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Flyback Vs. Forward Converter Topology Comparison Based Upon Magnetic Design

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Flyback Vs. Forward Converter Topology Comparison Based Upon Magnetic Design ELECTRONICA DE POTENCIA - Revista de la SOBRAEP, vol. 5, núm. 1, 2000, pp. 16-27. FLYBACK VS. FORWARD CONVERTER TOPOLOGY COMPARISON BASED UPON MAGNETIC DESIGN . H. E. TACCA. Cita: H. E. TACCA (2000). FLYBACK VS. FORWARD CONVERTER TOPOLOGY COMPARISON BASED UPON MAGNETIC DESIGN. ELECTRONICA DE POTENCIA - Revista de la SOBRAEP, 5 (1) 16-27. Dirección estable: https://www.aacademica.org/hernan.emilio.tacca/7 Esta obra está bajo una licencia de Creative Commons. Para ver una copia de esta licencia, visite http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es. Acta Académica es un proyecto académico sin fines de lucro enmarcado en la iniciativa de acceso abierto. Acta Académica fue creado para facilitar a investigadores de todo el mundo el compartir su producción académica. Para crear un perfil gratuitamente o acceder a otros trabajos visite: http://www.aacademica.org. 1 FLYBACK VS. FORWARD CONVERTER TOPOLOGY COMPARISON BASED UPON MAGNETIC DESIGN Hernán Emilio TACCA Universidad de Buenos Aires , Facultad de Ingeniería LABCATYP - Depto. de Electrónica [email protected] Abstract - Based on approximative equations for single la air gap step calculation design procedures, a simple method l average mean turn length useful to adopt the most suitable topology in low power eav DC to DC conversion is derived from the volume lem mean turn length calculation of the magnetic cores needed. lFe effective magnetic length n primary turns Index terms - Low power magnetic components, switching P power converters, flyback and forward magnetics design. nS secondary turns PCu winding losses NOMENCLATURE P device rated switching power D P core losses Bmax peak value of the induction Fe P converter output power Bmin induction minimum value O D duty-cycle factor Rac a.c. resistance f switching frequency Rdc d.c. resistance Fc window filling factor of the primary/secondary PS/ ℜVFW/ FB total forward core volume to flyback core coil (also known as copper factor) : volume ratio FnSS= cPPS///SCuW PS PS/ Rθ thermal resistance f voltage form factor S inductor wire cross section fV CuL F partition factor of the primary windings : S primary wire cross section P CuP FSSPWW= S secondary wire cross section P CuS f power switch profit factor (or power device pr Sdis heat dissipation surface utilization factor) SFe minimum core section Fr total winding eddy currents factor SFeef effective core section FW window factor : FSSWWF= e SFe flyback core section required I average value of the inductor current FB Lav SFe inductor core section required I effective value of the inductor current L Lef SFe forward transformer core section required I peak value of the inductor current TFW Lmax SW window area I average value of the primary current Pav S primary window area WP I effective value of the primary current Pef S secondary window area WS I P peak value of the primary current max tC power switch conduction time kC core sizing characteristic converter topology V core volume of the flyback coupled inductor FeFB coefficient (usually named flyback “transformer”) k ES effective core shape factor V total volume occupied by the cores of the FeFW k skin effect factor rS forward converter krX proximity effect factor V core volume of the smoothing inductor FeL kS geometrical core shape factor V core volume of the forward transformer FeTFW ku transformer utilization factor T VP primary supply voltage L inductance of the smoothing inductor Δ penetration depth 2 ΔB maximum induction increment δ iII=Δ (2.2) PPPmax δ i normalized amplitude of the inductor ripple L DtT= C (2.3) current and from the current waveforms it follows : δ i P normalized primary current variation ⎛ δ i ⎞ ID=−I⎜1 P ⎟ (2.4) η converter efficiency PPav max ⎝ 2 ⎠ Φ magnetic flux 1 2 μ o magnetic field constant ID=−I1 δδ ii+ (2.5) PPef max PP3 μ relative static permeability (derived from the rs Then, the output power is : static magnetization curve) ⎛ δ i ⎞ ρ conductor resistivity PPVID==ηη = η⎜1 −P ⎟ VI (2.6) OPPPav⎝ 2 ⎠ PP max σ L inductor current density + Vp D iO σ P primary current density iS I. INTRODUCTION nP n S Vo RL In DC to DC converters and off-line switching power i P supplies for low power applications, the most used topologies are the flyback and the forward converters [1]. The flyback structure has the advantage of requiring only a single magnetic component. This one, if designed for minimum size, results smaller than the overall volume (a) occupied by both the smoothing inductor plus the power i P transformer of the equivalent forward converter. However, Ip when the flyback coupled inductor size is minimum, the max profit factor of the power switch becomes poor [2][3]. If an Ip improved profit of the flyback power device is required, it min results mandatory to supersize the magnetic component . So, 0 a trade-off arises between the core size and the rated tc = DT T t iS switching power (maximum theoretical switching power) of the power transistor [4]. The better the profit factor, heavier I Smax the magnetic cores become and this apply to both topologies here compared. Nevertheless, the required core volumes I result from different laws, so for a wanted profit factor, one Smin topology will be the most suitable regarding the core weight. In this work, the total magnetic material volume required T t tc T - tc for both alternatives are computed and related. The mm... f comparison criterion is stated as the ratio of core sizing mm... f max approximative equations, which become justified by the niS S ni closed matching with results obtained using manufacturer P P magnetomotive force mm... f min design data and recommended procedures. mm... f= nPP i+ n SS i Derivation of some equations involved on design procedures are presented in appendices (including some T t tc T - tc application examples agreeing with manufacturer data). DT In order to compare topologies, first, the required core sections are obtained and then, the core volumes are (b) computed assuming identical core shapes for all the magnetic components involved. Figure 1 : Flyback converter, (a) basic circuit, (b) basic Finally, the volume rate is plotted to bring an easy method waveforms. to know wich topology will be the lightest. B. Core sizing II. FLYBACK CONVERTER The primary current density is : I P σ = ef (2.7) A. Basic flyback circuit P S Fig. 1.a depicts the basic circuit of a flyback converter and CuP where S is the cross section of the primary wire that fig. 1.b shows the corresponding waveforms. From fig. 1.b it CuP may be defined : must verify : ΔIIPP=− I P (2.1) SF= FSn (2.8) max min CuPP P c W P 3 In accordance with the Faraday law : G ≅ 1 δ i ΔB ()p Vn= S (2.9) PPt Fe as it was done with flyback converters. C The equations 3.1 and 3.2 are particular cases of where, ΔBB=−max B min and generalized expressions valid for many other converter μ μ topologies (Apendix II). B = o nI ≅ o nI (2.10) max PPmaxPP max L l D Fe la FW iO la + μ rs + Vp because usually : i ll>> μ L aFers Vo nP DL nS R where μ rs is the relative static permeability. L i By a similar way, P μ o v ΔΔB ≅ nIPP (2.11) CE Dm la Relating 2.10 and 2.11 yields : (a) ΔB ΔI P ==δ i P (2.12) iP Bmax I P max using this equation (with the simplified notation Ipmax BBmm= ax) the expression 2.9 yields : Ip f min VniB= δ S (2.13) PPPmFD e 0 DT T t With eqs. 2.5 , 2.6 , 2.7 , 2.8 and 2.13 , using the window i i S L factor definition FSSWWF= / e, it results : Is = I max Lmax DP i L SG= O (2.14.a) FeFB i ()δ ip ηδiBf σ F FF S Pm PcP PW I Lmin where, 1 2 DT T 1 −+δδii v mm... f t PP3 CE G = (2.14.b) V δ i CEmax v ()p ⎛ δ i P ⎞ CE ⎜1 − ⎟ ⎝ 2 ⎠ For all the possible values 01≤≤δ iP it results mm... f Vp 11≤<G .075, so the expression 2.14.a may be ()δ ip DT T t simplified assuming G ≅ 1 . tm ()δ ip To complete the design, it is necessary to adopt the (b) partition factor of the primary windings (see section IV), the primary current density (section V) and the maximum value Figure 2 : Forward converter, (a) basic circuit, (b) basic of the induction (Appendix I). waveforms. III. FORWARD CONVERTER B. Inductor core sizing The effective value of the inductor current can be A. Basic circuit and transformer core sizing expressed as : The typical circuit of a forward converter is presented in S S WLLFe fig. 2.a , while its waveforms are depicted in fig. 2.b . The ISLL==σσCuL Fc = σLcWFF (3.3) ef L n n equation of the primary voltage becomes : L L B 1 On the other hand, Vn==m S nBfS (3.1) nBS PP Fe P m Fe nL Φ LmFeL tC D L == (3.4) i I from which, the sizing equation results : L Lmax Using eqs. 3.3 and 3.4 : DPO SGFe = (3.2) LILL I TFW ()δ ip ησBf F FF ef max mPcPWP S = (3.5) FeL σ FF B where it may be approximated LcW m From fig. 2.b it follows : 4 1 and secondary coils, while FP is the partition factor of the II=−1 δδ i+ i2 (3.6) LLef max L3 L primary windings defined as the ratio between the window area occupied by the primary winding and the total window ⎛ δ i ⎞ II=−⎜1 L ⎟ (3.7) area , FSS= .
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