Trade-off between noise figure (NF) and input return loss (RL or |S 11|) imposes a fundamental limitation on the design of low noise amplifiers (LNA) for ultra-wideband (UWB) applications. A graph-based approach using Smith Chart to achieve optimum values for both NF and input RL over the desired LNA bandwidth is presented. The proposed method and device optimization technique are systematically incorporated to enhance the overall LNA performance in terms of gain, noise, linearity, and power consumption. An UWB LNA prototype is implemented in a 0.13pm CMOS process to demonstrate the use of this methodology. It shows a gain of 11.3 dB, a NF of 3.9-4.6 dB, and an IIP3 of 3.2-5dBm over a -3dB bandwidth of 2.2-9GHz while consuming 30mW from a 1.2V DC supply.