Paper presents a Neural Network Modelling approach to microwave LNA design. To acknowledge the specifications of the amplifier, Mobile Satellite Systems are analyzed. Scattering parameters of the LNA in the frequency range 0.5 to 18 GHz are calculated using a Multilayer Perceptron Artificial Neural Network model and corresponding smith charts and polar charts are plotted as output to the model. From these plots, the microwave scattering parameter description of the LNA are obtained. Model is efficiently trained using Agilent ATF 331M4 InGaAs/InP Low Noise pHEMT amplifier datasheet and the neural model's output seem to follow the various device characteristic curves with high regression. Next, Maximum Allowable Gain and Noise figure of the device are modelled and plotted for the same frequency range. Finally, the optimized model is utilized as an interpolator and the resolution of the amplifying capability with noise characteristics are obtained for the L Band of MSS operation.