DD5-c9-高频电感与变压器的设计

1、Chapter 9：Design of High-Frequency Inductors and Transformers9-1 Introduction9-2 Basics of Magnetic Design9-4 Area-Product Method9-5 Design Example of an Inductor9-6 Design Example of a Transformer for a Forward Converter9-7 Loss mechanisms in magnetic circuitsFrom Reference 2-First Course on Power

2、Electronics9-1 Introduction High-frequency inductors and transforms are generally not available off-the-shelf, and must be designed based on the application specifications. So far, we have mostly considered analysis. Design is more challenging, and is partly an art. In this chapter, a simple and a c

3、ommonly 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)9-2 BASICS OF MAGNETIC DESIGN In designing high frequency inductors and transforms, a designer is faced with countless

4、 choices, including: Core materials (permeability is dependent of materials)Core shape (some offer better thermal conduction whereas others offer better shielding to stray flux)Cooling methods (natural convection versus forced cooling)Losses (lower losses offer higher efficiency at the expense of hi

5、gher size and weight)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 winding2 Overview of core material: (1) Iron-based alloy la

6、minated 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 Bs=11.8T Used in low-

7、frequency applications.(2) Powdered iron alloy 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(3) Ferrite cores Various compositions Iron oxi

8、des Fe-Ni-Mn oxides Important properties Resistivity very large (insulator)-no ohmic losses and hence skin effect problems at high frequencies. Bs=0.3T (T= tesla)Core materials comparison3 Magnetic core shapes Ferrite cores available as U, E, and I shapes as well as pot cores and toroids. Laminated

9、(conducting) materials available in E, U, and I shapes as well as tape wound toroids and C-shapes.insulating layer magnetic steel lamination Open geometries such as E-core make for easier fabrication and better thermal conduction but more stray flux and hence potentially more severe EMI problems. Cl

10、osed geometries such as pot cores make for more difficult fabrication and worse thermal conduction but much less stray flux and hence EMI problems.4 Two basic quantities need being calculated in design-optimization problems: The peak flux density Bmax in the magnetic core (we most not exceed the all

11、owed flux density of the material. BmaxBsat) to limit core losses, andThe peak current density Jmax in the winding conductors (wine must thick enough to carry current without overheating) to limit conduction losses. In general, JmaxBmax A pot core 2616, which is shown in Fig. 9-4 for a laboratory ex

12、periment, has the core Area Acore=93.1 mm2 and the window Area Awindow =39mm2 . Therefore, we will select this core, which has an Area-Product Ap =93.139 = 3631mm4 3583mm4.Soluction: 3 selecting core shape to ensure practical Apcalculated Ap. Soluction: 4 calculating N. 23.12310.1935.2075.351010066m

13、axcoreABILN Winding wire cross sectional area Acond = Irms / Jmax = 5.0 / 6.0 =0.83mm2. We will use five strands of American Wire Gauge AWG 25 wires 3, each with a cross-sectional area of 0.16mm2 , in parallel.Soluction: 5 selecting Acond. Soluction: 6 calculating lg. )(2.601010010.19310423667202mmL

14、ANlcoreg9-6 DESIGN EXAMPLE OF A TRANSFORMER FOR A FORWARD CONVERTER The required electrical specifications for the transformer in a Forward converter are as follows: fs =100kHz and V1 =V2 =V3 = 30V . Assume the rms value of the current in each winding to be 2.5 A . We will choose the following value

15、s for this design: Bmax=0.25T, Jmax=5A/mm2, kw=0.5, kconv=0.5.）（）（41263maxmax,1800101055.2010100.50.52303.50)(mmfBJkIVkAswyrmsyyconvpSoluction: 1 Calculating Ap. Soluction: 2 selecting core shape to ensure practical Apcalculated ApSelect pot core 2213, Acore=63.9mm2, Awindow=29.2mm2, and therefore A

16、p=1866mm41800mm4.10109.391010010.9635.2030.5032136max1NNNfABVkNscoreconvySoluction: 3 calculating NUse three strands of AWG 25 wires 3, each with a cross-sectional area of 0.16mm2 , in parallel for each winding.Soluction: 4 selecting Acond)(5 . 055 . 22max, 11 ,mmJIArmscond9-7 Loss mechanisms in mag

17、netic 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. 1 Winding loss At low frequency (including dc), winding loss is just due to the dc resistance in the winding and is e

18、asy to calculate. Pdiss=(irms)2RwireAt higher frequency, there are additional effect we must consider of: skin effect and proximity effect.Skin effectSkin effect is the “self-shielding” effect of conductors: Due to eddy currents generated by changes in magnetic field of an ac current, the fields and

19、 currents may not penetrate inside a conductor at high frequency.I(t)H(t)I(t)J(t)J(t)0Eddy currentsraa(a)(b)(c)Time-varying current i(t) Magnetic fields H(t) Eddy currentsAccording to Lenzs law, magnetic fields within the core induce currents (“eddy currents”) to flow within the core. The eddy curre

20、nts 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.Eddy Currents Increase Winding Losseseddy currents cause a nonuniform current density in the conductor. Effective resistance of conductor incre

21、ased over dc value.fkfcucuFor 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.Numerical example using copper at 100C.Frequency50Hz5kHz20kHz500kHzSkin Depth10.6mm1.06mm0.

22、53mm0.106mm)(.57cmfFor copper at room temperature: So, if we need to carry high frequency current, wine of radiusis 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(

23、t).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

24、and avoided highs of layer.Example: a two-winding transformerPrimary 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 illustra

25、ted. Each layerhas thickness h .(1) Distribution of currents on surfaces of conductors: Skin effect causes currents to concentrate on surfaces of conductors Surface current inducesequal and opposite currenton adjacent conductor Net conductor current isequal to i(t) for each layer,since layers are co

26、nnected in series Circulating currents within layers increase with the numbers of layers(2) Estimating proximity loss: high-frequency limitThe 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: Rac = (h/)RdcThis induc

27、es copper loss P1 in layer 1: P1 = I2RacPower loss P2 in layer 2 is: P2 = P1 + 4P1 = 5P1Power loss P3 in layer 3 is:P3=(22 + 32)P1 = 13P1)() 1(222dcmRhmmIPAdd up losses in each layer:) 12(3)() 1()(221222MMRhImmRhIPdcMmdcCompare with dc copper loss:If foil thickness were H=, then at dc each layer wou

28、ld produce copper loss P1. The copper loss of M-layer winding would be Pdc=I2MRdcSo the proximity effect increases the copper loss by a factor of: ) 12)(312MhPPFdcRThe solution to minimize proximity losses is: In inductors, windings can be with single-layer construction.In transforms, windings can b

29、e interleaved and avoided highs of layer.(3) Two-winding transformer MMF diagramWinding layoutMMF diagram(a) without proximity effect(b) with proximity effect(c) Interleaving the windings: MMF diagramGreatly reduces the peak MMF, leakage flux, and proximity losses2 Core loss = Eddy current loss + hy

30、steresis lossSkin effectdB/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! xdx-xLdwBsin(wt)xyzEddy current flow pathxdx-xLdwBsin(wt)xyzEddy current flow pathTime-varying magnetic fields B(t) Eddy currents Secondary magnetic fields that oppose the applied magnetic field.Eddy Currents effects(1) Cause eddy current losses!coreeddyeddyRifdtdBi2(2) Cause the flux to be rejected from the core! The t