AST356/326CoherentDetection&

ThermalNoise

Oct16,2017

Announcements• Lab#1optionalextension,checkyouremail.• You’restuckwithmeforthenext3weeks,officehoursstillFri@3-4pm,nowinAB126.

• Lab#2beginstoday,dueNov15th.– Godownload,print,andreadthelabmanualifyouhaven’tyet!

– Don’tleavethingstothelastminute,trytopaceyourself.Notgoingtobeextendedlike#1…

• PresentationgroupsnextMonday:EGADIJ

FigurecourtesyNASA

Atmopsheric Windows

Excellentseeingoverahugeband!

1mm– 10m(300GHz– 30MHz)

Wavelengthsvs.FrequenciesUnfortunately,radiopeopletendtouseboth.

Remember:c=ln =3x108 m/s

n =300MHz=3x108 Hzó l =1mn =300GHz=3x1011 Hzó l =1mm

Handyreferencepoints:

Ppeta1015

Eexa1018

ffemto10-15

aatto10-18

LowEnergyLight

1mm(300GHz)photon:• 200yoctojoules• 2x10-22 Joules• 0.001eV

Insufficientforphotoelectric

effect!

1m(300MHz)photon:• 0.2yoctojoules• 2x10-25 Joules• 0.000001eV

E=hn

ThreeWaystoDetectLight

1.PhotonDetectors2.ThermalDetectors3.CoherentDetectors

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DetectingRadioLight:Thermal

Bolometers:• justfancythermometers• heatupinresponsetopower• Presentlythemostsensitive

detectorsformicrowavelight• Stillnotenoughpowerinmost

radiosignalstobeviable

ImagefromWikipedia

Wave-particleDuality

• Optical:eV – canphoto-ionize• Radio:µeV – negligibleenergy/photon

Thinkwaves,notparticles.

Waves

...... ...

DetectingRadioLight:Coherent

Forgetparticlesandpower– justrecordthewaves.

Afeed couplesfreespacewavesintowaveguide.Thatmakesiteasiercontrolandmanipulatethelight.

Fromthere,wecan:• amplify• delay(phaseshift)

• filter• mix

• sample• correlate

CoherentdetectionrecordsElectricfields,bothamplitude andphase.

Coherent&IncoherentCoherentisunlikephotoncountingorthermaldetection.Thoseeachmeasurethepower intheincominglight,andareincoherent formsofdetection.

Coherent detectorsmeasureE(t)=SwA sin(wt+fw,t).Variationsinphasef containlotsofinformation,buttheoverallf isusuallyarbitrary&meaningless.

ThepowerofthesourceP µ <E2>µ |A|2 isoftenmoreusefulthantherawamplitudes,asitrelatestosourcetemperature,energyconservation,…

FeedsIn radio, large light, small focal planes – no Megapixel CCDs.• Radio “cameras” are still in the single- (or few-) pixel regime.• Feeds collect radiation from free space

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-I=sin(2pnt)

V=sin(2pnt+f)

Forhighefficiency(toberesonant),afeed’ssizemustbeoforderl.

Receivers(Everythingbehindthefeed.)

WaveguideWeusuallythinkoflightinfreespaceorbulkmaterial.EMfieldswillalsopropagateinwaveguides.Awaveguideconfinesthesignaltotravelinonedirection.

Optical:Fiber

Microwave:MetalTubes/ microstrip

Radio:TransmissionLines/Cables/Microstrip

RFAmplifiersSemiconductorsarefastnow.

Manycommercialamplifiersexist,capableofamplifyingsignalsupto≈100GHz.

Incoherentdetection,wedirectlyamplify anEMwaveinwaveguide. MicrowaveDynamics

AlexanderGrahamBell

• Hugely influentialinradio.• Unitofsignalattenuation

namedafterhim.• 1Bel =10-foldlossofsignal• MorecommonlyusedB

• Nowwidelyusedlog-relative

DeciBels

PracticaldB dB Relative

Level

0 1x+10 10x+20 100x+30 1000x-10 0.1x-20 0.01x-30 0.001x+3 2x+26 400x

• dBnowusedeverywherelogscalesareneeded.

• cosmictimeoftengivenindBs,decibelsrelativetoasecond

• RadiopowergivenindBm (dB-milliWatts)ordBW (dB-Watts).

1dBW=+30dBm

DigitizersOnceit’sanicebigsignal,weconnectahighspeedvoltmeter(anAnalogtoDigitalConverter,ADC)toreaditout!

Aliasing&NyquistCanonlydistinguishfsamp/2totalbandwidth.

Power

Freq

Mixers

sin(w1t+f1)sin(w2t+f2)=½[cos((w1- w2)t+(f1- f2))-

cos((w1+w2)t+(f1+f2))]

HeterodyneDetectors

(GMRTuses5stagesofup- &down-mixing.)

HeterodyneBatDetector

DesignProblems!

Iwanttorecord120-150MHzasefficientlyaspossible.WhatmixersandsamplingratedoIuse?

Iwanttorecord20-220MHzasefficientlyaspossible.WhatmixersandsamplingratedoIuse?

30MHzBandwidthà 60MSps120-150MHzbandà LOat120MHz,150MHz,or90MHz.

200MHzBandwidthà 400MSps20-220MHzbandà LOat220MHz.

DigitalLightAfterdigitization,dowhateveryouwanttothelight.

Forexample:

• Channelize:FourierTransformtosplitfrequencies(ArbitrarilyfineDn resolution,noneedforprisms.)

• Integrate:sumupincomingpower|E|2(Equivalenttoathermaldetection.)

• Correlate:combinethelightfromfarawayantennas(Moreifyoueverstudyinterferometry.)

RJTemperature

Forradio&mm,usuallykT >>hn,sowe’reinRayleigh-Jeansregime.

Withinaband,blackbodypowerislinearlyrelatedtotemperature.

“Temperature”isafrequentunitofsignal&noisepower.

P =kTDn(AlsomeansthermalnoisefromourinstrumentTrcvr issignificant.)

SystemTemperature

We want to measure

We can measure the total system power:

Psource =kTsourceDn

Includesallpowerbeforeandaftertheantenna,includingamplifiers,cables,pickup,crosstalk,ADCs,etc.Atlowfrequencies,everything isglowingthermally.

HowdowegetTsource?

RadiometerEquation

Bandwidth(Dn)andtime(t)giveindependentmeasurements,andtheRadiometerEquation givesfundamentalnoise:

Low-energydetectorsdon’thave“readnoise”inelectrons.Theymeasurelightinyourwaveguide.

NotethatALL powerinthesystemaddstothenoise.Thegoalforalow-noisesystemistominimizepower.

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RadioFrequencyInterference(RFI)Lightpollutionatlongwavelengths.

• AMRadio• FMRadio• BroadcastTV• RADAR• CellPhones• CBRadio• Electronics• Etc…

3kHz100km

300kHz1km

3MHz100m

30MHz10m

300MHz1m

3GHz10cm

30GHz1cm

UnitedStatesRFSpectrumAllocation

Howbadisit?HowhotaretheFMbroadcastsfromtheCNtower?

Total:350kW Wikipedia

Wikipedia

Back-of-the-Envelope!Whatistheflux(inJy)ofthe350kWofFMradiocomingofftheCNtoweratUofT?Assumeanisotropictransmitter.

BandwidthofFM:20MHzDistancetotheCN:≈2km1Jy=10-26 W/m2/Hz

S=350kW/(4p x(2km)2)/20MHz=3x10-10 W/m2/Hz=3x1016 Jy =30PJy

Wikipedia

Brightcelestialsourcesareoforder1Jy.ThebrightestcelestialsourceisCassiopeiaA,about105 Jy at100MHz.TheCNtowerisBRIGHT.

Lab#2

Radiometers&ThermalNoise

PartI:Receivers,Stats&Spectra

TheAirSpy Receiver

TheAirSpy Receiver

TheAirSpy Receiver

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

USB- microUSB

IMPORTANT:RECORDDATAINTO/tmp ONTHELAPTOPS!

YOURHOMEDIRECTORYWILLNOTWORK.Youcancopy

itoverforposterityonceyouhaveagooddataset.

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

ADCsRevisited

• MeasureVoltage,expressinbits.

• Repeataftersometime,typically≈ms.

• Usedeverywhere:thermometers,motors,magneticfields,etc.

• Radiojustdoesitfaster.

Volta

ge

t

0V

5V

0

63

t

ADCsRevisited2-bitDigitizer

ADCsRevisited3-bitDigitizer

ADCsRevisited4-bitDigitizer

000012-bitADCvalmy_data.dat

• AirSpy uses12-bitADC.

• PCsusuallydealwith8bit=1Bytechunks.

• AirSpy packsits12bnumbersinto16b=2B,soPCscanhandlemoreeasily.

Padding Data

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

my_data.dat

• AirSpy ADCissymmetric:0Vishalf-waybetweenminandmaxvalues.

• 12-bitrange:0-4095

• 0Vßà 211 =2048

• Togetvoltageinbits,needADCval – 211

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

my_data.dat

In [1]: import numpy as np

In [2]: data = np.fromfile('my_data.dat',dtype='int16') - 2**11;

In [3]: data.shapeOut[3]:(1000000,)

In [4]: data.mean()Out[4]: 13.6037

airspy_rx –f 1000 –a 1 –t 4 –v 15 –m 15 -l 14–n 1000000 –d –r my_data.dat

In [5]: import matplotlib.pyplot as plt

In [6]: plt.plot(data[10000,11000],'.');In [7]: plt.xlabel('Sample number');In [8]: plt.ylabel('ADC Reading [bits]');In [9]: plt.title(’Raw samples from AirSpy');In [10]: plt.show();

CentralLimitTheoremForany underlyingprobabilitydistribution,thedistributionofasumofrealizationstendstowardGaussianasthenumberbecomeslarge.

Example:(fair)coinflip.heads=0,tails=1.

Normal‘ol EMWaves• Most(natural)thingsthatgenerateradiophotonsare

complicated,drivenbyQMandthermalprocesses.• CLT:neteffectwillbeanormallydistributedE-field.• Averageanddeviationmayvarywithfrequency,time,

direction,polarization,….• CLT:sumstillnormal!

TemperatureofaRadioWave

Tµ Pµ <E2>

RJtemperatureisthevarianceofourcoherentsignal!

c2 DistributionsSum-of-squaresofk samplesdrawnfromanormaldistribution.

Comeupfrequentlyinerroranalysis!(CLT:ck2à Gaussianforlargek)

Mean à kVariance à 2k

In [11]: f=np.fft.fft(d[0:2**19].reshape(-1,1024),\axis=1 );

In [12]: s=(f.real**2+f.imag**2).sum(axis=0);In [13]: plt.plot(10*np.log10(s[0:512]), '.');In [14]: plt.xlabel('Frequency Bin');In [15]: plt.ylabel('Power [dB arb]');In [16]: plt.title('Spectrum from AirSpy');In [17]: plt.show();

TestingNormality

IfthesignalisGaussian,theRadiometerEquation willhold:

Low-energydetectorsdon’thave“readnoise”inelectrons.Theymeasurelightinyourwaveguide.

ALL powerinthesystemaddstothenoise.Youshouldchecktherelationinnarroworbroadfreq bands.

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GoodLuck!