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EECS 142Lecture 12: Noise in Communication SystemsProf. Ali M. NiknejadUniversity of California, BerkeleyCopyrightA. M. Niknejadc2005 by Ali M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 1/31– p.

Degradation of Link QualityAs we have seen, noise is an ever present part of allsystems. Any receiver must contend with noise.In analog systems, noise deteriorates the quality of thereceived signal, e.g. the appearance of “snow” on theTV screen, or “static” sounds during an audiotransmission.In digital communication systems, noise degrades thethroughput because it requires retransmission of datapackets or extra coding to recover the data in thepresence of errors.A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 2/31– p.

BER PlotBit Error Rate10. 10.010.0010.000101020304050SNR (dB)It’s typical to plot the Bit-Error-Rate (BER) in a digitalcommunication system.This shows the average rate of errors for a givensignal-to-noise-ratio (SNR)A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 3/31– p.

SNRIn general, then, we strive to maximize the signal tonoise ratio in a communication system. If we receive asignal with average power Psig , and the average noisepower level is Pnoise , then the SN R is simplySSN R NPsigSN R(dB) 10 · logPnoiseWe distinguish between random noise and “noise” dueto interferers or distortion generated by the amplifierA. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 4/31– p.

Spurious Free Dynamic RangeS(ω)fundSF DRspurSN RdistortionωThe spurious free dynamic range SF DR measures theavailable dynamic range of a signal at a particular pointin a system. For instance, in an amplifier the largestsignal determines the distortion “noise” floor and thenoise properties of the amplifier determine the “noisefloor”A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 5/31– p.

Noise FigureThe Noise Figure (N F ) of an amplifier is a block (e.g.an amplifier) is a measure of the degradation of theSN RSN RiF SN RoN F 10 · log(F ) (dB)The noise figure is measured (or calculated) byspecifying a standard input noise level through thesource resistance Rs and the temperatureFor RF communication systems, this is usually specifiedas Rs 50Ω and T 293 K .A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 6/31– p.

Noise Figure of an AmplifierSuppose an amplifier has a gain G and apply thedefinition of N FPsigSN Ri NsGPsigSN Ro GNs Namp,oThe term Namp,o is the total output noise due to theamplifier in absence of any input noise.SN Ro A. M. NiknejadPsigNs University of California, BerkeleyNamp,oGEECS 142 Lecture 12 p. 7/31– p.

Input Referred Noise (I)Let Namp,i denote the total input referred noise of theamplifierPsigSN Ro Ns Namp,iThe noise figure is thereforePsigր Ns Namp,iSN Ri F SN RoNsPsigրNamp,iF 1 1NsAll amplifiers have a noise figure 1. Any real systemdegrades the SN R since all circuit blocks add additionalnoise.A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 8/31– p.

Input Referred Noise (II)Pin Ns GNamp,iThe amount of noise added by the amplifier isnormalized to the incoming noise Ns in the calculationof F . For RF systems, this is the noise of a 50Ω sourceat 293 K.Since any amplification degrades the SN R, why do anyamplification at all? Because often the incoming signalis too weak to be detected without amplification.A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 9/31– p.

Noise Figure of Cascaded BlocksPin NsG1F1G2F2G1 G2FIf two blocks are cascaded, we would like to derive thenoise figure of the total system.Assume the blocks are impedance matched properly toresult in a gain G G1 G2 . For each amplifier incascade, we haveNamp,iFi 1 NsA. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 10/31–p

Total Input Noise for CascadeBy definition, the noise added by each amplifier to theinput is given byNamp,i Ns (F 1)where Ns represents some standard input noise. If wenow input refer all the noise in the system we have′Namp,iNs (F2 1) Ns (F1 1) G1Which gives us the total noise figure of the amplifierF 1 A. M. Niknejad′Namp,iNsF2 1F2 1 1 (F1 1) F1 G1G1University of California, BerkeleyEECS 142 Lecture 12 p. 11/31–p

General Cascade FormulaApply the formula to the last two blocksF23F3 1 F2 G2F23 1F F1 G1F2 1 F3 1 F1 G1G1 G2The general equation is written by inspectionF2 1 F3 1F4 1 F1 ···G1G1 G2G1 G2 G3A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 12/31–p

Cascade Formula InterpretationLNARest ofFront-EndWe see that in a cascade, the noise contribution ofeach successive stage is smaller and smaller.The noise of the first stage is the most important. Thus,every communication system employs a low noiseamplifier (LNA) at the front to relax the noiserequirementsA typical LNA might have a G 20 dB of gain and anoise figure N F 1.5 dB. The noise figure depends onthe application.A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 13/31–p

NF Cascade ExampleLOVGALNAG1F1G2F2G3F3The LNA has G 15 dB and N F 1.5 dB. The mixerhas a conversion gain of G 10 dB and N F 10 dB.The IF amplifier has G 70 dB and N F 20 dB.Even though the blocks operate at different frequencies,we can still apply the cascade formula if the blocks areimpedance matchedA. M. Niknejad10 1 100 1F 1.413 2.4 dB6060 · 10University of California, BerkeleyEECS 142 Lecture 12 p. 14/31–p

Minimum Detectable SignalSay a system requires an SN R of 10 dB for properdetection with a minimum voltage amplitude of 1mV. If afront-end with sufficient gain has N F 10 dB, let’scompute the minimum input power that can supportcommunication:PminSN RiSN Ro Ns 10FForPin 10 · F · Ns 10 · F · kT Bwe see that the answer depends on the bandwidth B .Pin 10 dB N F 174 dBm 10 · log BA. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 15/31–p

Minimum Signal (cont)For wireless data, B 10MHz:Pin 10 dB 10 dB 174 dB 70 dB 84 dBmWe see that the noise figure has a dB for dB impact onthe minimum detectable input signal. Since the receivedpower drops 20 dB per decade of distance, a fewdB improved NF may dramatically improve thecoverage area of a communication link.Otherwise the transmitter has to boost the TX power,which requires excess power consumption due to theefficiency η of the transmitter.A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 16/31–p

Equivalent Noise Generatorsvn2NoisyTwo-Porti2nNoiselessTwo-PortAny noisy two port can be replaced with a noiselesstwo-port and equivalent input noise sourcesIn general, these noise sources are correlated. For nowlet’s neglect the correlation.A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 17/31–p

Equivalent Noise Generators (cont)observeoutputnoisevn2i2nA. M. NiknejadNoiselessTwo-Portnoiseonlyf (vn2 )open inputNoisyTwo-Portequate noiseshort inputThe equivalent sources are found by opening andshorting the 2i2nUniversity of California, BerkeleyNoiselessTwo-Portnoiseonlyf (i2n )EECS 142 Lecture 12 p. 18/31–p

Example: BJT Noise Sourcesvr2bCµrbi2brπCπ vπgm vπroi2cIf we leave the base of a BJT open, then the total outputnoise is given byi2o i2c β 2 i2b i2n β 2or2ii2n c2 i2b i2bβA. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 19/31–p

BJT (cont)If we short the input of the BJT, we have2 2i2o gmvn ZπZπ r b 22vn β2(Zπ rb )22vrb2 β2ic(Zπ rb )2Solving for the equivalent BJT noise voltage2 (Z r )2iπbc22vn vrb β22Z 2ivn2 vr2b c 2πβA. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 20/31–p

BJT Generators at Low Freqat low frequencies.2ivn2 vr2b 2cgmvn22qIC B 4kT Brb 2gmi2nA. M. Niknejad2qIc βUniversity of California, BerkeleyEECS 142 Lecture 12 p. 21/31–p

Role of Source ResistanceRsVsvn2i2nNoiselessTwo-PortIf Rs 0, only the voltage noise vn2 is important.Likewise, if Rs , only the current noise i2n isimportant.Amplifier Selection: If Rs is large, then select an ampwith low i2i (MOS). If Rs is low, pick an amp with low vn2(BJT)For a given Rs , there is an optimal vn2 /i2n ratio.Alternatively, for a given amp, there is an optimal RsA. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 22/31–p

Equivalent Input Noise Voltagevn2RsVsNoiselessTwo-Porti2nLet’s find the total output noise voltagevo2 (vn2 A2v2 A2 ) vRvs A. M. Niknejad(vn2 RinRin Rs i2n Rs22 ) vRs 2 RinRin RsRinRin RsUniversity of California, Berkeley 2 2Rs2 i2n A2vA2vEECS 142 Lecture 12 p. 23/31–p

Noise FigureRsVs2veqNoiselessTwo-PortWe see that all the noise can be represented by asingle equivalent source2 v 2 i2 R2veqnn sApplying the definition of noise figure2veqNamp,i 1 F 1 Nsvs2A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 24/31–p

Optimal Source ImpedanceLet vn2 4kT Rn B and i2n 4kT Gn B . ThenRnRn G n Rs 1 G n Rs F 1 RsRsLet’s find the optimum RsRndF Gn 2 0dRsRsWe see that the noise figure is minimized forsrRnvn2 Ropt Gni2nA. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 25/31–p

Optimal Source Impedance (cont)The major assumption we made was that vn2 and i2n arenot correlated. The resulting minimum noise figure isthusRnFmin 1 Gn Rs RsrrRnGn Rn 1 GnGnRnp 1 2 Rn G nA. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 26/31–p

FminConsider the difference between F and FminF FminpRn 2 Rn G n G n Rs RsRnGn Rs2Rs pRn G n (1 2RsRnRn! 2Rn2RsRs 1 RsRoptRoptRn Rs 1 Rs Ropt2 Rn Rs Gopt Gs 2A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 27/31–p

Noise Sensitivity ParameterSometimes Rn is called the noise sensitivity parametersinceF Fmin Rn Rs Gopt Gs 2This is clear since the rate of deviation from optimalnoise figure is determined by Rn . If a two-port has asmall value of Rn , then we can be sloppy and sacrificethe noise match for gain. If Rn is large, though, we haveto pay careful attention to the noise match.Most software packages (Spectre, ADS) will plot Yoptand Fmin as a function of frequency, allowing thedesigner to choose the right match for a given biaspoint.A. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 28/31–p

BJT Noise FigureWe found the equivalent noise generators for a BJT22qIC Bic22vn vrb 2 4kT Brb 2gmgmi2n i2bThe noise figure isF 1 4kT rb 2qIC2gm4kT Rs2qIC Rs2rb1gm Rs 1 β4kT RsRs 2gm Rs2βAccording to the above expression, we can choose anoptimal value of gm Rs to minimize the noise. But thesecond term rb /Rs is fixed for a given transistordimensionA. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 29/31–p

ErcA. M. NiknejadBrbscalable lengthemitterCbasecollectorBJT Cross SectionThe device can be scaledto lower the net currentdensity in order to delaythe onset of the Kirk EffectThe base resistance alsodrops when the device ismade largerUniversity of California, BerkeleyEECS 142 Lecture 12 p. 30/31–p

BJT Device SizingWe can thus see that BJT transistor sizing involves acompromise:The transconductance depends only on IC and notthe size (first order)The charge storage effects and fT only depend onthe base transit time, a fixed vertical dimension.A smaller device has smaller junction area but canonly handle a given current density before Kirk effectreduces performanceA larger device has smaller base resistance rb butlarger junction capacitanceA. M. NiknejadUniversity of California, BerkeleyEECS 142 Lecture 12 p. 31/31–p

Cascade Formula Interpretation Rest of LNA Front-End We see that in a cascade, the noise contribution of each successive stage is smaller and smaller. The noise of the ﬁrst stage is the most important. Thus, every communication system employs a low noise ampliﬁer (LNA) at t