Lecture05_Electronic_Noise_6up

EECS240 – Spring 2010 Lecture 5: Electronic Noise Elad Alon Dept. of EECS EECS240 Lecture 5 2 Electronic Noise • Why is noise important? • Sets minimum signals we can deal with – often sets lower limit on power • Signal-to-noise ratio • Signal Power Psig ~ (VDD)2 • Noise Power Pnoise ~ kBT/C • SNR = Psig / Pnoise • Technology Scaling • VDD goes down Æ lower signal • Increase C to compensate Æ increases power EECS240 Lecture 5 3 Types of “Noise” • Interference • Not “fundamental” – deterministic • Signal coupling • Capacitive, inductive, subtrate, etc. • Supply noise • Device noise • Caused by discreteness of charge • “fundamental” – thermal noise • “manufacturing process related” – flicker noise EECS240 Lecture 5 4 Noise in Amplifiers • All amplifiers generate noise • Comes from carrier random thermal motion and discreteness of charge • Noise is random • Has to be treated statistically – can’t predict actual value • Deal with mean (average), variance, spectrum EECS240 Lecture 5 5 Thermal Noise of a Resistor • Origin: Brownian Motion • Thermally agitated particles • E.g. ink in water, electrons in a conductor • Available noise power: • Noise power in bandwidth ∆f delivered to a matched load • Example: ∆f = 1Hz Æ PN = 4 x 10-21W = -174 dBm • Reference: J.B. Johnson, “Thermal Agitation of Electricity in conductors,” Phys. Rev., pp. 97-109, July 1928. N BP k T f= ∆ EECS240 Lecture 5 6 Resistor Noise Model 2 4 n N B vP k T f R = ∆ = 2 4n Bv k TR f= ∆ Mean square noise voltage: EECS240 Lecture 5 7 Thermal Noise • Present in all dissipative elements • I.e., resistors • Independent of DC current flow • Random fluctuations of v(t) or i(t) • Mean is 0 • Distribution (pdf) is Gaussian • Power spectral density is “white” • Up to ~THz frequencies • kBT = 4 x 10-21 J (T = 290K = 16.9oC) • Example: R = 1kΩ Æ 4nV/rt-Hz 1MHz bandwidth Æ σ = 4uV 2 2 44 Bn B n k TBv k TRB i R = = EECS240 Lecture 5 8 Thermal Noise in Capacitors? EECS240 Lecture 5 9 Noise Calculations • Noise calculations • Instantaneous voltages add • Power spectral densities add • RMS voltages do NOT add • Example: R1+R2 in series EECS240 Lecture 5 10 Calculating Noise in Passive Networks • Capacitors and inductors only shape spectrum: ( ) ( )∑ = = x xjfsxTon fvsHfv 22 2 2 , )( π EECS240 Lecture 5 11 Noise in Diodes • Shot noise • Zero mean, Gaussian pdf, white • Proportional to current • Independent of temperature • Example: ID = 1mA Æ 17.9pA/rt-Hz 1MHz bandwidth Æ σ = 17.9nA • Shot noise versus thermal noise • gdiode = Id/(kbT/q) • Thermal noise density: 4kbTgdiode = 4qId • Shot noise half of this (current flow in 1 direction) fqIi Dn ∆= 2 2 EECS240 Lecture 5 12 BJT Noise fqIi f fIKfqIi fTrkv Cc BBb bBb ∆= ∆ +∆= ∆= 2 2 4 2 1 2 2 α • Just like diodes: shot noise • Collector and base noise partially correlated • Extrinsic resistors contribute noise • Small signal resistors (e.g., ro) don’t • These aren’t physical resistors EECS240 Lecture 5 13 Triode MOSFET Noise • Channel resistance contributes thermal noise • Channel conductance when Vds = 0: • Device is truly a resistor when Vds = 0, so: ( )0ds ox GS thWg C V VLµ= − 2 04d dsi kTg f= ∆ EECS240 Lecture 5 14 Saturation Noise • Noise distributed along the channel: • For long channel model, can substitute γgm for gds0 • More correct formulation uses inversion charge in the channel [Tsividis] • This is what SPICE/BSIM use 2 4d mi kT g fγ= ∆ EECS240 Lecture 5 15 Thermal Noise for Short Channels • Strong inversion Æ thermal noise • Drain current: gds0 is what you really care about • gm more convenient for input-referred noise • For low field (long L), γ = 2/3 relates gm to gds • For high field, use α to capture increase in noise • High-field noise can be 2-3 times larger than low field • MOS actually has intrinsic gate induced noise (142/242 topic) • Gate leakage Æ shot noise EECS240 Lecture 5 16 Weak Inversion Noise EECS240 Lecture 5 17 FET Noise Model • Model neglects intrinsic gate noise • BSIM3 does not directly include α EECS240 Lecture 5 18 1/f Noise • Flicker noise • Kf,NMOS = 2.0 x 10-29 AF Kf,PMOS = 3.5 x 10-30 AF • Strongly process dependent • Example: ID = 10µA, L = 1µm, • Cox = 5.3fF/µm2, fhi = 1MHz flo = 1Hz Æ σ = 722pA flo = 1/year Æ σ = 1083pA EECS240 Lecture 5 19 1/f Noise Corner Frequency • Definition (MOS) • Example: • V* = 200mV, γ = 1 NMOS PMOS L = 0.35µm Æ 192kHz 34kHz L = 1.00µm Æ 24kHz 4kHz 2 2 14 4 f D f D B r m co ox co ox B r m K I K If k T g f f L C f L C k T g γ γ ∆ = ∆ = 2 * 2 1 1 4 8 m D f g IB r ox f B r ox K k T C L K V k T C L γ γ = = EECS240 Lecture 5 20 Noise Calculations with Actives • Method: 1) Create small-signal model 2) All inputs = 0 (linear superposition) 3) Pick output vo or io 4) For each noise source vx, ix Calculate Hx(s) = vo(s) / vx(s) (… io, ix) 5) Total noise at output is: • Tedious but simple … ( ) ( )∑ = = x xjfsxTon fvsHfv 22 2 2 , )( π ( ) ( )2 ,simpler notation: on T nv f S f= EECS240 Lecture 5 21 SPICE Noise Analysis 100/1 1000/10 50/2