. Use this to develop aalytical ethods ad defiitios. Without too uch iaiatio, oe ca the exted toay proble. The ece594 oise otes provide uch ore detail, but thekey stepsare here all siply show.

4 C145C /18C otes, M. odwell, copyrihted 007 oal: Coputi ial/noise atio ad esitivity adio eceiver si cos clock ad data recovery Optical eceiver clock ad data recovery To copute the receiver sesitivity, weust fid the sial/oi se ratio at thedecisio circuit iput. t is ofte coveiet tocopare theiput sial to the equivalet iput - referred oise. aitude

5 Circuit oise aalysis: oals C145C /18C otes, M. odwell, copyrihted 007 The circuit output has out A v i oise,output both sial ad oise. Noise arises fro the eerator, the aplifier, oise,output oise,eerator oise,aplifier oise,load ad the load These oise ters ca out A v i oise,output be represeted by fictitious iput ters : A v i oise,iput, where oise,iput oise,output / A v How do we calculate the output- referred oise?

6 Noise odel of this circuit C145C /18C otes, M. odwell, copyrihted 007 f 4kT/f e i B bb 49 C cbx 6.4 ff c C cbi ff cbo qcbo C 4kT out e 4kTe 4kTbb kt/bb or qb C diff 18 ff C je 38 ff b ' e 350 ex 4. 3 kt/ or qc b ' e 4kTex 4kTee ee The circuit has a lare uber of oise eerators. Noise aalysis of ost practical circuits is of foridable Brute- force ethods are too hard for had aalysis. We will lear ore efficiet techiques. We will illustrate calculatio s with a very siple circuit. coplexity.

7 Circuit Noise Aalysis: 1st xaple a C145C /18C otes, M. odwell, copyrihted 007 e i out e e N,e C s s Nd D N out e i N, s iple aplifier, with siplified oise odel. Notatio: ile - sided, Hz - based spectral desities d df 4kT or d df 4kT for all resistors d d d df 4kT for the FT chael oise.

8 Circuit Noise Aalysis: 1st xaple b C145C /18C otes, M. odwell, copyrihted 007 e N,e C s s Nd D N out e i N, s Now calculate out 1 C out, sial out,ap_oise out, e_oise where d d N, d out, sial d e e d df the output voltae : N, N, C N, N, e N, out,ap_oise e out, e_oise 1 1 C 1 1 C df 4kT s s s 4kT or e for the FT chael s e e d e oise. df N, d N, 4kT for all resistors

9 eider C145C /18C otes, M. odwell, copyrihted 007 f y H x The y x x y H yx * H x y ad y y H x x

10 Circuit Noise Aalysis: 1st xaple c C145C /18C otes, M. odwell, copyrihted 007 e N,e C s s Nd D N out e i N, s o : d out, sial ap, out e, out d d d e 1 1 C df N, N, e 1 1 4kT fc fc df 4kT or s s s e e e d for the FT chael oise. N, d N, df 4kT for all resistors

11 Circuit Noise Aalysis: 1st xaple d C145C /18C otes, M. odwell, copyrihted 007 e N,e C s s Nd D N out e i N, s The output sial out, sial A e v 1 1 C e s e The output oise *due to theaplifier ap, out 4kT 1 fc s * e 4kT 4kT The output oise *due to the eerator e, out 4kT e 1 fc s * e

12 Circuit Noise Aalysis: 1st xaple e C145C /18C otes, M. odwell, copyrihted 007 e N,e C s s Nd D N out e i N, s Now Defie * equivalet iput oise* out A A v This eas * e * e siply : out, ap_ oise i, ap_ oise i, e _ oise out, e _ oise i, e _ oise N, e ad i, ap_ oise out, ap_ oise / A v o the aplifier iput - referred ap, out ap i, A oise is : 1 fc, ap out v s e Ad theiput oise *due to the eerator 4kT e, i e *is :

13 Circuit Noise Aalysis: 1st xaple f C145C /18C otes, M. odwell, copyrihted 007 e N,e C s s Nd D N out e i N, s ap, i 4kT iput - referred oise fro 4kT 1 1 fc s e iput referred chael oise 4kT 1 1 fc s e iput - referred load resistor oise put oise * fro the eerator 4kT e, i e *

14 Circuit Noise Aalysis: 1st xaple C145C /18C otes, M. odwell, copyrihted 007 Noise Fiure e, i F defiitio : e, i ap, i e e N,e i N, C s s s Nd D N out Fro which we ca write 4kT F i, total _ oise e ial/noi se ratio : sial N i, total _ oise Where sial is theiput sial' s power spectraldesity

15 C145C /18C otes, M. odwell, copyrihted 007 Circuit Noise Aalysis: 1st xaple: uary e N,e C s s Nd D N out e i N, s referred These are the exact stepsfor calculatio of iput - output- referred oise, N, ad oise fiure. oise, This is how a coputer iht calculate these. The ethod is extreely tedious, eve for a sall circuit. Note that,i coputi iput - referred oise, ay of stepswere cacelled oe we foud thefial aswer. our calculatio Clearly, the, our ethod ust be iefficie t.

16 C145C /18C otes, M. odwell, copyrihted 007 Circuit Noise Aalysis: 1st xaple: uary Aalysis was hard because we...propaated the circuit oise eerators to the circuit output,...the propaated the back to the iput. This ivolves cacelled steps- - - extra work. t is particularly iefficie t because ***The ost iportat oise sources are ear the iput***

17 C145C /18C otes, M. odwell, copyrihted 007 Circuit Noise Aalysis: ource Traspositio Method et use ove all We ust restrict ourselves the circuit oise eerators - port iput - output characters tics of to the circuit iput. to trasforatios which do ot chae the the etwork betwee iput ad output. e N,e C s s Nd D N out e i N, s This eas, ake trasforatios oly iside red box

18 C145C /18C otes, M. odwell, copyrihted 007 Circuit Noise Aalysis: ource Traspositio Method Thevei - Norto MoviCurret Across AN Brach N N = N N N Output- put out = N N = N / Movioltae Throuh A Node N N N /A v N N A v A v

19 C145C /18C otes, M. odwell, copyrihted 007 Circuit Noise Aalysis: ource Traspositio Method " Walk" N to theiput e C s s D N out e i s N / e s e i s N / C s e e i C s

20 C145C /18C otes, M. odwell, copyrihted 007 Circuit Noise Aalysis: ource Traspositio Method e e N *1/ 1+ C s N *C s / e e N *1/ 1+ C s N *C s / N *[1/ 1+ C s +1/ C s e ] = N *[1/ + C s + e / ]

21 C145C /18C otes, M. odwell, copyrihted 007 Circuit Noise Aalysis: ource Traspositio Method fc 4kT 1 s e ; oise iput This was certaily ot a easy calculatio, but because it was thesile hardest calculatio to ake. is far fro the iput, The chael oise curret eerator is i parallel with that of iput ; chael_ oise 4kT 1 fc s e so,

22 C145C /18C otes, M. odwell, copyrihted 007 Circuit Noise Aalysis: ource Traspositio Method e N,e C s s Nd D N out e i N, s this particularly easy 4kT iput ; exaple, iput ; eerator we ca also see that 4kT e so iput hece F 1 ; aplifier iput iput ; aplifier ; eerator 4kT 1 4kT e 1 e 4kT 1 4kT 4kT fc 1 s fc s e e

23 C145C /18C otes, M. odwell, copyrihted 007 put Noise oltae / put Noise Curret Model Z e i out Z e e e jx e N,e C s s Nd D N out i N, s e We frequetly wish tospecify oise of a device or circuit with the eerator ipedace ukow ad uspecified The represetatio allows this.

24 - Model: ource Traspositio Aai C145C /18C otes, M. odwell, copyrihted 007 Oce aai, " walk" sources toiput - -but ot ito theeerator illustratio of load resistor oise oly. C s s D N out i s N / s i s N / C s i C s

25 - Model: ource Traspositio Aai C145C /18C otes, M. odwell, copyrihted 007 i N / C s i N *1/ 1+ C s N *C s / N *C s / i The output oise is represeted N / N *C s / at i by a cobiatio of voltae source ad a curret source. a i N / N * C s / N *C s / As they are both related 1:1 to N, they are 100% correlated.

26 - Model: With All ources C145C /18C otes, M. odwell, copyrihted 007 i N + Nd *1/ 1+ C s + N Becuase, total, total N N C 1 C C / C / s s d d s N + Nd *C s / s N Ad Becuase N 4kT N 4kT / Nd 4kT, total, total, total, total 4kT 4kT 4kT 4kT 1 4kT 1 4, kt total, total Notei particular the cross spectral desity. fc s 1 / fc s 1 C C s 4kT s *

27 Usi the - Model C145C /18C otes, M. odwell, copyrihted 007 N,e e jx e e i N N N,e e jx e e i N + N Z e ive a circuit withspecified, total, total ad ive a specified eerator ipedace Z, e, total, total e, ad jx e, total, total, o, total, aplifier, total, aplifier N Z Z Z e e Z * e jx e

28 Usi the - Model--Coclusio C145C /18C otes, M. odwell, copyrihted 007 f we use the circuit relatioship e,, Z total aplifier Z e ad the device relatioships, total, total, total, total 4kT 4kT 4kT 4kT 1 4kT 1 * 4 1, kt, j fcs j fc total total s The by varyiz calculus, we ca fid the device iiu oise fiure ad the optiusource ipedace which provides this, i.e. we ca calculate the Fukui FT oise fiure expressio. fc s Z * e 1 / jx fc e s 4kT