This paper presents a generalized charge-based EKV MOSFET model that includes the effects of trapped charges in the bulk oxide and at the silicon/oxide interface. It is shown that in the presence of oxide- and interface-trapped charges, the mobile charge density can still be linearized but with respect to both the surface potential and the channel voltage. This enables us to derive closed-form expressions for the mobile charge density and the drain current. These simple formulations demonstrate the effects of charge trapping on MOSFET characteristics and crucial device parameters. The proposed charge-based analytical model, including the effect of velocity saturation, is successfully validated through measurements performed on devices from a 28-nm bulk CMOS technology. Ultrahigh total ionizing doses up to 1 Grad(SiO2) are applied to generate oxide-trapped charges and activate the passivated interface traps. Despite a small number of parameters, the model is capable of accurately capturing the measurement results over a wide range of device operation from weak to strong inversion. Explicit expressions of device parameters also allow for the extraction of the oxide- and interface-trapped charge density.