Noise Power, Noise Figure and Noise Temperature March 21, 2014 Sujeong Lee Noise • Any unwanted input - UNDESIRABLE portion of an electrical signal • Limits systems ability to process weak signals Noise Power • Most of input noise = Thermal Noise • Noise power N = k T B p B -23 J/K kB = Boltzmanns constant 1.38x10 T = Absolute temperature of device B = Circuit bandwidth Noise Power • Signal to Noise Ratio (SNR) S( f ) average − signal − power SNR = = N( f ) average − noise − power The concept of noise figure TheThe concept concept of noiseof noise figure figure – 40 – 40 The most basic definition of noise figure came into popular use – 40 – 40 The most basic definition of noise figure came into popular use – 40 – 40 inThe the most 1940’s basic when definition Harold of Friis noise [8] figuredefined came the noiseinto popular figure Fuse of – 60 – 60 in the 1940’s when Harold Friis [8] defined the noise figure F of – 60 – 60 ain network the 1940’s to bewhen the Haroldratio of Friis the signal-to-noise[8] defined the noisepower figure ratio atF of – 60 – 60 a network to be the ratio of the signal-to-noise power ratio at thea network input to to the be signal-to-noisethe ratio of the powersignal-to-noise ratio at the power output. ratio at – 80 – 80 the input to the signal-to-noise power ratio at the output. – 80 – 80 the input to the signal-to-noise power ratio at the output. – 80 – 80 – 100 – 100 Si/Ni – 100 – 100 FS =/N Input Power Level (dBm) – 100 – 100 i S――――i/N Output Power Level (dBm) F = i i Input Power Level (dBm) ―――― Output Power Level (dBm) F = Input Power Level (dBm) S――――/N Output Power Level (dBm) o o (1-1) – 120 – 120 S o/NS o/N (1-1) – 120 2.6 2.65 2.7 – 120 2.6 2.65 2.7 o o (1-1) –2.6 120 2.65 2.7 –2.6 120 2.65 2.7 2.6 Frequency 2.65 (GHz) 2.7 2.6 Frequency 2.65 (GHz) 2.7 Frequency (GHz)(a) Frequency (b)(GHz) Thus the noise figure of a network is the decrease or degrada- Frequency(a) (GHz) Frequency(b) (GHz) ThusThus the noisethe noise figure figure of a ofnetwork a network is the is thedecrease decrease or degrada- or degrada- (a) (b) tiontion in the in thesignal-to-noise signal-to-noise ratio ratio as theas thesignal signal goes goes through through the the network.tion in the A signal-to-noiseperfect amplifier ratio would as the amplify signal the goes noise through at its in-the network. A perfect amplifier would amplify the noise at its in- Figure 1-2. Typical signal and noise levels vs. frequency (a) at an amplifier’s putnetwork. along Awith perfect the signal,amplifier maintaining would amplify the same the noise signal-to-noise at its in- Figure 1-2. Typical signal and noise levels vs. frequency (a) at an amplifier’s put along with the signal, maintaining the same signal-to-noise inputFigure and 1-2. (b) Typical at its signaloutput. and Note noise that levels the noise vs. frequency level rises (a) more at an than amplifier’s the put along with the signal, maintaining the same signal-to-noise input and (b) at its output. Note that the noise level rises more than the ratio at its input and output (the source of input noise is often input and (b) at its output. Note that the noise level rises more than the ratio at its input and output (the source of input noise is often signalsignal level level due dueto added to added noise noise from from amplifier amplifier circuits. circuits. This This relative relative rise risein in ratio at its input and output (the source of input noise is often signal level due to added noise from amplifier circuits. This relative rise in thermalthermal noise noise associated associated with with the theearth’s earth’s surface surface temperature temperature noisenoise level level is expressed is expressed by the by amplifierthe amplifier noise noise figure. figure. orthermal with losses noise associatedin the system). with A the realistic earth’s amplifier, surface temperaturehowever, noise level is expressed by the amplifier noise figure. or withor with losses losses in the in thesystem). system). A realistic A realistic amplifier, amplifier, however, however, alsoalso adds adds some some extra extra noise noise from from its ownits own components components and and degradesalso adds thesome signal-to-noise extra noise from ratio. its A own low noisecomponents figure meansand degradesdegrades the signal-to-noisethe signal-to-noise ratio. ratio. A low A lownoise noise figure figure means means thatthat very very little little noise noise is added is added by the by thenetwork. network. The The concept concept of of Note that if the input signal level were 5 dB lower (35 dB that very little noise is added by the network. The concept of NoteNote that that if the if theinput input signal signal level level were were 5 dB 5 dBlower lower (35 (35 dB dB noisenoise figure figure only only fits fitsnetworks networks (with (with at least at least one one input input and and one one above the noise floor) it would also be 5 dB lower at the out- noise figure only fits networks (with at least one input and one aboveabove the thenoise noise floor) floor) it would it would also also be 5be dB 5 dBlower lower at theat the out- out- outputoutput port) port) that that process process signals. signals. This This note note is mainly is mainly about about put (25 dB above the noise floor), and the noise figure would output port) that process signals. This note is mainly about put put(25 (25dB dBabove above the thenoise noise floor), floor), and and the the noise noise figure figure would would two-porttwo-port networks; networks; although although mixers mixers are arein general in general three-port three-port still be 10 dB. Thus noise figure is independent of the input two-port networks; although mixers are in general three-port stillstill be 10be dB.10 dB.Thus Thus noise noise figure figure is independent is independent of theof the input input devices, they are usually treated the same as a two-port device signal level. devices,devices, they they are usuallyare usually treated treated the thesame same as a as two-port a two-port device device signal level. with the local oscillator connected to the third port. signal level. withwith the localthe local oscillator oscillator connected connected to the to thethird third port. port. A more subtle effect will now be described. The degradation in A moreA more subtle subtle effect effect will will now now be described.be described. The The degradation degradation in in It mightIt might be worthwhile be worthwhile to mention to mention what what noise noise figure figure does does not not a network’s signal-to-noise ratio is dependent on the tem- It might be worthwhile to mention what noise figure does not a network’sa network’s signal-to-noise signal-to-noise ratio ratio is dependent is dependent on onthe the tem- tem- characterize.characterize. Noise Noise figure figure is not is nota quality a quality factor factor of networks of networks perature of the source that excites the network. This can be characterize. Noise figure is not a quality factor of networks peratureperature of the of thesource source that that excites excites the the network. network. This This can can be be withwith one oneport; port; it is itnot is nota quality a quality factor factor of terminations of terminations or of or of proven with a calculation of the noise figure F, where S and N with one port; it is not a quality factor of terminations or of provenproven with with a calculation a calculation of the of the noise noise figure figure F, where F, where Si andSi and Ni Ni oscillators.oscillators. Oscillators Oscillators have have their their own own quality quality factors factors like like represent the signal and noise levels i i oscillators. Oscillators have their own quality factors like representrepresent the thesignal signal and and noise noise levels levels “carrier-to-noise“carrier-to-noise“carrier-to-noise ratio” ratio” and and “phase “phase noise”. noise”. But But receiver receiver noise noise generatedgenerated in the in thesidebands sidebands of the of thelocal local oscillator oscillator driving driving the the S /N S /N mixer,mixer, can canget getadded added by the by themixer. mixer. Such Such added added noise noise increases increases F = i Si/Ni i mixer, can get added by the mixer. Such added noise increases F ――――= ―――― the thenoise noise figure figure of the of thereceiver. receiver. S /NS /N the noise figure of the receiver. o So/No o NoiseNoise figure figure has hasnothing nothing to do to withdo with modulation modulation or demodula- or demodula- tion.tion. It is It independent is independent of the of themodulation modulation format format and and of the of the Si /N Si/Ni i tion. It is independent of the modulation format and of the = ―――――――――― =――――――――――i i fidelityfidelityfidelity of modulators ofof modulatorsmodulators and and anddemodulators. demodulators.demodulators. Noise NoiseNoise figure figurefigure is, is, =―――――――――― GS GSi/(Ni/(Na +a GN+ GNi) i) therefore,therefore,therefore, a more aa moremore general generalgeneral concept conceptconcept than thanthan noise-quieting noise-quietingnoise-quieting used used to to i a i indicateindicateindicate the thesensitivitythe sensitivitysensitivity of FM ofof FMFMreceivers receiversreceivers or BER oror BERBER used usedused in digital inin digitaldigital communications.