Modeling and Simulation of Non-ideal Buck Converter in DCM

ISSN 2249-6343International Journal of Computer Technology and Electronics Engineering (IJCTEE)Volume 2, Issue 2Modeling and Simulation of Non-ideal BuckConverter in DCMSheng-yu Gong, Lin Chen, Chang-hu Yu, Guang-jun Xie*Abstract— The modeling method is exemplified by Buckconverter operating in the discontinuous conduction mode(DCM), taking into account all parasitic resistances, thresholdvoltage of diode and inductor current ripples existing in actualconverters. Based on the theory of switch average model, timeaverage method of equivalent circuit, the theory of energyconservation, a circuit averaging method is studied to modelnon-ideal Buck converters operating in DCM, and a duty ratioconstraint which leads to a full order model is introduced. Onthe basis of DC circuit model and large and small-signalequivalent circuit model, the modeling and simulation analysisof non-ideal Buck converters are presented. Therefore, thederived models are convenient for modeling and designing ofDC-DC converter and its control system.Index Terms— Buck, Non-ideal, DCM, Modeling, SimulationI. INTRODUCTIONThe continuous conduction mode (CCM) and discontinuousconduction mode are two basic operations in DC-DC PWMconverters. Compared with the CCM, the average inductorcurrent is lower during the entire switching period of DCMdue to exit a zero inductor current sub-interval. Therefore, thedc-dc switching converter operating in DCM is widelyapplied in light load conditions with small load current. Theinductor current in reverse direction can be avoided in thelarge heavy load current converter in DCM, then to improvethe efficiency of energy transfer. So modeling of the converterin DCM is necessary. However, additional constraints inDCM make the modeling process more complex, and theaccuracy higher. In this paper, the equivalent transformationof non-ideal parasitic components (the on-resistance of activeswitching power MOSFET, passive switching diode forwardvoltage drop and on-resistance, the equivalent seriesresistances of the inductor and capacitor, the inductor currentripple) is based on the principle of energy conservation. And aduty ratio constraint which leads to a full order model isintroduced. A circuit averaging method is studied to buildlarge signal averaged, DC and small signal circuit models ofnon-ideal BUCK converter in DCM, then analysis of steadystate and dynamic small signal characteristics is implemented,which can derive the open-loop transfer function forsimulation.Manuscript received Mar 24, 2012.Sheng-yu Gong is with School of Electronic Science and AppliedPhysics, Hefei University of Technology, Hefei 230009, Anhui, China.Gang-jun Xie is with School of Electronic Science and Applied Physics,Hefei University of Technology, Hefei 230009, Anhui, China(corresponding author, e-mail: gjxie8005@hfut.edu.cn).II. CIRCUIT OF NON-IDEAL BUCK CONVERTERThe equivalent circuit with parasitic components of BUCKconverter is shown in Fig.1.Suposed that the switching periodis T s , Tonis the on-time of switch S, and the duty cycleD T T1 on /'Ton ,sD T Tv g'2on/ siS, the freewheeling diode conduction time isS.RSDR DV Di DFig.1 The equivalent circuit with parasitic components of BuckconverterConsidered the influence of inductor current ripple in DCM,the current waveforms through the inductor, the switch andthe diode are shown in Fig.2.i Li Si DImax0 D 1T S( D 1D2) TSI LLT SRLi LCR CRvOFig.2 The current waveforms of Buck converter in DCMIII. THE MODELING OF NON-IDEAL BUCKCONVERTER IN DCMA. The Principle of Energy ConservationThe average current through inductor during a switchingperiod is:T1S( D1D2)IL iL()t dt ImaxTs20(1)The rms value of the inductor current is:T1S2( D1D2)1L, rmsL( ) max 2LTs3 3( D01D2)(2)I i t dt I IThe power loss inresistance of inductor is:RLwhich is the equivalent seriesttt72

ISSN 2249-6343International Journal of Computer Technology and Electronics Engineering (IJCTEE)Volume 2, Issue 2d ( D dˆ)( I iˆ)i d( D dˆ ) ( D v dˆ iˆ)1 1 1 L LL1dD22D2 D2ˆ112g1LVgD1ILD D D I 2D I ˆ D ˆD D D D V D D D Dd1d d21 1 2 L2 L1I ˆLv2 gd2 1i2 L12(12) g(12) (12)1 2( D ˆ ˆ1d1)( Vgvg)vg( ˆ D D) ( ˆ ˆ DD d D v d iˆ)2 2 21 1 2 g 1 LVgD1ILD D ( D 2 D ) 2D VˆˆD D V V v d iˆD D D D D D D D I1 1 1 22 g1 2 gg 2 g 2 12 L12(12) (12) (12)L(16)(17)Neglecting the small signal perturbations, DC equivalentcircuit model of non-ideal Buck converter in DCM as shownin Fig.5:I I RLE V ESV gD1D D12I LD1D DFig.5 DC equivalent circuit model of Non-ideal Buck converterin DCMVODD1Vg VE1D2RE1RE. Small-signal Equivalent Circuit Model12V gR(18)Removed the DC component in the equation (16) & (17),the small-signal equivalent circuit model of non-ideal Buckconverter in DCM as shown in Fig.6:vˆgî Savˆga ˆd 21 1a iˆ3 LîLb vˆ1 gb 2 ˆd 1b iˆ3 LFig.6 Small-signal equivalent circuit model of Non-ideal Buckconverter in DCMFrom Fig.6, the open loop transfer function of Buckconverter from duty cycle to output voltage in DCM can beobtained:LR ECR CRV ovˆoovˆ () sG () s vd odˆ 1 () svˆ g ( s) 0b2R(1 sRCC)2E 3(C(C)(E 3) ) (C)R R b s RR C R R R b C L s R R LCs1bR2z1 (19)2R REb3s s 1 QooWhere,R REb3( R R ) LCC,( R RE b3)( R RC)LCQ R ( RE b3) C RRC C ( RE b3)RC C ,L1z1 .RCCIV. SIMULATIONIn this paper, a Buck converter with the followingparameters is assumed:V 10V, V 5V, R 25 , L 2 ,goR 3.5m , C 3mF, R 20m , R 10m ,RfLDS1m , V 0.4V 200kHZDC, the switching frequency. The simulation result as follows:Fig.7 The simulation results (the solid line is for considering theparasitic components, dash line is for without considering theparasitic components)Compared with the ideal model, there is a zero in thetransfer function of non-ideal model. So in theamplitude-frequency curve, the solid line declines at the slope6of 20 dB / dec after 10 H z , while the dash line dose atthe slope of 40 dB / dec .S74

ISSN 2249-6343International Journal of Computer Technology and Electronics Engineering (IJCTEE)Volume 2, Issue 246In the phase-frequency curve, from 10 H z to10 H z , the0 0phase margin of non-ideal model rises from -90 to 0 ,0while the ideal model remains -90 . The simulation resultshows that considering the parasitic components and the dutycycle constraint, the high-frequency performance of BUCKconverter is more accurate.V. CONCLUSIONIn the paper, the equivalent circuit with parasiticcomponents of Buck converter agrees with the theoreticalanalysis well, the simulation result confirms the validity ofthis modeling method in DCM; the full order model reflectsthe actual converter characteristics more accurately, inparticular high-frequency performance. It is very importantfor improving the accuracy of the model.ACKNOWLEDGMENTThis work was supported by the Intercollegiate Key Projectof Nature Science of Anhui Province under Grant No.KJ2011A213.REFERENCES[1] Robert W. Erickson, Dragan Maksimovic. Fundamentals of PowerElectronics (Second Edition). Kluwer Academic Publishers, 2001.[2] J Sun, D. M. Mitchell. Averaged Modeling of PWM ConvertersOperating in Discontinuous Conduction Mode, IEEE Trans. PowerElectronics, Vol.16, No.4, 2001, 482-492.[3] D. Maksimovic, A. M. Stankovic. Modeling and Simulation of PowerElectronic Converters, Proc of the IEEE, Vol.89, No.6, 2001, 898-912.[4] Zhang Weiping. Modeling and Controlling of Switching Converter.China Power Press, 2006.[5] Hou Zhenyi. Technology and Applications of DC Switching PowerSupply. Electronic Industry Press, 2006.[6] Ou Yang Changdi. Modeling Analysis and Simulation of DC-DCSwitching Converter. Aeronautics and Astronautics of NanjingUniversity, PhD thesis, 2004.[7] Cheng Xin. Modeling and Simulation of Non-ideal DC-DC Converters.Hefei University of Technology, Master thesis, 2009.[8] Xu Huifang. Modeling and Controlling of Current Program ModeNon-ideal Buck Converter. Hefei University of Technology, Masterthesis, 2011.75