Broadband polarimeter receivers at 30 and 40 GHz for cosmic microwave background measurement

Broadband radiometers at 30 and 40 GHz for QUIJOTE radio astronomy experiment are very sensitive receivers to perform scientific sky observations of the Cosmic Microwave Background (CMB). The aim of this experiment is the linear polarization percentage measurement of the received signals. Radiometers have cryogenically cooled Front-End Modules followed by room temperature amplification, correlation and detection modules. Their relative bandwidth is around 30%. There are 30 receivers (pixels) at 30 GHz and 29 receivers at 40 GHz. The radiometer scheme is based on two balanced branches, microwave correlation and direct detection. The manufactured receivers measure Stokes polarization parameters I, Q, and U simultaneously. This paper describes the principle of operation of polarimeter receivers, and present details of manufactured subsystems, integration and test results. Receivers integrate different technologies: waveguides, microstrip, Monolithic Microwave Integrated Circuits (MMIC) and active and passive devices. The receivers are currently under installation in El Teide Observatory, Tenerife (Canary Islands, Spain).


INTRODUCTION
The Thirty and Forty GHz polarimeters for the Q-U-I JOint TEnerife (QUIJOTE) CMB radio astronomy experiment, 1,2 are broadband very sensitive receivers to perform scientific sky observations of the Cosmic Microwave Background (CMB). The aim of the QUIJOTE experiment is the measurement of the linear polarization percentage of the received waves from the sky. Scientific data will be used for cosmological analysis of the Universe and the indirect detection of gravitational waves. The receivers are radiometers based on cryogenically cooled front-end modules followed by room temperature back-end modules performing amplification, correlation and detection. Relative bandwidth is around 30%. The radiometers scheme is based on two balanced branches and direct detection. Thirty GHz Instrument (TGI) and Forty GHz Instrument (FGI) are multipixel radio telescope receivers composed of about 30 pixels. Each pixel has an individual receiver.

TELESCOPES
The QUIJOTE CMB experiment consists of two identical telescopes installed inside a unique enclosure, Figure 1, in El Teide Observatory, Tenerife, Spain. The layout of both telescopes is based on an altazimuth mount supporting a primary reflector and a secondary reflector oriented as an offset Gregorian Dragon scheme. 3 There are two off-axis parabolic reflectors: primary reflector of 2.25 m and secondary reflector of 1.85 m. Telescope design provides low cross-polarization and a symmetric radiation beam.
The system is under-illuminated to minimize side-lobes and ground spillover. Each telescope is mounted on its own platform that can rotate around the vertical axis at a maximum frequency of 6 rpm (i.e., 36 deg/s). Instruments are located on the telescope focal plane, attached to the rear side, Figure 2, and then they move with the telescope according azimuth and elevation settings. Both telescopes have an unlimited rotation capacity in azimuth axis and a range of movement between 25° to 95° in elevation axis. An integrated rotary joint transmits fluid, power and signal to the rotary elements. The pointing and tracking accuracies are better than 1.76 arcmin and 44 arcsec, respectively.

RECEIVER SCHEMES
The TGI and FGI receivers 4, 5 are polarimeters to obtain three (of four) Stokes parameters (I, Q, U). The Cosmic Microwave Background (CMB) has a very weak linear polarization. The designed receivers measure the Q, U and I Stokes parameters simultaneously. The remaining Stokes parameter is V = 0, because the CMB does not have circular polarization. Stokes parameters are calculated from the incoming signal field components. TGI and FGI have almost identical schemes, with only a difference in the type of 3 dB hybrid couplers in the correlation stage. Block diagrams in Figure 4 show the configuration of each receiver. Each pixel of a receiver is composed of a cold Front-End Module (FEM) at 20 K, and a room temperature (298 K) Back-End Module (BEM). The cryogenic part is made up of a feedhorn, a polarizer, an Ortho-Mode Transducer (OMT) and two cryogenic low-noise amplifiers (Cryo-LNA). Passive components in the FEM are cryogenically cooled to minimize their contribution to the system noise temperature.
Outside the cryostat, two Gain and Filtering Modules, Phase Switches Module and Correlation and Detection Module operate at room temperature, in which the microwave signal is amplified, filtered, decorrelated by 180º or 90º hybrids and, finally, converted into DC voltages using square-law detectors. These signals are collected by a data acquisition system (DAS). The Phase Switches Modules comprise a four phase-state circuit generating four polarization states. Their performance is crucial in order to obtain the Stokes parameters, minimizing the leakage among them and, at the same time, overcoming the 1/f noise and different systematic errors in the receiver. In front of the BEM, adjusting phases are located to balance the insertion phase between both branches. This adjustment must be done experimentally for each pixel in the integration and verification phase.
The combination of a 90º polarizer and the OMT give two signals at the output of the OMT. Each signal is proportional to the left hand (L) and right hand (R) circularly polarized components of the electric field received by the feedhorn antenna. Two separate branches amplify and filter L and R signals. Ideally, both branches should have identical amplitude and phase responses. A fine adjustment for a balanced phase response in both branches is made by adjusting phase components.
A Correlation-Detection module performs signals decorrelation and direct detection (rectification and filtering of the microwave signal) to low frequency. In order to allow the correction of systematic errors of each receiver, both signals are phase modulated before their correlation. The Phase-Switches Module make this phase modulation in two identical branches, containing 180º and 90º broadband phase-switches. Signal correlation consists basically in addition and subtraction of broadband microwave signals, by a system based on 3 dB/90º or 3 dB/180º hybrid couplers and a fixed 90º phase shifter in a branch.
According to the Phase-Switches state, of the four possible states (0º, 90º, 180º and 270º), the output detected signals from the Correlation-Detection module, are proportional to different combinations of Stokes parameters (Q, U, I), which define the degree of polarization of an electromagnetic wave. The extraction of those Stokes parameters magnitudes, from observations with the instruments, is the experiment main objective.

PRINCIPLE OF OPERATION
Stokes parameters are calculated from the incoming signal field components. Using a circular basis of coordinates for the electromagnetic fields: the total electric field received by the feedhorn is a combination of left hand and right hand circular electric fields: The electric field in rectangular coordinates is: where these components can be expressed as The Stokes parameters I, Q and U are obtained from left and right hand circular polarized components of the electric field: The combination of a 90º polarizer and the OMT give two signals at the output of the OMT. Each signal is proportional to the electric field components El or Er of the total electric field received by the feedhorn antenna. In Figure 4 there is a sketch of the signals A and B obtained at the output of the assembly feedhorn-polarizer-OMT. In the case of FGI, the correlation is based on 3 dB/90º hybrids. The scheme and ports numbers for the 90º hybrid and its S-parameters matrix are shown in Figure 6. Assuming as initial state a null phase in the Phase-Switches the input voltages into the Correlation and Detection Module are A and B. Solving the equations with S-parameters, the final result for the voltages at the outputs in Figure 5(b) are: These signals are detected by square-law Schottky diode detectors and amplified by DC amplifiers. The signals at the BEM output are proportional to the squared amplitudes of signals in equations (7) to (10). Discarding the ½ factor, the voltage at the BEM outputs, scheme in Figure 3(b), are as follows: From the expression (5) The Stokes parameters values are obtained as: Stokes parameters are normalised values ranging from -1 to +1. The intensity I is always equal to +1, then the expressions (16) to (18) should be normalized accordingly.
Introducing the different phase states and assuming that only the upper branch will change its phase, then: ∅ is the phase difference between both receiver branches. The calculation of output voltages for the different states (0º, 90º, 180º and 270º) give the results contained in Table 1.
Finally, the Stokes parameters calculation is made in a similar way as it is done in equations (16), (17) and (18) for the different phase states. Stokes parameters in terms of output detected voltages are in Table 2.
Making a similar analysis for the TGI receiver, with correlation based on 3 dB/180º hybrids, Figure 5(a), the Stokes parameters, in terms of output detected voltages, for each phase state are shown in Table 3. Table 2. Stokes parameters at different phase states in FGI receivers

POLARIZATION SEPARATION: PASSIVE COMPONENTS
Each receiver is composed of a Front-End Module (FEM), cooled cryogenically, and a Back-End Module (BEM) operated at room temperature. The FEM contains passive waveguide components from the antenna to the input of cryogenic lownoise amplifiers (cryo-LNA): feedhorn, polarizer and OMT. A 3D view of the FEM subsystems of FGI receiver is depicted in Figure 7. In the case of TGI receiver the FEM concept is identical. The polarizer is a differential 90º phase shifter for the two orthogonal propagation modes (TE10 and TE01) in the square waveguide. The polarizer is rotated 45º in relation to the y-axis of the feed-horn. The constant phase difference, between both modes, is achieved by internal stepped ridges in the square waveguide, placed in its four internal walls. When the electric field at the polarizer input has a linear horizontal or vertical orientation (Figure 8), each orthogonal component propagates along the ridged square waveguide with a different insertion phase. At the polarizer output, field components have 90º phase difference between them. The OMT is based on a turnstile junction with an inserted scatterer. Its design consists of a circular waveguide input and two WR22 rectangular waveguide in-phase outputs. The assembly polarizer-OMT (Figure 9) has three physical ports and four electrical ports, since at the polarizer input there are two orthogonal modes. Port numbers for the S-parameters matrix are as follows: The reference phase (0º) is taken for the transmission parameter relating the polarizer input H with the OMT output H. According to (20) with an input horizontal electric field E coming into port #3, the two OMT output signals have the same amplitude but are phase shifted by 90º. The same happens if an input vertical electric field E comes into port #4, then the two OMT output signals have the same amplitude and are phase shifted by 90º. Figure 9. Assembly Feedhorn-Polarizer-OMT of FGI receiver.

Thirty GHz Instrument cryogenic LNA
Cryogenic LNA is a two stages low noise amplifier: a first MMIC low noise amplifier on 100 nm MHEMT technology from the Fraunhofer IAF, Freiburg, Germany, and a second MMIC low noise amplifier on 130 nm MHEMT technology from the OMMIC foundry, France. A 5 dB attenuator is between both amplifiers, in order to reduce gain and to assure stability. An internal view of this amplifier and an external view of three units are in Figure 10. DC bias circuitry warrants out of band stability and protection against over-voltages. All the DC circuitry as well as the RF part are included in the same box with a WR-28 waveguide input and output connections. Figure 11 shows in band (26 to 36 GHz) noise temperature and average gain values obtained from 62 tested units at 12 K. Figure 11. Cryogenic LNA for TGI receiver. Average of 62 tested units at 12 K in 26-36 GHz band. Noise Temperature ≈ 25 K, Gain ≈ 43 dB.

Forty GHz Instrument cryogenic LNA
Cryogenic LNA is a two stages low noise amplifier containing two MMIC low-noise amplifiers on 100 nm mHEMT technology from the Fraunhofer IAF (Freiburg, Germany). The MMIC amplifier has four stages with mHEMT transistors having a 4x15 μm gate periphery. An equalizer is placed between both MMIC amplifiers to assure stability and to improve the gain versus frequency slope. A total compensation of the slope could not be achieved because it would have implied a higher noise temperature of the whole module. The RF input and output are through WR-22 waveguide connectors.  Further signal amplification is done in the Back-End Module at room temperature, Figure 3

(b). The Gain and Filtering
Module is composed of two cascaded MMIC commercial LNA, with an equalizer in-between and a microstrip filter to define the 35 to 47 GHz bandpass. Its gain is around 30 dB. A detailed view is in Figure 14. This module has a positive gain slope to flatten the amplitude response of the overall receiver.

Thirty GHz Instrument Phase Switches
Phase switches module comprises two cascaded circuits, which individually introduces a relative phase difference of 90º and 180º. A driver integrated circuit (DR65-0109 from MACOM) controls phase states from appropriate TTL bias signals. The 90º phase switch uses single-pole double-throw (SPDT) switches and two microstrip band-pass filters (BPFs). SPDT is a combination of coplanar waveguide (CPW) and slotline transmission lines, in which microwave PIN diodes perform switching between paths. PIN diodes are connected in precise circuit positions. 6 The whole circuit uses 10-mils thick Alumina (A996) substrate. A picture of the 90º phase switch is in Figure 15. The 180º phase switch is a circuit based on coplanar waveguide (CPW) and slotline technologies, in which the phase shift is the phase difference of the electromagnetic waves feeding a CPW output line, transitioned from slotline. 7 The circuit uses also 10-mil thick Alumina (A996) substrate. In the slotline transmission path, there is a T-junction enabling to change the transmission path of the microwave signal, prior to CPW line transition. Transmission path selection is also done by microwave PIN diodes. The combination of 90º and 180º phase switches performs four different phase states (0º, 90º, 180º and 270º). A picture of a branch of TGI Phase Switches Module is in Figure 17. Typical phase difference values of a representative unit, average from tests in 26 to 36 GHz band, are in Table 4.

Forty GHz Instrument Phase Switches
The Phase Switches module has two separate and identical branches. Each branch has a microstrip circuit containing a power divider, a 180º phase switch, a fixed 90º differential phase shifter and a power combiner. This circuit introduces a relative phase difference of 90º, 180º and 270º by using TTL control signals. The switching devices are beam lead PIN diodes. Figure 18 shows a view of the phase switch and its equivalent block diagram. The Phase Switch has four phase states (0º, 90º, 180º and 270º). Each phase state is the combination of the two independent 0º/180º phase switches states. At the power combiner output, the phase of the combined signal changes. Taken as 0º phase reference state when the two 0º/180º are in 0º state, then the phase difference introduced by the full circuit is 180º when both 180º phase switches are individually actuated, while when only one of 0º/180º phase switches, the upper or the lower, is actuated, then the phase difference is 90º or 270º.

Thirty GHz Instrument Correlation and Detection
Correlation and Detection subsystem in the TGI follows the scheme shown in Figure 3(a). Input signals are correlated by 180º broadband hybrids in microstrip lines technology. Figure 20 shows a picture of one of the hybrids within the module. Schottky diode detectors directly convert the microwave correlated signals to low frequency. Figure 21 shows a picture of one of these detectors.

Forty GHz Instrument Correlation and Detection
This module consists of four 90º hybrid couplers, a 90º phase shifter and four Schottky diode detectors. Its block diagram scheme is in Figure 3(b). Low noise video amplifiers provide signal conditioning and low pass filtering. Hybrid couplers and 90º phase shifter are rectangular waveguide subsystems. Diode detectors are microstrip circuits. Waveguide components are built in two halves, Figure 23 shows both, being the rectangular waveguide cut in the E-plane. The four output detected voltages are amplified by low-noise DC amplifiers located in the module back side.

BACK END MODULE RACKS
The installation of receivers in the telescopes requires the integration of several Back-End Modules, one per pixel, in standard 19 inches racks, containing all the mechanical and electrical interfaces for the appropriate operation of both instruments; Thirty and Forty GHz Instruments.
Thirty GHz Instrument has sixteen BEM pixels integrated per rack, in each BEM pixel there are three main separated subsystems: two RF Gain Modules, a Phase Switches Module and a Correlation-Detection Module. Figure 24 shows the assembly of these modules per pixel and the sixteen BEM pixels integrated in the rack. Input microwave interfaces are 2.92 mm (f) coaxial connectors. The TGI has two BEM racks containing 32 pixels in total.
Forty GHz Instrument has ten BEM pixels integrated per rack, in each BEM pixel there are also two Gain modules, a Phase Switches module and a Correlation-Detection module. Figure 25 shows the assembly of these modules per pixel and the ten BEM pixels integrated in the rack. Input microwave interfaces are WR22 rectangular waveguides with standard flanges. The FGI has three BEM racks containing 30 pixels in total.
For temperature control of all modules inside the rack, every pixel has attached a silicon heater mat and a temperature sensor. This temperature control permits the operation of all modules at a fixed temperature higher than ambient temperature at the observatory. The goal of this temperature control is to keep a fixed gain in the BEM along the time.
The four output signals per pixel in both instruments, TGI and FGI, are the inputs for the Data Acquisition Electronics (DAE), for signal conditioning and data recording. The description of these subsystem is out of scope of the present paper.

CONCLUSION
The objective of this paper is the description of two broadband and low noise instruments, at 30 and 40 GHz, addressed to CMB polarization measurements. Each instrument has about 30 pixels and provides direct detection signals containing combinations of the Stokes parameters I, Q and U. Phase switching in the Back-End Module permits polarization modulation and gives redundant information to extract the Stokes parameters by reducing systematics effects. Each receiver has a cryogenic Front-End Module, to minimize the system noise temperature, followed by a room temperature Back-End Module performing microwave signals amplification, filtering, correlation and detection.