AampA 520 A6 (2010)DOI 1010510004-6361200912860ccopy ESO 2010

Astronomyamp

AstrophysicsPre-launch status of the Planck mission Special feature

Planck pre-launch status Calibration of the Low FrequencyInstrument flight model radiometers

F Villa1 L Terenzi1 M Sandri1 P Meinhold2 T Poutanen3 45 P Battaglia6 C Franceschet7 N Hughes8M Laaninen8 P Lapolla6 M Bersanelli7 R C Butler1 F Cuttaia1 O DrsquoArcangelo9 M Frailis10 E Franceschi1S Galeotta10 A Gregorio11 R Leonardi2 S R Lowe12 N Mandolesi1 M Maris10 L Mendes13 A Mennella7

G Morgante1 L Stringhetti1 M Tomasi7 L Valenziano1 A Zacchei10 A Zonca14 B Aja15 E Artal15M Balasini6 T Bernardino16 E Blackhurst12 L Boschini6 B Cappellini14 F Cavaliere7 A Colin16 F Colombo6

R J Davis12 L De La Fuente15 J Edgeley12 T Gaier17 A Galtress12 R Hoyland18 P Jukkala8 D Kettle12V-H Kilpia8 C R Lawrence16 D Lawson12 J P Leahy12 P Leutenegger6 S Levin16 D Maino7 M Malaspina1A Mediavilla15 M Miccolis6 L Pagan6 J P Pascual15 F Pasian10 M Pecora6 M Pospieszalski19 N Roddis12

M J Salmon16 M Seiffert17 R Silvestri6 A Simonetto9 P Sjoman8 C Sozzi9 J Tuovinen20 J Varis20A Wilkinson12 and F Winder12

(Affiliations can be found after the references)

Received 9 July 2009 Accepted 3 May 2010

ABSTRACT

The Low Frequency Instrument (LFI) on-board the ESA Planck satellite carries eleven radiometer subsystems called radiometer chain assemblies(RCAs) each composed of a pair of pseudo-correlation receivers We describe the on-ground calibration campaign performed to qualify the flightmodel RCAs and to measure their pre-launch performances Each RCA was calibrated in a dedicated flight-like cryogenic environment with theradiometer front-end cooled to 20 K and the back-end at 300 K and with an external input load cooled to 4 K A matched load simulating ablackbody at different temperatures was placed in front of the sky horn to derive basic radiometer properties such as noise temperature gainand noise performance eg 1 f noise The spectral response of each detector was measured as was their susceptibility to thermal variation Alleleven LFI RCAs were calibrated Instrumental parameters measured in these tests such as noise temperature bandwidth radiometer isolationand linearity provide essential inputs to the Planck-LFI data analysis

Key words cosmic microwave background ndash space vehicles instruments ndash instrumentation detectors ndash techniques miscellaneous

1 Introduction

The Planck mission1 has been developed to provide a deep full-sky image of the cosmic microwave background (CMB) in bothtemperature and polarization Planck incorporates an unprece-dented combination of sensitivity angular resolution and spec-tral range ndash spanning from centimeter to sub-millimeter wave-lengths ndash by integrating two complementary cryogenic instru-ments in the focal plane of the Planck telescope The LowFrequency Instrument (LFI) covers the region below the CMBblackbody peak in three frequency bands centered at 30 44and 70 GHz The spectral range of the LFI is also suitable fora wealth of galactic and extragalactic astrophysics The LFImaps will address studies of diffuse Galactic free-free and syn-chrotron emission emission from spinning dust grains and dis-crete Galactic radio sources Extragalactic radio sources will

Present address Astrium GmbH Friedrichshafen Germany1 Planck (httpwwwesaintPlanck) is a project of theEuropean Space Agency ndash ESA ndash with instruments provided by two sci-entific Consortia funded by ESA member states (in particular the leadcountries France and Italy) with contributions from NASA (USA) andtelescope reflectors provided in a collaboration between ESA and a sci-entific Consortium led and funded by Denmark

also be observed particularly those with flat or strongly invertedspectra peaking at mm wavelengths Furthermore the Planckscanning strategy will also allow monitoring of radio sourcevariability on a variety of time scales While these are highly in-teresting astrophysical objectives the LFI design and calibrationis driven by the main Planck scientific scope ie CMB science

The LFI is an array of cryogenic radiometers based on in-dium phospide (InP) cryogenic HEMT low noise amplifiers(Bersanelli et al 2010) The array is composed of 22 pseudo-correlation radiometers mounted in eleven independent radiome-ter units called ldquoradiometer chain assembliesrdquo (RCAs) two cen-tered at 30 GHz three at 44 GHz and six at 70 GHz2 To optimizethe sensitivity and minimize the power dissipation in the frontend each RCA is split into a front-end module (FEM) cooledto 20 K and a back-end module (BEM) operating at 300 Kconnected by a set of composite waveguides

Accurate calibration is mandatory for optimal operation ofthe instrument during the full-sky survey and for measuring pa-rameters that are essential for the Planck data analysis

2 The chains are numbered as RCAXX where XX is a number from 18 to23 for the 70 GHz RCAs from 24 to 26 for the RCAs at 44 GHz andfrom 27 to 28 for the RCAs at 30 GHz

Article published by EDP Sciences Page 1 of 14

AampA 520 A6 (2010)

Fig 1 Scheme of the RCA and its flight-like thermal interfaces The FEM is at 20 K while the BEM is at 315 K At 30 and 44 GHz the thermalinterface attached to the third and coldest V-groove (VG-3) is controlled at a temperature near 60 K while for the 70 GHz RCA the VG-3 interfacewas not controlled in temperature Both loads ndash the sky load and the reference load ndash are controlled in a temperature of approximately 4 K to 35 K

The LFI calibration strategy has been based on a comple-mentary approach that includes both pre-launch and post-launchactivities On-ground measurements were performed at all-unitand sub-unit levels both for qualification and performance ver-ification Each single FEM and BEM as well as the passivecomponents (feed horn orthomode transducers waveguides 4 Kreference loads) were tested in a stand-alone configuration be-fore they were integrated into the RCA units

The final scientific calibration of the LFI was carried out attwo different integration levels depending on the measured pa-rameter First each RCA was tested independently in dedicatedcryofacilities which are capable of reaching a temperature ofsim4 K at the external input loads These conditions were nec-essary for an accurate measurement of key parameters such assystem noise temperature bandwidth radiometer isolation andlinearity Subsequently the eleven RCAs were integrated intothe full LFI instrument (the so-called radiometer array assem-bly RAA) and tested as a complete instrument system in a largecryofacility with highly stable input loads cooled down to 20 K

We reports on the calibration campaign of the RCAs whileMennella et al (2010) report on the RAA calibration The pa-rameters derived here are crucial for the Planck-LFI scientificanalysis Noise temperatures bandwidths and radiometer isola-tion provide essential information to construct an adequate noisemodel which is needed as an input to the map-making processAny non-linearity of the instrument response must be accuratelymeasured because corrections may be needed in the data analy-sis particularly for observations of strong sources such as plan-ets (crucial for in-flight beam reconstruction) and the Galacticplane As part of the RCA testing we also performed an end-to-end measurement of the bandshape inside the cryofacilityFinally for comparison and as a consistency check the RCAtest plan also included measurement of parameters whose pri-mary calibration relies on the RAA test campaign such as op-timal radiometer bias (tuning) 1 f noise (knee frequency andslope) gain and thermal susceptibility

The 30 and 44 GHz RCAs were integrated and tested inThales Alenia Space Italia (TAS-I) formerly Laben from thebeginning of January 2006 to end of May 2006 using a dedi-cated cryofacility (Terenzi et al 2009b) to reproduce flight-likethermal interfaces and input loads The 70 GHz RCAs were in-tegrated and calibrated in Yilinen Electronics (Finland) from the

end of April 2005 to mid February 2006 with a similar cry-ofacility but with simplified thermal interfaces (Terenzi et al2009b) The differences between the two cryofacilities resultedin slightly different test procedures because the temperatureswere not controlled in the same way

Section 2 of the paper describes the concept of RCA cali-bration while Sect 3 illustrates the two cryofacilities In Sect 4we describe each test the methods used in the analysis and theresults The conclusions are given in Sect 5

2 Main concepts and calibration logic

21 Radiometer chain assembly description

A diagram of an RCA is shown in Fig 1 A corrugated feedhorn (Villa et al 2009) which collects the radiation fromthe telescope Tsky is connected to an ortho-mode transducer(DrsquoArcangelo et al 2009b) which divides the signal into twoorthogonal polarizations namely ldquoMrdquo (main) and ldquoSrdquo (side)branches The OMT is connected to the front-end section (Daviset al 2009 Varis et al 2009) in which each polarization of thesky signal is mixed with the signal from a stable reference loadTref via a hybrid coupler (Valenziano et al 2009) The signal isthen amplified by a factor Gfe and shifted in phase by 0ndash180 de-grees at 8 kHz synchronously with the acquisition electronicsFinally a second hybrid coupler separates the input sky signalfrom the reference load signal

175 m long waveguides (DrsquoArcangelo et al 2009a) are con-nected to the FEM in bundles of four elements providing thethermal break between 20 K and 300 K where the ambient tem-perature back-end section of the radiometer is located (Artalet al 2009 Varis et al 2009) The waveguides are thermally at-tached to the three thermal shields of the satellite the V-groovesThey act as radiators to passively cool down the payload to about50 K They drive the thermal gradient along the waveguides

Inside the BEM the signal is further amplified by Gbe andthen detected by four output detector diodes3 In nominal con-ditions each of the four diodes detects a voltage alternatively(each 122 μs which corresponds to 18192 Hzminus1) proportional

3 According to the name convention diodes refer to the Main-polarization are labeled as M-00 M-01 and those referring to the Side-polarization are labeled as S-10 S-11

Page 2 of 14

F Villa et al Calibration of LFI flight model radiometers

by a factor a to the sky load and reference load temperature Bydifferencing these two signals a very stable output is obtainedwhich allows the measurement of very faint signals

Assuming negligible mismatches between the two radiome-ter legs and within the phase switch the differenced radiometeroutput at each detector averaged over the bandwidth β can bewritten in terms of overall gain Gtot in units of VK and noisetemperature TN as

Vout = Gtot

[(Tsky + TN

)minus r middot

(Tref + TN

)]timesGtot = a middot k middot β middotGfeLwgGbe

timesTN T (fe)N +

T (be)N

Gfemiddot (1)

Here we further define the waveguide losses as Lwg the front-endnoise temperature a T (fe)

N and the back-end noise temperature as

T (be)N and with k the Boltzmann constant The noise contribution

of the waveguides due to its attenuation is negligible and notconsidered here

The ohmic losses of the feedhorn ndash OMT assembly Lfo andof the 4K Reference load system L4 K modify the actual skyand reference load through the following equations

Tsky =Tsky

Lfo+

(1 minus 1

Lfo

)Tphys (2)

Tref =Tref

L4 K+

(1 minus 1

L4 K

)Tphys (3)

where Tphys its the physical temperature (close to 20 K at opera-tional conditions)

The r factor in Eq (1) is the gain modulation factor calcu-lated as

r =Tsky + TN

Tref + TN

(4)

which nulls the radiometer output A more general form of theaveraged power output which takes into account various non-ideal behaviors of the radiometer components can be found inSeiffert et al (2002) and Mennella et al (2003) The key parame-ters needed to reconstruct the required signal (differences of Tskyfrom one point of the sky to another) are therefore the photo-metric calibration Gtot and the gain modulation factor r whichis used to suppress the effect of 1 f noise Deviations from thisfirst approximation are treated as systematic effects

22 Signal model

To better understand the purpose of the calibration it is usefulto write Eqs (1) to (4) appropriately so that the attenuation co-efficients are taken into account in the RCA parameters insteadof considering their effects as a target effective temperature Forthe sky signal the output can be written as

Vskyout = Gsky

tot

(Tsky + T sky

N

) (5)

Gskytot = a middot k middot β 1

LfoGfe

1Lwg

Gbe (6)

T skyN = TN +

[(Lfo minus 1) Tphys

] (7)

and equivalently for the reference signal

V refout = Gref

tot

(Tref + T ref

N

) (8)

Greftot = a middot k middot β 1

L4 KGfe

1Lwg

Gbe (9)

T refN = TN +

[(L4 K minus 1) Tphys

] (10)

Differencing Eqs (5) and (8) we obtain the differenced (sky ndashref) output similar to Eq (1)

Vout = Glowasttot

[(Tsky + T sky

N

)minus rlowast

(Tref + T ref

N

)] (11)

Glowasttot = Gtot1

Lfo (12)

rlowast = rLfo

L4Kmiddot (13)

Equations (5) (8) and (11) are the basis for the RCA calibra-tion because all parameters involved were measured during theRCA test campaign by stimulating each RCA at cryo tempera-ture (close to the operational in-flight conditions) with severalknown Tsky and Tref values

23 Radiometer chain assembly calibration plan

Each RCA calibration included (i) functional tests to verify thefunctionality of the RCA (ii) bias tuning to set the best am-plifier gains and phase switch bias currents for maximum per-formance (ie minimum noise temperature and best radiometerbalancing) (iii) basic radiometer property measurements to es-timate Glowast T sky

N T refN (iv) noise performance measurements to

evaluate 1 f white noise level and the rlowast parameter (v) spec-tral response measurements to derive the relative bandshape (vi)susceptibility measurements of radiometer thermal variations toestimate the dependence of noise and gain with temperature Thelist of tests is given in Table 1 together with a brief descriptionof the purpose of each test

Although the calibration plan was the same for all RCAs thedifferences in the setup between 3044 GHz and 70 GHz resultedin a different test sequence and procedures which retained theobjective of RCA calibration unchanged

At 70 GHz the RCA tests were carried out in a dedicatedcryogenic chamber developed by DA-Design4 (formerly YlinenElectronics) which was capable of accommodating two RCAsat one time Thus the RCA test campaign was planned for threeRCA pairs namely RCA18 and RCA23 RCA19 and RCA20 RCA21and RCA22 At 30 and 44 GHz only one RCA at a time was cali-brated Due to the different length of the waveguides the thermalinterfaces were not exactly the same for different RCAs whichresulted in a slightly different thermal behavior of the cryogenicchamber and thus slightly different calibration conditions

3 Radiometer chain assembly calibration facilities

In both cases the calibration facilities used the cryogenic cham-ber described in Terenzi et al (2009b) a calibration load theskyload (Terenzi et al 2009a) electronic ground support equip-ment (EGSE) and software (Malaspina et al 2009) The heartof the EGSE was a breadboard of the LFI flight data acquisi-tion electronics (DAE) with LabwindowTM5 software to controlthe power supplies to the FEMs and BEMs read all the house-keeping parameters and digitize the scientific signal at 8 KHzwithout any average or time integration The EGSE sent datacontinuously to a workstation operating the Rachel (RAdiometer

4 httpwwwda-designfispace5 httpwwwnicomlwcvi

Page 3 of 14

AampA 520 A6 (2010)

Table 1 Calibration test list

Test id DescriptionFunctionality

RCA_AMB Functional test at ambientRCA_CRY Functional test at cryo

TuningRCA_TUN Gain and offset tuning of the DAE

Tuning of the front end module(phase switches and gate voltages)Basic Properties

RCA_OFT Radiometer offsetmeasurement

RCA_TNG Noise temperature andphotometric gain

RCA_LIS Radiometer linearityNoise Properties

RCA_STn Noise performances testsWN fk and α β r

RCA_UNC Verification of the effectof the radiometer switchingon the noise spectrum

Band Pass ResponseRCA_SPR Bandpass

SusceptibilityRCA_THF Susceptibility to

FEM temperature variationsRCA_THB Susceptibility to

BEM Temperature variationsRCA_THV Susceptibility to V-groove

temperature variations

Notes The first column reports the test identification In the secondcolumn the purpose of each test is described WN is the white noiselevel fk α are the 1 f knee frequency and slope respectively β is theequivalent radiometer bandwidth derived from noise r is the modula-tion factor Apart from the first test RCA_AMB which is performed atambient temperature all the other tests are performed at the operationaltemperature (ie at a temperature as close as possible to in-orbit condi-tions)

CHain EvaLuator) software for quick-look analysis and datastorage (Malaspina et al 2009) The data files were stored inFITS format As two chains were calibrated at the same time at70 GHz separate EGSEs and analysis workstations were usedfor each RCA Below the cryofacilities and skyloads are sum-marized with the emphasis on the issues related to the analysisof the calibration data

31 The cryofacility for the 30 and 44 GHz RCAs

The chamber with its overall dimensions of 20times12times10 m3 wasable to accept one RCA at a time The chamber was designed toallow the pressure to reach less than 10minus5 mBar and containedseven thermal interfaces to reproduce the flight-like thermal con-ditions of an RCA During tests it was possible to control and sta-bilize the BEM temperature the waveguide-to-spacecraft inter-face temperature and the FEM temperature In addition the tworeference targets (the reference load and the sky load) were con-trolled in temperatures in the range 4minus35 K to allow temperaturestepping for radiometer linearity tests (RCA_LIS) In addition tothe electrical connections for the DAE breadboard and to controlthe thermal interfaces two thermal-vacuum feedthroughs (onefor the 30 GHz and the other one for the 44 GHz RCAs) withKapton windows were provided to allow access for the RF sig-nal for the bandpass tests (RCA_SPR)

Fig 2 Radiometer chain assembly integrated into the 30 and 44 GHzcryofacility for calibration In the picture at the top the skyload fac-ing the horn is visible together with the FEM insulated from the 50 Kshroud (the copper box) In the bottom picture the BEM and its thermalinterface are shown See the text for details of the cryochamber

During the RCA27 and RCA28 calibrations an uncertainty inthe reference targetsrsquo temperature was experienced A visual in-spection of the cryochamber after the RCA28 test gave a possi-ble explanation and in the RCA27 test an additional sensor wasput on the back of one of the reference targets in order to ver-ify the probable source of the problem The observed behaviorwas consistent with an excess heat flow through the 4 K refer-ence load (4KRL) via its insulated support caused by a contactcreated during cooldown A dedicated thermal model was thusdeveloped to derive the Eccosorb 4KRL temperature Tref fromthe back plate controller sensor temperature T ctrl

ref (Terenzi et al2009b) A quadratic fit was found with Tref = a + b middot T ctrl

ref + c middot(T ctrl

ref

)2for each pair of detectors coupled to the same radiometer

arm and for each 30 GHz RCA The coefficients derived fromthe fit are shown in Table 2

32 Sky load at 30 and 44 GHz

The calibrator consisted of a cylindrical cavity with walls cov-ered in Eccosorb CR1106 (see Fig 6) The back face of the

6 Emerson amp Cuming httpwwweccosorbcom

Page 4 of 14

F Villa et al Calibration of LFI flight model radiometers

Table 2 Reference load target temperature

RCA27M S

a 57 plusmn 02 25 plusmn 01b 058 plusmn 002 081 plusmn 001c 000686 plusmn 58 times 10minus4 000322 plusmn 32 times 10minus4

RCA28M S

a 247 plusmn 005 550 plusmn 009b 0799 plusmn 0007 057 plusmn 001c 000407 plusmn 25 times 10minus4 000831 plusmn 41 times 10minus4

Notes Quadratic fit coefficients

Fig 3 Thirty minutes of data acquired during RCA28 Noise tempera-ture and linearity tests are shown with T ctrl

sky in red Tsky in green and

T sidesky in blue This represents the worst case of these differences The

stability of the temperatures with the values T ctrlsky = 850000 plusmn 000006

Tsky = 90981 plusmn 00004 and T sidesky = 99560 plusmn 00007 are also evident

cavity was covered with Eccosorb pyramids to guarantee a re-turn loss of about minus30dB Details of the skyload are reportedin Cuttaia (2005) Four temperature sensors were placed on thesky load but only two cernox sensors were taken as referencefor calibration The first one was placed on the back plate of thesky load to measure the temperature of the PID control loop ofthe sky load T ctrl

sky The second was placed on the Eccosorb pyra-mids inside the black body cavity and was assumed as the black-body reference temperature Tsky The contribution to the effec-tive emissivity due to the pyramids was estimated by Cuttaia(2005) to be 09956 for the 30 GHz channel and 09979 for the44 GHz channel The effective emissivity was calculated assum-ing the horn near field pattern and the emissivity of the materialIn the case of the skyload side walls the effective emissivity is429times 10minus3 and 207times 10minus3 for the 30 GHz and 44 GHz respec-tively In the data analysis only the contribution of the pyramidswas considered assuming its emissivity equal to 1 Assuming theemissivities reported above and the temperatures as in Fig 3the approximation leads to an uncertainty in the brightness tem-perature of about 004 K and the same uncertainty in the noisetemperature measurements

Due to a failure in the sensor on the pyramids an analyt-ical evaluation of Tsky temperature from T ctrl

sky temperature wasperformed during the calibration of RCA24 and RCA27 Thedata are shown in Fig 4 Although the data show a linear be-havior the differences between T ctrl

sky and Tsky decrease as the

Table 3 Temperarture of the sky load pyramids Quadratic fit coeffi-cients

30 GHz 44 GHza 09185 plusmn 00006 05430 plusmn 0008b 09540 plusmn 00001 09795 plusmn 00008c 00008460 plusmn 44 times 10minus6 0000217 plusmn 19 times 10minus5

Fig 4 Tsky as a function of back plate controller skyload temperatureT ctrl

sky The left plot refers to the 30 GHz RCAs based on RCA28 data(circles) The right plot refers to the 44 GHz RCAs based on RCA25and RCA26 data (squares) The lines are the quadratic fit to the data

Fig 5 Differences between Tsky and T ctrlsky as a function of T ctrl

sky showingthe non-linear behavior of the difference Circles are for 30 GHz RCAsand squares for 44 GHz RCAs

temperature increases (see Fig 5) as expected from the ther-mal behavior of the system suggesting that a quadratic fit with

Tsky = a+bmiddotT ctrlsky+cmiddot

(T ctrl

sky

)2is more representative This quadratic

fit was performed and the coefficients are reported in Table 3

33 The cryofacility of the 70 GHz RCAs

This cryofacility has the dimensions 16 times 10 times 03 m3 Thefacility has a layout similar to that at 30ndash44 GHz although the70 GHz facility was designed to house two radiometer chainssimultaneously (Fig 7)

Page 5 of 14

AampA 520 A6 (2010)

Fig 6 Bologna design of the RCA sky load calibrator The overall di-mensions in mm are reported in the drawing on the left The pyramidson the bottom of the skyload are clearly visible on the right picture

The smaller dimensions of the feedhorns and front end mod-ules and the decision to use two small dedicated sky loads di-rectly in front of the horns allowed the cold part of the two RCAsunder test to be contained in a volume similar to that of the 30and 44 GHz chamber Temperature interfaces such as FEMssky load and reference load were coupled together by means ofcopper slabs and then connected to the 4 K and 20 K coolersThe FEMs were controlled at their nominal temperature of 20 Ksky and reference loads were controlled in the range 10ndash25 Kwith a stability better than 10 mK the back end modules wereinsulated from the chamber envelope by means of a supportingstructure without temperature control which was considered un-necessary

34 The skyloads at 70 GHz

The design for the 70 GHz RCA skyload was made by YlinenElectronics The basic design is shown in Fig 8 The load config-uration is a single folded conical structure in Eccosorb mountedin an aluminum housing It is attached to a brass back plate Asingle waveguide input is mounted through the back plate pro-viding the method of applying RF stimulus signals through theabsorber for the RCA_SPR test (see Sect 45) Load performanceswere measured over the whole V-band showing a return loss bet-ter than minus20 dB Two sensors were placed on the sky load oneat the controller stage referred to as Tctrl and one inside the ab-sorber Tsky Although the temperature along the skyload wasexpected to be uniform due to its small dimensions this was notthe case due to the cool down effects the thermal junction be-tween the temperature control and the load was not efficient asexpected A typical difference in temperature within 4minus7 K wasobserved between the two thermometers This cool-down effectwas not predictable so that the sky load was considered as a rel-ative instead of an absolute temperature reference

4 Methods and results

41 Functional tests

Functional tests were performed at ambient and at cryo tem-perature All the RCAs were biased with nominal values andthe power consumption was verified In addition each phaseswitch was operated in the nominal mode to check its function-ality As an example the functional test performed at cryogenictemperature on RCA26 is shown in Fig 9 The figure reports

FFront End Modules

Waveguides

Back EndModules

Fig 7 Top two 70 GHz RCAs integrated in the Ylinen Electronics cry-ofacility The two BEMs (on the right) are connected to the waveguideshere surrounded by aluminum mylar On the left the shroud contains thetwo horns facing the ldquoYlinenrdquo skyload at about 50 K Bottom detail ofthe front end The two FEMs and the pair of horns are facing the twoskyload containers

Fig 8 Ylinen design of the RCA sky load calibrator This design pro-duced a load with minus20 dB of return loss over the whole bandwidth Thetwo light blue shaded regions represent the horn mouth at the left and therectangular waveguide injector on the right The absorber is enclosed ina metallic box except for the part facing the horn which is closed witha Teflonrcopyplate

Page 6 of 14

F Villa et al Calibration of LFI flight model radiometers

Fig 9 Functional test performed at cryogenic temperature on RCA26The two lines (orange and cyan) refer to the sky and load signals whenthe 4 KHz switching is activated Outside the interval 310ndash350 s the twocurves are indistinguishable

the output voltage of the detector S-10 when the functional testis run the BEM is switched on the FEM is biased at nominalconditions and the fast 4 KHz switching is activated on the phaseswitches It is evident that most of the change in signal is expe-rienced when the BEM is on and the phase switches are biasedcorrectly These functional tests were also used as a referencefor further tests up to the satellite-level verification campaignbesides checking the functionality of the RCA to proceed withthe calibration

42 Tuning

Before tuning the RCA the DAE was set-up to read the voltagefrom each detector of the BEM VBEM with appropriate resolu-tion The output signal from the DAE VDAE is given by

VDAE = GDAE middot (VBEM minus ODAE) (14)

The DAE gain GDAE was set to ensure that the noise inducedby the DAE did not influence the noise of the radiometric signalfrom the BEM detectors The voltage offset ODAE was adjustedto guarantee that the output voltage signal lay well within the[minus25+25] Volts range when the gain was set properly for theinput temperature range GDAE and ODAE were set for each of thefour detectors and employed during all noise property tests

The aim of the RCA tuning procedure (RCA_TUN) was tochoose the best bias conditions for each FEM low noise am-plifiersrsquo (LNA) gate voltage and phase switch current Each ofthe four LNAs in a 30 GHz FEM consists of four amplificationstages (five for the FEM at 44 GHz) each driven by the samedrain voltage Vd The gate voltage Vg1 biases the first amplifica-tion stage while Vg2 biases the successive three (or four) stagesThe phase switches are driven by two currents (I1 and I2) bias-ing each diode The currents determine the amount of attenuationby each diode and thus are adjusted to obtain the final overall ra-diometer balance

The phase switches between the LNA and the second hybriduse the interconnection of two hybrid rings to improve the band-width and the matching with two Shunt PIN diodes Dependingon the polarization of the diodes the signal travels into a circuitwhich can be λ2 longer so that it is shifted by 180 Detailscan be found in Hoyland (2004) and in Cuttaia et al (2009) In

Fig 10 Conceptual scheme of the phase switch integrated into the ra-diometers Each phase switch is composed of two diodes commandedby the currents I1 and I2 They act as a onoff switch Depending onthe polarization state of the diodes the signal follows the magenta pathor the cyan λ2 shifted path The two currents at which the diodes aretuned determine the attenuation of each path represented here by thedifferent thickness While the phase matching depends on the particularRF design the amplitude matching depends on the (I1 I2) bias supplyof the diodes which is the goal of the phase switch tuning

Fig 10 we report the conceptual schematic diagram of the phaseswitch

At 30 and 44 GHz the phase switches were tuned withone radiometer leg switched off In these conditions the signalentering each phase switch diode is the same and the output sig-nal at the DAE can be used directly to precisely balance the twostates of the phase switch Any differences in the sky and refsignal are caused only by the phase switches and not by othernon-idealities of the radiometers nor by different input targettemperatures The two currents were chosen to minimize thequadratic differences δPSW between odd and even samples ofthe signal (corresponding in Fig 10 to the magenta and cyanpath respectively) If for example the phase switch was tuned onthe same leg as the amplifier M1 the following expression wasminimized

δPSWM1 =

radic(S o

00 minus S e00

)2+

(S o

01 minus S e01

)2 (15)

where S 00 S 01 are the two DAE outputs related to the ldquoMrdquo halfFEM In this case o and e refer to odd and even signal sam-ples The same differences for the other phase switches δPSW

M2 δPSW

S1 and δPSWS2 were calculated in the same way The I1 and

I2 were varied around the best value obtained during the FEMstand-alone tests (Davis et al 2009) The phase switches of the70 GHz RCAs were not tuned To reduce the transient the phaseswitches were always biased at the maximum allowable current

The front-end LNAs were tuned for noise temperature per-formance Tn and isolation I For each channel Tn and I weremeasured as a function of the gate voltages Vg1 and Vg2

Firstly the minimum noise conditions were found by varyingVg1 while keeping Vg2 and Vd fixed The noise temperature wasmeasured with the Y-factor method (see Appendix A for the de-tails of this method) Because only relative estimates of Tn arerelevant for tuning purposes we did not correct for the effect ofnon-linearity in the 30 and 44 GHz RCAs

Once the optimum Vg1 was determined the optimum Vg2 wasfound by maximizing the isolation I

I =ΔVsky minusG0 middot ΔTsky(

ΔVref minusG0 middot ΔTsky

)+ ΔVsky

(16)

Page 7 of 14

AampA 520 A6 (2010)

measured by varying Tref with Tsky kept fixed The term minusG0 middotΔTsky is a correction factor for any unwanted variation of Tskyoriginating chiefly from thermal non-ideality of the cryofacility

At 70 GHz the best working conditions were found by mea-suring the noise temperature and the isolation as a function ofthe gate voltages Vg1 and Vg2 but with a slightly different ap-proach mainly for schedule reasons to that of the lower fre-quency chains The procedure required two different tempera-tures for the reference load (about 10 K in the low state and about20 K in the high state) and Vg1 Vg2 and Vd were varied indepen-dently on the half FEM Then the procedure was repeated withboth FEM legs switched on The noise temperature was mea-sured with the Y-factor method from the signals coming fromthe two temperature states and the isolation was calculated withEq (16)

Although the bias parameters found during the RCA tuningare the optimal ones we found that different electrical and cryo-genic conditions induce uncertainties in the bias values This isdue to the different grounding and the impact of the thermal gra-dient along the bias cables To overcome this problem tuningverification campaigns are planned at LFI integrated level andinflight In both cases the RCA bias values have been assumedas reference values

43 Basic properties

The basic properties of the radiometers namely noise tempera-ture isolation gain and linearity were obtained in a single test

The RCA_LIS test was performed varying Tsky (and subse-quently Tref) in steps while keeping the Tref (and subsequentlyTsky) constant In Fig 11 we give the temperature range spannedduring the tests Due to the different thermal behavior of eachRCA the range was not the same for all the chains The bright-ness temperature was calculated from temperature sensors lo-cated in the external calibrators (both sky and reference) andthe output voltages of the four detectors were recorded Themain uncertainty was in the determination of the actual bright-ness temperature seen by the radiometer At 30 and 44 GHz thebrightness temperature of the skyload was derived from the ther-mometer located inside the pyramids from where the main ther-mal noise emission originated For 70 GHz both the backplatethermometer and the absorber thermometer were used to derivethe brightness temperature However the backplate and the ab-sorber temperatures were found to introduce a significant sys-tematic error in the reconstructed physical temperature of theload as explained in Sect 34 It was decided to calibrate the70 GHz RCAs using the reference load steps instead

We denote here for simplicity the value of either Vskyout or V ref

outwith Vout in Eqs (5) and (8) alternatively Tsky or Tref with Tinand the corresponding T sky

N or T refN with Tsys With G we denote

the corresponding total gainFor a perfectly linear radiometer the output signal can be

written as

Vout = G middot (Tin + Tsys) (17)

and the gain and system temperature can be calculated by mea-suring the output voltage for only two different values of theinput temperature (Y-factor method) This was indeed the casefor the 70 GHz RCAs For the 30 and 44 GHz RCAs the deter-mination of the basic properties was complicated by a signifi-cant non-linear component in the response of the 30 and 44 GHzRCAs This was discovered during the previous qualificationcampaign and has been well characterized during these flight

Fig 11 Physical temperature ranges for the RCA_LIS tests Black linesrefer to the reference load temperature steps Gray lines refer to theskyload temperature steps

Fig 12 Typical temperature behavior of sky load (blue) reference load(green) and FEM body (red) during the RCA_STn test The temperaturestability is better than 1 mK

model RCA tests The non-linearity effects in LFI are discussedin Mennella et al (2009) together with its impact on the sci-ence performances For a radiometer with compression effectsthe radiometer gain G is a function of total input temperatureT = Tin + Tsys and is given by

Vout = G(T ) middot (Tin + Tsys) (18)

Particular care was required in the determination of the noisetemperature of the 30 and 44 GHz RCAs To overcome theproblem the application of four different types of fit were per-formed

1 Linear fit This fit was always calculated as a reference evenfor non-linear behavior of the radiometer so that

Vout = Glin middot T (19)

The linear gain Glin and the noise temperature were derivedThe fit was applied to all available data not only to the twotemperature steps as in the Y-factor method to reduce theuncertainties for the linear 70 GHz RCAs and to evaluate thenon-linearity of the 30 and 44 GHz chains

2 Parabolic fit This was applied to understand the effect ofthe non-linearity for the evaluation of which the quadraticfit is the simplest way The output of the fit were the threecoefficients from the equation

Vout = a0 + a1T + a2T 2 (20)

Page 8 of 14

F Villa et al Calibration of LFI flight model radiometers

Table 4 Receiver basic properties

Isol (dB)LinearModel

M-00 M-01 S-10 S-11RCA18 ndash135 ndash130 ndash111 ndash109RCA19 ndash155 ndash159 ndash153 ndash139RCA20 ndash158 ndash159 ndash127 ndash142RCA21 ndash130 ndash124 ndash101 ndash104RCA22 ndash128 ndash111 ndash124 ndash113RCA23 ndash126 ndash118 ndash133 ndash143RCA24 ndash117 ndash123 ndash104 ndash105

(ndash133) (ndash136) (116) (ndash119)RCA25 ndash108 ndash107 ndash120 ndash115

(ndash146) (ndash144) (ndash155) (ndash145)RCA26 ndash108 ndash119 ndash137 ndash137

(ndash97) (ndash104) (ndash139) (ndash140)RCA27 ndash130 ndash128 ndash147 ndash146

(ndash112) (ndash110) (ndash117) (ndash118)RCA28 ndash109 ndash103 ndash103 ndash105

(ndash116) (ndash112) (ndash120) (ndash122)

Notes Isolation in dB The values found during the Vg2 tuning are alsoreported in brackets for comparison

In this case the noise temperature was employed as the solu-tion of the equation a2T 2

sys + a1Tsys + a0 = 03 Inverse parabolic fit This was used because the noise tem-

perature was directly derived from

T = a0 + a1Vout + a2V2out (21)

where Tsys = a04 Gain model fit A new gain model was developed based

on the results of Daywitt (1989) modified for the LFI (seeAppendix B) The total power output voltage was written as

Vout =

⎡⎢⎢⎢⎢⎢⎢⎣ G0

1 + b middotG0 middot(Tin + Tsys

)⎤⎥⎥⎥⎥⎥⎥⎦ middot (Tin + Tsys

) (22)

where G0 is the total gain in the case of a linear radiometerb is the linear coefficient (b = 0 in the linear case b = infin forcomplete saturation ie G(T ) = 0)

The values obtained for gain linearity and noise temperature arereported in Table 5 The isolation values were calculated withEq (16) based on all possible combinations of temperature vari-ation on the reference load The results are given in Table 4where the values obtained during the tuning of the Vg2 are alsoreported for the 30 and 44 GHz RCAs While at 30 GHz thedifferences are due mainly to the reference load thermal modelapplied in this case for the 44 GHz RCAs the differences aredominated by the gain used to compensate for thermal couplingin Eq (16)

44 Noise properties

Radiometer noise properties were derived from the RCA_STntest This test consisted of acquiring data under stable thermalconditions for at least three hours Then the temperature of theloads were changed to measure the noise properties at differentsky and reference target temperatures As expected the best 1 fconditions were found when the difference between the sky andreference load temperatures was minimal This occurred at thefirst and last step as seen in Fig 12 which represents a typical

Table 5 Receiver basic properties gain noise temperature andlinearity

Gain (VK) Tn (K) and LinM-00 M-01 S-10 S-11

RCA18 G0 00173 00195 00147 00143Tn 360 361 339 351

RCA19 G0 00161 00174 00176 00196Tn 331 315 322 336

RCA20 G0 00186 00164 00161 00165Tn 352 342 369 350

RCA21 G0 00161 00154 00119 00114Tn 273 284 344 364

RCA22 G0 00197 00174 00165 00163Tn 309 303 303 318

RCA23 G0 00149 00171 00271 00185Tn 359 341 339 311

RCA24 G0 00048 00044 00062 00062Tn 155 153 158 158b 179 149 144 145

RCA25 G0 00086 00085 00079 00071Tn 175 179 186 184b 122 117 080 101

RCA26 G0 00052 00067 00075 00082Tn 184 174 168 165b 109 142 094 122

RCA27 G0 00723 00774 00664 00562Tn 121 119 130 125b 012 012 013 014

RCA28 G0 00621 00839 00607 00518Tn 106 103 99 98b 019 016 019 020

Notes For the 70 GHz RCAs the gain G0 and the noise temperatureTn were derived from the linear fit and the linearity coefficient is notreported For 30 and 44 GHz G0 Tn and the linearity coefficient bwere derived from the gain model-fit

temperature profile of the test The amplitude spectral densitywas calculated for each output diode The 1 f component (kneefrequency fk and slope α) the white noise plateau and the gainmodulation factor r were derived At 70 GHz the 1 f spectrumwas clearly dominated by thermal instabilities of the BEM whichwas not controlled in temperature There the measured knee fre-quency values were over-estimated while at 30 and 44 GHz thecryofacility was sufficiently stable to characterize the 1 f perfor-mances of the radiometers From the white noise and DC levelthe effective bandwidth was calculated as

β = K2 middot V2out

ΔV2out middot τ

(23)

where ΔVout is the white noise level Vout is the DC level τ theintegration time and K = 1 for a single detector total powerin the unswitched condition K =

radic2 for a single detector to-

tal power in the switched condition K = 2 for a single detec-tor differenced data K =

radic2 for double-diode differenced data

This formula does not include the non-linearity effects that arediscussed in detail by Mennella et al (2009) The overall noiseperformances of all eleven RCAs are reported in Table 6 whileFig 13 shows the typical amplitude spectral density of the noisefor each frequency channel

Apart from 1 f noise and white noise spikes were observedin all RCAs at 70 GHz they were caused by the electrical inter-action between the two DAE units which were slightly unsyn-chronised at 30 and 44 GHz they were due to the housekeeping

Page 9 of 14

AampA 520 A6 (2010)

Fig 13 Log-log plot of the amplitude spectral density of the differential detector output noise The left plot refers to the RCA27M-00 detector withthe sky and the reference loads both at 20 K the plot in the center refers to the RCA26M-00 detector with sky and reference loads at 8 K and 13 Krespectively the plot on the right refers to the RCA23S-11 with the sky and reference loads at 15 K and 9 K respectively

acquisition system Because it was clear that the spikes were al-ways due to the test setup and not to the radiometers themselvesthe spikes were not considered critical at this stage even if theyshowed up in frequency and amplitude

As an example of the dependence of the noise performanceon the temperature the antenna temperature pairs used duringthe the tests of the RCA28 are reported in Table 7 These temper-atures were calculated with the coefficients reported in Tables 2and 3 of Sect 31 with the physical temperatures converted intoantenna temperatures The differences between the Tref and theTsky were calculated for each arm of the radiometer The result-ing 1 f knee frequency the slope of the 1 f spectra and thegain modulation factor r are reported in Fig 14 as a function ofthe temperature differences It is evident from these plots that theknee frequency is increasing with the temperature difference asexpected Moreover the gain modulation factor is approachingunity as the input temperature difference becomes zero whichagrees with Eq (4) The slope α does not show any correlationwith the temperature differences because it depends on the am-plifiers rather than on the

(Tref minus Tsky

) This behavior was also

found in the other RCAs

45 Bandpass

A dedicated end-to-end spectral response test RCA_SPR wasdesigned and carried out to measure radiometer RF bandshapein operational conditions ie on the integrated RCA with thefront-end at the cryogenic temperature An external RF sourcewas used to inject a monochromatic signal sweeping through theband into the sky horn Then the DC output of the radiometerwas recorded as a function of the input frequency giving the rel-ative overall RCA gain-shape Gspr(ν) The equivalent bandwidthwas calculated with

βspr =

(intGspr(ν)dν

)2

intGspr(ν)2dν

middot (24)

Different setup configurations were used At 70 GHz the RF sig-nal was directly injected into the sky horn The input signal wasvaried by 50 points from 575 GHz to 825 GHz At 30 GHzand 44 GHz the RF signal was injected into the sky horn af-ter a reflection on the sky load absorberrsquos pyramids scanningin frequency from 265 GHz to 40 GHz in 271 points and from33 GHz to 50 GHz in 341 points The flexible waveguides WR28and WR22 were used to reach the skyload for the 30 and 44 GHzRCAs (Fig 15) The input signal was not calibrated in powerbecause only a relative band shape measurement was requiredThe stability of the signal was ensured by the use of a synthe-sized sweeper generator guaranteeing the stability of the output

Fig 14 1 f knee frequency (asterisk on the left) gain modulation fac-tor (diamonds in the center) and the slope of the 1 f spectrum (trian-gles on the right) as a function of

(Tref minus Tsky

) Sixteen points (four pairs

for each detector) were reported The spread of knee frequency valuesis due to the intrinsic difficulty of fitting the lower part of the powerspectral density

within 10 The attenuation curve of the waveguide carrying thesignal from the sweeper to the injector was treated as a rectan-gular standard waveguide with losses during the data analysis

All RCA bandshapes were measured but for the two 30 GHzRCAs only half a radiometer was successfully tested due to asetup problem that appeared when the RCAs were cooled downFor schedule reasons it was not possible to repeat the test at theoperational temperature and only a check at the warm temper-ature was performed This warm test was not used for calibra-tion due to different dynamic range amplifier behavior and biasconditions Results are reported in Table 8 and plots of all themeasurements in Figs 16ndash18 All curves reported in the plotsare normalized to the area so that

Gnspr(ν) =

Gspr(ν)intGspr(ν)dν

middot (25)

The bandshape is mainly determined by the filter located insideeach BEM whose frequency response is independent of the tun-ing of the FEM amplifiers The dependence of the bandshape onthe amplifier biases has been checked on the 30 GHz radiome-ters (De Nardo 2008) showing that at first order the responseremains unchanged A similar situation occurs on the RCAs at

Page 10 of 14

AampA 520 A6 (2010)

Fig 13 Log-log plot of the amplitude spectral density of the differential detector output noise The left plot refers to the RCA27M-00 detector withthe sky and the reference loads both at 20 K the plot in the center refers to the RCA26M-00 detector with sky and reference loads at 8 K and 13 Krespectively the plot on the right refers to the RCA23S-11 with the sky and reference loads at 15 K and 9 K respectively

acquisition system Because it was clear that the spikes were al-ways due to the test setup and not to the radiometers themselvesthe spikes were not considered critical at this stage even if theyshowed up in frequency and amplitude

As an example of the dependence of the noise performanceon the temperature the antenna temperature pairs used duringthe the tests of the RCA28 are reported in Table 7 These temper-atures were calculated with the coefficients reported in Tables 2and 3 of Sect 31 with the physical temperatures converted intoantenna temperatures The differences between the Tref and theTsky were calculated for each arm of the radiometer The result-ing 1 f knee frequency the slope of the 1 f spectra and thegain modulation factor r are reported in Fig 14 as a function ofthe temperature differences It is evident from these plots that theknee frequency is increasing with the temperature difference asexpected Moreover the gain modulation factor is approachingunity as the input temperature difference becomes zero whichagrees with Eq (4) The slope α does not show any correlationwith the temperature differences because it depends on the am-plifiers rather than on the

(Tref minus Tsky

) This behavior was also

found in the other RCAs

45 Bandpass

A dedicated end-to-end spectral response test RCA_SPR wasdesigned and carried out to measure radiometer RF bandshapein operational conditions ie on the integrated RCA with thefront-end at the cryogenic temperature An external RF sourcewas used to inject a monochromatic signal sweeping through theband into the sky horn Then the DC output of the radiometerwas recorded as a function of the input frequency giving the rel-ative overall RCA gain-shape Gspr(ν) The equivalent bandwidthwas calculated with

βspr =

(intGspr(ν)dν

)2

intGspr(ν)2dν

middot (24)

Different setup configurations were used At 70 GHz the RF sig-nal was directly injected into the sky horn The input signal wasvaried by 50 points from 575 GHz to 825 GHz At 30 GHzand 44 GHz the RF signal was injected into the sky horn af-ter a reflection on the sky load absorberrsquos pyramids scanningin frequency from 265 GHz to 40 GHz in 271 points and from33 GHz to 50 GHz in 341 points The flexible waveguides WR28and WR22 were used to reach the skyload for the 30 and 44 GHzRCAs (Fig 15) The input signal was not calibrated in powerbecause only a relative band shape measurement was requiredThe stability of the signal was ensured by the use of a synthe-sized sweeper generator guaranteeing the stability of the output

Fig 14 1 f knee frequency (asterisk on the left) gain modulation fac-tor (diamonds in the center) and the slope of the 1 f spectrum (trian-gles on the right) as a function of

(Tref minus Tsky

) Sixteen points (four pairs

for each detector) were reported The spread of knee frequency valuesis due to the intrinsic difficulty of fitting the lower part of the powerspectral density

within 10 The attenuation curve of the waveguide carrying thesignal from the sweeper to the injector was treated as a rectan-gular standard waveguide with losses during the data analysis

All RCA bandshapes were measured but for the two 30 GHzRCAs only half a radiometer was successfully tested due to asetup problem that appeared when the RCAs were cooled downFor schedule reasons it was not possible to repeat the test at theoperational temperature and only a check at the warm temper-ature was performed This warm test was not used for calibra-tion due to different dynamic range amplifier behavior and biasconditions Results are reported in Table 8 and plots of all themeasurements in Figs 16ndash18 All curves reported in the plotsare normalized to the area so that

Gnspr(ν) =

Gspr(ν)intGspr(ν)dν

middot (25)

The bandshape is mainly determined by the filter located insideeach BEM whose frequency response is independent of the tun-ing of the FEM amplifiers The dependence of the bandshape onthe amplifier biases has been checked on the 30 GHz radiome-ters (De Nardo 2008) showing that at first order the responseremains unchanged A similar situation occurs on the RCAs at

Page 10 of 14

F Villa et al Calibration of LFI flight model radiometers

Fig 15 Setup of the RCA_SPR tests The picture and the sketch on the left report the test setup of the 30 and 44 GHz RCAs The flexible waveguideis clearly visible on the picture on the side of the horn The picture and the sketch on the right report the setup of the 70 GHz RCAs There thesignal was injected infront of the horn through the sky load and copper rigid waveguides were used to carry the signal form the generator to theRCAs

Fig 16 Measured relative gain function (bandpass) of the 8 detectorsat 30 GHz The curves that show big ripples are those caused by thesetup problem (see text) The bandpasses are normalized to the area asexplained in the text

44 GHz and 70 GHz where the tuning has second order effectson the overall frequency response

46 Susceptibility

Any variation in physical temperature of the RCA Tphys willproduce a variation of the output signal that mimics the variationof the input temperature Tsky so that

δTsky = Tf middot δTphys (26)

Fig 17 Measured relative gain function (bandpass) of all 12 detectorsat 44 GHz The bandpasses are normalized to the area as explained inthe text

where Tf is the transfer function A controlled variation of FEMtemperature was imposed to calculate the transfer function ofthe front end modules T FEM

f This was done for all RCAs and alldetectors The chief results are given in Table 9 while the detailsof the applied method and of the measurements are reported byTerenzi et al (2009c)

The susceptibility of the radiometer signal to temperaturevariations in the BEM and 3rd V-groove were measured onlyfor the 30 and 44 GHz chains because at 70 GHz it wasnot possible to control the temperatures of these interfaces intheir cryofacility Here we report on the BEM susceptivity tests

Page 11 of 14

AampA 520 A6 (2010)

Table 6 Receiver noise properties 1 f knee frequency slope andr factor

1f spectrum r factor and βM-00 M-01 S-10 S-11

RCA18 fk 92 92 140 190α ndash162 ndash171 ndash149 ndash171r 117 117 117 116β 957 1030 853 1078

RCA19 fk 130 96 144 143α ndash175 ndash193 ndash180 ndash185r 112 112 114 113β 890 910 900 1106

RCA20 fk 557 637 1193 985α ndash163 ndash148 ndash136 ndash132r 103 102 103 104β 1074 946 1086 1048

RCA21 fk 109 85 109 97α ndash159 ndash190 ndash161 ndash117r 121 121 118 118β 1002 1008 979 879

RCA22 fk 116 108 80 113α ndash159 ndash190 ndash161 ndash165r 121 121 118 118β 1002 108 979 879

RCA23 fk 97 89 101 109α ndash141 ndash192 ndash190 ndash183r 107 107 108 108β 1131 1302 1105 1189

RCA24a fk 139 102 97 133α ndash113 ndash126 ndash115 ndash118r 0991 0974 0971 0962β 613 412 521 659

RCA25b fk 180 219 96 47α ndash112 ndash128 104 ndash089r 10289 1059 ndash0859 1041β 687 688 496 682

RCA26c fk 210 232 154 231α ndash102 ndash072 ndash067 ndash081r 1085 1061 1131 1119β 567 552 501 740

RCA27d fk 67 101 249 311α ndash102 ndash119 ndash139 ndash090r 1012 1004 1093 1075β 777 770 873 718

RCA28e fk 199 194 407 411α ndash139 ndash120 ndash157 ndash160r 1058 1050 0955 0939β 791 794 878 823

Notes Data were taken setting the temperature of the loads at the lowestpossible values The 70 GHz 1 f knee frequencies are dominated by thethermal instabilities of the cryochamber (a) Tref = 85 K Tsky = 85 K(b) Tref = 80 K Tsky = 105 K (c) Tref = 80 K Tsky = 130 K (d) Tref =95 K Tsky = 128 K (e) Tref = 86 K Tsky = 85 K

only it is the prominent radiometric effect between both be-cause the diodes are thermally attached to the BEM body Thetotal power output voltage on each BEM detector can then beexpressed by modifying Eq (18)

Vout = Gtot

(T bem

0

)middot[1 + Tf middot

(T bem minus T bem

0

)]middot(Tin + Tsys

) (27)

Fig 18 Measured relative gain function (bandpass) of all 24 detectorsat 77 GHz The bandpasses are normalized to the area as explained inthe text

Table 7 Receiver noise properties Long duration test antennatemperature pairs for the RCA28

Tsky[K] Tref[K](Tref minus Tsky

)M S M S

848 1021 885 173 037907 1516 1466 610 559974 1945 1936 970 9621963 1945 1936 ndash018 ndash027

Table 8 Spectral response test results

SPR Bandwidth and central frequencyM-00 M-01 S-10 S-11

RCA18 βspr 1240 1114 1084 1025RCA19 βspr 1045 1074 800 991RCA20 βspr 1119 1221 1257 1082RCA21 βspr 1119 1221 1257 1082RCA22 βspr 1149 1038 1111 1044RCA23 βspr 1035 1152 1162 1144RCA24 βspr 515 408 526 582

ν0 4575 424 456 453RCA25 βspr 442 449 417 591

ν0 4575 4525 4585 4490RCA26 βspr 610 486 426 548

ν0 4435 4485 4490 4420RCA27 βspr ndash ndash 389 371

ν0 ndash ndash 3045 3070RCA28 βspr 494 512 ndash ndash

ν0 314 3135 ndash ndash

Notes The numbers are bandwidth values βspr and central frequencyν0 both in GHz

There Gtot

(T bem

0

)is the total power gain when the BEM is at

nominal physical temperature T bem0 while T bem is the BEM

physical temperature that was varied in steps Non-linear effectswere not considered because they were mainly caused by thechange in Tin which was fixed in this case By exploiting the lin-ear dependence between the voltage output and the BEM physi-cal temperature as

Vout = m middot T bem + q (28)

Page 12 of 14

F Villa et al Calibration of LFI flight model radiometers

Table 9 The transfer function of the susceptibility of FEM to tempera-ture variations

FEM susceptibilityTransfer Function cKK

M-00 M-01 S-10 S-11RCA18 ndash848 ndash913 ndash677 ndash767RCA19 ndash943 ndash928 ndash120 ndash949RCA20 ndash661 ndash569 ndash593 ndash579RCA21 ndash301 ndash185 ndash0770 ndash0930RCA22 567 521 569 604RCA23 ndash207 ndash441 ndash407 ndash392RCA24 ndash121 ndash0610 ndash203 ndash0964RCA25 ndash151 ndash133 ndash287 ndash221RCA26 ndash622 ndash610 ndash657 ndash631RCA27 ndash168 ndash105 ndash364 ndash306RCA28 ndash0266 ndash0519 ndash185 ndash105

Table 10 The transfer function of the susceptibility of BEM to temper-ature variations

BEM susceptibilityTransfer Function 1K

M-00 M-01 S-10 S-11 T bem0 C

RCA24 ndash0008 ndash0009 ndash0008 ndash0008 34292RCA25 ndash0020 ndash0021 ndash0022 ndash0021 35237RCA26 ndash0018 ndash0018 ndash0018 ndash0017 31810RCA27 ndash0006 ndash0006 ndash0009 ndash0007 40178

Notes The physical temperature of the BEM is also reported in the lastcolumn

with the transfer function Tf calculated from a linear fit to thedata as

Tf =m

m middot T bem0 + q

middot (29)

The values are reported in Table 10

5 Conclusions

The eleven LFI RCAs were calibrated according to the over-all LFI calibration plan The front end low-noise amplifiersand phase switches were properly tuned to guarantee mini-mum noise temperature and best isolation Basic performances(noise temperature isolation linearity photometric gain) noiseproperties (1 f spectrum noise equivalent bandwidth) relativebandshape and susceptibility to thermal variations were mea-sured in a dedicated cryogenic environment as close as possi-ble to flight-operational conditions All radiometric parameterswere measured with excellent repeatability and reliability ex-cept for 1 f noise at 70 GHz and some of the bandpasses at30 GHz The measurements were essentially in line with thedesign expectations indicating a satisfactory instrument perfor-mance Ultimately all RCA units were accepted because themeasured performances were in line with the scientific goal ofLFI The RCA test campaign described here represents the pri-mary calibration test for some key radiometric parameters of theLFI because they were not accurately measured as part of theRAA calibration campaign nor can they be measured in-flightduring the Planck nominal survey

ndash Tuning results were used to set the subsequent tuning verifi-cation procedure up to the calibration performance and veri-fication phase (CPV) in flight

ndash Non-linear behavior of the 30 and 44 GHz RCAs was ac-curately measured and characterized and used to estimatethe impact in flight (Mennella et al 2009) Moreover eachradiometer system noise temperature was accurately deter-mined

ndash Except for some of the measured spectral responses inwhich systematic effects arising from standing waves in thesky load were experienced the RCA band shapes were onlymeasured and characterized during the RCA tests Togetherwith the independent estimates of the band shape based ona synthesis of measured responses at unit level (Zonca et al2009) they are essential for the flight data analysis

ndash Susceptivity to thermal variation of the FEM and BEMwas measured and represents the reference values becauseonly the FEM susceptivity was measured during RAA tests(Terenzi et al 2009a) but under worse thermal conditions

In conclusion we can state that even if the RCA calibration cam-paign was an intermediate step in the LFI development the re-sults obtained and presented here will be used in conjunctionwith the performance measured in flight to the exploitation ofthe scientific goal of Planck

Acknowledgements Planck is a project of the European Space Agency withinstruments funded by ESA member states and with special contributionsfrom Denmark and NASA (USA) The Planck-LFI project is developed by anInternational Consortium lead by Italy and involving Canada Finland GermanyNorway Spain Switzerland UK USA The Italian contribution to Planckis supported by the Italian Space Agency (ASI) In Finland the Planck LFI70 GHz work was supported by the Finnish Funding Agency for Technologyand Innovation (Tekes) TPrsquos work was supported in part by the Academy ofFinland grants 205800 214598 121703 and 121962 TP thank Waldemar vonFrenckells stiftelse Magnus Ehrnrooth Foundation and Vaumlisaumllauml Foundation forfinancial support The Spanish participation is funded by Ministerio de Ciencia eInnovacion through the projects ESP2004-07067-C03-01 and AYA2007-68058-C03-02

Appendix A Y-factor method

The classical Y-factor method is the simplest way to calculatethe noise temperature and it requires that radiometric data areacquired at two different (possibly well-separated) physical tem-peratures of one of the input loads Below we will assume a skyload temperature increase Clearly the treatment is completelysymmetrical if the reference load temperature is increased If wedenote with Tlow and Thigh as the antenna temperatures corre-sponding to the skyload physical temperatures we find that theratio between the output voltages is given by

Vlow

Vhigh=

Tlow + TN

Thigh + TNequiv 1

Ymiddot (A1)

The system noise temperature is then calculated as

TN equiv Thigh minus Y middot Tlow

Y minus 1middot (A2)

Appendix B Radiometer non-linear model (gainmodel)

A non-linear gain model was developed and applied to the 30and 44 GHz RCAs to model the observed behavior of the outputvoltages as a function of input temperature The model was de-veloped on the basis of Daywitt (1989) and specifically adoptedfor the LFI 30 and 44 GHz RCAs which exhibit a non-negligible

Page 13 of 14

AampA 520 A6 (2010)

compression effect in the BEMs The FEM is assumed to have aconstant gain and noise temperature

FEM

Gain = GFEM0

Noise = T FEMN

(B1)

The BEM (Artal et al 2009) shows an overall gain (includingthe detector diode) which depends on the BEM input power asfollows

BEM

Gain = GBEM =

GBEM0

1+bmiddotGBEM0 middotp

Noise = T BEMN

(B2)

where p is the power entering the BEM and b is a parameterdefining the non-linearity of the BEM For b = 0 the radiometeris linear for b = infin the BEM has a null-gain for any input powerfor p = infin the BEM is completely compressed and GBEM = 0 forany value of the non-linearity parameter

The power entering the BEM (we here neglect the attenua-tion of the waveguides whose effect can be modeled as a smallreduction of the FEM gain and a small increase of the FEM noisetemperature) can be written as

p = k middot B middotGFEM0 middot (TA + TN) (B3)

where

TN = T FEMN +

T BEMN

GFEM0

middot (B4)

The voltage at each output BEM detector (the detector diodeconstant is included in the BEM gain) can be written as

Vout = k middot B middotGFEM0 middot GBEM

0 middot (TA + TN)

1 + b middotGBEM0 middot (TA + TN)

= G0

[1

1 + b middotG0 middot (TA + TN)

]middot (TA + TN) (B5)

where

G0 = GFEM0 middotGBEM

0 middot k middot B (B6)

In a compact way Eq (B6) can be written as

Vout = Gtot middot (TA + TN) (B7)

Gtot = G0

[1

1 + b middotG0 middot (TA + TN)

] (B8)

where the Gtot is the total gain of the radiometer which dependson the input antenna temperature G0 is the radiometer lineargain and it coincides with the overall gain in case of perfect lin-earity (b = 0)

ReferencesArtal E Aja B de la Fuente M L et al 2009 JINST 4 T12003Bersanelli M Mandolesi N Butler R C et al 2010 AampA 520 A4

Cuttaia F 2005 PhD Thesis University of BolognaCuttaia F Mennella A Stringhetti L et al 2009 JINST 4 T12013DrsquoArcangelo O Figini L Simonetto A et al 2009a JINST 4 T12007DrsquoArcangelo O Simonetto A Figini L Pagana E Villa F Pecora

M Battaglia P Bersanelli M Butler R C Garavaglia S Guzzi PMandolesi N amp Sozzi C 2009b JINST 4 T12005

Davis R J Wilkinson A Davies R D et al 2009 JINST 4 T12002Daywitt W C 1989 NIST Tech Note 1327De Nardo S 2008 Masterrsquos Thesis Univeristagrave degli Studi di MilanoHoyland R 2004 US patent 6 803 838 B2Malaspina M Franceschi E Battaglia P et al 2009 JINST 4 T12017Mennella A Bersanelli M Seiffert M et al 2003 AampA 410 1089Mennella A Villa F Terenzi L et al 2009 JINST 4 T12011Mennella A Bersanelli M Butler R C et al 2010 AampA 520 A5Seiffert M Mennella A Burigana C et al 2002 AampA 391 1185Terenzi L Cuttaia F De Rosa A L V et al 2009a JINST submittedTerenzi L Lapolla M Laaninen M et al 2009b JINST 4 T12015Terenzi L Salmon M J Colin A et al 2009c JINST 4 T12012Valenziano L Cuttaia F De Rosa A et al 2009 JINST 4 T12006Varis J Hughes N J Laaninen M et al 2009 JINST 4 T12001Villa F DrsquoArcangelo O Pecora M et al 2009 JINST 4 T12004Zonca A Franceschet C Battaglia P et al 2009 JINST 4 T12010

1 INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica via PGobetti 101 40129 Bologna Italye-mail villaiasfboinafit

2 Department of Physics University of California Santa Barbara93106-9530 USA

3 University of Helsinki Department of Physics PO Box 64 00014Helsinki Finland

4 Helsinki Institute of Physics PO Box 64 00014 Helsinki Finland5 Metsaumlhovi Radio Observatory Helsinki University of Technology

Metsaumlhovintie 114 02540 Kylmaumllauml Finland6 Thales Alenia Space Italia SpA SS Padana Superiore 290 20090

Vimodrone (MI) Milano Italy7 Universitagrave degli Studi di Milano via Celoria 16 20133 Milano Italy8 DA-Design Oy (aka Ylinen Electronics) Keskuskatu 29 31600

Jokioinen Finland9 IFP-CNR via Cozzi 53 20125 Milano Italy

10 INAF - Osservatorio Astronomico di Trieste 11 via Tiepolo 34143Trieste Italy

11 University of Trieste Department of Physics 2 via Valerio 34127Trieste Italy

12 Jodrell Bank Centre for Astrophysics Alan Turing Building TheUniversity of Manchester Manchester M13 9PL UK

13 Planck Science Office European Space Agency ESAC PO box 7828691 Villanueva de la Cantildeada Madrid Spain

14 INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica via EBassini 15 20133 Milano Italy

15 Universidad de Cantabria Dep De Ingenieria de ComunicacionesAv Los Castros sn 39005 Santander-Spain

16 Instituto de Fisica de Cantabria (CSIC-UC) Av Los Castros sn39005 Santander Spain

17 Jet Propulsion Laboratory 4800 Oak Grove Drive PasadenaCalifornia 91109 USA

18 Instituto de Astrofiacutesica de Canarias C Via Lactea sn 38205 LaLaguna (Tenerife) Spain

19 National Radio Astronomy Observatory Stone hall University ofVirginia 520 Edgemont road Charlottesville USA

20 MilliLab VTT Technical Research Centre of Finland Tietotie 3Otaniemi Espoo Finland

Page 14 of 14

• Introduction
• Main concepts and calibration logic
• • Radiometer chain assembly description
  • Signal model
  • Radiometer chain assembly calibration plan
  • • Radiometer chain assembly calibration facilities
    • • The cryofacility for the 30 and 44 GHz RCAs
      • Sky load at 30 and 44 GHz
      • The cryofacility of the 70 GHz RCAs
      • The skyloads at 70 GHz
      • • Methods and results
        • • Functional tests
          • Tuning
          • Basic properties
          • Noise properties
          • Bandpass
          • Susceptibility
          • • Conclusions
            • Y-factor method
            • Radiometer non-linear model (gain model)
            • References

AampA 520 A6 (2010)

compression effect in the BEMs The FEM is assumed to have aconstant gain and noise temperature

FEM

Gain = GFEM0

Noise = T FEMN

(B1)

The BEM (Artal et al 2009) shows an overall gain (includingthe detector diode) which depends on the BEM input power asfollows

BEM

Gain = GBEM =

GBEM0

1+bmiddotGBEM0 middotp

Noise = T BEMN

(B2)

where p is the power entering the BEM and b is a parameterdefining the non-linearity of the BEM For b = 0 the radiometeris linear for b = infin the BEM has a null-gain for any input powerfor p = infin the BEM is completely compressed and GBEM = 0 forany value of the non-linearity parameter

The power entering the BEM (we here neglect the attenua-tion of the waveguides whose effect can be modeled as a smallreduction of the FEM gain and a small increase of the FEM noisetemperature) can be written as

p = k middot B middotGFEM0 middot (TA + TN) (B3)

where

TN = T FEMN +

T BEMN

GFEM0

middot (B4)

The voltage at each output BEM detector (the detector diodeconstant is included in the BEM gain) can be written as

Vout = k middot B middotGFEM0 middot GBEM

0 middot (TA + TN)

1 + b middotGBEM0 middot (TA + TN)

= G0

[1

1 + b middotG0 middot (TA + TN)

]middot (TA + TN) (B5)

where

G0 = GFEM0 middotGBEM

0 middot k middot B (B6)

In a compact way Eq (B6) can be written as

Vout = Gtot middot (TA + TN) (B7)

Gtot = G0

[1

1 + b middotG0 middot (TA + TN)

] (B8)

where the Gtot is the total gain of the radiometer which dependson the input antenna temperature G0 is the radiometer lineargain and it coincides with the overall gain in case of perfect lin-earity (b = 0)

ReferencesArtal E Aja B de la Fuente M L et al 2009 JINST 4 T12003Bersanelli M Mandolesi N Butler R C et al 2010 AampA 520 A4

Cuttaia F 2005 PhD Thesis University of BolognaCuttaia F Mennella A Stringhetti L et al 2009 JINST 4 T12013DrsquoArcangelo O Figini L Simonetto A et al 2009a JINST 4 T12007DrsquoArcangelo O Simonetto A Figini L Pagana E Villa F Pecora

M Battaglia P Bersanelli M Butler R C Garavaglia S Guzzi PMandolesi N amp Sozzi C 2009b JINST 4 T12005

Davis R J Wilkinson A Davies R D et al 2009 JINST 4 T12002Daywitt W C 1989 NIST Tech Note 1327De Nardo S 2008 Masterrsquos Thesis Univeristagrave degli Studi di MilanoHoyland R 2004 US patent 6 803 838 B2Malaspina M Franceschi E Battaglia P et al 2009 JINST 4 T12017Mennella A Bersanelli M Seiffert M et al 2003 AampA 410 1089Mennella A Villa F Terenzi L et al 2009 JINST 4 T12011Mennella A Bersanelli M Butler R C et al 2010 AampA 520 A5Seiffert M Mennella A Burigana C et al 2002 AampA 391 1185Terenzi L Cuttaia F De Rosa A L V et al 2009a JINST submittedTerenzi L Lapolla M Laaninen M et al 2009b JINST 4 T12015Terenzi L Salmon M J Colin A et al 2009c JINST 4 T12012Valenziano L Cuttaia F De Rosa A et al 2009 JINST 4 T12006Varis J Hughes N J Laaninen M et al 2009 JINST 4 T12001Villa F DrsquoArcangelo O Pecora M et al 2009 JINST 4 T12004Zonca A Franceschet C Battaglia P et al 2009 JINST 4 T12010

1 INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica via PGobetti 101 40129 Bologna Italye-mail villaiasfboinafit

2 Department of Physics University of California Santa Barbara93106-9530 USA

3 University of Helsinki Department of Physics PO Box 64 00014Helsinki Finland

4 Helsinki Institute of Physics PO Box 64 00014 Helsinki Finland5 Metsaumlhovi Radio Observatory Helsinki University of Technology

Metsaumlhovintie 114 02540 Kylmaumllauml Finland6 Thales Alenia Space Italia SpA SS Padana Superiore 290 20090

Vimodrone (MI) Milano Italy7 Universitagrave degli Studi di Milano via Celoria 16 20133 Milano Italy8 DA-Design Oy (aka Ylinen Electronics) Keskuskatu 29 31600

Jokioinen Finland9 IFP-CNR via Cozzi 53 20125 Milano Italy

10 INAF - Osservatorio Astronomico di Trieste 11 via Tiepolo 34143Trieste Italy

11 University of Trieste Department of Physics 2 via Valerio 34127Trieste Italy

12 Jodrell Bank Centre for Astrophysics Alan Turing Building TheUniversity of Manchester Manchester M13 9PL UK

13 Planck Science Office European Space Agency ESAC PO box 7828691 Villanueva de la Cantildeada Madrid Spain

14 INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica via EBassini 15 20133 Milano Italy

15 Universidad de Cantabria Dep De Ingenieria de ComunicacionesAv Los Castros sn 39005 Santander-Spain

16 Instituto de Fisica de Cantabria (CSIC-UC) Av Los Castros sn39005 Santander Spain

17 Jet Propulsion Laboratory 4800 Oak Grove Drive PasadenaCalifornia 91109 USA

18 Instituto de Astrofiacutesica de Canarias C Via Lactea sn 38205 LaLaguna (Tenerife) Spain

19 National Radio Astronomy Observatory Stone hall University ofVirginia 520 Edgemont road Charlottesville USA

20 MilliLab VTT Technical Research Centre of Finland Tietotie 3Otaniemi Espoo Finland

Page 14 of 14

• Introduction
• Main concepts and calibration logic
• • Radiometer chain assembly description
  • Signal model
  • Radiometer chain assembly calibration plan
  • • Radiometer chain assembly calibration facilities
    • • The cryofacility for the 30 and 44 GHz RCAs
      • Sky load at 30 and 44 GHz
      • The cryofacility of the 70 GHz RCAs
      • The skyloads at 70 GHz
      • • Methods and results
        • • Functional tests
          • Tuning
          • Basic properties
          • Noise properties
          • Bandpass
          • Susceptibility
          • • Conclusions
            • Y-factor method
            • Radiometer non-linear model (gain model)
            • References