SARAS is an ongoing experiment aiming to detect the redshifted global 21-cm signal expected from Cosmic Dawn (CD) and the Epoch of Reionization (EoR). Standard cosmological models predict the signal to be present in the redshift range $z sim $6--35, corresponding to a frequency range 40--200~MHz, as a spectral distortion of amplitude 20--200~mK in the 3~K cosmic microwave background. Since the signal might span multiple octaves in frequency, and this frequency range is dominated by strong terrestrial Radio Frequency Interference (RFI) and astrophysical foregrounds of Galactic and Extragalactic origin that are several orders of magnitude greater in brightness temperature, design of a radiometer for measurement of this faint signal is a challenging task. It is critical that the instrumental systematics do not result in additive or multiplicative confusing spectral structures in the measured sky spectrum and thus preclude detection of the weak 21-cm signal. Here we present the system design of the SARAS~3 version of the receiver. New features in the evolved design include Dicke switching, double differencing and optical isolation for improved accuracy in calibration and rejection of additive and multiplicative systematics. We derive and present the measurement equations for the SARAS~3 receiver configuration and calibration scheme, and provide results of laboratory tests performed using various precision terminations that qualify the performance of the radiometer receiver for the science goal.
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