  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.
