Generation of proper source/load pull impedances for a selected GaN device is essential to design a microwave power amplifier for optimum gain and power-added efficiency. As they are obtained, these impedances may not be realizable network functions over the desired frequency band. Therefore, in this paper, first, we introduce a new method to test if the given source and load pull impedances are realizable. Then, a novel numerical procedure is introduced to model the source and load pull impedances as realizable network functions, which in turn results in the optimum power intake and power delivering capacity for the GaN transistor used in the design. In the numerical modelling process, a robust tool called "Virtual Gain Optimization" is presented. Numerically generated realizable source and load impedances are modelled analytically. Eventually, these impedances are synthesized using our automatic Darlington Synthesis Robot software to yield the optimum input and output matching network topologies with component values. Examples are presented to test the realizability of the given source/load pull impedance data. Then, the power intake and delivery capacity of the active device are assessed for a 10W-GaN power transistor, namely "Wolfspeed CGH40010F" over 0.8-3.0 GHz bandwidth. Eventually, the power amplifier is designed and manufactured. It is shown that the computed and the measured performance of the amplifier is very close with 10 Watts output power, 11.4 +/- 0.6 dB gain and 49% to 76 % power added efficiency.