Low Noise Amplifiers (LNAs) are one of the most important components found in some of the radio receivers used in radio astronomy. A good LNA should simultaneously possess both a gain in excess of 25\,dB and as low a noise contribution as possible. This is because the gain is used to suppress the noise contribution of the subsequent components but the noise generated by the LNA adds directly to the noise of the overall receiver. The work presented in this thesis aimed to further enhance the noise performance through a variety of techniques with the aim of applying these techniques to the study of the polarisation of the Cosmic Microwave Background. One particular technique investigated was to cool the LNAs beyond the standard 20\,K typically used in experiments to 2\,K. In doing so it was found that the noise performance increased by between 20 and 30\% depending on the amplifier. Another technique investigated involved uniting the two technologies (MICs and MMIC) used in LNA fabrication to lower the noise performance of the LNA. Such an LNA, known as a T+MMIC LNA was successfully developed and possessed an average noise temperature of 9.4\,K and a gain in excess of 40\,dB for a 27-33\,GHz bandwidth at 8\,K physical temperature. Potential ``in field'' applications for these technologies are discussed, and a design for a variant of the T+MMIC LNA that utilises both of these technologies is presented. This particular LNA with a predicted average noise temperature of 6.8\,K for a 26-36\,GHz bandwidth, would if fabricated successfully represent the lowest noise Ka-band LNA ever reported.