In this work, a linear model of a 3-phase active power filter (APF) is obtained to design a DC link proportional--integral (PI) controller. The system is designed on the basis of a TMS320F2812 digital signal processer (DSP). The PI controller is implemented in the program of the DSP. The hysteresis controller and sampling frequency are also taken into account in the linear model. The effect of hysteresis bandwidth, filter inductance, DC link capacitor, and sampling frequency on the stability are investigated by using the Routh--Hurwitz method. The detailed simulation model in MATLAB and experimental results showed that the linear model can be used to specify the PI controller's parameters. \vs{-1mm}