Abstract: A reactor includes a toroidal coil including a winding wound to have an annular outer shape, a bus bar electrically connected to one end of the winding, and a current sensor that measures electric current flowing through the bus bar. The bus bar includes a crossing passing through a central area including an area inside an internal surface of the annular outer shape and an area in which the area extends along a central axis of the annular outer shape, and the current sensor measures electric current flowing through the crossing.

Abstract: The wound core of the present invention has at least one arbitrary bent region 5A, in a plurality of corner portions (3), in which the corner portion (3) bulges outward to confine the magnetic flux flowing in the wound core so that the angle ? formed by the straight line PQ and the straight line PR satisfies 23°???50°.

Abstract: One aspect of the invention provides an Fe-based amorphous alloy ribbon having a free solidified surface and a roll contact surface, in which the Fe-based amorphous alloy ribbon has plural laser irradiation mark rows each formed from plural laser irradiation marks on at least one surface of the free solidified surface or the roll contact surface, a line interval is from 10 mm to 60 mm, which is a centerline interval in a middle section in a width direction, between mutually adjacent laser irradiation mark rows, a spot interval is from 0.10 mm to 0.50 mm, which is an interval between center points of the plural laser irradiation marks in each of the plural laser irradiation mark rows, and the number density D (=(1/d1)×(1/d2), d1: line interval, d2: spot interval) of the laser irradiation marks is from 0.05 marks/mm2 to 0.50 marks/mm2.

Abstract: A transformer for use in a rail vehicle and/or for rail applications, including a core which is at least partially surrounded by at least one coil is, with regard to the objective of providing a transformer in which the geometry of a coil can be selected to be as variable as possible, characterized in that the core is produced from individual segments, wherein the total cross-sectional surface-area of the core is greater than or equal to the sum of the individual cross-sectional surface-areas of the segments and wherein at least two individual cross-sectional surface-areas differ from each other and/or from the total cross-sectional surface-area in terms of their size and/or geometric shape.

Abstract: A coil component is capable of suppressing permeation of liquid or gas into a magnetic portion and increasing mechanical strength of the magnetic portion. A coil component includes a magnetic portion including soft magnetic metal particles having an insulating oxide layer on a surface thereof, with the soft magnetic metal particles being bonded to each other with the insulating oxide layer interposed therebetween; and a coil portion provided inside or on the surface of the magnetic portion. A mixture containing a resin and inorganic particles is disposed between the soft magnetic metal particles.

Abstract: A resolver for detecting the displacement amount of a passive body is provided with an excitation winding or a detection winding. The detection is based on a detection signal outputted from the detection winding as a result of an excitation signal inputted to the excitation winding. The excitation winding and/or the detection winding are composed of a combination of one or more sheet coils having one or more bore portions. The sheet coils are arranged at prescribed intervals in the lengthwise direction of a magnetic core to which the sheet coils are attached. A plurality of coil-storing grooves formed in a direction perpendicular to the lengthwise direction are provided in the core surface of the magnetic core. The coil portions of at least two portions of the respective sheet coils are accommodated in the coil-storing grooves.

Abstract: An inductive filtering device includes a first toric magnetic core without an air gap formed around a central void; a first electrical conductor formed of turns that are wound around the first magnetic core without passing through the central void, wherein no electrical conductor passes through the central void.

Abstract: A magnetic core includes a nanocrystalline alloy ribbon having a composition represented by FeCuxBySizAaXb, where 0.6?x<1.2, 10?y?20, 0?(y+z)?24, and 0?a?10, 0?b?5, all numbers being in atomic percent, with the balance being Fe and incidental impurities, and where A is an optional inclusion of at least one element selected from Ni, Mn, Co, V, Cr, Ti, Zr, Nb, Mo, Hf, Ta and W, and X is an optional inclusion of at least one element selected from Re, Y, Zn, As, In, Sn, and rare earth elements. The nanocrylstalline alloy ribbon has a local structure such that nanocrystals with average particle sizes of less than 40 nm are dispersed in an amorphous matrix and are occupying more than 30 volume percent of the ribbon.

Abstract: Embodiments of the disclosure provide a current protection device with a mutual reactor including a first winding and a second winding. The current protection device is a subcomponent of a previously developed fault current limiter. The current protection device protects the superconductor from potential damage. The current protection device may include a coil electrically connected in series with the first winding or the second winding, an actuator mechanically coupled at an output of the coil, and an electrical interrupter electrically connected to the first and second windings, wherein the actuator is communicatively coupled with the electrical interrupter to actuate a moveable contact of a set of breaker contacts of the electrical interrupter. In some embodiments, the first and second windings are arranged in parallel to one another. In some embodiments, the coil is electrically coupled to an output of the first winding or the second winding.

Abstract: A magnetic core flux sensor assembly may include a flux sensor core portion and an elongated opening for receiving a conductor winding through the flux sensor core portion. The flux sensor core portion may include a width from a perimeter edge of the flux sensor core portion to the elongated opening that is constant. An electrical current flowing through the conductor winding generates a magnetic field about the conductor winding and a magnetic flux flow in the flux sensor core portion. One or more sensor holes may be positioned relative to the elongated opening for sensing the magnetic flux flow at different distances from the elongated opening. A sensor conductor winding may extend through each pair of sensor holes. The magnetic flux flow generates an electrical signal in each sensor conductor winding. The electrical signal corresponds to the magnetic flux flow at a location of the particular sensor conductor winding.

Abstract: An antenna magnetic core of an embodiment has a laminate of a Co-based amorphous magnetic alloy thin strip and a resin layer part having an average thickness in a range of from 1 to 10 ?m. Dispersion of thicknesses of the resin layer part is within ±40% in relation to the average thickness.

Abstract: Three-phase magnetic cores for magnetic induction devices (e.g., transformers, coils, chokes), and methods for manufacturing them, are disclosed. The magnetic cores are generally constructed from three generally rectangular magnetic core frames having a stair-stepped configuration extending along side portions of the frames. The frames are arranged to form a triangular prism structure such that side portions of locally adjacent frames are uniformly engaged to form three core legs over which coils of a three-phase magnetic induction device may be placed.

Abstract: An amorphous transformer which includes an amorphous core formed of an amorphous material with a lap provided at an upper portion and allowed to stand in substantially a vertical direction while being supported at a core support member, and a coil which is fitted with the amorphous core. The core support member is formed by integrating a core support member for supporting a side surface of the amorphous core and a corner support member for supporting a corner portion of the core. The core support member is provided in substantially a vertical direction along at least one of the side surfaces of the core.

Abstract: The disclosure relates to an amorphous transformer core including at least one transformer core disc with a plurality of layers of strip-like amorphous core material arranged concentrically around at least one winding window. At least one heat dissipating plate extends into an interior of the amorphous transformer core and is fed from there into at least one heat exchange region outside the amorphous transformer core. This can enhance dissipation of heat energy which is produced inside the amorphous transformer core.

Abstract: There is disclosed a transformer, comprising a triangular wound core; a low voltage LV winding; and at least one high voltage HV foil disc winding and a method for manufacturing a transformer coil, comprising providing a high voltage HV inner mold assembly; and winding at least one HV foil disc winding on the HV inner mold assembly. There is also disclosed a mold for manufacturing a transformer coil, comprising side gears respectively arranged at top and bottom positions of a triangular wound core; a high voltage HV inner mold assembly connected to the side gears; and a HV outer mold assembly connected to the side gears, wherein the HV outer mold assembly has a top opening across a length thereof.

Abstract: A ferromagnetic amorphous alloy ribbon includes an alloy having a composition represented by FeaSibBcCd where 80.5?a?83 at. %, 0.5?b?6 at. %, 12?c?16.5 at. %, 0.01?d?1 at. % with a+b+c+d=100 and incidental impurities, the defect length along a direction of the ribbon's length being between 5 mm and 200 mm, the defect depth being less than 0.4×t ?m and the defect occurrence frequency being less than 0.05×w times within 1.5 m of ribbon length, where t and w are ribbon thickness and ribbon width, respectively, and the ribbon in its annealed state and straight strip form of the ribbon, has a saturation magnetic induction exceeding 1.60 T, and exhibits a magnetic core loss of less than 0.14 W/kg when measured at 60 Hz and at 1.3 T induction level. The ribbon is suitable for use in transformer cores, rotational machines, electrical chokes, magnetic sensors and pulse power devices.

Abstract: A ferromagnetic amorphous alloy ribbon, a method of fabricating a ribbon and a wound transformer core are provided. The ribbon includes an alloy of FeaSibBcCd where 80.5?a?83 at. %, 0.5?b?6 at. %, 12?c?16.5 at. %, 0.01?d?1 at. % with a+b+c+d=100, and is cast from a molten state of the alloy, having a-surface tension of greater than or equal to 1.1 N/mi,. A defect length along a direction of the ribbon's length is between 5 mm and 200 mm, a defect depth less than 0.4 ×t ?m and a defect occurrence frequency less than 0.05 ×w times within 1.5 m of ribbon length, where t is the ribbon thickness and w is the ribbon width in mm. The ribbon has a saturation magnetic induction exceeding 1.60 T and a magnetic core loss of less than 0.14 W/kg when measured at 60 Hz and at 1.3 T induction level in an annealed straight strip form, and a core magnetic loss of less than 0.3 W/kg and an exciting power of less than 0.

Abstract: A ferromagnetic amorphous alloy ribbon includes an alloy having a composition represented by FeaSibBcCd where 80.5?a?83 at. %, 0.5?b?6 at. %, 12?c?16.5 at. %, 0.01?d?1 at. % with a+b+c+d=100 and incidental impurities, the ribbon being cast from a molten state of the alloy with a molten alloy surface tension of greater than or equal to 1.1 N/m on a chill body surface; the ribbon having a ribbon length, a ribbon thickness, and a ribbon surface facing the chill body surface; the ribbon having ribbon surface protrusions being formed on the ribbon surface facing the chill body surface; the ribbon surface protrusions being measured in terms of a protrusion height and a number of protrusions; the protrusion height exceeding 3 ?m and less than four times the ribbon thickness, and the number of protrusions being less than 10 within 1.5 m of the cast ribbon length; and the alloy ribbon in its annealed straight strip form having a saturation magnetic induction exceeding 1.

Abstract: An oil immersed stereo wound-core amorphous alloy transformer, comprising an iron core, a high-low voltage winding, leads and a tank. The core comprises three single frames made of amorphous alloy strips by winding and are identical in structure, and the single frames have a rectangular shape; the vertical sides of every two adjacent frames fit together fixedly to form a core pillar, and the horizontal sides of the single frame form iron yokes; the cross sections of the core pillars have an approximately circular or polygonal shape; the transformer further comprises a clamp, comprising a quasi-triangular upper and lower clamp, and posts, the lower clamp is provide with three food pads; the iron yokes in the lower portion of the iron core are located on the foot pads, and the high-low voltage winding is wound on the core pillars.

Abstract: A wound transformer core is provided with at least one core loop made of a magnetic material. The transformer core includes multiple thin amorphous band-like iron sheets which are concentrically stacked around at least one center axis. A lower yoke section, an upper yoke section, and at least two limb sections are formed. The transformer core includes a modular plate-like support structure which is affixed upright to the center axis on both face sides of the lower yoke section and on both face sides of each limb section such that neighbored iron sheets are affixed together at their outer edge. The modular plate-like support structure includes, for each face side of the corresponding core sections, at least two plate-like modules, which are each connected to each other by a first or second plug-in connection.

Abstract: Described herein are improved configurations for a wireless power transfer. Described are methods and designs to reduce and manage heating and heat dissipation in resonator structures. Configuration and orientation of magnetic material as well as heat sinking material with respect to the dipole moment of the resonator is used to reduce and control thermal properties of the resonator structure and reduce the effects of heating on the performance of wireless power transfer.

Abstract: An inductor comprises a magnetic core and a coil. The magnetic core has a wound portion around which the coil is wound, and a peripheral portion. The magnetic core is formed from two or more preliminarily-formed-bodies which are pressure-molded in a state where the coil winds one or more preliminarily-formed-bodies which form the wound portion. The preliminarily-formed-bodies include at least one preliminarily-formed-body which forms the peripheral portion while not form the wound portion. Each of the preliminarily-formed-bodies is made of a mixture of flat magnetic powders and an organic binder so as to have a plate-like shape. The flat magnetic powders are oriented so as to be parallel to the preliminarily-formed-body.

Abstract: A transformer of dry design is disclosed having a core composed of amorphous material, which is sensitive to mechanical loads, having at least one winding former which surrounds the core and is in each case formed from at least one primary winding and secondary winding, and having at least one holding apparatus. A method for transformer production is also disclosed, wherein the holding apparatus is used to fix the at least one primary winding and secondary winding in each case and for this purpose it acts on each of the end faces of the at least one winding former.

Abstract: A method of testing a transformer prior to installation in a high-pressure environment wherein the transformer comprises a transformer core comprising a stack of a plurality laminations, is provided. The method comprises applying a mechanical compression force to the stack, the force being at least equivalent to the ambient pressure of the high-pressure environment; and testing the electrical efficiency of the transformer.

Abstract: An apparatus and method for manufacturing a superconducting low-pass filter for quantum computing devices. The apparatus includes a plurality of containers and input and output ports connected to opposite ends of the apparatus. A plurality of coils of superconducting wire are wound using a mandrel. An adhesive is applied to the coils for maintaining a wound state. Each of the coils are positioned in each of the containers and electrically connected to each other with at least one coil being connected to the input port and at least one coil being connected to the output port. The coils are released or expanded from their wound state using an adhesive solvent. The containers are then filled with a conductive polymer and the containers are closed with one or more covers.

Abstract: A high leakage inductance transformer core device, and method of forming same, that has a core made of tape wound material, at least one set of concentric primary and secondary windings, and at least one flux shunt between the primary and secondary windings which is also made of tape wound material. The transformer core and flux shunts are arranged so that the transformer has a low external magnetic field, and substantially no excess core losses due to principal core flux flowing from one part of the core structure to another through the broad surface of the core tape.

Abstract: A wounded core Scott transformer configured so that opposed core legs of wounded cores corresponding to core legs mounted in a main coil and a teaser coil are arranged on the inside between the respective coils so as to be supported.

Abstract: A dual output autotransformer is realized by employing a novel topology in which three transformers are wound on a single, high permeability, ferrite, binocular core. The three transformers are (1) an autotransformer; (2) a coupled winding to the autotransformer; and, (3) a transmission line transformer. Within the topology employed, the outputs of the coupled line transformer and the transmission line transformer provide the balanced output (secondary) and the input to the autotransformer forms the unbalanced primary. Such an approach results in a wideband response of from 30 MHz to 3000 MHz or greater with the requisite amplitude and phase balance.

Abstract: An inductor core device, and method of forming same, that has at least a first inductor core section and typically has a second inductor core section, both formed of stacked layers of conductive material. The second core section may be positioned relative to the first core section to define an air gap therebetween and the sections are preferably profiled between their respective end faces and broad surfaces to reduce the eddy current losses induced in the core section(s) near the air gap. Various embodiments, “profile” shaping configurations, and core section arrangements are disclosed.

Abstract: A simple forming method capable of reducing an eddy current loss in a magnetic core formed by winding a foil body is provided. A magnetic core formed by folding a foil strip in the longitudinal direction thereof, winding and laminating the folded strip starting from one folded end after folding into a cylindrical body, and exciting the cylindrical body in the lateral direction of the foil strip for use.

Abstract: A core member (2) of the disclosed reactor (Da) comprises a magnetic wire material and is arranged outside a plurality of coils (1). As the core member (2) in the reactor (Da) having this structure is a wire material and is arranged outside the plurality of coils (1), the core member (2) can be formed by the winding of the wire material, simplifying manufacturing.

Abstract: A toroidal current transformer that can be used as a neutral current transformer in a single or three phase system as a result of its compactness is described. The core is made of ferromagnetic material having a primary winding and a secondary winding.

Abstract: An ignition transformer for a discharge lamp is provided having a transformer core whose material and dimensions are selected in such a manner that the Curie temperature of the material after the ignition which is achieved by means of the ignition transformer can be achieved by a voltage drop across a secondary winding of the ignition transformer.

Abstract: A transformer wherein the upper portions of cores are supported by a first supporting member disposed on first end surfaces of the upper portions of the cores, and a second supporting member disposed on second end surfaces of the upper portions of the cores, the first and second supporting members extend in the direction perpendicular to the faces of a magnetic material, and the cores are interposed between the first upper core supporting member and the second upper core supporting member; the first and second upper core supporting members are provided with hooks, the hooks of the first supporting member extending toward the second supporting member and the hooks of the second supporting member extending toward the first supporting member; bridging members are disposed on the opposing pairs of the hooks of the first and second upper core supporting members; and the cores are supported by the bridging members.

Abstract: A transformer arrangement comprising a transformer having a neutral and formed as a symmetrical transformer, in particular a cage transformer and having a reactor coil connected to the neutral of the transformer is provided. The transformer can be of any type having a neutral such as a Y-n/Y-n, Z-n/Z-n, Y-n/Z-n or a Z-n/Y-n transformer. By providing a transformer having symmetrical phases connected to a reactor coil a transformer arrangement having less weight is obtained. The lower weight is obtained because in comparison to using an E core for the transformer all phases will be symmetrical so that if a ground fault occurs in one of then phases there is no need for any compensatory windings regardless of which phase suffers the ground fault.

Abstract: The invention relates to a soft-magnetic metal strip for electromechanical components, wherein the soft-magnetic metal strip has a nanocrystalline or amorphous structure. The metal strip has strip thickness to roughness ratios d/Ra of 5?d/Ra?25.

Abstract: A method of assembling an electronic component in accordance with the invention comprises providing an electronic component having a body and a core and applying a film over at least a portion of the body and core so that the film secures the body and core to one another.

Abstract: A transformer of dry design is disclosed having a core composed of amorphous material, which is sensitive to mechanical loads, having at least one winding former which surrounds the core and is in each case formed from at least one primary winding and secondary winding, and having at least one holding apparatus. A method for transformer production is also disclosed, wherein the holding apparatus is used to fix the at least one primary winding and secondary winding in each case and for this purpose it acts on each of the end faces of the at least one winding former.

Abstract: Magnetic circuit comprising a gap bridging element made of a non-magnetic metal and a wound magnetic core comprising a plurality of stacked concentric ring layers of magnetic material having a high magnetic permeability. The magnetic core has a gap extending through a section of the stacked concentric ring layers of magnetic material, wherein the bridging element is welded to a lateral face of the wound magnetic core on either side of the gap. Welding connections between the bridging element and the magnetic core extend across the stacked concentric ring layers.

Abstract: A ferromagnetic amorphous alloy ribbon includes an alloy having a composition represented by FeaSibBcCd where 80.5?a?83 at. %, 0.5?b?6 at. %, 12?c?16.5 at. %, 0.01?d?1 at. % with a+b+c+d=100 and incidental impurities, the ribbon being cast from a molten state of the alloy with a molten alloy surface tension of greater than or equal to 1.1 N/m on a chill body surface; the ribbon having a ribbon length, a ribbon thickness, and a ribbon surface facing the chill body surface; the ribbon having ribbon surface protrusions being formed on the ribbon surface facing the chill body surface; the ribbon surface protrusions being measured in terms of a protrusion height and a number of protrusions; the protrusion height exceeding 3 ?m and less than four times the ribbon thickness, and the number of protrusions being less than 10 within 1.5 m of the cast ribbon length; and the alloy ribbon in its annealed straight strip form having a saturation magnetic induction exceeding 1.

Abstract: A ferromagnetic amorphous alloy ribbon includes an alloy having a composition represented by FeaSibBcCd where 80.5?a?83 at. %, 0.5?b?6 at. %, 12?c?16.5 at. %, 0.01?d?1 at. % with a+b+c+d=100 and incidental impurities; the ribbon being cast from a molten state of the alloy, with a molten alloy surface tension of greater than or equal to 1.1 N/m; the defect length along a direction of the ribbon's length being between 5 mm and 200 mm, the defect depth being less than 0.4×t ?m and the defect occurrence frequency being less than 0.05×w times within 1.5 m of ribbon length, where t is the ribbon thickness and w is the ribbon width, and the ribbon having a saturation magnetic induction exceeding 1.60 T and exhibiting a magnetic core loss of less than 0.14 W/kg when measured at 60 Hz and at 1.3 T induction level in an annealed straight strip form, and a core magnetic loss of less than 0.3 W/kg and an exciting power of less than 0.4 VA/kg in an annealed wound transformer core form.

Abstract: Disclosed herein is a ballast for multiple lamps and a method of manufacturing the ballast. A first coil is wound around a bobbin which has a partition formed in the center portion of an inner space thereof. An insulating sheet is stacked on the first coil, and a second coil is wound around the insulating sheet. Two paired core elements are vertically coupled to each other to form each core. Ends of the core elements disposed outside the bobbin are connected, and ends of the core elements disposed inside the bobbin are spaced apart from each other by the thickness of the bobbin partition, to form a path for magnetic flux.

Abstract: A slab having a predetermined composition is heated to 1280° C. or more. The slab is hot-rolled to obtain a hot-rolled steel sheet. The hot-rolled steel sheet is annealed to obtain an annealed steel sheet. The annealed steel sheet is cold-rolled to obtain a cold-rolled steel sheet. The cold-rolled steel sheet is decarburization annealed to obtain a decarburization annealed steel sheet. The decarburization annealed steel sheet is coiled in a coil state. The coil-state decarburization annealed steel sheet is finish-annealed. The cold-rolled steel sheet is heated to a temperature of 800° C. or more at a rate of 30° C./sec or more and 100° C./sec or less during increasing temperature of the cold-rolled steel sheet in the decarburization annealing or before the decarburization annealing. The decarburization annealed steel sheet is heated at a rate of 20° C./h or less within a temperature range of 750° C. or more and 1150° C.

Abstract: An inductor device is described. The inductor device includes a core comprising two core sections, at least one gap defined between the two core sections, and at least one cast coil and fringe shield assembly. The at least one cast coil and fringe shield assembly includes a conductor winding and a fringe shield sealed within an insulator. The at least one cast coil and fringe shield assembly is configured to at least partially surround portions of the two core sections.

Abstract: A coil module comprises a circular core and a winding is provided. The circular core comprises an outer circular portion and an inner circular portion. The winding is wound around the outer circular portion in a single-layer configuration and around the inner circular portion in a multi-layer configuration. The coil module comprises a first thickness after the winding is wound around the outer circular portion and comprises a second thickness after the winding is wound around the inner circular portion, wherein the first thickness is greater than or equal to the second thickness.

Abstract: An inductance element (1) includes a doughnut-shaped magnetic core (2) and a bottomed container (3) for housing the doughnut-shaped magnetic core (2). The bottomed container (3) has a cylindrical outer wall portion, a cylindrical inner wall portion, a bottom portion, an open section and a hollow portion. The open section of the bottomed container (3) is covered with an adhesive portion (4) for integrally fixing the doughnut-shaped magnetic core (2) and the bottomed container (3). The adhesive portion (4) has an extended portion (4a) extended in the cylindrical inner wall portion. The ratio (B/A) of a length (B) of the extended portion (4a) to a height (A) of the cylindrical inner wall portion is in a range of 0.1 to 0.5.

Abstract: A pulse transformer arrangement (100) is built from an uncut pulse transformer core (110) and at least one foil winding (120-A, 120-B) (each) comprising multiple insulated conducting strips arranged around the core and ending in foil winding terminals to form multiple independent primary windings. This new design principle has several advantages. Making the winding(s) of foil eliminates the need to cut the core, because of the ease of insertion of the foil winding(s) onto the core. The work to set up a plurality of primary windings is significantly reduced. In addition to the elimination of the costs for cutting the core, this also brings the further advantages of reduced DC reset current, reduced risk for electrical shorts and avoidance of excessive losses due to potential high frequency AC resistance problems.

Abstract: Disclosed is an electronic component, especially a coil with a coil core, in which the turns of the coil winding are spaced apart from each other at least at one point in the longitudinal direction of the coil. A plastic retaining element which overlaps both the coil core and at least the two adjacent turns of the coil winding in a longitudinal direction is sprayed on in the area of said point, whereby a connection between the coil core and the coil winding is created at the same time. The retaining element can be sprayed around a closed circumference of the coil while covering only a portion of the coil in the longitudinal direction thereof. Preferably, the retaining element is placed approximately in the center relative to the longitudinal extension of the coil.

Abstract: In a three phase wound transformer core three frames are connected in triangular fashion, each frame being made of multiple rings wound in off-set fashion on a common axis.

Abstract: A magnetic pole for magnetic levitation vehicles is described which pole comprises a core (1) and a winding (16) applied on it in form of a disc which is formed by a conductor strip (17) wound in several layers (10a) . . . 10k) around said core (1). According to the present invention, the conductor strip (17) is properly tailor-cut at its longitudinal rims (17a, 17b) so that its width increases from said core (1) towards the outside until it reaches a maximum value (b2).