IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 3, JUNE 1999 613 The Dynamics of a PWM Boost Converter with Resistive Input Sam Ben-Yaakov, Member, IEEE, and Ilya Zeltser Abstract— This paper investigates the large- and small-signal response issues and, in particular, the inner loop gain and outer loop response of an indirect control method for active power-factor correction. The control scheme is based on sens- ing the average inductor current and generating a (the complement of the switch duty cycle) which is proportional to the current. The method is demonstrated by considering the performance of a boost-type active power-factor corrector (APFC) that does not need to sense the input voltage. Theoretical and experimental results confirm the validity of the approach and demonstrate that the proposed method can be useful in the design of robust APFC with low total harmonic distortion. The indirect control method investigated in this paper is also compared to the classical direct APFC control method, pointing to the differences between the two. Index Terms— Active power-factor corrections, modeling, power converters, simulation. I. INTRODUCTION T HE current interest in active power-factor correction (APFC) [1]–[10] prompts investigators to look for im- proved methods to shape the input current of pulsewidth modulation (PWM) converters. Two groups of solutions have been proposed hitherto for continuous-current-mode (CCM) systems, those that rely on direct current feedback [2] and those that apply indirect input current control [3]–[10]. The main difference between the two groups is related to input voltage sensing. In the direct methods, the control of the input current is achieved by an “inner” feedback loop for which the rectified input voltage serves as the reference to the desired shape of the input current. In the indirect control method, the information regarding the desired input current shape is obtained by sensing the inductor current, the switch current, or the diode current [3]. This is possible, in theory, considering the fact that these currents are a function of the input voltage. The indirect control method has many advantages, such as being less susceptible to the switching noise which is normally superimposed on the rectified input voltage node. The indirect control scheme of APFC introduced in [11] is similar to the approach presented earlier in [6], the main difference being the way in which the input current is av- eraged. In [6], one-cycle averaging was used, whereas, in [11], a simply low-pass filtering is suggested. Other earlier Manuscript received October 30, 1997; revised January 31, 1998. Abstract published on the Internet March 1, 1999. The authors are with the Power Electronics Laboratory, Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel (e-mail: sby@bguee.ee.bgu.ac.il). Publisher Item Identifier S 0278-0046(99)04142-8. (a) (b) Fig. 1. (a) The boost converter and (b) its behavioral average model (after [9] and [10]). approaches of indirect APFC sensed the peak current [3]–[6] or switch current [7]. The objective of this paper was to study the large- and small-signal responses of a boost converter applying the indirect control APFC of [11]. This was accomplished by developing average models of the system and deriving their small-signal response. Finally, the difference between the proposed control scheme and the classical, inner current feedback method [2] is also explained in terms of basic control theory ideas. Although the main thrust of this paper is to discuss the dynamics of the system, we first summarize the concept of the control method—for the sake of completeness. II. THE BOOST TOPOLOGY The indirect APFC control method to be studied will first be described by a simple intuitive reasoning in relation to the boost converter [Fig. 1(a)]. It is assumed that the converter is driven by a duty cycle and that it operates under CCM conditions. As shown previously [13], [14], the function of the converter can be represented by the behavioral model of Fig. 1(b). One can now apply a power circuit theory corollary: under stable conditions, the average voltage across a power inductor must be zero (otherwise, the current will rise to infinity). Assuming that the circuit is stable (as will be shown below), this implies [Fig. 1(b)] (1) where is , is the average input voltage, and is the average output voltage. Averaging is over 0278–0046/99$10.00  1999 IEEE