Feedback Loop Analysis for AC/DC Rectifiers Operating in Discontinuous Conduction Mode James Lazar and Slobodan Cuk Power Electronics Group, 116-81, Caltech, Pasadena, CA 91125 Tel: (818)395-4711, Fax: (818)395-2944 Abstract- High power factor rectifiers employing converters operating in discontinuous conduction mode (dcm) exhibit "automatic" current shaping and use output voltage feedback to regulate the output voltage. Analysis of this feedback control loop requires derivation of the control-to-output transfer function in the presence of the rectijied ac source voltage. In this paper, linear, line frequency averaged control-to-output transfer functions are derived for some common dcm converter based rectifier topologies. Also, a new control scheme is analyzed which provides open loop correction for the nonideal input current of the dcm boost converter, giving it unity power factor. Finally, a simple method of providing 'yast " output voltage regulation under transient conditions is introduced. I. Introduction For certain converters operated in dcm, high power factor can be obtained without directly controlling the input current. This approach to power factor correction is called automatic current shaping. In these converters, the switching frequency average input current can be expressed in terms of the slowly changing duty ratio, input voltage, and perhaps output voltage, and thus the resulting input current is a consequence of only these quantities. The topological structure of such a system is shown in figure 1. Some of these converters provide unity power factor when the duty ratio is constant, while others less than unity. The first case is called "ideal" automatic current shaping, and the latter "non-ideal". While a non-ideal current shaper does not provide unity power factor, the harmonic content of the input current is often low enough to be useful in many applications. It may be used in lieu of an ideal shaper for other considerations, for example efficiency or isolation. Also, the power factor of such a shaper can be corrected in an open loop manner [ 11. Rectifiers of this type require output voltage feedback to regulate the output voltage, since the output voltage strongly depends on load. The gain of this feedback loop should roll off well below twice the line frequency to avoid line current distortion. To analyze the voltage This work was conducted under the Power Electronics Program at Caltech supported by grants from Rockwell Intemational Inc., Apple Computer Inc., GEC Ferranti Defense Systems Ltd., Dong Ah Electric Co., Ltd., Southern California Edison, International Rectifier Corp., and the Sorensen Fellowship Foundation. 0-7803-3044-7196 $5.00 0 1996 IEEE 797 I 1 CONTROLLER Figure 1. Topological structure of a DCM converter based rectifier with output voltage feedback and (possibly) source voltage feedforward. loop, the control-to-output transfer function is needed. This calculation is complicated by the presence of a rectified sine wave input voltage, which doesn't allow use of the transfer functions derived for dcm dc-dc converters, such as in [2]. The transfer functions derived in this paper are small-signal, linearized transfer functions, valid at frequencies well below twice the line frequency. The control-to-output transfer function is affected by the type of load the rectifier is presented. In order to cover the most common cases, the load used in the analysis is the parallel combination of a constant power load and a resistive load. The constant power load emulates the effect of loading the rectifier circuit with a switching regulator. This models systems where the rectifer is used as a preregulator, followed by a switching postregulator. A switching postregulator presents a negative incremental resistance to the rectifier output at low frequencies [3]. Since the bandwidth of the rectifier voltage loop must be kept well below the line frequency to avoid input current distortion, the switching regulator can probably be modelled as a constant power load in this frequency range. 11. Power Balance All of the rectifier circuits analyzed here consist of a dc-dc converter operating in dcm, with a large energy storage capacitor across the output. In the context of this paper, the large output capacitor does not belong to the converter, and is considered separate. Thus, it is the pupose of the converter to interface between the rectified ac source voltage and the dc output voltage across the large output capacitor. This is depicted in figure 2.