<p>This paper presents a black-hole optimization (BHO) based parameters extraction method. The developed method was applied on distributed small-signal equivalent circuit models of GaN HEMT. The BHO as a global technique generates initial values for the model elements that can be tuned in a later step using gradient or simplex local optimization. The reliability of extraction was improved by using measurement-based boundaries for the initially generated candidate solutions. Physics-based restriction conditions were implemented through the optimization process to avoid any nonrealistic values. The developed procedure was demonstrated by modeling different sizes devices on SiC, Diamond and Si substrates at different bias conditions. The modeling accuracy was validated by means of S-premasters simulations, which show a very good fitting to measured data. The extracted values of the models’ elements are consistent with the devices physics and scaling well with the device size. In general, the results obtained prove the applicability of the proposed approach for small-modeling and liner circuit design and providing an accurate and physically consistent framework within the operating conditions considered.</p>