# Difference between revisions of "LFI design, qualification, and performance"

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− | + | ==<span id="LFIDescription">Instrument description</span>== | |

− | == | + | The LFI instrument (see Fig. 1 in the [[LFI overview]]) consists of a 20 K focal plane unit hosting the corrugated feed horns, the orthomode transducers (OMTs) and the receiver front-end modules (FEMs). Forty four composite waveguides{{BibCite|darcangelo2009a}} are interfaced with three conical thermal shields and connect the front-end modules to the warm (~300 K) back-end unit (BEU) containing a further radio frequency amplification stage, detector diodes and all the electronics for data acquisition and bias supply. |

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− | The LFI instrument (see | ||

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Best LFI noise performance is obtained with receivers based on InP High Electron Mobility Transistor (HEMT) low noise amplifiers (LNAs) for minimal power dissipation and best performance. To further minimise power consumption in the focal plane, the radiometers are split into two sub-assemblies connected by waveguides, one located at the telescope focal area, the other on the 300 K portion of the Planck satellite. These design features allow the entire front-end LNAs dissipation to be <0.55 W, which enables the active cooling of the focal assembly. This is achieved with a vibration-less hydrogen sorption cooler, which also provides 18 K pre-cooling to the HFI helium J-T cooler. Two sorption cooler units are included in the flight hardware. | Best LFI noise performance is obtained with receivers based on InP High Electron Mobility Transistor (HEMT) low noise amplifiers (LNAs) for minimal power dissipation and best performance. To further minimise power consumption in the focal plane, the radiometers are split into two sub-assemblies connected by waveguides, one located at the telescope focal area, the other on the 300 K portion of the Planck satellite. These design features allow the entire front-end LNAs dissipation to be <0.55 W, which enables the active cooling of the focal assembly. This is achieved with a vibration-less hydrogen sorption cooler, which also provides 18 K pre-cooling to the HFI helium J-T cooler. Two sorption cooler units are included in the flight hardware. | ||

− | As shown schematically in | + | As shown schematically in Fig. 1 below, the LFI consists of the following subsystems: |

* Radiometer Array Assembly (RAA) | * Radiometer Array Assembly (RAA) | ||

* Sorption Cooler Subsystem (SCS) | * Sorption Cooler Subsystem (SCS) | ||

* Radiometer Electronics Box Assembly (REBA) | * Radiometer Electronics Box Assembly (REBA) | ||

− | The RAA includes the Front End Unit (FEU) and the Back End Unit (BEU), connected via waveguides. The FEU is located at the focus of the telescope, as one component of the joint LFI/HFI focal assembly (see sections below). The BEU is mounted on the top of the Planck SVM. | + | The RAA includes the Front End Unit (FEU) and the Back End Unit (BEU), connected via waveguides. The FEU is located at the focus of the telescope, as one component of the joint LFI/HFI focal assembly (see sections below). The BEU is mounted on the top of the Planck service module (SVM). |

− | The Radiometer Electronics Box Assembly | + | The REBA (Radiometer Electronics Box Assembly) and the warm parts of the Sorption Cooler System (SCS) are located on one of the lateral panels of the SVM. The FEU and the Sorption Cooler Compressor (SCC) are connected by concentric stainless steel tubes. The smaller tube carries hydrogen at ∼60 atmospheres from the cooler compressors to the FEU, while the larger tube returns the hydrogen at ∼0.3 atmospheres. These units are described in following sections and in the [[LFIAppendix|Annexes]], the SCS is described in details in the [[LFI design, qualification, and performance#The Sorption Cooler|Sorption Cooler]] section. |

All LFI units are linked together by the LFI harness, which also connects to the spacecraft interface. | All LFI units are linked together by the LFI harness, which also connects to the spacecraft interface. | ||

− | [[File:schema.jpg|thumb|center|500px|Figure | + | [[File:schema.jpg|thumb|center|500px|'''Figure 1. Block Diagram of LFI''']] |

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=== ''Radiometer Array Assembly (RAA)'' === | === ''Radiometer Array Assembly (RAA)'' === | ||

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The time scale of the stability of the receiver is driven by the 1 rpm rotation speed of the spacecraft, which requires a very low 1/f-noise or gain variation of the low noise amplifiers and other components. | The time scale of the stability of the receiver is driven by the 1 rpm rotation speed of the spacecraft, which requires a very low 1/f-noise or gain variation of the low noise amplifiers and other components. | ||

− | The LFI uses a pseudo-correlation receiver concept ( | + | The LFI uses a pseudo-correlation receiver concept (Fig. 2 below). This radiometer concept is chosen to maximise the stability of the instrument by reducing the effect of non-white noise generated in the radiometer itself. In this scheme, the difference between the inputs to each of the chains (the signal from the telescope and that from a reference black body respectively) is continuously being observed. To remove the effect of instability in the back-end amplifiers and detector diodes, it is necessary to switch the signal detected at the diodes at high rate. |

The signals from the sky and from a reference load are combined by a hybrid coupler, amplified in two independent amplifier chains, and separated out by another hybrid. The sky and the reference load power can then be measured and differenced. Since the reference signal has been subject to the same gain variations in the two amplifier chains as the sky signal, the true sky power can be recovered. | The signals from the sky and from a reference load are combined by a hybrid coupler, amplified in two independent amplifier chains, and separated out by another hybrid. The sky and the reference load power can then be measured and differenced. Since the reference signal has been subject to the same gain variations in the two amplifier chains as the sky signal, the true sky power can be recovered. | ||

The differencing receiver greatly improves the stability if the two input signals are almost equal, at | The differencing receiver greatly improves the stability if the two input signals are almost equal, at | ||

a cost of a factor of <math>\sqrt 2 \; </math> in sensitivity compared to a perfectly stable total-power radiometer with the same noise temperature and bandwidth. This radiometer concept is capable of greatly reducing the knee frequency. | a cost of a factor of <math>\sqrt 2 \; </math> in sensitivity compared to a perfectly stable total-power radiometer with the same noise temperature and bandwidth. This radiometer concept is capable of greatly reducing the knee frequency. | ||

− | We define as Radiometer Chain Assembly (RCA, see | + | We define as Radiometer Chain Assembly (RCA, see Fig. 2) each functional unit from the feed horn to the BEM. The RAA therefore includes a set of 11 RCAs and the Data Acquisition Electronics (see also Fig. 1 above), all mounted on a suitable mechanical structure. Although there are differences in the details of the radiometer chains at different frequencies, their overall configuration is similar, and a general description of its design is provided in this section. |

Planck LFI has 11 Radiometer Chain Assembly (RCA). Each RCA is constituted by feed horn and FEM in the FEU (at 20 K), BEM (at 300 K) in the BEU and four waveguides that connect each FEM-BEM couple. The frequency distribution of the RCA is the following: | Planck LFI has 11 Radiometer Chain Assembly (RCA). Each RCA is constituted by feed horn and FEM in the FEU (at 20 K), BEM (at 300 K) in the BEU and four waveguides that connect each FEM-BEM couple. The frequency distribution of the RCA is the following: | ||

− | * 2 RCAs at | + | * 2 RCAs at 30 GHz; |

− | * 3 RCAs at | + | * 3 RCAs at 44 GHz; |

− | * 6 RCAs at | + | * 6 RCAs at 70 GHz. |

− | [[File:rca_schematic.jpg|thumb|center| | + | [[File:rca_schematic.jpg|thumb|center|640px|'''Figure 2. A complete RCA from feed-horn to analog voltage output. The insets show the OMT, the details of the 20 K pseudo-correlator and of the back-end radio-frequency amplification, low-pass filtering, detection and DC amplification.''']] |

==== ''Radiometer Chain Assembly (RCA)''==== | ==== ''Radiometer Chain Assembly (RCA)''==== | ||

− | Every RCA consists of two radiometers, each feeding two diode detectors (see | + | Every RCA consists of two radiometers, each feeding two diode detectors (see Fig. 2 above), for a total of 44 detectors. The 11 RCAs are labelled by a numbers from 18 to 28 as outlined in Fig. 1 in [[LFI overview]], right panel. |

− | + | Fig. 2 provides a more detailed description of each radiometric receiver. In each RCA, the two perpendicular linear polarisation components split by the OMT propagate through two independent pseudo-correlation differential radiometers, labelled as ''M'' or ''S'' depending on the arm of the OMT they are connected to (''Main'' or ''Side'', see lower-left inset of Fig. 2). | |

− | In each radiometer the sky signal coming from the OMT output is continuously compared with a stable 4 K blackbody reference load mounted on the external shield of the HFI 4 K box | + | In each radiometer the sky signal coming from the OMT output is continuously compared with a stable 4 K blackbody reference load mounted on the external shield of the HFI 4 K box{{BibCite|valenziano2009}}. After being summed by a first hybrid coupler, the two signals are amplified by ~30 dB, see upper-left inset of Fig. 2. The amplifiers were selected for best operation at low drain voltages and for gain and phase match between paired radiometer legs, which is crucial for good balance. Each amplifier is labelled with codes ''1'', ''2'' so that the four outputs of the LNAs can be named with the sequence: ''M1'', ''M2'' (radiometer ''M'') and ''S1'', ''S2'' (radiometer ''S''). |

Tight mass and power constraints called for a simple design of the Data Acquisition Electronics (DAE) box so that power bias lines were divided into five common-grounded power groups with no bias voltage readouts; only the total drain current flowing through the front-end amplifiers is measured and is available to the house-keeping telemetry (this design has important implications for front-end bias tuning, which depends critically on the satellite electrical and thermal configuration and was repeated at all integration stages, during on-ground and in-flight satellite tests). | Tight mass and power constraints called for a simple design of the Data Acquisition Electronics (DAE) box so that power bias lines were divided into five common-grounded power groups with no bias voltage readouts; only the total drain current flowing through the front-end amplifiers is measured and is available to the house-keeping telemetry (this design has important implications for front-end bias tuning, which depends critically on the satellite electrical and thermal configuration and was repeated at all integration stages, during on-ground and in-flight satellite tests). | ||

− | A phase shift alternating between <math> 0^\circ \; </math> and <math>180^\circ \; </math> at the frequency of 4096 Hz is applied in one of the two amplification chains and then a second hybrid coupler separates back the sky and reference load components that are further amplified and detected in the warm BEU, with a voltage output ranging from -2.5 V to +2.5 V. | + | A phase shift (or phase switch) alternating between <math> 0^\circ \; </math> and <math>180^\circ \; </math> at the frequency of 4096 Hz is applied in one of the two amplification chains and then a second hybrid coupler separates back the sky and reference load components that are further amplified and detected in the warm BEU, with a voltage output ranging from -2.5 V to +2.5 V. |

Each radiometer has two output diodes which are labelled with binary codes ''00'', ''01'' (radiometer ''M'') and ''10'', ''11'' (radiometer ''S''), so that the four outputs of each radiometric chain can be named with the sequence: ''M-00'', ''M-01'', ''S-10'', ''S-11''. | Each radiometer has two output diodes which are labelled with binary codes ''00'', ''01'' (radiometer ''M'') and ''10'', ''11'' (radiometer ''S''), so that the four outputs of each radiometric chain can be named with the sequence: ''M-00'', ''M-01'', ''S-10'', ''S-11''. | ||

− | After detection, an analog circuit in the DAE box removes a programmable offset in order to obtain a nearly null DC output voltage and a programmable gain is applied to increase the signal dynamics and optimally exploit the ADC input range. After the ADC, data are digitally | + | After detection, an analog circuit in the DAE box removes a programmable offset in order to obtain a nearly null DC output voltage and a programmable gain is applied to increase the signal dynamics and optimally exploit the ADC input range. After the ADC, data are digitally down-sampled, re-quantised and compressed in the REBA according to a scheme described in{{BibCite|herreros2009}}{{BibCite|maris2009}}, before preparing telemetry packets. On ground, telemetry packets are converted to sky and reference load time ordered data after calibrating the ADU samples into volt considering the applied offset and gain factors. |

− | To first order, the mean differential power output for each of the four receiver diodes can be written as follows | + | To first order, the mean differential power output for each of the four receiver diodes can be written as follows{{BibCite|seiffert2002}}{{BibCite|mennella2003}}{{PlanckPapers|bersanelli2010}}:: |

− | + | <math> \label{eq:power} | |

P_{\rm out}^{\rm diode} = a\, G_{\rm tot}\,k\,\beta \left[ T_{\rm sky} + T_{\rm noise} - r\left( | P_{\rm out}^{\rm diode} = a\, G_{\rm tot}\,k\,\beta \left[ T_{\rm sky} + T_{\rm noise} - r\left( | ||

T_{\rm ref} + T_{\rm noise}\right) \right] | T_{\rm ref} + T_{\rm noise}\right) \right] | ||

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where <math>G_{\rm tot} \;</math> is the total gain, <math>k \;</math> is the Boltzmann constant, <math>\beta \;</math> the receiver bandwidth and <math>a \;</math> is the diode constant. <math>T_{\rm sky} \;</math> and <math>T_{\rm ref}\; </math> are the average sky and reference load antenna temperatures at the inputs of the first hybrid and <math>T_{\rm noise} \;</math> is the receiver noise temperature. | where <math>G_{\rm tot} \;</math> is the total gain, <math>k \;</math> is the Boltzmann constant, <math>\beta \;</math> the receiver bandwidth and <math>a \;</math> is the diode constant. <math>T_{\rm sky} \;</math> and <math>T_{\rm ref}\; </math> are the average sky and reference load antenna temperatures at the inputs of the first hybrid and <math>T_{\rm noise} \;</math> is the receiver noise temperature. | ||

− | The gain modulation factor | + | The gain modulation factor{{BibCite|mennella2003}}{{PlanckPapers|planck2011-1-6}}, <math>r</math>, is defined by: |

− | + | ||

+ | <math> \label{eq:erre1} | ||

r = \frac{T_{\rm sky} + T_{\rm noise}}{T_{\rm ref} + T_{\rm noise}} | r = \frac{T_{\rm sky} + T_{\rm noise}}{T_{\rm ref} + T_{\rm noise}} | ||

</math> | </math> | ||

and is used to balance (in software) the temperature offset between the sky and reference load signals and minimise the residual 1/<math>f \;</math> noise in the differential datastream. This parameter is calculated from the average uncalibrated total power data using the relationship: | and is used to balance (in software) the temperature offset between the sky and reference load signals and minimise the residual 1/<math>f \;</math> noise in the differential datastream. This parameter is calculated from the average uncalibrated total power data using the relationship: | ||

− | + | ||

+ | <math> \label{eq:erre2} | ||

r = \langle V_{\rm sky} \rangle/ \langle V_{\rm ref}\rangle, | r = \langle V_{\rm sky} \rangle/ \langle V_{\rm ref}\rangle, | ||

</math> | </math> | ||

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where <math><V_{\rm sky}> \;</math> and <math><V_{\rm ref}> \;</math> are the average sky and reference voltages calculated in a defined time range. | where <math><V_{\rm sky}> \;</math> and <math><V_{\rm ref}> \;</math> are the average sky and reference voltages calculated in a defined time range. | ||

The white noise spectral density at the output of each diode is essentially independent from the reference-load absolute temperature and is given by: | The white noise spectral density at the output of each diode is essentially independent from the reference-load absolute temperature and is given by: | ||

− | + | ||

+ | <math> \label{eq:dt1} | ||

\Delta T_0^{\rm diode} = \frac{2\,(T_{\rm sky}+T_{\rm noise})}{\sqrt{\beta}}. | \Delta T_0^{\rm diode} = \frac{2\,(T_{\rm sky}+T_{\rm noise})}{\sqrt{\beta}}. | ||

</math> | </math> | ||

− | If the front-end components are not perfectly balanced, then the separation of the sky and reference load signals after the second hybrid is not perfect and the outputs are mixed. First-order deviations in white noise sensitivity from the ideal behaviour are caused mainly by noise temperature and phase-switch amplitude mismatches. Following the notation used in | + | If the front-end components are not perfectly balanced, then the separation of the sky and reference load signals after the second hybrid is not perfect and the outputs are mixed. First-order deviations in white noise sensitivity from the ideal behaviour are caused mainly by noise temperature and phase-switch amplitude mismatches. Following the notation used in{{BibCite|seiffert2002}}, we define <math>\epsilon_{Tn} \; </math>, the imbalance in front end noise temperature, and <math>\epsilon_{A1} \; </math> and <math> \epsilon_{A2} \;</math> , the imbalance in signal attenuation in the two states of the phase switch. Equation above for the two diodes of a slightly imbalanced radiometer then becomes |

− | + | <math> \label{eq:dt2} (\Delta T^{diode} )^2 ≈ (\Delta T_0^{diode})^2 ( 1± \frac{\epsilon_{A1}- \epsilon_{A2}}{2} | |

+ \alpha \epsilon_{Tn}) | + \alpha \epsilon_{Tn}) | ||

</math> |