This work presents the design of a single-stage, low noise, stable and matched amplifier at 5 GHz. The amplifier is designed around the Agilent ATF-551M4 low noise enhancement mode pseudomorphic HEMT (EpHEMT). An Artificial Neural Network (ANN) model of the Smith Chart is proposed for an alternative solution to impedance matching of this LNA (Low Noise Amplifier) design which has been entitled, "Neural Smith Chart (NSC)" shortly. The input and the output impedance matching networks are performed using NSC outputs and MATLAB (R) RF Toolbox simulation solutions for comparison.