IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 2, MARCH 2006 549 Three-Level Buck Converter for Envelope Tracking Applications Vahid Yousefzadeh, Student Member, IEEE, Eduard Alarcón, Member, IEEE, and Dragan Maksimovic ´ , Member, IEEE Abstract—This letter proposes a three-level buck converter for tracking applications such as envelope-tracking in radio frequency power amplifiers (RFPAs). It is shown that the three-level buck converter can offer advantages in terms of switching ripples, losses, bandwidth, or the size of magnetic components compared to a stan- dard buck or a two-phase buck converter. Experimental results il- lustrate improved efficiency and ripple rejection in an RFPA enve- lope-tracking application representative for low-power battery-op- erated systems. Index Terms—Envelope elimination and restoration (EER), radio frequency power amplifier (RFPA), three-level buck con- verter. I. INTRODUCTION E NVELOPE elimination and restoration (EER) techniques or, more generally, polar modulation techniques, have been proposed to improve the efficiency and linearity of radio frequency power amplifier (RFPA) systems [1]. In such systems, as shown in Fig. 1, an efficient, wide-bandwidth envelope-tracking power supply modulates the supply voltage for the RFPA. Various approaches have been proposed to address the tradeoff between the wide-bandwidth tracking capability and the efficiency, including pulsewidth modulated (PWM) [2]–[4] or delta–sigma modulated buck converters [5], a single-ended primary inductance converter (SEPIC) with average current-mode control [6], a cascade of buck and boost converters [7], a multiphase converter [8], or linear-assisted switched-mode converters [9], [10]. Multilevel converters with flying capacitors, such as the three-level (i.e., two-cell) buck converter shown in Fig. 2, have been proposed for high-voltage high-power applications [11]. In this letter, we propose the use of the three-level buck con- verter configuration to achieve favorable tradeoffs in terms of the switching ripple, efficiency, bandwidth, or decreasing filter element sizes in envelope-tracking power supplies, including RFPA systems in low-power, battery-operated electronics. Operation of the three-level converter is briefly summarized in Section II. Section III compares the three-level converter to the two-phase buck converter. An example of time-varying Manuscript received June 11, 2005; revised June 28, 2005. This work was supported by the Defense Advanced Research Projects Agency (DARPA) under the Intelligent RF Front Ends (IRFFE) Program under Grant N00014-02-1- 0501. This letter was presented in part as “Three-Level Buck Converter for En- velope Tracking in RF Power Amplifiers” at APEC’05. Recommended by As- sociate Editor J. A. Cobos. V. Yousefzadeh and D. Maksimovic ´ are with the Colorado Power Electronics Center, Electrial and Computer Engineering Department, University of Col- orado, Boulder, CO 80309 USA (e-mail: yousefza@colorado.edu). E. Alarcón is with the Department of Electronic Engineering, Technical Uni- versity of Catalunya, Barcelona 08034, Spain. Digital Object Identifier 10.1109/TPEL.2005.869728 Fig. 1. Envelope-tracking technique for RFPAs. Fig. 2. Three-level buck converter [11]. modulation is presented in Section IV. Experimental results are shown in Section V. II. THREE-LEVEL BUCK CONVERTER OPERATION The power stage of the three-level buck converter is shown in Fig. 2. Two pairs of complementary switches, and , are operated at the same duty cycle , and phase shifted by 180 (similar to the operation of a two-phase con- verter), as illustrated by the waveforms in Fig. 3. Assuming that the flying capacitor voltage equals 2, the switch node voltage can take one of three possible levels: 0, 2, or . Furthermore, by phase shifting the switching of the two pairs of transistors, the frequency of the pulses is 2 , where is the switching frequency. The three-level operation, in combination with the effective doubling of the switching fre- quency, results in favorable trade offs in terms of decreasing the switching ripples, decreasing the switching frequency, reducing the size of the filter elements, increasing the converter open-loop bandwidth, or increasing the converter efficiency [12]. For ex- ample, assuming the same switching frequency and the same maximum switching ripples, the three-level converter requires 4 times smaller inductance and two times smaller capacitance compared to the standard buck converter. In our experimental prototypes, described in more detail in Section V, the switching frequency of the standard buck converter must be increased by a factor of 2 2 from 200 to 560 kHz to obtain the same max- imum output voltage ripple of 12 mV as in the three-level con- 0885-8993/$20.00 © 2006 IEEE