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An optimum design of a low noise amplifier (LNA) in S-band working at 2-4 GHz is described. Choosing FHC40LG high electronic mobility transistor (HEMT), the noise figure of the designed amplifier simulated by Microwave Office is no more than 1.5 dB, meanwhile the gain is no less than 20 dB in the given bandwidth. The simulated results agree with the performance of the transistor itself well in consideration of its own minimum noise figure (0.3 dB) and associated gain (15.5 dB). Simultaneously, the stability factor of the designed amplifier is no less than 1 in the given bandwidth.