SYSTEM NOISE AND LINK BUDGET - Sonoma State University

SYSTEM NOISE ANDLINK BUDGETUpdates: 9/24/13; 10/6/14

Introduction Any system (wired or wireless) receives and generatesunwanted signals Natural phenomena or man-made (Noise) Unwanted signals from other systems (Interferences) Man-made Noise: due to other subsystems (e.g.; powersupply) Natural Noise: due to random movements and agitation ofelectrons in resistive components (e.g., due totemperature)We focus on system thermal noise!

Thermal Noise Characteristics Thermal noise due to agitation of electrons Except at absolute zero temperature, the electrons inevery conductor (resistor) are always in thermal motion Function of temperature Present in all electronic devices and transmissionmedia Cannot be eliminated Particularly significant for satellite communication The Sun contributes to the thermal noise at the receiverhttp://homes.esat.kuleuven.be/ cuypers/satellite noise.pdf

Spectral Power Density of (white)Noise Amount of thermal noise to be found in abandwidth of 1Hz in any device or conductoris:N 0 kT ( W/Hz) N0 noise power density (in watts) per 1 Hz ofbandwidth k Boltzmann's constant 1.3803 10-23 J/K (or W/(K.Hz)) T temperature, in kelvin (absolute temperature) Note Watt J/sec J.Hz

Thermal Noise Noise Power Noise is assumed to be independent of frequency Thermal noise present in a bandwidth of B Hertz (inwatts):N 0 kT (W/Hz )à N kTBor, in decibel-wattsN 10 log k 10 log T 10 log B

Thermal or White Noise From the plot of the spectral density of thermal noise overfrequency, can see that the noise is flat frequencyspectrum till around 100GHz or so and starts to fall off ataround 1TeraHz

Thermal Noise Model At any temperature, thermal motion of electrons result inthermal noise This is due to difference between the resistor’s terminals The thermal noise source in the resistor delivers apower to the load (watt)N kTB Or in Watt/Hz: We call this noise power density :N 0 kT (W/Hz )Noise randomprocess hasGaussianDistribution withzero mean andsome SD

Modeling the ThermalNoise (Open Circuit – No Load)RVrmsTrue RMSMultimeterEquivalent Thermal Noise Model The noise generated due to temperature T by a resistivecomponent has normalized power spectrum (also calledmean-square voltage spectrum): 2RkT(V 2/Hz) k Boltzmann's constant 1.3803 10-23 J/K T temperature, in kelvin (absolute temperature) Therefore the average power that a voltage or currentsource can deliver (available) is: 2RkT.2B 4RkTB (V 2) The RMS voltage equivalent of the thermal noise will beVrms AveragenoisePower 4kTRB (V )Example A: Calculate the open-circuit Vrms reading when we connect a true RMSvoltmeter to a 100Kohm resistor at room temperature (20 deg. C) with BW 1MHz tomeasure the generated thermal noise. Draw the equivalent circuit.

Noise Power Delivered to the Load The voltage delivered to the load is maximum whenRs RL R Thus, VL(t) Vs(t)/2 à PLoad2VL (t)2 [Vs (t) / 2]2 Vs (t)2 Vrms 2R4R4R Spectral Noise Density at the load will be:kT/2 No/2 (W/Hz)VL(t)RsVs(t)Equivalent Thermal Noise ModelSubsystemRL

Thermal Noise PowerImpact of temperature in generating thermal noise in dB2.15-102.16-10Thermal Noise in dB%MATLAB CODE:T 10:1:1000;k 1.3803*10 -23;B 10 6;No k*T;N k*T*B;N in dB 10*log10(N);semilogy(T,N in dB)title(‘Impact of temperature ingenerating thermal noise in dB’)xlabel(‘Temperature in Kelvin’)ylabel(‘Thermal Noise in 00Temperature in Kelvin7008009001000

Two-Ports Sub-System Noise Characterization A subsystem’s noise behavior can be characterized byseveral parameters:VL(t) Available Gain (G) Noise Bandwidth (B) Noise Figure or Factor (F)RsSubsystemVs(t)Equivalent Thermal Noise ModelInput signal &noiseoutput signal &noiseG, B,FRL

Two-Ports Sub-System Noise Characterization A subsystem’s noise behavior can be characterized byseveral parameters: Available Gain (G)Input signal &noise Noise Bandwidth (B)output signal &noiseG, B,F Noise Figure or Factor (F)No /2Sao & Pao Available Gain: The available output noise spectral density due to input white noisewill be:Sao G N 0 / 2 ( W/Hz) The available output noise power due to input white noise will be:Pao G 2B N 0 / 2 ( W)

System Noise Bandwidth (B)Two-Ports SystemSo ( f ) G( f )Si ( f ) G( f ) Assuming the system isdriven by white noise! So is the availableoutput power spectraldensity (W/Hz) Pao is the availableoutput power (W) G Go is the mid-bandavailable gain (DC gain)No2 No Pao So ( f )df G( f )df 2 Pao G 2B N 0 / 2 ( W)1 B G( f )df 2G The availableoutput noisepower due toinput white noiseOutput PowerSpectrum DensitySo(f)Input PowerSpectrum DensitySi(f)G(f)

Example A (1) Find the BW for a first-order low-pass Butterworth filterwhose gain is given as follow (assume DC gain Go 1):1G( f ) 1 ( f / f3dB )2 (2) Assuming the input of the system above is driven bywhite noise, find the output available power.Output PowerSpectrum DensitySo(f)Input PowerSpectrum DensitySi(f)G(f)f3dB

Remember:Two-Ports Sub-System Noise Characterization A subsystem’s noise behavior can be characterized byseveral parameters:VL(t) Available Gain (G) Noise Bandwidth (B) Noise Figure or Factor (F)Let’s talk aboutthis!RsSubsystemVs(t)Equivalent Thermal Noise ModelInput signal &noiseoutput signal &noiseG, B,FRL

System Noise Figure (F) The most basic definition of noise figure came intopopular use in the 1940’s when Harold Friis defined thenoise figure F of a network to be the ratio of the signal-tonoise power ratio at the input to the signal-to-noise powerratio at the output.F SNRi / SNRoTe 1 -8255E.pdf

System Noise Figure (F) We define the Noise Figure (Noise Factor) as: à We often express F in dB Note that F 1 Nr is the available output noise power due to the two-portsub-system Te is effective (internal) temperature of the subsystem To is output equivalent temperature into the subsystemInput Signal Power PsiInput Noise PowerSpectrum DensitySni kTSubSystemG, B,F, TePsi.GAvailable Noise PowerDue to input thermal noise:kTGBAvailable Noise PowerDue to internal noise:kToGB(F-1) NrF SNRi / SNRo 1 TeToPao(noise) kTGB kToGB(F 1) kGB(T To(F 1))) k(T Te) G BNote: T ToFind the expression forSNRi? SNRi Psi/kToB

Example B Assume the antenna contributes to the input thermal noise of the system byT 10K Find the available input noise spectral density (Sai) Find the available output noise spectral density (Sao) Find the available output noise power (Pao) Find the noise figure for the system (F) Draw the thermal noise circuit model for the antennaAntennaGain 100dBB 150 KHzTe 140 Koutput signal &noise

Cascaded SystemAntenna(G,To,R)Orà (G,T)Unit 1(F1, G1, B1)Unit 2(F2, G2, B2)Unit 3(F3, G3, B3)PaoR is the equivalent antenna resistanceT is effective temperature resulting in noise Cascadedsub- sandnoiseproper7es(B B1 B2 B3 .) G total Go G1.G2.G3 . F total F1 (F2- ‐1)/G1 (F3- ‐1)/(G1.G2) . Te total (F total–1).Toà F total 1 [Te total/To] Notethat:Total Gain

Example CAntenna(G,T)Cascaded SystemReceivedPowerAntennaNoiseMixer(F2, G2, B2)Low Noise Amp(F1, G1, B1)RX Model(F total, G total, Te, B)ToIFAmpPndPsdPnd Pao T ant 20K ForLNA:G1 10dB,F1 3dB ForMixer:G2 9dB,F2 6.5dB FindG total,F total,Te,NoisePower,Pnd SimplifiedModel: G total G1.G2 F total F1 (F2- ‐1)/G1 Te (F total–1).ToSee notes!

ExampleDWirelessTransmi erDigitalDataFreq. ConverterPower Amplifier(PA)PtRFTransmitterMatchedNetworkFeedline AssumePA 40dBm,fortheantennaGt 10dBd,Feedlineloss 3dB,Lossthroughthematchednetworkis0.5dB. FindEIRPandERPforadipoleantenna. IsthisRFtransmi ermorelikelytobeahandsetorabasesta7on?Do it on yourown!

Expression Eb/N0 Ratio of signal energy per bit (J/b) to noise power densityper Hertz (W/Hz)Eb S / RS N0N0kTR R 1/Tb; R bit rate; Tb time required to send onebit; S Signal Power Given a value for Eb/N0 to achieve a desired error rate,parameters of this formula can be selected As bit rate R increases, transmitted signal power mustincrease to maintain required Eb/N0Eb S . Tb W x Sec / bit Energy (J) / bit

Probability of Bit Error Rate(PBER)Question: Assume we requireEb/No 8.4 dB for bit error of10 -4. Assume temperature is290 Kelvin and data rate is setto 2.4 Kbps. Calculate therequired level of the receivedsignal.10 -48.4 dB

ownload) Link characteristics (in terms of power, capacity, and frequency ofoperation) Noise Analysis is generally significant to characterize the received signalby the receiver System is generally balanced in term of dynamic range (in TX and RXdirections) Design Objective:––––Offer good quality of service (QoS)Provide high signal level (SNR and SNIR)Guarantee intelligibility and fidelity (PBER)High accuracy (BER) Conflicting Parameters (next slide)

Link BudgetDetailed ViewPtDigitalDataFreq. ConverterPower AmplifierRF TransmitterPrFeedlineRF UnitReceiver(F, Go, B)PnDecoderDigitalDataFeedline

Budget Link Analysis Conflicting Parameters BW&QoS&ThermalNoise SNR&QoS/Fidelity&Pt&Cost BER&QoS&SNR&Pt&Cost Freq.&Fidelity&DynamicRange SystemLoss&DynamicRange&QoS&Material&Cost QuiescentPowerDissipa7on&LifeTime&Cost&Complexity Bitrate&Noise Temperature&SNR Let us see how through an example! à

PrExampleEAntenna(Go,To,R)Feedline(F1,G1) Assume the frequency ofoperation is 1900 MHz. Thefollowing parameters are given Antenna gain is 0dBd Feedline loss is 0.5 dB Noise figure of the RF unit is 8 dB RF Unit gain is 40 dB Antenna noise temp is 60 Kelvin Detector BW is 100 kHz Detector’s SNR is 12dB Use a design margin of 3 dB(above the required sensitivity) Transmit power is 43 dBmRF UnitReceiver(F2, G2, B2)PsdPndDecoderDigitalData Part I: Find the following– Total system noise figure– Total system gain– Noise power at the detector (Pn) Part II: Find the signal powerrequired into the detector indBm Part III: Find the RX power intothe receiver (Pr) such that thedetector operates properly(Psen of the receiver) Part IV: The maximum dynamicrange

PrExampleE–Antenna(Go,T)PartISolu7on No KT F1 FeedlineLossFeedline(F1,G1)RF UnitReceiver(F2, G2, B2)ReceivedPowerAntennaNoise Go 0dB;G total Go.G1.G2 Pnd k.To.G total.B.F total Te (F total–1).ToPndDecoderRX Model(F total, G total, Te, B) G1 1/F1 forTransmissionLine F total F1 (F2- ‐1)/G1PsdDigitalDataPsdPndPartIISolu on: SignalPowerRequiredfortheDetector–NoisePower Psd–Pnd SNRdBPartIIISolu on: Pr(min) G total Psdà Psens Psd–G totalPartIVSolu on: L path Pt–P marg Psens(dB)

Budget Link Analysis - ReviewConflicting Parameters BW&QoS&ThermalNoise SNR&QoS/Fidelity&Pt&Cost BER&QoS&SNR&Pt&Cost Freq.&Fidelity&DynamicRange SystemLoss&DynamicRange&QoS&Material&Cost QuiescentPowerDissipa7on&LifeTime&Cost&Complexity Bitrate&Noise Temperature&SNR

Other Types of Noise Intermodulation noise – occurs if signals with differentfrequencies share the same medium Interference caused by a signal produced at a frequency thatis the sum or difference of original frequencies Crosstalk – unwanted coupling between signal paths Impulse noise – irregular pulses or noise spikes Short duration and of relatively high amplitude Caused by external electromagnetic disturbances, or faultsand flaws in the communications systemQuestion: Assume the impulse noise is 10 msec. How manybits of DATA are corrupted if we are using a Modem operatingat 64 Kbps with 1 Stop bit?64000 x 7/8 56000 bit / sec56000 x .01 560 data bits effected

Other Types of Noise - ExampleIntermodulation noise(Diff. signals sharing theSame medium)Impulse noiseCrosstalk(coupling)

What Next? Other types of impairments . Channel characteristics

Other Impairments Atmospheric absorption – water vapor and oxygencontribute to attenuation Multipath – obstacles reflect signals so thatmultiple copies with varying delays are received Refraction – bending of radio waves as theypropagate through the atmosphere

ImpairmentsWhy are they important?

References Black, Bruce A., et al. Introduction to wireless systems.Prentice Hall PTR, 2008, Chapter 2 Stallings, William. Wireless Communications & Networks, 2/E.Pearson Education India, 2009; Section 5.3 M F Mesiya, Contemporary Communication Systems, First editionChapter 6.

System Noise Figure (F) F SNR i /SNR o 1 Te To The most basic definition of noise figure came into popular use in the 1940’s when Harold Friis defined the noise figure F of a network to be the ratio of the signal-to-noise power ratio at the input to the signal-to-noise power ratio at the output.