ECEN474/704: (Analog) VLSI Circuit Design Spring 2016

Transcription

1 ECEN474/704: (Analo) LSI Circuit Desin Sprin 016 Lecture 11: Noise Sam Palermo Analo & Mixed-Sinal Center Texas A&M Uniersity

2 Announcements HW3 is due today HW4 is due Mar 30 Exam is on Apr 4 9:10-10:35PM (10 extra minutes) Closed book w/ one standard note sheet 8.5 x11 ront & back Brin your calculator Coers material throuh lecture 11 Preious years exam s are posted on the website or reerence

3 Aenda & Reerences Noise Types Noise Properties Resistor Noise Model Diode Noise Model MOSFET Noise Filtered Noise OTA Noise Example Readin Razai Chapter 7 3

4 Noise Siniicance Why is noise important? Sets minimum sinal leel or a ien perormance parameter Directly trades with power dissipation and bandwidth Reduced supply oltaes in modern technoloies derades noise perormance Sinal Power dd SNR P si / P Noise is oten proportional to kt/c noise dd noise Increasin capacitance to improe noise perormance has a cost in increase power consumption or a ien bandwidth 4

5 Intererence Noise Intererence Man-Made Noise Deterministic sinal, i.e. not truly random Could potentially be modeled and predicted, but practically this may be hard to do Examples Power supply noise Electromanetic intererence (EMI) Substrate couplin Solutions Fully dierential circuits Layout techniques Not the ocus o this lecture Unless the deterministic noise is approximated as a random process 5

6 Inherent Noise Electronic or Deice Noise Random sinal Fundamental property o the circuits Examples Thermal noise caused by thermally-excited random motion o carriers Flicker (1/) noise caused by material deects Shot noise caused by pulses o current rom indiidual carriers in semiconductor junctions Solutions Proper circuit topoloy More power!!! Is the ocus o this lecture 6

7 Noise Properties Noise is random [Johns] Instantaneous noise alue is unpredictable and the noise must be treated statistically Can only predict the aerae noise power Model with a Gaussian amplitude distribution Important properties: mean (aerae), ariance, power spectral density (noise requency spectrum) 7

8 RMS alue I we assume that the noise has zero mean (enerally alid) RMS or sima alue is the square-root o the noise ariance oer a suitable aerain time interal, T n 1 T T 0 rms n t Indicates the normalized noise power, i.e. i n (t) is applied to a 1 resistor the aerae power would be P n 1 n rms dt n rms 1 8

9 Sinal-to-Noise Ratio (SNR) SNR sinal power 10lo noise power For a sinal with normalized power o x SNR 10lo n rms rms 0lo x n rms rms x rms Quantiied in units o db 9

10 Thermal Noise Spectrum The power spectral density (PSD) quantiies how much power a sinal carries at a ien requency Thermal noise has a uniorm or white PSD The total aerae noise power P n in a particular requency band is ound by interatin the PSD P n 1 PSD d For white noise spectrum : P n n n

11 Thermal Noise o a Resistor The noise PSD o a resistor is where k is the Boltzmann PSD n 4kT 0 constant and T is the absolute temperature (K) The total aerae power o a resistor in a ien requency band is P n kt ktd 4kT Example: =1Hz P n =4x10-1 W=-174dBm 11

12 Resistor Noise Model An equialent oltae or current enerator can model the resistor thermal noise 4kT R n Rn Pn R 4kTR I Rn P R [Johns] Recall the PSD is white (uniorm w/ requency) 1

13 Noise Summation no no no t t t 1 T T rms n1 t n t 0 n1 n T rms n 1rms nrms n 1 t n t T 0 dt dt Same procedure applies to noise current summin at a node 13

14 Correlation Last term describes the correlation between the two sinals, deined by the correlation coeicient, C no C 1 T T 0 n1 n1 t n t rms nrms C rms n1rms nrms n1rms nrms dt Correlation always satisies -1 C 1 C=+1, ully-correlated in-phase (0) C=-1, ully-correlated out-o-phase (180) C=0, uncorrelated (90) 14

15 Uncorrelated Sinals For two uncorrelated sinals, the meansquared sum is ien by no rms n1rms nrms Add as thouh they were ectors at riht anles For two ully correlated sinals, the meansquared sum is ien by no rms n1rms nrms Sin is determined by phase relationship RMS alues add linearly (alined ectors) 15

16 Noise Example #1: Two Series Resistors n C rms n1rms nrms n1rms n rms The noise o the two resistors is uncorrelated or statistically independent, so C=0 n rms n 1rms nrms 4kTR1 R Always add independent noise sources usin mean squared alues Neer add RMS alues o independent sources 16

17 TAMU-ELEN Jose Sila-Martinez Noise Example #: oltae Diider Lets compute the output oltae: Apply superposition (noise sources are small sinals, you can use small sinal models)! + in - n1 R 1 R n 0 R R1 R R R1 R R1 R1 R 0 in n1 n Aboe is what you do or deterministic sinals, but we cannot do this or the resistor noise But noise is a random ariable, power noise density has to be used rather than oltae; then the output reerred noise density (noise in a bandwidth o 1 Hz) becomes 0n 0n R R1 R R R1 R n1 4kTR1 R1 R1 R R1 R1 R n -17-4kTR on, T General Case : H s x x s j x

18 Diode Noise Model Shot noise in diodes is caused by pulses o current rom indiidual carriers in semiconductor junctions White spectral density [Johns] Where q=1.6x10-19 C and I D is the diode DC current 18

19 TAMU-ELEN Jose Sila-Martinez Thermal Noise => Spectral Density o the thermal noise drain current (CMOS transistor linear reion) B S G D i d N+ P+ P+ substrate N Channel Resistor i n1 =4kT/R1 R 1 R DS C i ox Transistor d W L 4kT R 1 GS DS T DS -19-

20 TAMU-ELEN Jose Sila-Martinez White Noise i Triode reion 4kT R DS i d 4kTC ox W L GS T DS Low current noise => W/L => m or o i d 8 Saturation kt m o i d 1 R DS 3 8kT 3 m C ox W L GS T -0-

21 MOSFET 1/ (Flicker) Noise Caused by traps near Si/SiO interace that randomly capture and release carriers i d K F WLC m ox K F is stronly dependent on the technoloy 1

22 1/ Noise Corner Frequency This is the requency at which the licker noise density equals the thermal noise density K F WLC ox m co 4kT m co K F 4kTC ox m WL K F 4kTC ox 1 L I m D I D W For a ien m /I D (which sets I D /W), the only way to reduce co is to use loner channel deices

23 TAMU-ELEN Jose Sila-Martinez Output and input reerred noise Current noise is the real one oltae noise representation is an artiact to acilitate system analysis Thermal Noise i d d i seq m m 8 3 s s kt m eq i d Flicker Noise Reerred to the input -3- eq i eq d K F WLC K F WLC K C F ox ox m ox m 1 WL 1 m 1

24 TAMU-ELEN Jose Sila-Martinez Equialent input reerred oltae noise eq eq i dth i m d Equialent input reerred noise oltae means that all current noise sources are accounted as drain current and represented by an equialent noise oltae at transistor ate eq eqtotal 8 3 kt m K C F ox 1 WL RMS BW 1 eq ( ) d -4-

25 TAMU-ELEN Jose Sila-Martinez NOISE COMPONENTS (alues proided are or a 0.8 m technoloy) K C F OX i d eq M1 9.8x10 0.5x eq eq / m Hz(NMOS) / m Hz(PMOS) Noise density ( /Hz) Spice model th 1/ 8 kt d 3 m K WLC F OX d FOR LOW-FREQUENCY APPLICATIONS, WHEREIN 1/F NOISE IS DOMINANT, PMOS DEICES MUST BE USED. Corner requency n Flicker Thermal -5-

26 Filtered Noise no A j ni Aj ni Noise output spectral density is a unction only o the manitude o the transer unction, and not its phase With multiple uncorrelated noise sources, combined output is also uncorrelated n 1 [Johns] no ni n A j no no i1,,3 i ni n 3 [Johns] 6

27 First-Order RC Circuit Example [Razai] What is the total output noise power? 7

28 First-Order RC Circuit Example [Razai] out out A s s Aj kt tan C out 1 Usin 0 out R R RC 4kTR 1 4 R 1 1 src dx tan x 1 0 C 1 kt C x R C 0 4kTR To calculate Total Noise Power interate oer all requencies kt C 8

29 TAMU-ELEN Jose Sila-Martinez Noise is enerated by R but interated noise is unction o C (??) + in - n R C 0 1 total 0 1 RC 4kTR d kt C To et more insiht, lets hae a closer look on the operations! Thermal noise (lo) 4kTR 1 RC - (lo) Notice that: When R increases thermal noise increases too but the corner requency decreases, leadin to a constant area under the cures! -9-

30 Noise Bandwidth [Razai] The noise bandwidth is equal to the requency span o a brickwall ilter hain the same output noise rms alue 0 B n For a irst - order ilter Bn p alidatin with preious slides deriation : Total Noise Output 0 B n 0 no d 1 4kTR RC kt C 30

31 TAMU-ELEN Jose Sila-Martinez Output reerred noise: Take adantae o SYMMETRIES! M M Output reerred current noise density Superposition: Eery transistor contributes; consider one at the time. X 0.5i d1 0.5i d1 i out Analysis: You can use standard circuit analysis techniques but at the end o the day you hae to consider POWER. M1 i d1 M1 Output noise density: Each noise component represent the RMS alue o random uncorrelated noise! Then add the power noise components IB Noise injected into the common-source node equally splits into the two branches i out1 8 3 kt m1-31-

32 TAMU-ELEN Jose Sila-Martinez Output reerred noise: Take adantae o SYMMETRIES! M M i d i d Output reerred current noise density due to the P- type deices: X I d ~0 i out Let hand side transistor: i out i d 8 3 kt m M1 M1 Riht hand side transistor IB Noise injected into the common-source node equally splits into the two branches i 8 3 out kt m Noise due to the current source is mainly common-mode noise -3-

33 TAMU-ELEN Jose Sila-Martinez Output and input reerred noise M X M i out i out Output reerred current noise density kt 3 kt m1 m i d1 i d Input reerred noise density ( /H Z ) 1 M1 M1 in,eq 8 3 kt m1 8 3 kt m1 m m1 IB In this case, noise due to the current source is mainly common-mode noise Be careul because this is not always the case! -33-

34 TAMU-ELEN Jose Sila-Martinez Interated Input reerred noise Input reerred thermal noise density ( /Hz) M X M i out in,eq 8 3 kt m1 8 3 kt m1 m m1 Input reerred noise leel (olts) i d1 i d 1 M1 M1 IB I should adise you to use: Noise( Noise( RMS Noise( RMS ) BW in,eq d Example: or thermal noise, the noise leel becomes (assumin a sinle-pole system) ) RMS ) 8kT m1 16kT m1 m m1 1 m m1 BW BW 4kT16x10-1 coul. -34-

35 Next Time Three Current Mirror OTA 35