A new model for triodes of type 12AX7 is presented, featuring simple and continuously differentiable equations. The description is physically-motivated and enables a good replication of the grid current. Free parameters in the equations are fitted to reference data originated from measurements of practical triodes. It is shown, that the equations are able to characterize the properties of real tubes in good accordance. Results of the model itself and when embedded in an amplifier simulation are presented and align well.