Unified small‐signal model for DC‐DC converters based on the three‐state switching cell operating in discontinuous conduction mode

Abstract

SummaryUnified small‐signal modeling approaches are of paramount importance for the design of controllers and closed‐loop control systems in power electronic converters. In this sense, this work proposes the small‐signal analysis of non‐isolated dc‐dc converters employing the three‐state switching cell (3SSC) in discontinuous conduction mode (DCM). The modeling technique relies on the very same principles of the pulse width modulation (PWM) switch while not involving matrix operations, but only basic concepts related to electric circuits. Considering that the waveforms associated with the terminals of the 3SSC in DCM have a common behavior in all basic dc‐dc converters, it is possible to derive the small‐signal models for both operating regions of the 3SSC, that is, non‐overlapping mode (NOM) and overlapping mode (OM). Thus, one can effectively demonstrate that the same circuit can represent both modes, even though the coefficients that describe the models are calculated from distinct equations. The theoretical claims are validated in the frequency and time domains while comparing the model with the converter. The obtained results evidence that the unified model can accurately represent converters based on the 3SSC in DCM.

Generalized Pulse Width Modulation Switch Model for Converters Based on the Multistate Switching Cell in Discontinuous Conduction Mode

“…Substituting all the parameters in (59) allows for obtaining the numerical representation of the input-to-output transfer function, which is validated in both frequency and time domains in Figure 8 considering that the model follows the behavior of the switched converter accurately. It is also noteworthy that substituting M = 3 and Rn = 1 or M = 3 and Rn = 2 in the equations that provide the coefficients of the ac model represented in Figure 5 will lead to the very same results found in [40] for the 3SSC-based buck converter in DCM operating in the nonoverlapping mode (NOM) or the overlapping mode (OM), respectively. Now, let us assess the dc-dc buck converter based on the 4SSC described in [42] operating in DCM and region R2 (M = 4, Rn = 2, 1/3 ≤ D ≤ 2/3) to demonstrate that the model is valid for other configurations of the MSSC while considering the following specifications: Vi = 50 V, Vo = 25.88 V, D = 0.45, Ro = 30 Ω, fs = 30 kHz, L = 10 µH, RL = 1 mΩ, C = 100 µF, and RSE = 10 mΩ.…”

“…Substituting all the parameters in (59) allows for obtaining the numerical representation of the input-tooutput transfer function, which is validated in both frequency and time domains in Figure 8 considering that the model follows the behavior of the switched converter accurately. It is also noteworthy that substituting M = 3 and R n = 1 or M = 3 and R n = 2 in the equations that provide the coefficients of the ac model represented in Figure 5 will lead to the very same results found in [40] for the 3SSC-based buck converter in DCM operating in the non-overlapping mode (NOM) or the overlapping mode (OM), respectively. 61) to design the voltage and current control loops, respectively, considering the converter operating in average current mode control [44].…”

“…After thorough analysis of the literature, it can be concluded that there is a lack of comprehensive representation of converters employing the multistate switching cell (MSSC), which is an extension of the 3SSC designed to derive multiphase converters intended for high-power, high-current applications. Considering the aforementioned gap, this study serves as a continuation of the research presented in [40], while presenting the following contributions to the state of the art of small-signal analysis:…”