This thesis presents elevated temperature modeling of the 3rd generation wide bandgap GaN High Electron Mobility Transistors (HEMTs). In AlGaN/GaN HEMTs, Two Dimensional Electron Gas (2-DEG) can be achieved without having a dopant layer, because of the piezoelectric e ect found inherently in GaN semiconductor. This provides an increased saturation velocity and GaN HEMT, therefore, is a considered promising candidate for microwave power applications. In therst part of thesis, an analytical model is developed to predict temperature dependent DC characteristics of AlGaN/GaN HEMTs. The model comprehensively incorporates, temperature dependent variation in Schottky barrier height,b(T); bandgap discontinuity,Ec(T); sheet carrier concentration of 2- DEG, ns(T); saturation velocity,sat(T) and carriers mobility,(T). It has been shown that by increasing the ambient temperature, there is a decrease inb; an increase in ns; a decrease insat of 2-DEG carriers and a decrease inT . A comparative analysis revealed that the proposed model''s accuracy is at least 30% better than its counterparts. In the second part of thesis, AlGaN/GaN HEMTs AC characteristics are modeled by developing an analytical technique. In the proposed technique, temperature dependent ns(T) of 2-DEG isrst assessed to predict the DC characteristics of AlGaN/GaN HEMTs. Engaging the modeled DC data and by evaluating depletion layer capacitors, device''s intrinsic small signal parameters are determined. By employing assessed small signal parameters, S-parameters of the device are calculated and their compliance with the measured data ensures the validity of the proposed mechanism. In the third part of thesis, a numerical model to simulate output and transfer characteristics of GaN HEMTs is developed. The model takes into account dependence of output conductance on the device drain and gate bias, and simulates both positive and negative conductance to a good degree of accuracy. Appearance of peak transconductance to a relatively higher negative gate bias is a routinely observed phenomenon in GaN HEMTs, and the proposed model has the ability to simulate such 2nd order e ects with a good degree of accuracy. A comparative study revealed that the proposed model o ers at least 17% improved accuracy compared to other such models reported in literature. The accuracy of the model was also checked at elevated temperature and found signi cantly better than its counterparts. As, the model is based on a single expression, it is therefore easy to handle with and can comfortably be used in computer aided design software to assess the temperature dependent performance of GaN HEMTs for their possible integration into power circuitries.