Equivalent circuit modelling of biopolar transistors

Existing equivalent circuit models of bipolar transistors are reviewed together with techniques for the evaluation of suitable values of the model elements. A method enabling the optimisation of the element values of any particular model in order to match the measured S parameters of a device that is to be modelled is described. This method uses a modified Gauss Newton algorithm to minimise an objective function defined as the sum of the squares of the weighted errors between the required S parameters and those of the model. Details are then given of a new modelling algorithm for the development of accurate equivalent circuit models which was developed from this original optimisation method. The new modelling algorithm requires some S parameter measurements of the device to be modelled' over an appropriate range of frequencies, together with a potentially suitable model. The initial model elements are optimised and then, if necessary, suitable topological changes, involving the addition or deletion of both elements and nodes, are made until a model having the. required accuracy or complexity is obtained. A number of examples are given of small-signal equivalent circuit models of bipolar transistors developed using the algorithm. These particular transistors were operating at frequencies up to lGHz .A further example is given of the use of the modelling algorithm in the development of a bias dependent small-signal model of two similar bipolar transistors operating at frequencies up to 2GHz . Additional S parameter data for the same two transistors is also used to demonstrate that the algoritim can be used successfully for the development of non-linear models.