Parameter extraction of microwave transistors using tree annealing

The authors have developed an alternative formulation of simulated annealing using a tree-based Metropolis procedure called tree annealing. Tree annealing is suited to continuous optimization problems and, in particular, to transistor parameter extraction. The tree annealing optimization algorithm was used to extract the parameters of the HBT (heterojunction bipolar transistor) of U.K. Mishra et al. (IEDM Tech. Dig., p.180-3, Dec. 1988) using a physically based equivalent circuit and deembedded scattering parameter measurements from 45 MHz to 26.5 GHz. Good results were obtained from the parameter extraction technique, and the ability of MFA not to be locked in local minima enabled a physically based equivalent circuit model to be used. Tree annealing is essentially a smart random search technique and so requires many more functional evaluations than do gradient-based minimization algorithms. However, no startling guess is required, and the bounds on parameter values can be widely separated with little effect on optimization time