IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 9, NO. 2, MAY 2013 1029 Extension of Pulsewidth Modulation From Carrier-Based to Dither-Based Shiang-Hwua Yu, Member, IEEE, Ting-Yu Wu, and Sing-Han Wang Abstract—The carrier-based pulsewidth modulation (PWM) is extended to a dither-based PWM by replacing a conventional triangular carrier with a binary dither signal. Such a simple extension is generally impractical due to serious performance degradation. However, this paper presents a novel binary dither generator that helps enhance the performance of the dither-based PWM and makes the idea possible. The binary dither is generated as determined by the sign of the filtered modulation noise. The dither generated in this way automatically eliminates low-fre- quency modulation noise and randomizes the switching frequency. As indicated by experiments, the resulting dither-based PWM has relatively lower THD N and less pronounced high-frequency switching harmonics, as compared with the conventional fixed-fre- quency triangular carrier PWM. Index Terms—Dither, inverters, pulsewidth modulation, relay control, sliding mode control. I. INTRODUCTION P ULSE WIDTH modulation (PWM) is a method for carrying information on a train of pulses by varying pulsewidth. To the best of the authors’ knowledge, it was first described in 1931 by American engineers H. Shore and his colleagues as a means of transmitting intelligence [1]. Not very long thereafter, the PWM method was developed for radio and telephone communication [2], [3], and later, with the introduction of sampled-data control, the method also found an application in control systems as a way to sample regulation errors and generate relay control forces [4], [5]. In the late 1960s, some pioneering research on PWM motor drive led to the realization of the vast potential and utility of PWM in power amplification and conversion [6]–[8], and since then, PWM has been an invaluable technique in the field of power electronics. Popular PWM schemes fall into three main categories: car- rier-based PWM [9]–[11], delta-sigma modulation [12], [13], space vector modulation [14], [15]. Among these methods, car- rier-based modulation is the simplest and most widely used. This paper intends to improve the carrier-based PWM by ex- tending it to a dither-based PWM scheme, as shown in Fig. 1. The extension is motivated by two observations. First, among various dispositions of multicarrier PWM schemes [10], [11], Manuscript received November 29, 2011; revised February 02, 2012 and March 17, 2012; accepted September 17, 2012. Date of publication September 24, 2012; date of current version January 09, 2013. This work was supported by National Science Council, Taiwan, under Grant NSC101-2221-E-110-088. Paper no. TII-11-849. The authors are with the Electrical Engineering Department, National Sun Yat-Sen University, Kaohsiung, 804, Taiwan (e-mail: shaun@mail.ee. nsysu.edu.tw; b943011020@student.nsysu.edu.tw; m983010040@stu- dent.nsysu.edu.tw). Digital Object Identifier 10.1109/TII.2012.2220555 Fig. 1. (a) Carrier-based PWM. (b) Dither-based PWM. the phase-disposition modulation has the lowest line-to-line har- monic voltage distortion [11] and can be realized using a uni- form quantizer that is injected by a single triangular carrier, as displayed in Fig. 1(a) (see Fig. 7 for more details of the im- plementation.) Second, the variable-frequency carrier is now well established to help to reduce switching harmonics [16], [17] or other harmonics that are generated by circuit nonideal- ities [18]. These two observations motivate the modification of single-carrier PWM in Fig. 1 with replacement of the fixed-fre- quency triangular carrier by a variable-frequency binary dither signal. The idea of dithering of a quantizer to generate PWM is not new [19], [20]. The main problem is how to enhance the performance of dither-based PWM and make this idea prac- tical. A binary dither generator recently developed by the first author [21] is suitable for this purpose. With this dither gen- erator, the resulting dither-based PWM may yield lower total harmonic distortion plus noise (THD N) and less pronounced high-frequency switching harmonics than the conventional car- rier-based PWM. The rest of the paper is organized as follows. Section II presents a practical dither-based PWM method with a means of generating a binary dither that cancels the quantization error and thereby minimizes the modulation noise in the signal band. Section III elucidates a method for designing the optimal dither generator. Section IV applies the optimal sinusoidal dither-based modulation scheme to a single-phase full-bridge voltage source inverter and compares its performance with that of conventional carrier-based PWMs. Experimental results verify the superiority of the proposed modulation scheme. II. FEEDBACK DITHERING MODULATION Fig. 2 presents a dither-based modulation scheme, called feedback dithering modulation. The core of the design is a dither generator, in which a binary dither is generated based on the sign of the filtered modulation noise , hopefully to eliminate modulation noise in a frequency band of interest. To see how this goal can be achieved, the relationship between 1551-3203/$31.00 © 2012 IEEE