This work presents an application of Normalized Gain Function (NGF) method to the design of linear wideband microwave amplifiers based on small-signal model of a device. NGF has been originally developed to be used together with an S-parameter (*.s2p) file, whereas this work enables the NGF to be able to work with explicit S-parameter formulae derived from the small-signal model of the device. This approach provides the designer to be able to use simple set of S-parameter equations instead of S-parameter file of the device. Representation of the device simply by several model equations not only eliminates the need of carrying large number of data but also provides the capability of equation-based easy, realistic and equispaced S-parameter data generation in any desired resolution in frequency axis without requiring interpolation. NGF is defined as the ratio of T and |S-21|(2), i.e. T-N = T/|S-21|(2), gain function of the amplifier to be designed and transistor forward gain function, respectively. Synthesis of output/input matching networks (OMN/IMN) of the amplifier requires two target gain functions in terms of T-N, to be used in two sequential non-linear optimization procedures, respectively. An amplifier with a flat gain of similar to 10 dB operating in 0.8-2.35 GHz is designed using a small-signal model of an experimental GaN-HEMT. Theoretical amplifier performance obtained in Matlab is shown to be in excellent agreement with the simulated performance in MWO (Microwave Office, AWR Inc.). A prototype low-power amplifier having a similar to 10 to 12 dB gain, operating in (0.9-1.5 GHz) is also produced and measured which yielded good performance results.