This paper describes a method for designing cryogenic silicon-germanium (SiGe) transistor low-noise amplifiers and reports record microwave noise temperature, i.e., 2 K, measured at the module connector interface with a 50-Ω generator. A theory for the relevant noise sources in the transistor is derived from first principles to give the minimum possible noise temperature and optimum generator impedance in terms of dc measured current gain and transconductance. These measured dc quantities are then reported for an IBM SiGe BiCMOS-8HP transistor at temperatures from 295 to 15 K. The measured and modeled noise and gain for both a single- and two-transistor cascode amplifier in the 0.2-3-GHz range are then presented. The noise model is then combined with the transistor equivalent-circuit elements in a circuit simulator and the noise in the frequency range up to 20 GHz is compared with that of a typical InP HEMT
