The Spectrometer Development of CosmoCube, Lunar Orbiting Satellite to Detect 21-cm Hydrogen Signal from Cosmic Dark Ages

The cosmic Dark Ages represent a pivotal epoch in the evolution of the Universe, marked by the emergence of the first cosmic structures under the influence of dark matter. The 21-cm hydrogen line, emanating from the hyperfine transition of neutral hydrogen, serves as a critical probe into this era. We describe the development and implementation of the spectrometer for CosmoCube, a novel lunar orbiting CubeSat designed to detect the redshifted 21-cm signal within the redshift range of 13 to 150. Our instrumentation utilizes a Xilinx RFSoC, which integrates both Analog-to-Digital Converters (ADCs) and Digital-to-Analog Converters (DACs), tailored for the spectrometer component of the radiometer. This system is characterized by a 4096 FFT length at 62.5 kHz steps using a Polyphase Filter Bank (PFB), achieving an average Effective Number of Bits (ENOB) of 11.5 bits throughout the frequency of interest, from 10 MHz to 100 MHz. The spectrometer design is further refined through loopback tests involving both DAC and ADC of the RFSoC, with DAC outputs varying between high (+1 dBm) and low (-3 dBm) power modes to characterize system performance. The power consumption was optimized to 5.45 W using three ADCs and one DAC for the radiometer. Additionally, the stability of the ADC noise floor was investigated in a thermal chamber with environmental temperatures ranging from 5{\deg}C to 40{\deg}C. A consistent noise floor of approximately -152.5 dBFS/Hz was measured, with a variation of $\pm$0.2 dB, ensuring robust performance under varying thermal conditions.