The performance of broadband, Low-Noise, Low DC consumption cryogenic amplifiers was studied in detail with emphasis to minimize the power consumption and optimize the amplifier performance at cryogenic temperature. A general approach used in the modeling and amplifier design can help to minimize the power consumption and optimize the performance of the amplifier. A noise temperature below 6K and 25 dB gain was experimentally obtained in the frequency range 4-8 GHz with total power consumption of 4 mW with commercial GaAs transistor.