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SUMMARYAn improved non-linear high-frequency model for the bipolar transistor is presented, based on considerations of the dynamics of the charge stored in the base region. The model incorporates higher-order circuit elements in order to obtain increased accuracy in circuit simulation at high frequencies. The model is derived from device physics by solving the diffusion equation in the base region by means of a quasi-static expansion. The result is a more accurate circuit representation, which can be added to existing bipolar transistor models. Simulation examples are given and the possible convergence problems associated with the model are discussed. . INTRODUCTIONBipolar transistors are used today in a wide range of applications from power electronics and fast digital circuits to microwave amplifiers, both in discrete and integrated form. Considering the increasing level of integration to lower the costs, it is essential to use efficient CAD tools to achieve good design productivity and to predict the performance of the circuit under construction.For reliable circuit simulation, accurate models of devices t o be used are essential. The modelling of bipolar transistors has been the subject of extensive study during the last few decades. Ebers and Moll developed a model to describe the essential features of transistor operation. ' The charge control concept' was later used to formulate the Gummel-Poon model, which is the basis of most of the non-linear bipolar transistor models in use today.In spite of these advances, it is difficult to combine non-linear and high-frequency effects into a single model. This would be especially important with regard to microwave power transistors in class C operation near the transition frequency fT. One possibility is to use the Gummel-Poon model with external parasitic elements to increase its accuracy at high frequencie~.~ There are, however, reasons to believe that this approach is not entirely satisfactory.It is required to use frequency-dependent element values in the circuit models of microwave transistors if the models have to cover a wide range of frequencies. On the other hand, the small-signal diffusion conductance and capacitance of a p-n junction are also frequency-dependent, a fact derivable from the semiconductor equations.' It is clear that this phenomenon must also appear in the bipolar transistor. However, in time domain and harmonic balance analysis we cannot use models with frequency-dependent elements, because their constitutive relations cannot easily be given in the time domain.The use of higher-order and dynamic circuit elements opens up new possibilities in accurate non-linear modelling. Philippow and Jakubenko have presented a bipolar transistor model using higher-order elements. ' Chua and Chang have demonstrated the applicability of these elements to the high-speed nonlinear modelling of p-n junction diodes. * Sipila el a/. have extended the analysis to the bipolar t r a n s i~t o r .~ This paper contains a more complete description of the model. In con...

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