Average Modeling Technique for Switched Capacitor Converters Including Large Signal Dynamics and Small Signal Responses Michael Evzelman Sam Ben-Yaakov Student member, IEEE Fellow, IEEE Power Electronics Laboratory, Department of Electrical and Computer Engineering Ben-Gurion University of the Negev P.O. Box 653, Beer-Sheva, 84105 Israel evzelman@ee.bgu.ac.il; sby@ee.bgu.ac.il Website: www.ee.bgu.ac.il/~pel/ Abstract — A generic average model that is capable of predicting the static, large signal dynamics and small signal response of Switched Capacitor Converters (SCC) was developed and tested. The proposed model was verified by full circuit simulation and experimentally, and good agreement was found between the results. The model was used to study dynamic behavior of SCC systems including the small signal responses, which are required for designing control loops. The model can be of great design value as it can be used to optimize the dynamic design of SCC systems and to design the compensator for closed loop operation. Index Terms — Switched Capacitor Converter, SCC, modeling, dynamic behavior, power converter, small signal, large signal. I. INTRODUCTION Switched capacitor converters (referred further as SCC, for singular and plural), also known as a charge pumps, are a family of DC-DC converters that transfer a charge between input and output of the converter employing one, or a number of flying capacitors. The flying capacitor is first connected to the input charging the capacitor, and then connected to an output, or the next flying capacitor in chain to transfer the charge towards the output, or the load. SCC are preferred in a number of power management systems due to their small size, the absence of inductors and integration compatibility. The static behavior of SCC systems was analyzed in numerous earlier studies (e.g. [1-13]), in which the expressions of the voltage transfer ratios and the expected losses were derived. The objective of this study was to investigate the dynamic behavior of SCC systems including the small signal responses, which are required for designing control loops. This was accomplished by developing a generic average model of SCC systems that is capable of predicting not only the static, but also the large signal dynamic behavior and small signal responses of SCC converters. The model is an extension of the analytical findings of [12], [13] and includes the dynamic aspects. The proposed model covers hard switched SCC topologies and charge pumps that are built around active switches, or diodes, or both. The model is also applicable to multi phase, multi capacitors SCC if it can be assumed that each of the subcircuits of the modeled SCC can be described, or approximated, by a first order RC circuit which, as described in [12], is possible in many practical cases. The model covers all operational modes of SCC, Complete Charge – CC (Fig. 1a), Partial Charge – PC (Fig. 1b), and No Charge – NC (Fig. 1c) as discussed in [13]. II. BASIC ASPECTS OF THE PROPOSED SCC MODELING APPROACH For the sake of brevity, the model development is presented by considering an inverting 1:1 charge pump converter (Fig. 2). The converter consists of a flying capacitor C f , with a lossy component R ESR , two switches S 1 and S 2 with "ON" resistance of R s1 and R s2 respectively, an output filter capacitor C o with R ESRo and load resistance R o . It should be noted that the model treats the switches as a resistive elements when "ON" and conducting, and discontinuity while "OFF", any possible non- linearity of the switches, like entering saturation mode for example during the turn on of the converter, due to the high inrush current, are not taken into account in this model. The switches are operated complementary to each other, running at switching frequency, f s . Switches operation brings to periodical charge of the flying capacitor during T 1 , when S 1 is "ON", and discharge of the flying capacitor during T 2 , when S 2 is "ON". The equivalent charge and discharge circuits are presented in Fig. 3 as the charge subcircuit (i = 1, Fig. 3a), and discharge subcircuit ( i = 2, Fig. 3b). Fig. 1. Possible charge current shapes: (a) Complete charge-CC; (b) Partial charge-PC; (c) No charge-NC.