This paper presents a new carrier based pulse-width modulation (PWM) method for matrix converters. By using the concept of average over one switching period, the modulation algorithm and the required equations are derived to synthesize the desired output voltage and to achieve the controlled input power factor. The proposed method uses a continuous carrier and the predetermined duty ratio signals to directly generate the gating signals and, thus, is referred to as "direct duty ratio PWM (DDPWM)". The feasibility and validity of the proposed method were verified by simulation and experiment.