P1-5-Ch9-高频电感和变压器的设计.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,*,Chapter 9,：,Design of High-Frequency Inductors and Transformers,9-1 Introduction,9-2 Basics of Magnetic Design,9-4 Area-Product Method,9-5 Design Example of an Inductor,9-6 Design Example of a Transformer for a,Forward Converter,9-7 Loss mechanisms in magnetic circuits,From Reference 2-,First Course on Power Electronics,1,9-1 Introduction,High-frequency inductors and transforms are generally not available off-the-shelf,and must be designed based on the,application specifications,（应用要求，应用说明）,.,So far,we have mostly considered analysis.Design is more challenging,and is partly an art.,In this chapter,a simple and a commonly used approach called,Area-Product method,is presented,where the thermal considerations are ignored.(A detailed design discussion is presented in,Chapter 30 of the Textbook,),2,9-2 BASICS OF MAGNETIC DESIGN,In designing high frequency inductors and transformers,a designer is faced with,countless choices,including:,Core materials(,permeability,is dependent of materials),Core shape,(some offer better thermal conduction whereas others offer better shielding to,stray flux,杂散磁通,),Cooling methods,(natural convection versus forced cooling),Losses,(lower losses offer higher efficiency at the expense of higher size and weight),3,1 Design consists of:,(1)Selecting appropriate core material,geometry,and size,(2)Selecting appropriate copper winding parameters:wire type,size,and number of turns.,Core,(double E),Winding,Bobbin,Assembled,core and,winding,4,2 Overview of core material,(1),Iron-based alloy laminated,（铁合金片）,cores,(often termed,magnetic steels,):comprised of alloys principally of iron and small amounts of other elements,including:,Various compositions,Fe-,Si,(few percent,Si,),Fe-Cr-,Mn,Important properties,lower,Resistivity,=(10100),Cu,large values of saturation flux density B,s,=11.8T,Used in low-frequency,applications.,5,(2),Powdered iron alloy,（铁粉合金）,cores,:consist of small iron particles electrically isolated from each other.,Various compositions,Fe-,Si,(few percent,Si,),Fe-Cr-,Mn,Important properties,have larger effective,resistivity,than laminated cores,Used in low-frequency,applications,6,(3),Ferrite,（铁氧体）,cores,Various compositions,Iron oxides,Fe-Ni-,Mn,oxides,Important properties,Resistivity,very large(insulator)-no,ohmic,losses and hence skin effect problems at high frequencies.,B,s,=0.3T(T=,tesla,),7,Core materials comparison,8,3 Magnetic core shapes,Ferrite cores available as,U,E,and I shapes as well as,pot cores,and,toroids,.,Laminated(conducting)materials available in E,U,and I shapes as well as tape wound,toroids,and C-shapes.,insulating layer,magnetic steel lamination,9,10,11,Open geometries such as E-core make for easier,fabrication,（,装配）,and,better,thermal conduction,but more,stray flux,and hence potentially more severe EMI problems.,Closed geometries such as pot cores make for more difficult fabrication and worse,thermal conduction,but much less stray flux and hence EMI problems.,12,4 Two basic quantities need being calculated in design-optimization problems,The,peak flux density,B,max,in the magnetic core(we most not exceed the allowed flux density of the material.,B,max,B,sat,)to limit core losses,and,The,peak current density,J,max,in the winding conductors(winding must thick enough to carry current without overheating)to limit conduction losses.In general,J,max,B,max,25,A,pot core,2616,which is shown in Fig.9-4 for a laboratory experiment,has the core Area,A,core,=93.1,mm,2,and the window Area,A,window,=39,mm,2,.Therefore,we will select this core,which has an Area-Product,A,p,=93.139=3631,mm,4,3583,mm,4,.,Solution:,3 selecting core shape to ensure,practical,A,p,calculated,A,p,.,26,Solution:,4 calculating N.,Winding wire cross sectional area,A,cond,=,I,rms,/,J,max,=5.0/6.0=0.83,mm,2,.We will use,five strands,（,5,股）,of American Wire Gauge AWG 25 wires 3,each with a cross-sectional area of 0.16,mm,2,in parallel.,Solution:,5 selecting,A,cond,.,27,Solution:,6 calculating l,g,.,28,9-6 DESIGN EXAMPLE OF A TRANSFORMER FOR A FORWARD CONVERTER,The required electrical specifications for the transformer in a Forward converter are as follows:,f,s,=100,kHz,and,V,1,=,V,2,=,V,3,=30,V,.,Assume the,rms,value of the current in each winding to be,2.5,A,.We will choose the following values for this design:,B,max,=0.25T,J,max,=5A/mm,2,k,w,=0.5,k,conv,=0.5,.,29,Solution:,1 Calculating,A,p,.,30,Solution:,2 selecting core material and shape to ensure,B,select,B,max,and practical,A,p,calculated,A,p,Select pot core 22,13,A,core,=63.9mm,2,A,window,=29.2mm,2,and therefore,A,p,=1866mm,4,1800mm,4,.,31,Solution:,3 calculating N,32,Use,three strands,of AWG 25 wires 3,each with a cross-sectional area of 0.16,mm,2,in parallel for each winding.,Solution:,4 selecting,A,cond,33,9-7 Loss mechanisms in magnetic circuits,The size of a magnetic component is often determined by loss.,Generally,the losses can be divided into 2 components:,winding associated loss,and,core associated loss,.,34,1 Winding loss,At low frequency(including dc),winding loss is just due to the dc resistance in the winding and is easy to calculate.,P,diss,=(i,rms,),2,R,wire,At higher frequency,there are additional effect we must consider of:,skin effect,（集肤效应）,and,proximity effect,（邻近效应）,.,35,Skin effect,Skin effect,is the“self-shielding”effect of conductors:Due to,eddy currents,（涡流）,generated by changes in magnetic field of an ac current,the fields and currents may not penetrate inside a conductor at high frequency.,I(t,),H(t,),I(t,),J(t,),J(t,),0,Eddy currents,r,a,a,(a),(b),(c),Time-varying current,i(t,),Magnetic fields,H(t,),Eddy currents,36,According to Lenzs law,magnetic fields within the core induce currents(“eddy currents”)to flow within the core.The eddy currents flow such that they tend to generate a flux which opposes changes in the core flux,(t).,The eddy currents tend to prevent flux from penetrating the core.,37,Eddy Currents,Increase Winding Losses,eddy currents,cause a,nonuniform,current density in the conductor.Effective resistance of conductor increased over dc value.,For sinusoidal currents:current density is an exponentially decaying function of distance into the conductor,with characteristic length,known as the penetration depth or,skin depth,.,38,Numerical example using copper at 100C.,Frequency,50,H,z,5,k,H,z,20,k,H,z,500,k,H,z,Skin Depth,10,.,6,m,m,1,.,06,m,m,0,.,53,m,m,0,.,106,m,m,For copper at room temperature:,39,So,if we need to carry high frequency current,wire of radius,is not useful,since the current will be carried only on the surface of the wine.,The,solution,to this problem is to parallel isolated wire of,thickness,.Each layer carries net current,i(t,),.,41,Proximity effect,causes significant power loss in the windings of high-frequency transformers and ac inductors,especially in multi-layer windings,.,The,solution,to minimize,proximity losses,is:,In inductors,windings can be with single-layer construction.,In transforms,windings can be interleaved and avoided highs of layer.,42,Example:a two-winding transformer,Primary turns are wound in three layers,assume that each layer is one turn.The secondary is a similar three-layer winding.,Each layer carries net current,i,(,t,).Portions of the windings that lie outside of the core window are not illustrated.Each layer,has thickness,h,.,43,(1)Distribution of currents on surfaces of conductors:,Skin effect causes currents to concentrate on surfaces of conductors,Surface current induces,equal and opposite current,on adjacent conductor,Net conductor current is,equal to,i,(,t,)for each layer,since layers are connected in series,Circulating currents within layers increase with the numbers of layers,44,(2)Estimating proximity loss:high-frequency limit,The current,i,(,t,)having,rms,value,I,is confined to thickness,on the surface of layer 1.,Hence the effective“ac”resistance of layer 1 is:,R,ac,=(,h/,),R,dc,This induces copper loss,P,1,in layer 1:,P,1,=,I,2,R,ac,45,Power loss,P,2,in layer 2 is:,P,2,=,P,1,+4,P,1,=5,P,1,Power loss,P,3,in layer 3 is:,P,3,=(2,2,+3,2,),P,1,=13,P,1,46,Add up losses in each layer:,Compare with dc copper loss,:,If foil thickness were H=,then at dc each layer would produce copper loss P,1,.The copper loss of M-layer winding would be,P,dc,=I,2,MR,dc,So the proximity effect increases the copper loss by a factor of:,47,The,solution,to minimize,proximity losses,is:,In inductors,windings can be with single-layer construction.,In transforms,windings can be interleaved and avoided highs of layer.,48,(3)Two-winding transformer,MMF diagram,Winding layout,MMF diagram,(a)without proximity effect,49,(b)with proximity effect,50,(c)Interleaving the windings:MMF diagram,Greatly reduces the peak MMF,leakage flux,and proximity losses,51,2 Core loss,=,Eddy current loss+,hysteresis,loss,Skin effect,dB/,dt,through core generates voltage which drive eddy currents around core,these eddy currents flow such that they tend to generate a flux which,oppose,change core flue!,x,dx,-x,L,d,w,Bsin(,w,t,),x,y,z,Eddy current flow path,52,x,dx,-x,L,d,w,Bsin(,w,t,),x,y,z,Eddy current flow path,Time-varying m,agnetic fields,B(t,),Eddy currents,Secondary magnetic fields that oppose the applied magnetic field.,53,Eddy Currents,effects,(1)Cause,eddy current losses,!,(2)Cause the flux to be rejected from the core!The total magnetic field in the core decays exponentially with the distance into the core.,B,B/2.7,y,skin depth,:,54,The,solution,to this problem is to increase the,resistivity,of the core(adding small percentage of silicon to the iron),and to use core that made from stacks of many thin laminations.,Magnetic steel,lamination,Insulator,0.05 t,t(typically,0.3 mm),55,Magnetic steel,lamination,Insulator,0.05 t,t(typically,0.3 mm),Cores made from conductive magnetic materials must be made of many thin laminations.Lamination thickness skin depth.,Stacking factor,k,stack,=t/(t+0.05t),56,Hysteresis,loss,B,H,Minor,hysteresis,loop,B,s,-B,s,Core losses(,hysteresis,eddy currents)increase as B,2,(or greater),Area encompassed by,hysteresis,loop equals work done on material during one cycle of applied ac magnetic field.Area times frequency equals power dissipated per unit volume.,57,Typical waveforms of flux density,B(t,)versus time,in an inductor.,Only,B,ac,contributes to,hysteresis,loss.,t,B,ac,0,t,0,B(t,),B,avg,B,ac,Figure 30-1 Magnetic flux density waveforms,58,