Table Of Content

PreprinttypesetinJINSTstyle-HYPERVERSION 0 1 Advanced modelling of the Planck-LFI radiometers 0 2 n a J 6 2 P.Battaglia1∗,C.Franceschet2 ,A.Zonca3 ,M.Bersanelli2 ,R.C.Butler4 , ] O.D’Arcangelo5 ,R.J.Davis6 ,S.Galeotta7 ,P.Guzzi8 ,R.Hoyland9 ,N.Hughes10 , M P.Jukkala10 ,D.Kettle11 ,M.Laaninen12 ,R.Leonardi13 ,D.Maino2 ,N.Mandolesi4 , I . P.Meinhold13 ,A.Mennella2 ,P.Platania5 ,L.Terenzi4 ,J.Tuovinen14 ,J.Varis14 , h p F.Villa4 ,A.Wilkinson6 - o 1 ThalesAleniaSpaceItaliaS.p.A., r t s S.S.PadanaSuperiore290,20090Vimodrone(Mi),Italy a 2 UniversitádiMilano,DipartimentodiFisica, [ ViaG.Celoria16,I-20133Milano,Italy 1 3 INAF-IASFMilano, v 9 ViaE.Bassini15,I-20133Milano,Italy 5 4 INAF-IASFBologna, 6 ViaP.Gobetti,101,I-40129Bologna,Italy 4 5 IFP-CNR . 1 viaCozzi53,20125Milano 0 0 6 JodrellBankCentreforAstrophysics 1 AlanTuringBuilding,TheUniversityofManchester,Manchester,M139PL,UK v: 7 INAF-OATs, i ViaG.B.Tiepolo11,I-34131,Trieste,Italy X 8 Numonyx,R&DTechnologyCenter, r a ViaC.Olivetti2,20041AgrateBrianza(MI),Italy 10 DA-DesignOy Jokioinen,Finland 11 SchoolofElectricalandElectronicEngineering, TheUniversityofManchester,Manchester,M601QD,UK 12 YlinenElectronicsOy Kauniainen,Finland 13 DepartmentofPhysics, UniversityofCalifornia,SantaBarbara,CA93106-9530,USA 14 MilliLab VTTTechnicalResearchCentreofFinland,Espoo,Finland 9 InstitutodeAstrofÃnˇsicadeCanarias, C/ViaLÃa˘cteaS/N,E-38200,LaLaguna(Tenerife),Spain –1– Abstract: The Low Frequency Instrument (LFI) is a radiometer array covering the 30-70 GHz spectral range on-board the ESA Planck satellite, launched on May 14th, 2009 to observe the cosmicmicrowavebackground (CMB)withunprecedented precision. In this paper we describe the development and validation of a software model of the LFIpseudo- correlation receivers which enables to reproduce and predict all the main system parameters of interest as measured at each of the 44 LFI detectors. These include system total gain, noise temperature, band-pass response, non-linear response. The LFI Advanced RF Model (LARFM) has been constructed by using commercial software tools and data of each radiometer component as measured atsingleunitlevel. The LARFM has been successfully used to reproduce the LFI behavior observed during the LFI ground-test campaign. The model is an essential element in the database of LFI data processing centerandwillbeavailable foranydetailed studyofradiometerbehaviour duringthesurvey. Keywords: Instruments forCMBobservations; Spaceinstrumentation; Microwaveradiometers; Modeling ofmicrowavesystems. CorrespondingAuthor,e–mail:[email protected] ∗ Contents 1. Introduction 1 2. ThePlanckLFIdesign 2 2.1 TheoverallLFIconfiguration 2 2.2 TheLFIradiometer design 3 3. Theanalytical LFIAdvancedRFmodel 4 3.1 Implementation 5 3.1.1 Devicesimplementation 5 3.2 Modelverification 8 3.2.1 Componentlevelverification 8 3.2.2 Systemlevelverification 10 3.3 Applications 10 3.3.1 Instrument performances withtwoFEMprototypes 10 3.3.2 EffectsofOMTasymmetry 12 4. TheReal-DataLFIAdvancedRFModel 13 4.1 Implementation 14 4.1.1 FeedhornandOMT 14 4.1.2 FEM 14 4.1.3 BEM 15 4.2 Results 16 5. Conclusions 18 1. Introduction ThepropertiesoftheCosmicMicrowaveBackground(CMB)containawealthofinformationabout physical conditions in the early universe and a great deal of effort has gone into measuring those properties since its discovery. Numerous ground based and balloon borne experiments, as wellas space missions havebeen devised toobtain measurements ofCMBspectrum, spatial anisotropies, andpolarisationoverawiderangeofwavelengthsandangularscales. FollowingtheCosmicBack- ground Explorer (COBE1) and the Wilkinson Microwave Anisotropy Probe (WMAP2) satellites, launched by NASA in 1989 and 2001 respectively, Planck3 is an ESA space mission designed to 1http://lambda.gsfc.nasa.gov/product/cobe/ 2http://map.gsfc.nasa.gov/ 3http://www.esa.int/planck –1– extract essentially all information encoded in the temperature anisotropies and to measure CMB polarisation tohighaccuracy. Planck,successfully launched on2009 May,the14th, willobserve theentire skyfromaLis- sajousorbitaroundthesecondLagrangepointL2oftheEarth-Sunsystem. Thefocalplaneformed by the 1.5 m off-axis telescope hosts two cryogenic instruments: the Low Frequency Instrument (LFI),covering30-70 GHzinthreebands Bersanelli etal.[2009], andtheHighFrequency Instru- ment (HFI)which covers the range 100 GHzto 857 GHzin six bands Lamarre et al. [2009]. The twoinstruments operate at20K andat0.1K respectively. Suchtemperatures are achieved through acombinationofpassiveradiativecoolingandthreeactivecoolersTauberetal.[2009]. WhileLFI and HFI alone have unprecedented capabilities, it is the combination of data from the two instruments that gives Planck the imaging power, the redundancy and the control of systematic effects andforeground emissionsneededtoachievethescientificgoalsofthemission. The LFI has been designed to cover the low frequency portion of the Planck spectral range withthreebandscentredat30,44and70GHzusingpseudo-correlation receiversbasedonIndium Phosphide cryogenic highelectronmobilitytransistors (HEMT)lownoiseamplifiers(LNA). In order to support the radiometers design and testing phase as well as the study the instrument behaviour and potential systematic effects during the survey wehave constructed asoftware modelofthereceivers,theLFIAdvancedRFModel(LARFM).Inthispaperwedescribethedevel- opment and validation ofthe LARFM,which has been constructed by using commercial software tools. Themodelwasdevelopedintwostages: thefirststage,theAnalyticalLARFM(section3),is ananalytical, parametricmodelbuiltupontherequirements andspecifications oftheLFIreceivers frequency byfrequency. Itsdevelopment started beforethehardware wasbuiltandproveditsuse- fulness inpredicting radiometers performance and toprovide first-order estimates of theexpected impactofpotential systematics. The second stage is the Real-Data LARFM(section 4), implemented after the LFIwas built, whichincludes thedataofeachradiometer component asmeasured atsingleunitlevelchannel by channel. Themodeliscapable ofreproducing indetail the mainsystem parameters ofeach ofthe 44 LFI channels “as built ”, including total gain, noise temperature, bandpasses, non-linearity of the response. The Real-Data LARFMhas been successfully used to reproduce the LFIbehaviour observed during the LFI ground-test campaign Mennella et al. [2009a], Villa et al. [2009]. Cur- rently, theReal-DataLARFMisanessentialelementinthedatabaseofLFIdataprocessing centre andisavailable fordetailed studiesofradiometerbehaviour duringthePlancksurvey. 2. The Planck LFI design 2.1 Theoverall LFIconfiguration LFI(Figure1)isanarrayof11horns,eachfeeding2orthogonallinearlypolarisedchannelscentred at30,44and70GHz,onthefocalplaneofanaplanatic gregorian telescope. TheLFIradiometers include the Front End Unit (FEU) and the Back End Unit (BEU), connected via 44 rectangular waveguides. Such a division into FEU and BEU has been performed in order to minimise the effectsofpowerdissipation inthecriticalfocalplanearea. The Front End is cooled down to 20K by one of two Sorption Coolers, while the Back End, which is located in the body of the satellite, is at ambient temperature. The Front End Unit is the –2– SPACECRAFT INTERFACES HOLE FOR HFI LOCATION 11 LFI 30, 44 AND 70GHZ FEED HORNS IN THE FEU 44 WAVEGUIDES CONNECTING FEU AND BEU BEU CONTAINING BEMS, REBA AND DAE Figure1. AdrawingoftheLFIwithitsspacecraftinterfaces. heart of the LFI instrument and it contains the feed array and associated OrthoMode Transducers (OMTs), hybrid couplers and amplifiers blocks. The Back End Unit comprises the Back End Modules(BEM)andtheDataAcquisition Electronics. 2.2 TheLFIradiometerdesign The LFI array is made up of eleven Radiometric Chain Assembly (RCA) (Figure 2) each incor- porating the two radiometers connected to the feed horn. Each radiometer includes a pair of am- plification/detection chainscorrelatedthroughapairofhybridcouplers, constituting acontinuous- comparisondeviceBersanellietal.[2009]. Inthisscheme,thedifferencebetweentheinputstoeach ofthechains(thesignalfromthetelescopeandthatfromareferenceblackbodyload,respectively) iscontinuouslybeingtaken. Thisschemestronglysuppresses1/fnoisegeneratedbyinstabilitiesin theRFamplifiers,butnotinthereceiverelementsfollowingthesecondhybridcoupler. Toremove this Back End 1/f, it is necessary to modulate the sign of the comparison using solid-state phase- shifters within the correlation section. Thedifferencing receiver improves the stability atacostof afactorof √2insensitivity compared withatotalpowerscheme. Anydifference betweenthesky andreference inputsignals cangiveriseto1/fnoise,intheLFIreceiversthisisfurtherreducedby scaling one of the output data streams by a gain modulation factor "r". The blackbody reference itselfmustremainataverystabletemperature (seeValenziano etal.[2009]). The intensity ∆T of the smallest detectable signal is given by the radiometer equation (from Skou[1989]): T +T ∆T = √2 in noise, (2.1) √B τ eff · whereT istheinputtemperaturetotheradiometer, T istheradiometernoisetemperature in noise andτistheintegrationtime. Radiometersarecharacterised byaspectralresponseg(ν)throughthe radiometer band. Theeffectivebandwidthisdefinedas: –3– Figure2. TheLowFrequencyInstrumentRadiometricChainAssembly(LFIRCA)withtheDataAcquisi- tionElectronicsdiagram. 2 ∞ g(ν)dν   Beff = R0  . (2.2) ∞g2(ν)dν R0 3. The analyticalLFI Advanced RF model The need to analyse the effect of LFInon-ideal response and to estimate the impact of systematic effects lead to the development of a radiometer system simulator Battaglia [2002], using the Agi- lent Advanced Design System (ADS) software. ADS provides Radio Frequency (RF) models for development of system specifications. It contains an RF simulator that predicts performance of completeRFsystemsandincludesasetofblock-levelRFmodelsforlinearandnon-linearcompo- nents. TheADSDesignEnvironment,DataDisplay,RFSystemSimulatorandModelstoolsenable the graphic implementation of the receiver components and the possibility to obtain information abouttheRCAmainproperties, suchassystemgainandnoisetemperature. –4– 3.1 Implementation The radiometer model is built as a network whose electromagnetic properties can be expressed usingscatteringparameters,takingintoaccountthelossesandreflectionsoftheinputsignal,when itpassesthrougheachnetworkelement. For a generic multi-port network definition, it is assumed that each of the ports is allocated an integer n ranging from 1 to N, where N is the total number of ports. The insertion loss is the loss in load power due tothe insertion ofa component atsome point in atransmission system. In measured insertion loss tables found in literature, the S 2 is given rather than the pure insertion 21 | | lossvalue. Inordertoevaluatethepureinsertionloss,themeasuredreturnlosshastobetakeninto account. The S 2 ismeasuredexperimentally, indecibel, as 21 | | P S 2= out. (3.1) 21 | | P in S includes boththeeffectoftheinsertion andthereturnloss,infact: 21 S21=10IL2d0B q1−10RL1d0B, (3.2) andthepureinsertion lossisgivenby: S 2 IL = 10Log | 21| . (3.3) dB 10 Returnloss,instead, isgivenby: 1−10RL1d0B  RL = 10Log S 2, (3.4) dB 10 11 | | andtotalsystemgainisobtainedby: P G(dB) =10Log out , (3.5) 10 K ∆ν(T +T )! B noise in whereT istheinputloadtemperatureandP thecorrespondingpoweratdetectoroutput;∆ν in out istheeffectivebandwidthandK istheBoltzmann’sconstant. T ,thesystemnoisetemperature B noise istheinputload temperature necessary togenerate, inanoiseless system, thesameoutput voltage ofthenoisydevicewithzeroinputload. 3.1.1 Devicesimplementation Figure 3 shows a schematic of the implementation of the Analytic LARFM. The elements that constitute the RCA receiver shown in Figure 2 have been modelled in ADS starting from n-port devicemodels,amplifiers,hybrids, wave-guides modelsandequation-based models. –5– Figure3. TheAnalyticalLARFMgraphicalrepresentationintheADSdesignenvironment. Eachcompo- nentisaportdevicecompletelycharacterisedbytheparametersdisplayedinthefigure. –6– Input Loads. The receiver input load is generated by the port component termination. It is a 50Ω resistance at temperature T that produces a power noise equal to P= K T ∆ν, where, ant B ant in order to simulate the power absorbed by the sky and reference feed horns, T is the antenna ant temperature relatedtothethermodynamic temperature T by: hν T = kT T. (3.6) ant hν ekT 1 − Feed Horn and OMT. The sky and reference feed horns, as well as the OMT, are modelled as two-port devices, completely characterised by their scattering parameters - expressed in terms of insertion loss and return loss - and by their physical temperature, taking into account the noise temperature T generatedbythecomponentitselfintothenetwork. GivenaninputsignalT at noise in theinputportof,e.g.,afeedhorn,thesignalattheoutputoftheelementisgivenby: T = S 2T +T . (3.7) out 21 in noise | | Hybrids. ThehybridismodelledbeafourportS-parametersetofequationsusingtwovalues of magnitude and phase. They are set to correctly reproduce the in-phase and anti-phase addition oftheinputs. Thehybridmodelbydefaulthasaperfectportisolation, butwetestedalsotheeffect ofacrosstalk betweenthetwopathsofthesignal(thatsimulates anon-ideal isolation betweenthe twochannelsoftheradiometer). Thehybrid,beinganoisycomponent, isalsocharacterised bythe physical temperature ofthedevice. FrontEndandBackEndLowNoiseAmplifiers. TheLowNoiseAmplifier(LNA)ismod- elled using the amplifier component of the ADS object library. The LNA model uses scattering parameters for modelling the amplifier gain (S ) and reflections at the input and output ports of 21 the device (S and S ); minimum noise figure (NF ) at optimum source reflection (S ) and 11 22 min opt equivalent noise resistance R are used instead of noise figure to characterise the amplifier noise, n providing alsoacorrectreturnlossmodellingresponse4. Phase Switch. The phase switch model is a two ports system. Scattering parameters are defined in polar coordinates, so that the change in phase is obtained by setting the S parameter 21 phase to 180 degrees. The temperature parameter characterises the noise properties of the phase switchmodel,asforthefeedhornandOMTmodels. Waveguides. TheRCAwaveguidesaremodelledintotwoparts,thecopperwaveguidemodel and the gold-plated/stainless-steel waveguide model. Given the high thermal conductivity of copper, the copper waveguide model consists in a single rectangular waveguide element at the same temperatureoftheFrontEndModule,i.e. 22K.Attheinputandoutputportstwoimpedancetrans- formersplayadoublerole: theyenablethewaveguidematchingtothecharacteristic impedanceof thenetwork(50Ω)andtheymodelthewaveguideflangesreturnloss. The gold-plated and stainless-steel waveguide model, although characterised by the same parameters, is more complex than the copper one, including several rectangular waveguide elements, takingintoaccountthelineartemperature gradientbetweenthetwoflanges. Infactthestainlesssteelsectioninterfacestotwoheatsinksateitherend,oneat300Kandthe otherat22K.Thethermaldistribution alongthestainlesssteelwaveguideiscriticalduetoitshigh 4http://edocs.soco.agilent.com/display/ads2009/Amplifier2+(RF+System+Amplifier) –7– Figure 4. Schematic of the temperaturedistributionalongthe waveguides. V-groovesare thermalshields thatisolatethecoldFrontEnd(22K)fromthewarmBackEndUnit(293K). electrical resistivity. So, with reference to Figure 4, the stainless steel section has been modelled so that the temperature at the flanges and shields (V-groove) interfaces is preserved. For the gold platedsections thevalueforgoldresistivity hasbeenused. By setting the dimensions (width and height) of the waveguides section, the temperatures at theinterfacesandthereturnlossattheflanges,themodelisabletoreproduceacryogenicresponse ofthewaveguides, intermsoftheinsertion lossinthesimulatedfrequency band. Bandpass filter. Its design is a Chebyshev response bandpass filter and its parameters (see Figure 3 for a complete list) completely constrain the insertion loss in the passband and the slope at the cut-off frequency. From the noise temperature analysis point of view, the band pass filter behaves likeanattenuator, suchasOMTandfeedhorns. Detector. The detector has been modelled with a two ports system characterised by a return loss value. The power conversion and integration over the band are performed by an appropriate calculation envelope, available in ADS, so that the output voltage integrated over the frequency band∆νoftheradiometer isgivenby: V = G P (ν)dν, (3.8) out out Z∆ν · where G is a gain factor and P (ν)=V (ν)2/R, being V (ν) the simulated output voltage out out out asafunction ofthefrequency andR=50Ωtheimpedance ofthenetwork. RunningADSsimulations itispossible tocalculate: scatteringparametersoverthebandforthewholeRCAmodelandcomponentbycomponent; • output voltageovertheband; • integrated outputvoltage. • 3.2 Modelverification Themodelisverifiedfirstatsinglecomponent levelandthenatRCAlevel. 3.2.1 Componentlevelverification Thefunctionalconsistency ofeachradiometercomponentisverifiedevaluatingscatteringparame- ters,outputvoltageandnoisetemperature. AtsinglecomponentleveltheS-parametersareverified –8–