This paper presents a method to design a wide-band noise figure (NF) low noise amplifier (LNA) for 3.5–4.5 GHz. The quality factor method has been used to achieve better bandwidth of noise figure. To design low noise amplifier circuit in Radio Frequency (RF), trade-off between noise figure, gain, stability and input return loss should be considered. Two configurations of amplifiers are presented. The first configuration is a single-stage amplifier with input and output matching networks according to noise and gain consideration respectively. It has the noise figure of 1.062db and the gain of 10.288db. The second configuration is a cascade amplifier that, in addition to the first one, an inter-stage matching network is used for it. It has the noise figure of 1.123db and the gain of 20.317db. Agilent Advanced Design System (ADS) EM/circuit co-simulation has been used to perform simulation.