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Nuclear Instruments and Methods in Physics Research A 520 (2004) 396–401

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051-639-872

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0168-9002/$

doi:10.1016

Analysis of the radiometer—reference load system on boardthe Planck/LFI instrument

Francesco Cuttaiaa,*, Luca Valenzianoa, Marco Bersanellib, Reginald C. Butlera,Ocleto D’Arcangeloc, Danielle Kettled, Steven Levine, Nazareno Mandolesia,Aniello Mennellaf, Gianluca Morgantea, Gabriele Morigia, Neil Roddisd,Alessandro Simonettoc, Luca Terenzia, Maurizio Tomasif, Fabrizio Villaa

a IASF-CNR, Sezione. di Bologna, Via P. Gobetti 101, I-40129, Bologna, ItalybDipartimento di Fisica, Univ. Degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy

c IFP-CNR, Via Cozzi 53, I-20125, Milano, ItalydJodrell Bank Observator, Macclesfield, Cheshire SK11 9DL, UK

eJet Propulsion Laboratory, 4800 Oak Grove Drive, CA 91109, Pasadena, USAf IASF-CNR, Sezione. di Milano, Via Bassini 15, I-20133, Milano, Italy

Abstract

The Low Frequency Instrument aboard the Planck satellite will employ pseudo-correlation radiometers, operating

over three broad bands centered at 30, 44, 70GHz. This choice is oriented to maximize the instrumental stability

reducing non-white noise effects produced inside the radiometers. The radiometer scheme allows the simultaneous

comparison of two input signals, one coming from the telescope and the other coming from a reference blackbody (the

‘‘reference load’’ RL) at a stable temperature near 4K. In order to minimize non-white noise, typically exhibiting a 1=f

spectrum, the Reference Load temperature must be as close as possible to the sky temperature (about 2.7K). The

accuracy of the measurement is tightly related to the ability of keeping under control and minimizing all systematic

effects potentially perturbing the RL signal, particularly those not easily removable in software during data analysis. A

model of the radiometer and RL system interface, based on the finite elements method, has been developed, together

with a detailed thermal modeling, to characterize the physical system and to optimize its performance. The function of

the radiometric chain, the modeling and the changes made in the baseline configuration to improve the system

performances are described. The impact of systematic effects on the optimized configuration are also quantitatively

investigated.

r 2003 Elsevier B.V. All rights reserved.

Keywords: Cosmology; Cosmic microwave background; Satellite; Planck; Radiometer; Blackbody; Finite element method

onding author. Tel.: +39-051-639-8734; fax: +39-

4.

ddress: cuttaia@bo.iasf.cnr.it (F. Cuttaia).

- see front matter r 2003 Elsevier B.V. All rights reserve

/j.nima.2003.11.344

1. Introduction

The Planck satellite [1], to be launched in 2007,represents the third generation of mm-wave

d.

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Fig. 1. Radiometer’s functioning schema.

F. Cuttaia et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 396–401 397

instruments designed for space observations ofCosmic Microwave Background (CMB) anisotro-pies, within the new Cosmic Vision 2020 ESAScience Programme.

To reach its ambitious scope, the state of the artof microwave radiometers (Low Frequency In-strument (LFI) [2]) and bolometers (High Fre-quency Instrument (HFI) [3]), operating in a rangebetween 30 and 900GHz in nine frequencychannels, will be employed.

2. The low frequency instrument

The LFI is a system of 22 wide-band radioreceivers covering the frequency range 30–70GHz:they employ very low noise amplifiers based onInSb HEMTs (High Electron Mobility Transis-tors).

The radiometers were designed in order toreduce the 1=f noise induced by gain and noisetemperature fluctuations in the amplifiers [4].

A differential pseudo-correlation scheme waschosen: the power coming from the sky is receivedby 11 corrugated, profiled feed horns (activelycooled at 20K by a vibrationless sorption cooler)and continuously compared with a reference blackbody signal (provided by a reference load ther-mally linked to the HFI 4K stage).

2.1. The radiometer scheme

The sky signal xðtÞ; through the orthomodetransducer (OMT), is separated [4] into two linearpolarizations, coupled to a reference load signalyðtÞ (one for each polarization) by a first hybridand then amplified by low-noise amplifiers; one ofthe signals runs through a switch that applies aphase shift, which oscillates at a frequency of4096Hz. The signals are then recombined by asecond hybrid coupler, leading to an output whichis a sequence of signals alternating at twice thephase switch frequency. The function of thesecond hybrid is to separate the signals again, inorder to have two output signals proportional tothe incoming ones; they are again amplified,detected by a diode, integrated, digitized andacquired. The phase-switcher introduces a p phase

difference between the two signals to compensatefluctuations in the diodes (Fig. 1).

The I–O sequence can be described by definingthe transfer function for each component of thechain:

fhybrid : fx; yg-x þ yffiffiffi

2p ;

x � yffiffiffi2

p( )

ð1Þ

fampðg1; g2; n1; n2;f1;f2Þ :

fx; yg-fg1ðx þ n1Þeif1 ; g2ðx þ n2Þeif2g ð2Þ

x-

ffiffiffiffiA

peiyx phase switch state 1ffiffiffiffiffi

A0p

eiy0x phase switch state 2

(ð3Þ

where g1 and g2 are the voltage gains of amplifiers1 and 2; n1ðtÞ and n2ðtÞ and f1 and f2 are,respectively, the noise voltages and the signalphases of the two amplifiers; y and y0 are the phaseshifts in the two switch states (in the baselineconfiguration, y ¼ 0 and y0 ¼ p), A and A0 are thesignal amplitudes. After a few approximations,putting x2 ¼ knDTx and y2 ¼ knDTy; the averageoutput power p can be written as:

%p ¼ akbG½Tx þ Tn � rðTy þ TnÞ: ð4Þ

The r factor is the ‘gain modulation factor’:

r ¼½Tx þ TnTy þ Tn

ð5Þ

analytically inserted to balance the temperaturedifferences between the two branches of theradiometer. Tx and Ty are, respectively, the skynoise temperature and the reference noise tem-perature.

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F. Cuttaia et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 396–401398

2.2. Systematic effects in the LFI radiometers

Measurements are sensitive to various systema-tic effects, producing different fluctuations inEq. (4): they generate an output signal that mimicsa true sky fluctuation, confusing the sky tempera-ture information. They may come from:

(i)

variations in the amplifier noise temperature, (ii) variations in the amplifier gain, (iii) fluctuations in r; (iv) RL fluctuations.

This paper is mainly devoted to investigate theradio-frequency signal fluctuations in the RL andto provide an overview of the RL thermalmodeling. Thermal induced fluctuations are de-scribed in Ref. [5].

3. Reference load design

Stringent requirements in terms of mechanicaldimensions, mass, electromagnetic and thermalproperties required the implementation of aninnovative design for the loads.

The reference loads for the LFI are composed ofsmall absorbing targets [6], mechanically andthermally connected to the cryostat of the HFI.Small pyramidal horns, located in front of theloads at a distance of 1.5mm, are machined inFront-End Modules (FEMs) containing radio-meters or connected with short waveguides. Thisdesign was required to maintain the thermal loadon the HFI cryostat (which provides the referencetemperature) below 1mW. Mechanical constraintsmade impossible the realization of other solutionsto thermally decouple loads from radiometers(at 20K).

Horn design is like a small waveguide flare onewavelength long. Each of the LFI bands has adifferent horn design, whose properties have beenoptimized together with the load. In the 70GHzchannel, reference horns (RH) are obtained insideFEMs. In the 30 and 44GHz channels, due to thelocation of FEMs far from the HFI cryostat,horns are connected through short, bent wave-guides. All horns are made of high reflectivity

metal to reduce emissivity. In order to reduceleakage from the horn-load gap, small l=4 grooveshave been machined around horn aperture.

The overall load mass must be small (less than0.5 kg), and physical dimensions and thermal loadon the HFI cryostat must be minimized. Thisresults in small targets (the envelope of largestloads, designed for the LFI 30GHz band, is asquare parallelepiped whose side is about 30mmand thickness about 20mm), made of ECCO-SORBt CR-series [7]. The design philosophybasically follows the idea of gradually increasingthe dielectric constant. The front section of eachload and the central pyramid are made of CR-110,while the back part is made of CR-117. Loads aresurrounded and backed by a thin metal enclosure,that is machined in the mounting structure whichallows mechanical attachment to the HFI. Adetailed design has been optimized by simulatingthe unit [6]. A trade-off between various effects isfound, taking into account mechanical constraints.

4. Reference load material

Targets are made of ECCOSORBTM CR-series.It is a castable epoxy resin loaded with small (inthe range 5–10 mm) iron spheres. It is widely usedas absorbing material in microwave applications,also on space platforms [8] at cryogenic tempera-tures. Thermal and electro-magnetic properties arepoorly documented in the literature at the LFIfrequencies [9–12]. While loads are usually quitelarge compared with the wavelength, ours are not,requiring a careful modeling and, therefore, anaccurate determination of material properties. Dueto lack of detailed literature data we haveperformed tests to measure thermo-physical prop-erties of ECCOSORBTM at low temperatures(data are available only for CR110 [10,11]).

5. Reference load modeling

An extensive modeling activity is required totune the performance of the 4K RL unit (4K RL).It is possible to model the radiometer performanceand to evaluate the effect of various systematiceffects on the final products, that is the CMBR

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anisotropies sky maps. An analysis of systematiceffects of the 4K RL is reported here.

Let us consider Eq. (4): for r ¼ 1; load tempera-ture fluctuations produce variations of the sameorder as the sky signal: in fact, by differentiatingwith respect to Tx and Ty and comparing the twoobtained expressions, we get

DTx ¼ �rDTy: ð6Þ

It is then crucial to hold the reference temperaturethe closest to the sky temperature and to minimize itsfluctuations. Moreover, for amplifiers using HEMTtechnology, the noise temperature is proportional tothe gain fluctuations [4]. The low frequency compo-nent dominates the total noise, with a 1=f spectrumproportional to the temperature difference betweenthe sky and the reference signal. Active cooling of theamplifiers to about 20K allows the reduction of the1=f noise to very low values.

5.1. Systematic effects in the reference load

It is possible to evaluate the power coming fromthe RL, reaching the waveguide ðPwgÞ feeding theRH. Because of the thermo-mechanical separation(between the RH 20K stage and the RL 4Kstage), two effects dominate:

(i)

some Spillover radiation (SPO) from theenvironment enters the reference arm of theradiometer through the gap and cannot bedisentangled from true sky signal;

(ii)

not all the radiation coming from the RL,infalling the RH, reaches the waveguidebecause of the mismatching RH–RL ðS2

11Þ:

Port 1

Port 2

Port 1

ABC surface

Fig. 2. FEM setup representation for both the complete and

the single model; ports and ABC surface are shown.

A part of the signal ðTnÞ emitted by the instrumentsbeyond the waveguide is reflected back from themismatching RH–RL; some ðeÞ radiation is emitteddirectly from the horn, with its thermal temperatureTHorn: Assuming the validity of the ‘reciprocitytheorem’ [13], we name Z the ratio between thepower radiated onto the surrounding to that emittedby the antenna, RH the mismatching horn-surround-ing, k the Boltzman constant, we obtain

Pwg ¼ ½TAENV�SPO þ TA

LOAD�ð1� ZÞ�ð1� RHÞ

þ ½Tn þ kTHornDn�eH�S211: ð7Þ

5.2. The FEM modeling

The 4K RL optimization started from thedesign phase, in order to suppress those systema-tics diversely removable in the data processingphase; for this scope, a Finite Elements Method

(FEM) approach was used, based on the partition(mesh) of a 3-D problem in tetrahedra of variablesize. It employs the HFSS (ANSOFTt) code:Maxwell’s field equations are solved in the nodalpoints of the tetrahedra, matching conditionsbetween two adjacent tetrahedra sharing a node.Each point of a tetrahedron is representative of afield value.

The accuracy of the solution is strongly relatedto the size of tetrahedra and, consequently, to theirnumber: a trade-off between accuracy requiredand number of tetrahedra is required.

Single and complete Reference Load Systems(two RL plus two RH plus mounting structure)were modelled, for all the LFI’s frequencies, usingthe FEM. Input mode from the waveguide isradiated through the horn towards the RL: thefraction of the signal back-reflected into thewaveguide is modeled as return loss radiation;the fraction scattered from the target and from theedges of the horn in the surrounding as spill-overradiation.

Ports are placed at the terminals of waveguidesfeeding the reference horns: it acts both as signalsources and detectors. We measured both the Sii

(Reflection) and the Sij parameters (cross talk

radiation coming from the port i detected from theport j when two coupled horns were modelled). Aradiation box (ABC surface) surrounding the

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Fig. 3. Cross talk simulation in a complete 4K reference load;

in a color scale is shown how the radiation coming from the

right RH propagates inside the left RT and RH.

Fig. 4. Left panel: integration schema of the 4K reference load

and baffle; right panel: E-total field distribution inside the

cavity; brighter colors corresponds to a higher intensity fields.

SPO lowers from �25 to �60 dB with the baffle shielding.

F. Cuttaia et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 396–401400

device (except ports) is defined to evaluate the SPO(Figs. 2 and 3).

To reduce the straylight component fromexternal sources, the effect of a ‘baffle’, put inthe cavity between the HFI 4K and the LFI 20Kshields, was also simulated (Fig. 4).

5.3. Thermal modeling

A detailed thermal model of loads has also beenobtained, using analytical and numerical methods.The first model considers the RL to be a 1-D bodylinked to a heat reservoir (HFI shield) and facing asource of heat power (LFI 20K RH). The secondmodel considers the RL to be a 2-D rectangularbody placed in thermal contact with two highlyconductive metallic plates. These models thepresence of the box used to hold the loads on theHFI external shield. The presence of HFI and LFIis considered the same as in the 1-D model.

The numerical thermal model of the RL hasbeen built using SINDA, a thermal analysissoftware by C&R Technologies. Thermal modelscreated with SINDAt are specified using anetwork abstraction where nodes exchange heatthrough conductors. The model considers both thepresence of the HFI external shield and the LFI20K RH; they face two opposite sides of the RL(both the HFI shield and the LFI horn aremodeled as single nodes). The HFI node isthermally linked to the RL nodes using perfectconductors, while the LFI node is connected to theRL by means of radiative conductors. Theeffective shape of the feed horn is not taken intoaccount; instead, the distance between each RLsurface node and the RH is supposed to benegligible (at the current stage of development)in order to avoid complex geometrical calculationsin the radiative heat propagation.

6. Conclusions

Sensitivity levels required for CMB experimentsare reachable only with an accurate control ofsystematic effects; the 4K RL provides the Planck-LFI radiometers with a reference temperature thatmust be studied very accurately. This may bepossible only taking into account, in the design,susceptibility to various systematic effects. TheFEM method supplied an effective solution tocharacterize and optimize the radio-frequencybehavior in non-standard mechanical and thermalconditions at cryogenic temperatures.

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