Experimental and analytical study of electrical crosstalk in CMB cold readout systems and implications for power spectra

The Cosmic Microwave Background Radiation (CMB) originated in the early phases of the life of the Universe, during the recombination epoch, when protons and electrons combined to form hydrogen, emitting photons that free-streamed to the present epoch. The CMB frequency and power spectra have been measured and characterized by groundbreaking space missions such as COBE, which first detected the CMB anisotropies, WMAP, which provided improved angular resolution, and Planck, which achieved the most precise measurements to date. Future missions, such as the LiteBIRD (space-based) and LSPE/SWIPE (balloon-borne), aim to measure the polarization of the CMB, in particular the so called B-modes, to provide evidence for the current inflationary models. The new generation of CMB experiments employ superconducting devices to improve the sensitivity of the observations. The detection chain of both LiteBIRD and SWIPE is based on Transition Edge Sensors (TESs), which exploit the superconductors’ strong variation of resistance with temperature, thereby converting the detector heating produced by the sky signal into an electrical signal. Due to the small size of the signal Superconducting QUantum Interference Devices (SQUIDs) are used as cryogenic amplifiers. To limit the thermal load on the cryogenic stages, Frequency Division Multiplexing (FDM) is employed to reduce the number of SQUIDs and readout cables. In this approach, each TES is connected in series with a band-pass LC filter and biased at a specific frequency, while the combined output signals from multiple detectors are read out through a single SQUID. FDM is most commonly implemented using fully lithographed LC filters, consisting of spiral inductors and planar parallel-plate or interdigitated capacitors. Nonetheless it carries instrumental systematic effects, among which electrical crosstalk is one of the most critical. This is related to the presence of the filters themselves which can create signal leakage among channels. There are three main sources of electrical crosstalk that were identified: carrier leakage crosstalk, associated with the bandwidth of the filters; mutual inductance crosstalk, arising from possible electromagnetic coupling between spiral inductors; and common impedance crosstalk, caused by the presence of a non-zero inductance in series with all the multiplexing branches. The LC filters chip design, together with the sequence of the multiplexing frequencies, affects the overall crosstalk level. Measuring and understanding the impact of crosstalk on the readout chain of these experiments is of utmost importance. The work presented in this thesis focuses on the cold readout chain for those CMB experiments, addressing both simulation and experimental aspects. Optimization studies were carried out for the design of an LC filter chip entirely fabricated using lithographic techniques and composed of spiral inductors and interdigitated capacitors. In particular, an algorithm was developed to determine the optimal configuration that minimizes electrical crosstalk, based on the focal plane layout. LC assignments, linking the sequence of multiplexing frequencies to that of the TESs, have a significant impact on the crosstalk level. Analytical methods for estimating crosstalk were applied to the LiteBIRD and SWIPE readout chains. The results show that the expected level of crosstalk depends strongly on the separation between multiplexing frequencies and on the value of the stray inductance associated with the SQUID input coil and the wiring. Finally, experimental measurements on LC chips representative of both experiments were performed to validate the developed models, showing a good match. In the case of LiteBIRD readout, tests on a complete end-to-end channel, including the warm electronics, were carried out. The impact of electrical crosstalk on the observational outcomes was eventually assessed by propagating its effects to the CMB power spectra, evaluating the potential influence on the LiteBIRD results.