On SPICE simulation of voltage-dependent capacitors

The capacitance of voltage-dependent capacitors can be defined in two ways: as 'total capacitance' C_t(v) = Q/v and 'local capacitance' C_d(v) = dQ/dv. The former is applicable to cases when the capacitance is measured by a charge injection or when the total capacitance is derived from the properties of the dielectric material. The 'local capacitance' is applicable in cases when the capacitor is measured by a small test signal for various bias voltages. Based on the capacitance definitions, SPICE compatible models are implemented either by applying local and integral operators or by a nonlinear reflection of a linear capacitor. These are demonstrated by PSPICE behavioral-dependent sources. When properly emulated, the C_t and C_d models are applicable for simulating both small and large signals across the nonlinear capacitor. It is further brought up that both models suffer from convergence problems that can be partially alleviated by slowly increasing the level of the excitation signal and by reducing the maximum step time.