2n~63~8 , PARTI~L GAP MAGNETIC CORE APPARATUS
Technical Field The invention is concerned with apparatus dependent upon wire-wound core structures. Concerned cores, generally of ferrite or other soft magne~ic material, S are constituted of segments which, together, form a closed nnagnetic loop with at least one partially gapped joint thereby resulting in a structure known as a "partial gap" or "variable gap" core.
Descripffoll oî the Prior Al t Wire-wound core devices serve a variety of fu;nctions. An ~mportant use 10 is in power supplies in which they may serve as transformers to change voltage level as well as to isolate output f~m input circuitly. As inductors, they may take ~eform of choke coils for minimizing a.c. ripple and other forrns of noise. They may serve, as well, for magnetic energy storage, e.g., in power supplies using ftyback converter circuits.
A design limitation for such apparatus is the consequence of non-linear effects - ultimately of magnetic saturation - which results in pronounced dependence of inductance on current. Fall-off in inductance in the presence of currents with large d.c. components is a ma30r consideration in ~e design of such apparatus.
Relevant p~ior art is discussed in conjunction with FIG. 1. This figure, 20 on coordinates of inductance and direct cu~ent, each on a logarlthmic scale, exhibits the general form of relationship of Ihose two parameters for three types of structures.
Curve 10, is descriptive of an ungapped loop core. Curve 11 shows the form of the relationship for a gapped structure - for a loop core having at least one gap extending across the entire core CTOSS section. C~rve 12 traces the general relationship for such 2S a loop core which is "partially gapped" - for usual fabrication, in which concerned regions are the conse~uence of ma~ing surfaces and in which the topography of one or both of such surfaces is such as to produce a mated joint which is partially gapped and par~ally continuous.
Curve 10, wi~h its high initial inductance value plotted as peaking at 30 near-zero current point 13, drops off rapidly to reach a low value at 14. The actual inductance value at 14, while ~o low to be of consequence for contemplated apparatus, is actually non-æro - is of a value approaching that of an air core structure. This steep drop-off in inductance is a~ too low a current to meet many apparatus requiremcnts. For example, operating as a choke, it may fail to provide 35 adequate smoothing at full contemplated output.
Curve 11 is based on a full gap structure otherwise structurally similar to that of curve 10. Presence Or such a non-ma~netic gap - e.g., of an "air" gap -since not magnetically sa~urable, results in near independence of inductance - in a constant or near-constant inductance plateau at 15. The full gap structure is S characterized by perseverance of significant inductance at hi~gher cu~rents, reaching a near-zero inductance value only at 16. However, lhe full gap stn~cture is characterized, as well, by a reduced initial, inductance value 17. For rnany purposes, this initial low value of inductance is inadequate for intended use.
It is kllOWn thaL desired characteristics of gapped and ungapped core 10 structures may, to some extent, be combined in a third type of structure. This latter sometimes referred to as "partial gap", "stepped gap" or "non-linear" core, takes the form of a core of reduced cross-section at some position. Ihis is often realizecl by joinder of core segments of recluced cross-section to, together, result in core joint having a central contacting region surrounded by a peripheral gap.
Curve 12 traces inductance-curfent characte~istics for a p~rtial gap core with a gap depth approximating that of the structure of curve 11. Its initial or "near-zero current" inductance of value 18 approaches that of the ungapped core of curve 10. With increasing current, inductance drops to a plateau value of 19, toultimately drop-of~ to a low, near-zero value 20, at a current level approaching that 20 of drop-off for ~he gapped structure of curve 11.
Such partial gap "non-linear" structures haYe satisfied some perfonnance requirements. Their use has resulted in initial inductance values approaching those of ungapped structures as well as retention of high-current induc~ance values characterls~ic of gapped struc~ures. However, they retain certain characteristics of 25 full gap structures which may be disadvantageous. From the performance standpoint, such stepped gap structures, like their full gap coun~erparts, also develop fringing magnetic fields at the gap. Coupling of such fringing fields with encircling windings result in decreased inductance per unit volume, in heating and, generally, in overall per~ormance loss. The disadvantage is aggravated for planar devices and 30 with increasing miniaturization. ~tructural variations may cause further problems.
As an example, use of windlngs, e.g. helical windings, made of rectangular or oval cross-section conductors (with ~he large dimension in the radial direction), while useful in reducing d.c. electrical resistance, is effectively precluded due to larger field coupling and resulting increased heating and power loss.
6 3 5 ~
A furlher disadvanlage of the prior art non-linear structure, in manner simiklr lO Ihe full gap struc~ure, lakes itS toll during fab~ication as well as in use.
Entry of potting compound into the exposed peripheral gap may cause physical failure. Curing or crystallization of the potting material may be attended by volume S change to disrupt the joint. In use, joint failure may be cau~sed by localized heating due to resistive losses in the windings and to electromagnetic losses in the core.
Failure may be caused by differential thermal expansion within different regions of the invading potting material, or even by uniform expansion of potting material differing from that of contacting regions of the core. Even if physical joint failure 10 does not occurt the differential thermal expansion of pOttillg material in the gap may lead to ~ unpredictable or unwanted effec.~ive temperature coefficietlt of inductance for the device.
The foregoing is treated in a number of articles and texts. See, for example, Soft Ferrites Prope ties and A~plications, Ei. C. Snelling, sec. ed~, at pp.
15 20-21, 139-143 and 274-283.
Summ~_f the In7~nt~;0n Xn general terms, the invention overcomes disadvantages of prior art structures by use of a core provided with an air gap which is both magnetically and physica11y shielded. Advantageous consequences of resulting partial gap devices 20 include both reasonable fabrication cost and irnproved performance characteristics.
Structures of the invention may profitably displace conventional full gap devices. As discussed under "Design Conside~ations", dimensions and other parame~ers may 'oeoptimized to retain inductance at high current and ~hereby to approach operatingc'naracteris~cs associated with ~ull gap cores. Permitted uninterrupted sur~ace 25 contour at the joint avoids practical problems associated with the reduced cross-scction of prior art partial gap joints.
Ihe variable gap core which characterizes all structures of the invention, in fact, retains the performance advantages of earlier variable gap core structures as well. Accordingly, use may be made both of the high initial (æro current) 30 inductance, charac.eristic o~ ungapped structures, and of the retained levels of inductance at high current, characteristic of gapped ssructures.
Joinder of core segments through surfaces together defining a region of peripheral contact to, in turn, enclose gapped region/s, overcomes art-recognized disadvantages vf previously descAbed non-linear core devices. Discussion is 35 conveniently in terms of a single centrally located depression totally enclosed within a peripheral contacting region, ~ereby defining a centrosymmetric joint of the same 4 ~ 3 ~ ~
exlernal shape and dimensions as those of the core portions which are joined. A
variety of considerations rnay dictate variations in location and shape of the resulting gap as well as use of multiple gaps.
I he approach lessens - may totally avoid - fringing fields to, both, S minimize heating through coupling with encircling windings and to improve performance efficiency via lessened eddy current loss and increased iilductance.Alternatively, increased inductance-to-volume ratio may permit further miniaturization. Ordinarily attained viscosity values for, e.g., uncured crosslinking polymeric potting material, as dependent upon intimacy of peripheral contact, are 10 sufficient to avoid entry into the gap, thereby preventing joint failure both in construction and during use. E~cclusion may be ~urther assured by bonding of contactin~g joint regions prior to potting.
Outlincd characteristics are generally advantageous in a large family of conductively wound core devices. Inductanc~/current characteristics a~ well as joint 15 stability are advantageous in a.c. apparatus - transformers and inductors. AS with prior art non-linear core devices, a particular interest concerns energy storageinductors as well as chokes for d.c. apparatus such as power supplies. Implications include tolerance for apparatus design con~sidered disadvantageous in the past. As an example, essential decoupling of closely spaced devices and leads, due to avoidance 20 of fringing fields, perrnits free use of pancake windings of rectangular or oval ~ross-section7 with implications including reduced volume and decrease in cos~
For expediency, discussion is in terms indicated - generally in t~rms of specific apparatus, e.g. inductors as used for choke coils - coils generally based on cores of a par~icular configuration, e.g. largely of circular cross-section, etc. The 25 inventive advance is of broader value generally in the whole spectrum of "wire-wound" core devices. In all such instances, the inventive advances, in terms of magnetic and physical shielding, are valuable. By the same token, windings may be of any desired cross-section - constant or varying in si~e and/or shape.
Brie~ Descrip~don of ~e Drawin~
FIG. l, on logarithm coordinates of inductance and direct current, is a plot relating these properties for prior art (as well as for inventive) partial gap stroctures as compared with prototypical full gap and ungapped structures.
FI(3. 2 is a cross-sectional view depicting an illustrative core structure designed in accordance with the inventive teachings.
FIG. 3, on coordinates of inductance index and ampere turns, is a plot relating those parameters for two similar structures - the first, that of curve 30, based on windings of round cross-section, the other, ehat of curve 31, based on windings of rectangular cross-section, both using ~he same core. Near coincidence of the twoS curves constitutes experimental evidence supporting suhstantial elimination of fringing fields.
FIG. 4, on coordinates of inductance and ampe,re-turns, is of clesign significance in showing performance characteristics of illustrative gapped, llngapped, and two partial gapped structures.
FIGS. SA through SF are perspective views of core segments o illustrative designs appropriate for use with the inventive teaching as mated with, e.g., planar mating surfaces not shown.
FIGS. 6A through 6D are cross-sectional views of unmated core surfaces to be joined with mating surfaces - e.g., with planar mating surfaces - and 15 are representative of suitable configurations alternative to those of E~lGS. SA through SF.
Detailed D~crip~on Terminology Description is for the most part in telms of included devices of ~0 p~icular interest at this time and using terminology familiar to present-day workers.
The general thrust has been described: devices of the învention depend upon inductive coupling for current flQw following a spiral conductor path encircli-ng releYant region/s of a magnetic core. Devices of the invention have a feature incommon - all entail a magnetic core which is continuous but for one or more 25 partially gapped - partially contacting core joints. Consistent with general usage "continuous" may refer to: (1) physically continuous as, e.g. a toroidal core; (2) or mated core segments, often described as "ungapped", but in reality only approaching a toroid to the extent the mating surfaces are absolutely smooth. (For many purposes, "ungapped" refers to an effective gap of less than 0.5x10-3 i~.) Such 30 joints are variously described as "partial gap", "stepped gap" and "variable gap", and are responsible for "non-linear" structure (refe~ing to a structure in which inductance manifests the forrn of dependence on current as that of curve 12 of FIG
By ~he same token, description, in familiar fashion, refers to "wire-35 wound". In common with general usage, use of this terminology contemplatesdevices, however made, which function in the manner of the prototypical core as .
-6- 2~358 literally encompassed by helical turns of wire. In fact, many "wire-wound" structures as presently manufaclured, depelld upon deposited or printed conductor segments,and not on literal "windings~'. It is likely that prevalent use of the invention will take the forrn of structures of this type. Terms such as "winding/s" and "coills" are to be 5 so construed~
, ~; , .
Desi~n Considerations To a significanl exlen~, design considerations are well-known.
Parameters of consequence - dimensions, compositions, etc. - at least in fundamental terms, are of the same impact as for earlier partial gap devices. An excellent 5 reference, Soft Ferrites Properties and Applications, cited above at pp. 274-283, considers such designs for one category of devices - for choke coils and storageinductors. Similar considerations for othcr categories of devices are treated elsewhere in the same text. For this reason, detailed deslgn is not considered anecessary part of this disclosure. Instead, discussion is in rnore general terms.
All structures of the invention have a feature in common - a core with a shielded gap. For this purpose, a sbielded "gap" is defined as a core-enclosed three-dimensional discontinuity as produced by joinder of core surfaces, one or bot'n of which are of topology to result in at least one such gap. To qualify as a "gap", it is required that retained inductance be at a function-conse~uential level for values of lS winding current beyond that characteristic of an ungapped stmcture otherwise of the same design parameters. For many purposes, this translates into a cross-sectional surface/surfaces defining a minimal gap of operational significance. Experimental work based on gap depth of a minimum of 0.5 x 10-3 in. assigns operational significance to a centrally located gap of area as small as 10% of that of the joint, 20 and to a non-centrally loca~ed gap of lesser area - as small as 5% of ~hat of the joint.
Ihis work was verified with mated RM10 cores with low profile. ~e RM 10 core structure is defined by EC Publication 431- 1983 (Geneva, Swit~erlalld) and JIS C
2516 - 1990 ~Tokyo, Japan). The cores in this work were modified to have a height of 50% of standard, i.e. 0.183 in. per core half, as compared with 0.365 in. standard.
Gap depth can be related to incremental inductance and other parame~ers irl accordance with the following equation:
llo N2 A
L = Inductance 30 N = Number of turns in the winding A = Cross-sectional area of the magnetic circuit e = Magnetic path length of the body of the circuit excluding the gap region ,B = Ratio of contact area at the gap region to the total Area A
,uO = I'enneabili~ of air ~ 2~963~ ~
,u e = Rela~ive incremen~l permeability of the magnetic malerial in the body of the circuit ~lm = Relalive incremen~l permeability of thc rnagsletic material in ~e region peripheral to the gap 5 ~ - Gap depth - The relative permeabilities ~ and ~Im are non-linear functions of field strength - of the H fields, He and Hm (relating to the fields in the body of the CiICUit, and in tbe region of the gap, respectively). l`he fields He and Hm are, in l;urn, related to NI, the dc ampere turns, via the permeability dependent flux distribution 10 between the gap and the con~acting wall.
Accordingly, the equation cannot be solved analytically. Num~ical methods such as finite element analysis, may be used to nbtain solutions with reasonable accuracy. Nevertheless, this equation, in conjunction with approximations for values of ,u~ and llm. may serve as a useful starting point for 15 emphic~l investigation of the valiation in, L, as dependent on values of ~"B, and IdC-Chosen dimensions are with a view to device function. Where thedesire is operation approaching that of a full gap structure. peripheral waU thickness is minimi~ed. In such instance, ~he primary purpose of the retained contacting regions of ~he final core joint is avoidance of fringirlg fields and physical joint 20 integrity. A wall thickness of 10-2 in. is functionally sufficient for field shielding.
Minimum wall thickness to avoid mechanical fallure is largely a matter of physical stability and fabrication expedience. Experimentally, fe~te of 10-2 in. wall thickness has been found adequate for structures studied.
In instances in which the device is to function in the manner of some 25 earlier partial gap devices, e.g., in instances in which high values of inductance at low current operation are of particular consequence, peripheral wall thickness is likely greater than the minimum values cs)nsidered in the previous paragraph.
Retained inductance a~ high current is, in such instances, as shown in FIG. 1, is somewhat reduced. However, a centrally loca~d gap of area as small as 38% of the30 total c~oss-sectional area of joinder results in a functionally significant increase in retained inductance at increased current for structures studied and, accordingly, qualifies for use in contemplated devices. For s~udied low profile core devices, e.g.
~or RM10 design as referenced above, such a minimal gap area, with gap depth of l9x10-3 in. results in device-significant inductance at currents approximately four 35 times greater than for the corresponding ungapped structure (plateau values corxesponding with region 19 of FIG. 1).
While starting design parameters are generally calculable, realistic considerations require some ~ial and error. For example, deviation from per~ect surface smoothness may require some empiricism (e.g., compare curve 10 of FIG. 1with curve 40 of FIG. 4, ~he first relating inductance to cu~rent for a true ungapped S core and the second based on related properties for a real structure inclucling joinder of two "smooth" surfaces). It may even be ~at with expelience gained, design of new skuctures may dispense wilh theoretical considerations altogether.
Included structures are of greatest advantage for closely spaced, low profile, small-dimensioned devices where temperature rise is of particular 10 consequence~ F;rom this standpoint, device dimensions of a fraction of an inch and as similarly spaced, in particular, gain from avoidance of heating due to fringing field coupling.
Fabrication Considerations under this heading are again well-understood for devices 15 meeting present requirements. Core composition requirements are somewhat eased in view of the inventive attribote of increased inductance per unit volume, palticularly with rectangular or oval cross-section windings. Structures for inclusion in usual wiring boa~d circuitry may make use of familiar ferrite compositions, e.g. of manganese-~inc or nickel-zinc based ferrites. Required magnetic characteristics and 20 fabrication requirements may resul~ in any of a variety of alternatives - e.g., elemental metals and alloys, as well as other ferrites. Recent advances in the construction of a major category of such structures may be of benefit. U.S.
applica~ion, serial no. 07/710,736, filed May 31, 1991, describes a relevant core structure fabricated from core segments through adhesive joinder. It has been noted 25 that coil windings are likely to take form other than that of literal wire-wourldings.
U.S. application, senal no. 07/835,793, filed February 14, 1992, describes joinder of partial tums to result in functioning windings. Other fabrica~ion approaches, some in commercial use, others described in the literature, may serve.
The Fi~ures FIG. 1 has been considered in earlier discussion. The ~ree curve forms presented, ~hose of curves 10, 11 and 12, are representative of the general fonn of inductance v. d.c. current, L; v. Id c, as plotted on log-log coordinates. These curves correspond with ungapped and partial gap core structures, respectively. For discussion purposes, axis-intercept values are ~reated as zero values of the other 35 coordhlate axis even though only approaching such values since on logarithmiccoordinates. The ultimate values of induc~ance at 14, 16 and 20, however approach, - lo- 2~963~
the non-zero values as obtainable from ~he air core device to which the stmctureunder s~u(ly is effective}y convel ted upon magnclic saturation of the core. The value of Id c, at which value 14 is attained varies - i.e. the severity of the fall-off of curve 10, for an otherwise similar structure including joinder of less-than-perf~t S "smooth" mating surfaces decçeases as surface irnperfections increase.
Curve 11, depicting the relationship of inductance and current for a full-gap structure, commences at initial inductance 17 for zero current, maintains constant or plateau value for the major part of the curve for region 15, and finally drops off to attain m~imal inductance value 16. The plateau value as well as the10 fall-off position varies with chan~ging gap. Increasing ~he size of the gap results in a decrease in induc~ce together with an increase in the value of current at fall-off.
Again, the relationship is known - a useful reference is the tex Soft Ferrites cited above (see, Figure 9.13, p. 277 and related text).
Curve 12, representative of par~ial gapped structures, commences at ~ero 15 current value of inductance at 18, thereafter ~alling off to plateau value 19, and ultima~ely to small inductance (air core value) at 20. As discussed, the form of the relationship as reptesented by curve 12 may be made to more closely approach curve 10 or 11. Briefiy, relative increase of contacting surface at joinder (of ratio, ~13 =
contact area/total area) as well as decrease of gap depth produces a characteristic 20 relationship more closely approaching of the ungapped structure of curve 10. I~e ac~ual zero cur~ent inductance value is mainly dependent on ~ei. The inverse, e.g~
reduction in ,B9 results in characteristics approaching the forrn of curre 11, e.g., in that region before its intercept with curve 10. The magnitude of inductance at plateau value, 19, decreases, and the current value at fall-off, 20 increases with gap depth, ~.
FIG. 2 is a perspective view in cross-æction of a mated E core structure 21 similar in cross section to that used in experiments upon which much of the reported data was measured. It, in turn, consists of mating segments 22 and 23, together defining gap 24, in this instance, the consequencc of joinder of recessed surface 26 and planar surface 27. In common with other contemplated structures, gap 30 24 is enclosed within core material, thereby forming wall 25 about its entireperiphery, including the ~ace portion of structure 21 removed in draft-sectioning.
FIG. 3 contains plotted inforrnation for two partial gapped structures providing for substantial elimination of fringing fields. Coordinates are inductance index, AL = L/N2 on the ordinate, (in which L is inductance in nanohenrys and N is 35 number of turns) and ampere-turns, NI on the abscissa. The two experimental struc~ures used the same cores, ~hé firs~, that of curve 30, having a 26-turn spiral 1, ~n~ ~3~
winding of round cross-section conductor, the second having a 3-turn helical ~pancake) winding of rectangular cross-section conductor. Substantial coincidence oE curves 30 and 31 is clear evidence of ab~sence of fringing fields since such fields would couple more strongly with pancake windings (as carrying current to result in 5 the same number of ampere turns), thereby resulting in a lowered plateau value for that structure - for the struc~ure of curve 31.
FIG. 4 is a log-log plot of inductance, L in microhenrys, on the ordinate, and of ampere-turns, NI, on the abscissa, for four low profile RM 10 (FIG. 5C) core stmctures, all of similar design but ~Eor gap presence and dimensions. Cur~e 40 10 relates these quantities for an ungapped structure, curve 41 is for a full gap of 2Q x lo-3 in. depth, curve 42 repor~s measurements for a 20 x 10-3 in. depth cylindrical gap encompassed by a 40 x 10-3 in. wall, curve 43 is for a structure similar to that of curve 42 but of 31 x 10-3 in. wall thickness. As discussed, characteristics oE the ungapped structure of curve 40 are more closely approached as relative contact area 15 increases, while full gap is more closely approached with decreasing area.
FIGS. SA through SF are perspective views of core loop segments presently in use. As before, shown segment surfaces may be mated with contoured surfaced segments, e.g. with mirror image segments, or alternatively, with planar (or ungapped) surface segments. l:)epicted structures, as well as a large number of 20 alternatives, are described in detail in Soft Ferrites, cited above. Views colTespond with s~Lructures as follows: 5A - U core~ 5B - F core, 5C - RM core, SD - low profile core, SE - EP core, and SF - pot core. As depicted, all structures shown are provided with a depression illustratively centrally located and of the cross-sectional shape of the containing core leg.
FIGS. 6A through 6D are perspective views in section of core segments representative of a much larger number of gap configurations, any of which may be joined with segments having contoured or with planar mating surfaces.
F~G. 6A depicts a multiple cavity gap - in this instance containing cavities 60 and 61 within unrecessed portion, or wall, 62.
FIG. 6B depends upon a stepped gap 63 consisting of gap regions 6 and 65, defined by wall 66.
FIG. 6C illustrates a structure providing for a gap 67 of varying depth as enclosed within wall 68. FIG. 6D depicts a structure dependent on an annular gap 67 enclosed within wall 68 and, in turn, enclosing unrecessed region 69.
35 Examples Example 1 -1~- 21~ 58 ï hree chnke coils of Ihe same shape, Si~R, composition and number of winding lurns were cnergized ~o result in data of lhe form depicted in FIG. 1. The cores used in all three, were low profile RM10 cores - as depicted in FIG. SC. mated with an ungapped core-half, and were provided with a 26 turn winding encircling the 5 center leg. The size of each mated core pair was approximately 1.09 in. x 0.52 in. x 0.37 in. with a round center leg of diameter 0.42 in. The first structure was Imgapped, ~e second was gapped with constant depth of 20 x 1o-3 ill. in tlle center leg and the third was provided with a shielded cylindrical gap of l9 x 10-3 in. depth encircled ~y a peripheral wall of 34x 10-3 in. thickness as depicted. As energized, 10 measured inductance value was as plotted on FIG. 1 with ;zero current inductance of 4470, 174 and 2360 microhenrys and with low induetance (70 IlH corresponding with points 14, 16 and 20) at Id c. = 0.9 amp.,7.0 amp. and 5.5 ~np., respectively. A
note in passing - both the curve ~orm and values repor~ed were approximately thesame for a prior art partial gap strocture (of peripheral rather than enclosed gap).
15 Exarnple 2 Two ayback transformers, the first fully gapped, the second of enclosed partial gap (wound coxe of round 0.416 in. diameter cross-section, of gap depth =
20x 10-3 in. and ,B - 0.27) otherwise of the same size ~low profile RM 10), corecomposition, primary and secondary coil structure, were activated in a flyback 20 converter circuit to determine perforrnance differences. Bo~h were operated at average input current of approximately 2 amperes as resulting frorn input at 500kHz, 40 volt. The transforrner with the enclosed partial gap showed a transformer loss of 3 watt, about 20% lower than tllat with the full gap, while maintaining converter performance in all other respects.
25 Example 3 Measured data curves as shown on FIG. 3 were based on two structures of the same shape, size and composition as that of the partial gap structure of Exarnple 1. The core used was gapped to a depth of 20x 10-3 in. The gap diameterwas 0.354 in. and was enclosed by a 31 x 1o-3 in. wall (to result in ~ = 0.28). The 30 coil in the first structure consisted of 26 turns of 17.9 x 10-3 in. diameter, round cross-section copper wire. The second was provided with three turns of 0.150 in. x 20 x 10-3 in. rectangular cross-section ("pancake") conductors with the long dimension radially disposed relative to the core. As recorded on FIG. 3, both curves plateaued at a value of inductance index, AL, of 200-300 nanohenrys per turn-35 squared over the range of from 6-100+ ampere-turns. As shown in that figure, inductance index was near-iden~ical so supporting assumed avoidance of fringing - 13 - ~ 0 ~ 8 field. (More intimate coupling of fringing field with the pancake windings wouldhave resul~cd in less ef~ctive opera~ion ~o lessen inductance.) Example 4 Four cores of the same shape, composition and dimensions, all provided S with a twenty-six turn winding were operated at 500 millivolt and at a frequency of 100 kilohert~ to result in the inductance characteristics repor~ed on FIG. 4. The first, ungapped, resulted in the measured values of culve 40. A fully gapped structure - of 20 X 10-3 in. const~nt gap depth - produced the characteristics plotted as curve 41.
Two partial gapped structures resulted in the performance of curves 42 and 43. The 10 putpose of the experiment was to verify the e~fect of varying ~ (the ratio ofcontacting to total surface at the joint, and, accordingly, only the diarneter of the gap varied as between the two3. The structure corresponding with curve 42 was provided with a cylindrical gap of 20x 10-3 in. depth as enclosed within a 40 x 10-3 in. wall for a value of ~ = 0.35. The second partial gap structure, on which data points for 15 curve 43 was measured, differed only in increased gap diarneter to leave a wall thickness of 31 x 10-3 in. (,B = 0.28). It is seen that increased ,B resulted in a partial gap structure more nearly approaching that of the ungapped structure with regard to inductance a~ lower current values. Decreased ~B resulted in inductance/arnpere-blrn ratio more closely approaching that of the full gap structure.