Circuit Modeling for In Situ 21 cm Radiometer Calibration

Abstract

Recent experiments in cosmology, particularly those aimed at detecting the faint, redshifted, global 21 cm hydrogen line (depth < ~200 mK, z > 7.5), have imposed stringent new requirements on radiometer calibration. In this work, we present a framework for circuit modeling and parameter inference to strengthen these calibration pipelines. This new approach enables in situ characterization of otherwise immeasurable systematics using physically motivated models. A combination of frequentist and Bayesian techniques are employed in a pipeline that supports iterative modeling, robust parameter estimation, and detailed uncertainty quantification. The framework is applied to the REACH telescope, where the precise correction of variations in the radio signal paths arising from component aging or environmental effects is critical. Circuit models of REACH's calibration sources are developed, with the goal of predicting source temperature corrections that are conventionally obtained from laboratory measurements. By fitting the models to measured data using a convolutional cost function, a strong agreement with RMS residuals no worse than -37 dB is obtained. However, Bayesian inference reveals that the resulting temperature corrections can have uncertainties on the order of 1 to 2 K, caused by reflection coefficient degeneracies, measurement noise, and errors in the models. To combat this, posteriors obtained from laboratory measurements are employed as updated priors, reducing correction uncertainties down to 75 mK. Ultimately, the framework provides a means of dynamically accounting for drift in system non-idealities over time, addressing the increasing precision demands of global 21 cm radio astronomy.

Figures (16)

• Figure 1: Models of the sky and signal temperatures, showing (\ref{['fig:21cm_signal']}) the magnitude of the expected sky temperature, modeled as a -2.5-power law, against the absolute magnitude of an example global 21 cm signal (adapted from Cumner2022CMB), and (\ref{['fig:21cm_line']}) a typical model of the global 21 cm signal, with (from left to right): collisional coupling (grey), onset of Ly-$\alpha$ coupling (yellow), onset of X-ray heating (orange) and photoionization (purple) (adapted from de2022reach).
• Figure 2: An overview of the REACH radiometer, showing (\ref{['fig:reach_frontend']}) the front-end receiver with 12 independent calibration sources and the antenna connected to the receiver via mechanical switches, and (\ref{['fig:reach_backend']}) the back-end receiver control system and RF-over-fibre link (adapted from roque2025receiver).
• Figure 3: An illustration of the switching procedure between the antenna and the calibration sources, which connect to the input of the radiometric receiver. $\Gamma_\mathrm{rec}$ represents the reflection coefficient observed looking into the receiver, while $\Gamma_\mathrm{ant}$ and $\Gamma_\mathrm{source}$ are the reflection coefficients looking back into the antenna and calibration sources. $T_\mathrm{A}$ represents the antenna temperature, comprised of the global 21 cm signal, $T_\mathrm{21}$, as well as foreground and background components, $T_\mathrm{f}$ and $T_\mathrm{b}$. When the antenna is connected, the output power, $P_\mathrm{out}$, consists of a sum of the mismatched antenna and internal receiver temperatures, $M T_\mathrm{A}$ and $T_\mathrm{rec}$, multiplied by Boltzmann's constant, $k_\mathrm{B}$, and the receiver's gain, $G_\mathrm{rec}$.
• Figure 4: A circuit diagram depicting the various reflection coefficients and mismatch impedances for an arbitrary noise generator connected via a two-port network to a load (adapted from miller1967noise). $P_\mathrm{1a}$/$P_\mathrm{1d}$ and $P_\mathrm{2a}$/$P_\mathrm{2d}$ are the available/delivered powers on the left/right of reference planes 1 and 2 respectively.
• Figure 5: An illustration of a typical source (heated load) connected to the receiver via an RF cable, with load reflection $\Gamma_R$, load and cable temperatures $T_R$ and $T_\mathrm{cab}$, source reflection $\Gamma_\mathrm{source}$, and effective temperature $T_\mathrm{source}$ (adapted from roque2025receiver). Note that $T_\mathrm{R}$, $T_\mathrm{cab}$ and $T_\mathrm{source}$ are not necessarily equal.