Following the reported detection of an absorption profile associated with the 21[Formula: see text]cm sky-averaged signal from the Cosmic Dawn by the EDGES experiment in 2018, a number of experiments have been set up to verify this result. This paper discusses the design process used for global 21[Formula: see text]cm experiments, focusing specifically on the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH). This experiment will seek to understand and compensate for systematic errors present using detailed modeling and characterization of the instrumentation. Detailed quantitative figures of merit and numerical modeling are used to assist the design process of the REACH dipole antenna (one of the two antenna designs for REACH Phase I). This design process produced a 2.5:1 frequency bandwidth dipole. The aim of this design was to balance spectral smoothness and low impedance reflections with the ability to describe and understand the antenna response to the sky signal to inform the critically important calibration during observation and data analysis.

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A fast full-wave simulation technique is presented for the analysis of large irregular planar arrays of identical 3-D metallic antennas. The solution method relies on the Macro Basis Functions (MBF) approach and an interpolatory technique to compute the interactions between MBFs. The Harmonicpolynomial (HARP) model is established for the near-field interactions in a modified system of coordinates. For extremely large arrays made of complex antennas, two approaches assuming a limited radius of influence for mutual coupling are considered: one is based on a sparse-matrix LU decomposition and the other one on a tessellation of the array in the form of overlapping sub-arrays. The computation of all embedded element patterns is sped up with the help of the non-uniform FFT algorithm. Extensive validations are shown for arrays of log-periodic antennas envisaged for the low-frequency SKA (Square Kilometer Array) radio-telescope. The analysis of SKA stations with such a large number of elements has not been treated yet in the literature. Validations include comparison with results obtained with commercial software and with experiments. The proposed method is particularly well suited to array synthesis, in which several orders of magnitude can be saved in terms of computation time.

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