A low noise amplifier is critical in providing us the capability of reading small signals, from various sources. For systems where the signal is transmitted along large distances, the signal power degrades; and thus in radar systems when the signal bounces off an object and back to the receiver, it is quite small. Therefore, a well designed low noise amplifier is needed at the receiver so that signal can be recovered and read clearly to extract the data. The main objective of this project was to gain experience in radio frequency amplifier design and to learn the concepts and tools to achieve a successful design. Using the ADS Design kit, we picked a Gallium Arsenide Hetero-junction field effect transistor from California Eastern Laboratories that has a typical Noise of 0.35dB and Gain of 13.5dB at a frequency of 12GHz. We determined the bias point for a power supply voltage of 3.0V at the frequency of 14 GHz that would provide low noise with a reasonable high gain. We designed an input matching network for low noise and output matching network for high gain, for both the first and second stage amplifiers. After we cascade them, we achieved a low noise of less than 2dB, a forward gain of 17dB, and an output return loss less than -40dB. This design will be helpful in producing low noise amplifiers to be used in many applications including part of a modular system for an adaptive automobile cruise control system.