A moving boundary problem in a distributed parameter system with application to diode modeling

Distributed parameter system modeling is motivated by a need to have high fidelity system simulation. A practical consequence is that irrational functions arise in the frequency domain model. This dissertation compares four different methods for approximating the irrational hyperbolic functions commonly met in distributed parameter transmission lines, and proposes a simple and concise approach for modal approximation, which can be helpful in general ‘wave’ type transmission lines. The approximation techniques discussed in this dissertation can also be extended to approximate a fractional differential operator, commonly found in continuous system control. The proposed method enhances the approximation accuracy over the Páde approximation method. By using a weak, or general, solution for the partial differential equation, it is shown that state space equations can be used to approximate a moving boundary problem. This technique can be readily implemented for a dynamic diode model as demonstrated in this dissertation. The dissertation shows that by including the effect of a moving boundary in the diode charge diffusion, the accuracy of a diode model is drastically improved.