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'Seminar 900 Topic 8 - Coupled Inductor Design'

May 93 Lloyd Dixonto minimize the number of winding layers andminimize the magnetic field strength between thewindings by stretching it out across a wide , in this application, there is little highfrequency current in the windings, so losses are notvery important, and there is no desire to minimizeleakage inductance but instead to utilize it for aspecific purpose. So the application is better satis-fied with a "low frequency" core with a moresquare window Parameters: Coupled Inductor windings L 1, (2:Uncoupled (leakage) inductance, LL:Total peak current, Ipk:Total full load current, In:Total ripple current, :Select the Proper Core Size:Referring to the design procedure in Ref. [3] ,core selection is facilitated by calculating the corearea product (AP) required by the application, andrelating this calculation to the APs of availablecores. This step is not necessary , it simple reducesthe number of trial solutions that would be requiredto find the optimum core.)

May 93 Lloyd Dixon to minimize the number of winding layers and minimize the magnetic field strength between the windings by stretching it out across a wide window.

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Transcription of 'Seminar 900 Topic 8 - Coupled Inductor Design'

1 May 93 Lloyd Dixonto minimize the number of winding layers andminimize the magnetic field strength between thewindings by stretching it out across a wide , in this application, there is little highfrequency current in the windings, so losses are notvery important, and there is no desire to minimizeleakage inductance but instead to utilize it for aspecific purpose. So the application is better satis-fied with a "low frequency" core with a moresquare window Parameters: Coupled Inductor windings L 1, (2:Uncoupled (leakage) inductance, LL:Total peak current, Ipk:Total full load current, In:Total ripple current, :Select the Proper Core Size:Referring to the design procedure in Ref. [3] ,core selection is facilitated by calculating the corearea product (AP) required by the application, andrelating this calculation to the APs of availablecores. This step is not necessary , it simple reducesthe number of trial solutions that would be requiredto find the optimum core.)

2 (The core area product isthe magnetic cross section area times the windowarea. Some manufacturers call this WaAc, othersAwAe.)At low frequencies, core size is dictated by F Rlosses in the windings and the saturation fluxdensity of the core material. At high frequencies,core losses dominate --the core cannot be operatedanywhere near saturation flux density .Different APcalculations are required for these two cases. Sincethe high frequency ripple current is small in thiscoupled Inductor application, the saturation limitedSummary: Coupled inductors have many applications inpower electronics. In a multiple-output buck derivedregulator. filter Inductor windings Coupled on acommon core provide vastly improved ac cross-regulation. and ripple current steeringfor improvedfiltering and reduced minimum loads!l] Couplingthe inductors in a SEPIC high power factor prereg-ulator can reduce noise by steering high frequencyripple away from the input!

3 2]This paper shows how to design a coupledinductor to achieve desired objectives. using tech-niques discussed in previous Unitrode the specific design example is the coupledinductor used in the SEPIC preregulator. thetechniques use are broadly Strategy:A Coupled Inductor version of the SEPIC con-verter used in a high power factor application isdescribed in a reference paper .12] In that circuit, aspecific uncoupled inductance is also required, inseries with input winding of the Coupled purpose is to steer the high frequency rippleCUlTent away from the input in order to minimizeinput noise filtering this paper, the uncoupled inductance will beobtained by integrating it into the same magneticstructure as the Coupled inductance, in the form ofleakage inductance between the Coupled structural design will (a) provide the desiredvalue of uncoupled inductance and (b) locate itproperly in the , in high frequency magnetics design ,considerable effort is expended to minimize leakageinductance and eddy CUlTent losses in the cores designed for switching power sup-plies have window areas that are long and narrow8-1 Coupled Inductor Acase applies.

4 The saturation limited fonnula (SIunits) K Bmaxcm4AP=felTite is insignificant. The gap alone detennines theenergy stored. and therefore the inductance penneability, pr, equals I in the gap:N2A~ = Po Pr e .10-2~gap L cm41t 010-2 = .415 cmfgap = .002 PQSO/SO CORE cm1 cm10 cm8 C/WMagnetic cross-section area, Ae:Winding window area, Aw:Window width, Ww:Winding width (bobbin), bw:Winding height (bobbin), hw:Mean length per turn, ML T:Free air thermal resistance, RJ:The gap must be placed entirely in the outer legs should be in intimate contact. Do notshim the core ha/ves apart. A/though the desiredinductance may be obtained this way, the /eakageinductance will not be in the desired circuit permissible power loss in the windings fora 32 C temperature rise is:Pw = L\TIRT = 32/8 = 4 WattsAt full power (2 OOW), the rms cun-ent in wind-ing 2 is 2 OOW /2 OOV = 1 A rms.

5 In winding 1,worst case rms current is at low line: 200W /l00V= 2 A rms. Since the turns are equal, we can thinkof this as 3 A rms through a single winding. Themaximum allowable resistance of this compositewinding is:Rwmax = Pw/IFL2 = 4/32 = .444 . resistance per centimeter wire length is:Rw/cm = Rw/(N. M T)= .444/(142 .10) = .313 simplicity, we will use the same wire sizefor both windings (most of the time the current in 1 is considerably less than 2 A). Thus each wirewill have half the copper area and twice the resis-tance: = .616 Looking in the wiretables, A WG22 (.64mm) has a resistance of . at 20 C, or. 708 at 100 to the winding structure in Figure 1,the two windings will be wound separately. ThefIrst winding, closest to the gapped center-leg, willbe winding 2. The leakage inductance energy isstored in the non-magnetic region within andbetween the two windings.

6 This leakage inductanceflux and its associated energy is linked to the outerThe next step is to calculate the minimumnumber of turns that will take the core to Bmax atthe peak current limit. (Fewer turns will require asmaller gap to achieve the required inductance andwill take the flux beyond Bmax.) .002-7 -lcfNMIN = = = 142 turnsBmaxAe the minimum number of turns, nextcalculate the center-pole gap length required toachieve the desired inductance Ll (same as L2).Compared to the gap, the energy stored in the8-2u NITRODE CORPORA TION~::~ 1. -Winding Structure41t-10-7-1422-{10-S) -10-2 = mHLL = , Ll, (assuming the outer legs are notgapped). The amount of leakage inductance isdetermined by the spacing between the the structure of the two windings is estab-lished. AWG22 insulated diameter is .71mm. Thebobbin width is 32mm, allowing 32 = 46 turnsper layer.}

7 142 turns will require layers. Why notgo to 4 full layers with larger wire to reducelosses? Working backwards, 4 full layers has 142/4or 36 turns per layer. 32mm/36t = .89mm wirediameter. According to the wire table, A WG20 hasan insulated diameter of .89mm and a resistance ofonly .445 m{}/cm at 100roC. The height of each 4-layer winding is = , or . total height available for both windings is 1cm., so there is plenty of the Leakage Inductance Value:Figure 1 shows that the flux representing theleakage inductance energy extends across the entirecore window. Even though these flux lines proceedthrough the outer core leg to form closed loops, theenergy stored within the core material is negligible.(Ferrite permeability is so high the field intensity isnegligible within the core.) So the length of theeffective leakage inductance field is the width of thecore window, Ww.

8 The cross-sectional area of theleakage inductance field is the cylindrical areabetween the windings, which equals the meanlength of a turn, ML T , multiplied by the separation,s, between the windings. The field actually extendsSince a leakage inductance of is desired:S = = = .286 cmTo obtain the actual spacing between the wind-ings, subtract 1/3 of the winding height (twice).Spacing = .286 -2(.284/3) = .097 a PQ core, the actual leakage inductancewill be perhaps 25% smaller than calculated can be corrected by a corresponding increasein the S value. The reason for the reduced induc-tance is that a considerable portion of the windingslie outside the core window, where the leakageinductance field is not bounded by the windowwidth Ww. These flux lines must bend around toreach the core, and the increased length of the fieldreduces the field strength and energy in this pot core will give a result much closer to thecalculated Modeling:A previous Seminar Topic [4] showed how to usereluctance modeling and duality to translate thephysical structure of a magnetic device into itsequivalent inductance values and their circuitlocations.

9 This technique is extremely valuable forunderstanding and optimizing the structure of anymagnetic 2 shows the structure of this coupledinductor with the various reluctances of the core legs is not shown-it is so8-3 Coupled Inductor Designinto each winding, tailing off from the center to theouter edges next to the core. As an approximation,the effective separation between the windingsincludes 1/3 of the height of each winding, asshown in The entire region where the leakageinductance energy is stored is non-magnetic, withJlr=l. The same inductance formula used before cannow be used to calculate the leakage inductancevalue. Only the terms representing the area andlength of the field have been changed:U)~Fig 2. -Modeling the Coupled InductorReferences:[1] L. H. Dixon, " Coupled Filter inductors inMultiple Output Buck Regulators ProvideDramatic Performance Improvement,"Unitrode Seminar Manual SEM500, 1986(Reprinted in SEM600, SEM7OO, SEM800 andSEM900.

10 [2] L. H. Dixon, "High Power Factor SEPICP reregulator," Unitrode Seminar ManualSEM-900, 1993[3] Dixon, "Filter Inductor and FlybackTransformer design for Switching PowerSupplies," Unitrode Seminar Manual SEM400,1985 (Reprinted in SEM600, SEM700,SEM800, and SEM900)[4] L. H. Dixon, "How to Place Leakage andWiring Inductances in the High FrequencyModel," Unitrode Seminar Manual SEM600,1988 (Reprinted in SEM700, SEM800, andSEM900.)small it is negligible. Duality converts the reluc-tances to permeances, with parallel reluctancesbecoming series permeances, etc. Permeance multi-plied by N2 becomes on the left that the reluctance of the strayfield is in parallel with the reluctance of the outerleg. The stray field reluctance is not negligible. It isin fact comparable to the reluctance of the center-leg gap which is the determinant of the coupledinductance value. However, with the outer legstightly mated to minimize the outer-leg gap, thereluctance of the outer leg is extremely low.


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