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The purpose of this project is to design a low noise amplifier (LNA) for a radio telescope. The LNA is an electronic amplifier used in communication systems to amplify extremely weak signals captured by antennae. This thesis describes the procedure of designing an LNA for 7 GHz frequency. Noise matching is an important technique which was considered in the design process. The designed LNA achieved a gain of 30 dB with 1 GHz bandwidth. The noise figure achieved was less than 2.9 dB. Return-losses were improved by 6 dB with a new proposed optimization method.