Polynomial splines for MOSFET model approximation

The approximation of MOSFET nonlinearities by use of polynomial splines was investigated for reducing both circuit model development time and model simulation cost. After a brief tutorial on spline functions, it is shown how the number of independent variables for the MOSFET simulation models in digital circuits is reduced by their use. A tableau formulation for generating splines is presented along with a storage-reduction technique for polynomial spline coefficients. Mathematical programming problems for one-, two-, and three-dimensional splines are given that result in accurate monotonic splines using few segments. Two spline segments are shown to provide sufficient accuracy in the one-dimensional case, while 4×4 and 2×5×5 segments provide sufficient accuracy in the two- and three-dimensional cases, respectively