Noise Power, Figure and

March 21, 2014 Sujeong Lee Noise

• Any unwanted input - UNDESIRABLE portion of an electrical signal • Limits systems ability to process weak signals

• 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 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――――o/No (1-1) – 120 Output Power Level (dBm) – 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 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 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 ) 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 “”. 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 = ―――――――――― = ―――――――――― Si/Ni 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. communications.communications. N N+ GN+ GN = a Na + GNi i ―――――― =―――――― NoiseNoise figure figure should should be thoughtbe thought of as of separateas separate from from gain. gain. Once Once GN GNi GN i (1-2) (1-2) Noise noiseFigurenoise is added is added to the to thesignal, signal, subsequent subsequent gain gain amplifies amplifies signal signal and andnoise noise together together and and does does not notchange change the thesignal-to-noise signal-to-noise ratio. available at the input to the device under test (DUT), So and No ratio.ratio. available at the input to the device under test (DUT), So and No representrepresent the thesignal signal and and noise noise levels levels available available at theat the output, output, Figure 1-2(a) shows an example situation at the input of an FigureFigure 1-2(a) shows an example situation at the input of an Na isN the is thenoise noise added added by theby the DUT, DUT, and and G is G the is the gain gain of theof the amplifier. The depicted signal is 40 dB above the noise floor: a amplifier. The depicted signal is 40 dB above the noise floor: DUT.DUT. Equation Equation (1-2) (1-2) shows shows the the dependence dependence on onnoise noise at theat the Figure 1-2(b) shows the situation at the amplifier output. FigureFigure 1-2(b) shows the situation at the amplifier output. inputinput Ni. TheN . The input input noise noise level level is usually is usually thermal thermal noise noise from from the the • Noise Figure The amplifier’s gain has boosted the signal by 20 dB. It also ii The amplifier’s gain has boosted the signal by 20 dB. It also sourcesource and and is referred is referred to byto kTbyo kTB. FriisB. Friis [8] [8]suggested suggested a refer- a refer- boosted the input noise level by 20 dB and then added its own o boosted the input noise level by 20 dB and then added its own enceence source source temperature temperature of 290Kof 290K (denoted (denoted by Tbyo ),T which ), which is is noise. The output signal is now only 30 dB above the noise equivalent to 16.8 °C and 62.3 °F. This temperatureo is close to noise. The output signal is now only 30 dB above the noise equivalent to 16.8 °C and 62.3 °F. This temperature is close to floor. Since the degradation in signal-to-noise ratio is 10 dB, the average temperature seen by receiving antennas directed floor.floor. SinceSince thethe degradationdegradation inin signal-to-noisesignal-to-noise ratioratio is 10 dB, the average temperature seen by receiving antennas directed the amplifier• Noise has a 10 dB noise figure figure. representsacross the the atmosphere at the transmitting antenna. thethe amplifieramplifier hashas aa 1010 dBdB noisenoise figure.figure. across the atmosphere at the transmitting antenna. degradation in signal/noise 6 ratio as the signal passes6 through a device.

output

input

• F is always greater than 1.

Noise Figure

Noise Factor • Noise Figure

Modern usage of “noise figure” usually is reserved for the quantity NF, expressed in dB units:

NF = 10 log F [dB] 10 NF = (Si/Ni)dB – (So/No)dB

S /N o o (Si/Ni)dB = 40 dB Si /Ni (So/No)dB = = 30 dB

Noise Figure = 10 dB

Noise Temperature

• Comes from the random motion of electrons ! Thermal Noise • Convenient! Common basis for measuring random electrical noise from any source

• Relation with Noise Figure

Te = To ( F – 1 )

Te : The effective noise temperature of device T0 : a reference temperature 290K (room temperature) Summary

• Noise Power – The magnitude of Noise Np = kBT B

• Noise Figure – Noise Factor

– Noise Figure : the degradation of SNR

NF = 10 log10 F [dB] • Noise Temperature – Basic tool of measuring any kind of noise

– Relation with Noise Factor Te = To ( F – 1 )