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A&A 520, A5 (2010)Isolation (dB)Isolation (dB)-5.0-10.0-15.0-20.0-25.0-5.0-10.0-15.0-20.0-25.0Detector M-00Receiver testsInstrument testsRequirementLFI18 LFI20 LFI22 LFI24 LFI26 LFI28Detector S-10Receiver testsInstrument testsRequirementLFI18 LFI20 LFI22 LFI24 LFI26 LFI28Isolation (dB)Isolation (dB)-5.0-10.0-15.0-20.0-25.0-5.0-10.0-15.0-20.0-25.0Detector M-01Receiver testsInstrument testsRequirementLFI18 LFI20 LFI22 LFI24 LFI26 LFI28Detector S-11Receiver testsInstrument testsRequirementLFI18 LFI20 LFI22 LFI24 LFI26 LFI28Fig. 3. Summary of measured isolation compared with the same measurementsperformed at receiver level (Villa et al. 2010).3. Spurious frequency spikes. These are a common-mode additiveeffect caused by interference between scientific andhousekeeping data in the analog circuits of the data acquisitionelectronics box (see Sect. 5.2.5).5.2.2. Test experimental conditionsThe test used to determine instrument noise was a long-duration(2-day) acquisition during which the instrument ran undisturbedin its nominal mode. Target temperatures were set at T sky = 19 Kand T ref = 22 K. The front-end unit was at 26 K, maintained tobe stable to ±10 mK.The most relevant instabilities were a 0.5 K peak-to-peak 24-hour fluctuation in the back-end temperature and a 200 mK driftin the reference load temperaturecausedbyaleakageinthegasgap thermal switch that was refilled during the last part of theacquisition (see Fig. 5).The effect of the reference load temperature variation wasclearly identified in the differential radiometric output (seeFig. 6) andremovedfromtheradiometerdatabeforedifferencing.The effect of the back-end temperature was removed by correlatingthe radiometric output with temperature sensor measurements.and another √ 2fromthehalvingoftheskyintegrationtime.When we average the two (calibrated) outputs of each radiometer,we gain back a factor √ 2, so that the final radiometer sensitivityis given by Eq. (3)withK = √ 2.Figure 4 shows the effectiveness of the LFI pseudocorrelationdesign (see Meinhold et al. 2009). After differencing,the 1/ f knee frequency is reduced by more than three ordersof magnitude, and the white noise sensitivity scales almostperfectly with the three values of the constant K. Thefollowingterminology is used in the figure:– Total power data:datastreamsacquiredwithoutoperatingthe phase switch;– Modulated data:datastreamsacquiredinnominal,switchingconditions before taking the difference in Eq. (1);– Diode differenced data: differenced datastreams for eachdiode;– Radiometer differenced data: datastreamsobtainedfromaweighted average of the two diode differenced datastreamsfor each radiometer (see Eq. (E.2)).5.2.1. Overview of main noise parametersIf we consider a typical differenced data noise power spectrum,P( f ), we can identify three main characterisics:1. The white noise plateau, where P( f ) ∼ σ 2 .Thewhitenoisesensitivity is given by σ (in units of K s 1/2 ), and the noiseeffective bandwidth byβ =(KV DC /σ V ) 2[1 + bG0 (T sky + T noise ) ] 2 , (4)where V DC is the voltage DC level, σ V the uncalibrated whitenoise sensitivity and the term in square brackets representsthe effect of compressed voltage output (see Appendix C).2. The 1/ f noise tail, characterised by a power spectrum P( f ) ∼σ 2 ( f / f k ) −α described by two parameters: the knee frequency,f k ,definedasthefrequencywherethe1/ f and white noisecontribute equally, and the slope α.5.2.3. White noise sensitivity and noise effective bandwidthThere are four sources of white noise that determines the finalsensitivity: (i) the input sky signal; (ii) the RF part of the receiver(active components and resistive losses); (iii) the back-endelectronics after the detector diode 5 ;and(iv)signalquantisationperformed in the digital processing unit.Signal quantisation can significantly increase the noise levelif σ/q < ∼ 1, where q represents the quantisation step and σthe noise level before quantisation. <strong>Pre</strong>vious optimisation studies(Maris et al. 2004) demonstratedthataquantisationratioσ/q ∼ 2isenoughtosatisfytelemetryrequirementswithoutsignificantly increasing the noise level. This has been verifiedduring calibration tests using the so-called “calibration channel”,i.e., a data channel containing about 15 minutes per dayof unquantised data from each detector. The use of the calibrationchannel allowed a comparison between the white noise levelbefore and after quantisation and compression for each detector.Table 9 summarises these results and shows that digital quantisationcaused an increase in the signal white noise of less than 1%.We report in Fig. 7 the white noise effective bandwidth calculatedaccording to Eq. (4).Ourresultsindicatethatthenoiseeffectivebandwidth is smaller than the requirement by 20%, 50%,and 10% at 30, 44, and 70 GHz, respectively. Non-idealities inthe in-band response (ripples) causing bandwidth narrowing arediscussed in Zonca et al. (2009).It is useful to extrapolate these results to the expected inflightsensitivity of the instrument at the nominal temperatureof 20 K when observing a sky signal of ∼2.73 K in thermodynamictemperature. This estimate has been performed in two differentways. The first uses measured noise effective bandwidthsand noise temperatures in the radiometer equation, Eq. (3). Thesecond starts from measured uncalibrated noise, which is thencalibrated in temperature units, corrected for the different focalplane temperature in test conditions, and extrapolated to ∼2.73 K5 The additional noise introduced by the analog electronics is generallynegligible compared to the intrisic noise of the receiver, and its impactwas further mitigated by the variable gain stage after the diode.Page 6 of 16
A. Mennella et al.: LFI calibration and expected performanceFig. 4. Amplitude spectral densities of unswitched and differenced data streams. The pseudo-correlation differential design reduces the 1/ f kneefrequency by three orders of magnitude. The white noise level scales almost perfectly with K.Table 5. White noise sensitivities per radiometer in µK · s 1/2 .From uncalib. noiseM-0 S-170 GHzLFI18 468 468LFI19 546 522LFI20 574 593LFI21 424 530LFI22 454 463LFI23 502 63544 GHzLFI24 372 447LFI25 501 492LFI26 398 39230 GHzLFI27 241 288LFI28 315 251From radiom. equationM-0 S-170 GHzLFI18 450 450LFI19 482 466LFI20 498 511LFI21 381 496LFI22 428 410LFI23 453 41944 GHzLFI24 404 407LFI25 451 462LFI26 455 42830 GHzLFI27 311 320LFI28 305 268Notes. Sensitivity values have been extrapolated at CMB input usingthe two methods outlined in the text and detailed in Appendix D.Fig. 5. Thermal instabilities during the long duration acquisition. Top:drift in the reference load temperature caused by leakage in the gas capthermal switch. The drop towards the end of the test coincides with refillof the thermal switch. Bottom: 24-h back-end temperature fluctuation.input using the radiometeric response equation, Eq. (2). The detailsof the extrapolation are given in Appendix D.Table 5 indicates the sensitivity per radiometer estimatedaccording to the two procedures. The sensitivity per radiometerwas obtained using a weighted noise average from the twodetectors of each radiometer (see Appendix E). Because radiometersLFI18M-0 and LFI24M-0 were not working duringthe tests, we estimated the sensitivity per frequency channel byconsidering the white noise sensitivity of LFI24M-0,whichwaslater repaired, measured during receiver-level tests, while forLFI18M-0,whichwaslaterreplacedbyaspareunit,weassumedthe same sensitivity as for LFI18S-1. Furtherdetailsaboutthewhite noise sensitivity of individual detectors are reported inMeinhold et al. (2009).We provide in Table 6 the sensitivity per frequency channelestimated using the two procedures and compared with the LFIrequirement.5.2.4. 1/f noise parametersThe 1/ f noise properties of the LFI differenced data were determinedmore accurately during instrument-level than receiverleveltests for two reasons: (i) the test performed in this phasewas the longest of all the test campaign; and (ii) because of thePage 7 of 16
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A&A 520, E1 (2010)DOI: 10.1051/0004
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ABSTRACTThe European Space Agency
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A&A 520, A1 (2010)- University of C
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