JOM
`DOI: 10.1007/s11837-012-0350-0
`Ó 2012 TMS
`
`Soft Magnetic Materials in High-Frequency, High-Power
`Conversion Applications
`
`ALEX M. LEARY,1,3 PAUL R. OHODNICKI,2 and MICHAEL E. MCHENRY1
`
`1.—Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes
`Avenue, Pittsburgh, PA 15213, USA. 2.—Division of Chemistry and Surface Science, National
`Energy Technology Laboratory (NETL), 626 Cochrans Mill Road, Pittsburgh, PA 15236, USA.
`3.—e-mail: leary@cmu.edu
`
`Advanced soft magnetic materials are needed to match high-power density
`and switching frequencies made possible by advances in wide band-gap
`semiconductors. Magnetics capable of operating at higher operating frequen-
`cies have the potential to greatly reduce the size of megawatt level power
`electronics. In this article, we examine the role of soft magnetic materials in
`high-frequency power applications and we discuss current material’s limita-
`tions and highlight emerging trends in soft magnetic material design for
`high-frequency and power applications using the materials paradigm of
`synthesis fi structure fi property fi performance relationships.
`
`INTRODUCTION
`Wilson1 defines power electronics as the technol-
`ogy associated with the efficient conversion, control,
`and conditioning of electric power by static means
`from its available input form into the desired elec-
`trical output form. Nearly all generated electricity
`requires some form of conversion. Power losses
`during conversion dissipate as heat during trans-
`mission and distribution to the end user and
`developments in soft magnetic materials resulted in
`significant reductions in these losses over this time.2,3
`Limited metering restricts precise measurement of
`transmission and distribution losses on a large
`scale.4 When generated commercial power does not
`exceed demand, the ratio of power sold to generated
`provides an estimate for these losses. Figure 1
`shows the total electrical power generated for the
`retail market compared with the percentage that
`was not sold between 1949 to 2010 in the United
`States.5 In addition to a direct economic impact
`totaling $25.8 billion in lost revenue for a nominal
`retail price of $0.0988/kWh, the generation of this
`wasted power also results in additional greenhouse
`gas emissions that negatively impact the environ-
`ment. These losses drive efficiency improvements
`and are a lower bound of the total transmission,
`distribution, and conversion losses since they do not
`include losses experienced by the consumer down-
`stream of the billing meter.
`
`The Department of Energy expects demand for
`electricity to rise by 30% and estimates a $1.5 tril-
`lion cost to modernize the existing United States
`electricity infrastructure over the next 20 years.6
`These upgrades and capacity expansions provide an
`opportunity to build and integrate new power elec-
`tronics to meet demand while reducing waste and
`inefficiencies. Movement toward grid-level integra-
`tion of renewable energy sources and distributed
`storage systems requires new topologies to handle
`transient sources and facilitate two-way power
`conversion.7 Flexible alternating current
`(AC)
`Transmission Systems (FACTS) and High Voltage
`DC (HVDC) technologies aim to improve the effi-
`ciency of power networks and benefit from high-
`frequency conversion.8
`Increases in DC power
`generation and loading also motivate research into
`new topologies containing high-frequency DC–DC
`power converters.9–13
`Independent of the power generation method, the
`laminated electrical steels traditionally used for
`power cores become inefficient at high switching
`frequencies. Additionally, soft magnetics used in
`power electronics can occupy significant space,
`require extensive cooling, and limit designs. New
`large-scale systems must be cost competitive with
`existing systems and further
`cost
`reductions
`require materials advancements. These advance-
`ments will dictate the most successful topologies to
`take advantage of material strengths and minimize
`
`Ex.1024 / IPR2022-00117 / Page 1 of 10
`APPLE INC. v. SCRAMOGE TECHNOLOGY, LTD.
`
`

`

`Leary, Ohodnicki, and McHenry
`
`components. Instead, an active switching circuit
`modifies the input signal using pulse width modu-
`lation by various techniques.20 Fourier analysis de-
`scribes this modulated signal as the superposition of
`a many frequencies, so optimally designed soft
`magnetic materials must have broadband capability.
`The semiconductors used in active switching cir-
`cuits have voltage and power limitations and high-
`voltage converters often divide the total output into
`manageable quantities with a multilevel circuit.21
`Multilevel circuits can have the added benefit of
`improving the harmonic quality of the drive current,
`but each additional level comes with a price as the
`semiconductors have associated switching and con-
`duction losses. New SiC and GaN semiconductors
`have wider band gaps than currently available Si
`devices that result in much lower on-resistance.22
`Lower losses in the active components of a power
`converter allow for higher power densities ðW=m3Þ:
`While several high-frequency converter designs
`operate without magnetics, considerations such as
`galvanic
`isolation and the scaling limitations
`associated with air core inductors suggest
`the
`need to further develop advanced magnetics.18
`Currently, no commercial magnetic materials can
`match the performance level of the wide band gap
`semiconductors.23
`A successful design minimizes the combined los-
`ses of the passive magnetic material, the windings,
`and the switching circuit for a given power output.
`Typically,
`loss mechanisms are complex and
`designers rely on empirical rather than analytical
`models. High-frequency losses in magnetic materi-
`als are dominated by classical and anomalous eddy
`currents caused by the motion of domain walls.24
`Eddy currents generate heat by I2R losses in the
`magnetic material. For continuous operation, this
`heat must be dissipated through the component
`surface to prevent excessive temperatures. Scaling
`limitations result when surface area decreases
`while the amount of generated heat remains con-
`stant. Improvements in power density for a given
`power rating and efficiency require increased cool-
`ing due to the reduced surface area available to
`smaller components. With currently available soft
`magnetic materials, thermal management limits
`converter power density below levels possible with
`advanced switching circuits. The steady-state tem-
`perature rise in the magnetic material for a given
`shape and power loss is a function of the material’s
`thermal conductivity and emissivity, the local heat
`transfer conditions surrounding the material, and
`the surface area of the material exposed to these
`conditions.
`Scaling models describe the effects of size reduc-
`tions for given design constraints and require
`descriptions
`of heat generation and thermal
`responses to losses. Passive components (inductors
`and capacitors) operate in concert with active com-
`ponents in a power converter and scaling relation-
`ships must consider both. A geometric factor, such
`
`Losses (%)
`
`12
`
`10
`
`8
`
`6
`
` Power
` Losses
`
`4000
`
`3500
`
`3000
`
`2500
`
`2000
`
`1500
`
`1000
`
`500
`
`Electrical Power Generated (Billion kWh)
`
`1950
`
`1960
`
`1970
`
`1980
`
`1990
`
`2000
`
`2010
`
`Fig. 1. Total retail electrical power generated (NAICS 22) in the
`United States and estimated transmission and distribution losses, as
`measured by the ratio of power sold to power generated. Data taken
`from Ref. 5 includes independent power producers starting in 1989.
`
`weaknesses. This article explores the use of soft
`magnetic materials in power conversion applica-
`tions. The first section describes the high-frequency
`limitations of soft magnetic materials, the ‘‘Materials
`Survey’’ section surveys the current state-of-the-
`art materials, and the ‘‘Future Processing Oppor-
`tunities’’ section highlights opportunities for future
`improvements.
`
`HIGH-FREQUENCY SWITCHING
`AND POWER CONVERSION
`
`¼ L
`
`dB
`dI
`¼ LI0x cosðxtÞ
`dt
`dt
`I0x cosðxtÞ
`
`(1)
`
`Soft magnetic materials enable low loss inductive
`switching, which is useful in inductor, transformer
`and filter applications. The basic design challenge
`for inductive components becomes evident after
`considering Eq. 1, which relates Faraday’s law of
`induction to the voltage response of an ideal toroidal
`core with inductance L driven by an AC current,
`I = I0 sin(xt).
`V ¼ NA
`¼ lN2A
`
`l
`
`For constant maximum voltage (V), permeability (l),
`number of turns (N), and effective length (l), the
`cross-sectional area (A) is inversely proportional to
`the frequency (x = 2pf). This relation motivates the
`use of high-frequency switching to reduce size and
`weight of passive inductive components in power
`converters. However, nonlinear material properties
`limit scaling reductions in power magnetics, espe-
`cially for applications above the kilowatt power
`range. Several studies examine these limitations to
`guide transformer and inductor design.14–19 Addi-
`tionally, high-frequency power converters rarely use
`purely sinusoidal currents to drive the magnetic
`
`Ex.1024 / IPR2022-00117 / Page 2 of 10
`APPLE INC. v. SCRAMOGE TECHNOLOGY, LTD.
`
`

`

`Soft Magnetic Materials in High-Frequency, High-Power Conversion Applications
`
`Fig. 2. Tape wound ring core geometry used for loss modeling.
`
`as the area product25 or a component volume, com-
`bines the dimensions of passive and active compo-
`nents into a single variable. Here, we consider
`magnetic material property effects on scaling for the
`simple tape wound core geometry shown in Fig. 2 of
`outer and inner diameters (R1 and R2) and the core
`depth d. We choose the outer diameter of the ring
`core R1 as the geometric variable and fix the inner
`diameter and depth to 0.7R1 and 0.3R1.
`The time averaged core loss is given by the well-
`known variation of the Steinmetz Eq. 2 where k, a,
`and b are empirical fits to loss data.
`PC ¼ kf aBb
`This loss, usually determined from a sinusoidal
`driving frequency, incorporates the hysteresis and
`eddy current losses due to changes of magnetization
`at a frequency f. The windings produce a field H
`that is amplified by B = lH in the core.
`H ¼ /IN
`l
`
`m
`
`(2)
`
`(3)
`
`where N is the number of turns over an effective
`length l and / is a geometric constant. We assume
`no DC bias and the useful portion of the induction is
`expressed as DB ¼ 2Bm. For a single layer of closely
`packed windings where l = Nw, winding losses for a
`
`
`given conductor resistivity (q) can be described as
`2 ql
`Ac
`
`rmsR ¼ 1
`PW ¼ I2
`2
`
`Bml
`l/N
`
`(4)
`
`Fig. 3. Power loss for R1 = 7 cm core for two relative permeabilities.
`Added power rating (orange) for a lower permeability material com-
`pared with additional winding losses (yellow) leads to higher effi-
`ciency for constant core loss (Color figure online).
`
`PW ¼ I2RFr where Fr ¼ 1 þ p2x2l20N2n2d6
`
`c k
`768q2b2
`c
`
`(5)
`
`The wire on the model core occupies a window with
`2 and uses Litz wire with
`an areal dimension bc
`n = 300 strands of diameter dc = 0.2 mm wire. We
`first consider a case where Litz wire windings fill
`the center core area with N ¼ ðpR2
`2=w2Þ and the
`wire crosssection is 50% copper ðq ¼ 2lX cmÞ. Each
`wire occupies a square area w2 within the winding
`2. To account for additionalwindow of size bc2 = p R2
`
`
`winding layers, the length per turn increases by 8w
`for each additional layer. The DC winding resis-
`tance is small compared with the AC resistance. A
`more detailed winding loss model for tape cores is
`found in Ref. 27.
`For magnetic materials with constant permeabil-
`ity over the flux range DB, the power rating (PVA)
`can be used to estimate the inductive efficiency for a
`single core (gc) of volume Vc
`PVA ¼ VrmsIrms ¼ p/AlB2
`mf
`l
`
`¼ dðBHÞ
`
`dt
`
`¼ VcB2
`mf
`2l
`
`(6)
`
`The conductor cross section (Ac) decreases with
`increasing frequency due to the skin effect.
`Increasing N decreases the maximum drive current,
`but for high-frequency and power applications,
`smaller cores may limit the available winding space.
`Multiple winding layers lead to additional losses
`due to AC proximity effects. Sullivan26 accounts for
`these losses by defining Fr, a dimensionless factor
`that relates DC to AC resistance for a core wound
`with Litz wire.
`
`gc ¼ PVA ðPC þ PWÞ
`
`PVA
`
`(7)
`
`Assuming Steinmetz coefficients to be constant over
`the frequency range of interest, core loss is linear on
`a log–log loss versus frequency plot. Winding losses
`change slope with increased frequency due to skin
`and proximity effects. Figure 3 shows these losses
`and the output of a core with R1 = 7 cm and 308
`
`Ex.1024 / IPR2022-00117 / Page 3 of 10
`APPLE INC. v. SCRAMOGE TECHNOLOGY, LTD.
`
`

`

`Leary, Ohodnicki, and McHenry
`
`Fig. 4. (a) Efficiency versus frequency and (b) power density in kW=dm3 for the core geometry of Fig. 2.
`
`turns for Bm = 0.5T with core loss values from
`Ref. 28. The two shaded areas show the difference
`between output power (VA) and total losses for two
`different relative permeabilities. We assume the
`same core loss for lower and higher permeability
`cores and discuss the assumption in the ‘‘Materials
`Survey’’ section. By lowering permeability, the
`material stores more inductive energy per cycle but
`also requires higher current (or more turns) to reach
`a desired induction. For this model, the additional
`stored inductive energy is greater than the added
`winding losses. If core loss is greater than winding
`loss, then materials with low permeability give
`efficiency benefits at high frequencies, as shown in
`Fig. 4a. For volume and weight limited applications,
`low permeability also gives high power density.
`Figure 4b shows the theoretical power density for
`this core geometry over a range of inductions and
`relative permeabilities. The 60 kW DC–DC converter
`in Ref. 29 has a 40 kW=dm3 power density. Kolar
`et al.23 show a 10-fold increase in converter power
`density every 20 years. Published power density
`values vary depending on the inclusion of a cooling
`system. Magnetic components occupy a significant
`portion of the volume. In the following, we extend this
`core model to estimate desirable magnetic material
`properties for high-frequency, high-power conver-
`sion. Reasonable designs must consider thermal
`limitations. In Refs. 14, 18, and 30, the relation
`between temperature rise and power loss relies on
`extrapolations from experimental data. We can also
`estimate the temperature rise DT for a material
`based on the thermal conductivity k as in Ref. 31.
`kDT ¼ PTh
`A
`
`(8)
`
`The cooling system determines the heat transfer
`conditions at the surface, but the heat generated by
`the power loss PT = Pc + Pw must first conduct
`
`through the thermal path h within the material. We
`assume a cooling system to be able to remove PT
`from the surface at T1 and use the thermal param-
`eter ðkDTÞ
`to describe the maximum possible
`efficiency of the inductive components in a 1 MVA
`power converter.
`Ring core geometries with many windings present
`a challenge because the windings limit heat transfer
`from the core. For this reason, we consider ring
`cores with three winding layers and define the
`thermal path length as h = R1 R2. Each core and
`winding form a subcomponent within the converter
`and losses for the model subcomponents were cal-
`culated using the Monte Carlo method by randomly
`assigning model parameters over the following de-
`sign space: (I) f ¼ 1 kHz ! 1 MHz; (II) Bm ¼ 0:5 !
`(III) lr ¼ 200 ! 5000; and (IV) R1 ¼ 7 !
`1:3T;
`20 cm. Core losses were calculated in mW=cm3 units
`from Eq. 2 using Finemet loss values from Ref. 28
`with k = 3.935, a = 1.585, and b = 1.88 where the
`frequency is in kHz and the induction in Tesla. The
`measured core losses were accurate within 1% to
`500 kHz. For converters that require multiple sub-
`components to achieve a desired power rating, the
`connection arrangement effects the overall efficiency
`(gt). Figure 5a shows the efficiencies for individual
`subcomponents compared with the thermal param-
`eter from Eq. 8. These efficiency values correspond to
`the gt for subcomponents connected in parallel and
`successful designs have high efficiencies and require
`low thermal parameters. The power ratings (PVA)
`form a banded pattern, and the 20 kVA and 80 kVA
`lines
`indicate
`the
`respective boundaries. For
`gc > 0.95, higher frequencies (Fig. 5b) and lower
`permeabilities (Fig. 5c) produced higher power rat-
`ings but require higher thermal parameters. The
`allowable temperature rise and thermal conductivity
`varies for different soft magnetic materials. Ferrites
`with k  4W=mK have operating limits below 200°C
`
`Ex.1024 / IPR2022-00117 / Page 4 of 10
`APPLE INC. v. SCRAMOGE TECHNOLOGY, LTD.
`
`

`

`Soft Magnetic Materials in High-Frequency, High-Power Conversion Applications
`
`Fig. 5. Performance measures for randomly designed sub-components with (a) efficiency versus thermal parameter and power rating (PVA)
`versus thermal parameter. Higher frequencies (b) and lower permeabilities (c) yield higher PVA ratings.
`
`MATERIALS SURVEY
`Magnetic materials store inductive energy ð1
`2 LI2Þ
`and filter unwanted signals in power converters. The
`majority of heat generated in a circuit arises from
`this storage function and a good inductive material
`stores the most energy with the lowest loss. As shown
`in Eq. 1, L is largely a function of the permeability (l).
`Figure 7 shows the energy stored for different per-
`meabilities. The area enclosed in the BH hysteresis
`curve for a material equals the core loss per cycle. The
`high induction levels approaching 2T commonly used
`at 50/60 Hz in Si steels are not achievable at higher
`frequency with currently available materials due to
`high coercivities (Hc). High-permeability materials
`(lr > 10,000) store very little energy prior to satu-
`ration. Materials with lower permeabilities store
`more energy per cycle at lower inductions but require
`higher driving fields and increased winding losses.
`Designers can achieve low-permeability cores by
`introducing an air gap or cutting a core made of high-
`permeability material. Cut cores introduce additional
`losses through flux fringing around the gaps that can
`also induce eddy currents in nearby conductive
`material.28 Poor manufacturing techniques greatly
`influence cut core properties and can lead to much
`higher losses than expected.33 Materials with low
`permeability with respect to the driving field direction
`are preferred in order to avoid complications due to cut
`cores. Cores with induced anisotropies transverse to
`the drive field restrict domain wall motion and show
`low losses at high frequency.34 Alves et al.35 demon-
`strated improved performance in a low power flyback
`converter design with a low permeability stress an-
`nealed Finemet core compared to a gapped ferrite
`core. The nanocomposite core was half the size of the
`ferrite core and produced 333% more power. For high-
`power, low-loss applications, low permeability is best
`achieved by inducing a controlled anisotropy perpen-
`dicular to the drive field in a material that exhibits a
`high permeability and low coercivity as measured
`along the easy axis. Therefore, figures of merit for low-
`frequency applications including high saturation
`
`1.00
`
`0.99
`
`0.98
`
`0.97
`
`0.96
`
` Efficiency
`
` f > 40 kHz
` 20 kHz < f ≤ 40 kHz
` f ≤ 20 kHz
`
`102
`
`104
`103
` 1 MVA Mass (kg)
`
`105
`
`Fig. 6. 1 MVA efficiency versus total mass of soft magnetic material
`required. With the modeled material, higher frequencies reduce the
`amount of material required but result in lower efficiencies.
`
`and nanocomposites maintain low losses above 200°C
`with k  9W=mK.32 The improved thermal proper-
`ties of nanocomposite materials greatly expand the
`envelope of acceptable designs. The total converter
`power level and the individual core power rating
`determine the number of subcomponents required
`for a converter design. Figure 6 shows the converter
`efficiency compared with the mass of soft magnetic
`material (density = 7.9 g/cm3) required to obtain 1
`MVA. For the modeled material, higher frequencies
`reduce the required mass but sacrifice efficiency.
`This illustrates the need for improved high-fre-
`quency magnetics to maintain high efficiency. A cost
`analysis is needed to determine the best overall de-
`sign and is the subject of future work. The shape
`ratios used to define R2 and d may not be optimal and
`were chosen based on assumed manufacturing limi-
`tations, such as ribbon width and structural integrity.
`
`Ex.1024 / IPR2022-00117 / Page 5 of 10
`APPLE INC. v. SCRAMOGE TECHNOLOGY, LTD.
`
`

`

`Leary, Ohodnicki, and McHenry
`
`The empirical constants are defined as in Ref. 28 to
`describe core loss in mW=cm3. Materials with a high
`power ratio must store large amounts of power
`efficiently. Although the actual amount of power
`stored in the material will differ due to the pulse
`width modulation and the duty cycle used, sinusoi-
`dal excitations are assumed here as most loss data is
`published using this waveform.
`Losses in soft magnetic materials consist of both
`static and dynamic hysteresis losses. To limit static
`hysteretic losses in bulk metal alloys such as silicon
`steels, metallurgists have sought to obtain large grain
`sizes in order to minimize domain wall pinning, lower
`coercivity, and hence reduce low-frequency losses.
`Hasegawa36 showed the advantages of magnetic
`materials with small crystalline grains within amor-
`phous alloys. The random anisotropy model developed
`by Alben et al.37 for amorphous ferromagnets was
`applied by Herzer38 to nanocrystalline ferromagnets
`and showed that a reduction in grain size well below
`the ferromagnetic exchange length can lead to a rapid
`decrease in coercivity. The review of amorphous and
`nanocomposite soft magnets in Ref. 39 describes the
`properties of these alloys in more detail.
`Dynamic losses consist of classical eddy current
`and anomalous or excess losses. Bertotti40 describes
`the classical eddy current power loss in Eq. 11,
`where t is the material thickness and q is the
`resistivity, as
`
`Pcl ¼ p2t2B2mf 2
`
`6q
`
`(11)
`
`This expression is valid when the material thick-
`ness is much less than the skin depth. Nanocom-
`posite materials with q  130 lX cm and lr = 1,000
`have a skin depth of 61 lm at 100 kHz and ribbons
`produced by rapid solidification are usually<30 lm
`thick suggesting that this expression is approxi-
`mately valid. Engineering approaches to limiting
`these losses focus on reducing thickness with thin
`laminations and increasing resistivity.
`Figure 8 shows the power ratio from 10 for dif-
`ferent soft magnetic materials described in Table I.
`Materials with poor performance at high frequen-
`cies, such as Si steels, and high permeability have
`low power ratios. The distributed air gap in powder
`cores allow for very low effective permeabilities
`and soft saturation, which can be beneficial for
`some applications. Ferrites can also achieve low
`permeability, but their low saturation induction
`and thermal conductivity restricts their use in
`high-power converters. Nanocomposite alloys con-
`sist of nanocrystals precipitated in an amorphous
`matrix and offer an extended set of processing
`dimensions such as grain size and volume fraction
`to tailor properties. Nanocomposite alloys of the
`FINEMET type41 have been most
`intensively
`studied, and hence, they represent the majority of
`data points in Fig. 8. The highest power ratios
`in the nanocomposites exhibit low permeabilities
`
`Fig. 7. Inductive energy storage for low-coercivity materials with
`different permeabilities. Low permeability materials store more en-
`ergy per cycle but must maintain low coercivity to prevent losses.
`
`magnetization and high permeability may not directly
`apply to power magnetic materials for relatively high
`frequency applications (10 kHz–1 MHz), though high
`permeability prior to inducing anisotropy is a good
`predictor of low losses. Therefore, materials with
`tunable permeabilities through carefully designed
`thermomagnetic or thermomechanical processing al-
`low designers to optimize the magnetic material to the
`active components.
`Several factors determine the performance of a
`magnetic material as a high-frequency inductor.
`The quality factor (Q) in Eq. 9 where l0 and l00 are
`the real and imaginary parts of complex perme-
`ability is a performance measure for an inductor.
`Q ¼ xL
`R
`
`¼ l0
`l00
`
`(9)
`
`High permeability materials saturate under low
`fields. For high power applications, the amount of
`energy stored must be considered as well as the
`losses, but the quality factor does not account for
`magnetic saturation. A figure of merit in Eq. 10
`compares the inductive energy stored per unit
`volume during a half cycle to the measured losses
`for a sinusoidal driving field during that period.
`Power Ratio ¼ Stored Power
`¼
`
`
`Power Loss
`1a
`
`
`
`12
`
`BmH2f
`
`
`
`1;000k
`
`f
`1;000
`
`¼ B2b
`
`m
`
`f
`1;000
`kl0lr
`
`a
`
`Bb
`m
`
`ð10Þ
`
`This quantity is valid for materials with constant
`permeability over the frequency range of interest.
`
`Ex.1024 / IPR2022-00117 / Page 6 of 10
`APPLE INC. v. SCRAMOGE TECHNOLOGY, LTD.
`
`

`

`Soft Magnetic Materials in High-Frequency, High-Power Conversion Applications
`
` Nanocomposite
` Ferrite
` Powder
` Amorphous
` Steel
` Cut Core
` Stress Annealed
` Field Annealed
`
`µr = 200
`
`µr = 2000
`
`2
`
`3
`
`4
`
`5 6 7 8 9
`105
`
`2
`
`3
`
`4
`
`5 6 7 8 9
`106
`
`2
`
`3
`
`4
`
`5
`
`Frequency (Hz)
`
`23456789
`
`23456789
`
`100
`
`10
`
`Power Ratio
`
`1
`
`104
`
`Fig. 8. Survey of published soft magnetic material performance. Dotted lines indicate Eq. 10 with k = 3.935, a = 1.585, and b = 1.888
`for l = 200, 2000 at Bm = 0.1T.
`
`thereby enhancing the maximum potential stored
`energy. In practice, this can be accomplished by
`cutting the core to induce an air gap or by engi-
`neering transverse anisotropy. Gapped Finemet
`cores42 and stress annealed material43,44 approach
`the calculated power ratio for the modeled material
`with low permeability and Bm = 0.1T as indicated.
`The field annealed Co-rich FeCo nanocomposite in
`Ref. 45 shows comparable performance with stress
`annealed Fe-rich alloys.
`
`Several published high frequency, high power
`converter designs demonstrate the advantages of
`et al.46
`nanocomposite
`core materials. Zhang
`describe a 100-kW bidirectional DC–DC power con-
`verter that switches at 25 kHz with 97.8% efficiency.
`This design uses three Finemet cores that account
`for 32% of the total loss. The advantages of high
`induction can be seen in Ref. 17, where a 30-kW
`converter with a Finemet core showed three times
`higher power density than a ferrite design at
`
`Table I. References and material descriptions from Fig. 8
`
`Reference
`
`Author
`
`Material
`
`[12] 1
`[12] 2
`[12] 3
`[49] 1
`[49] 2
`[42] 1
`[42] 2
`[43]
`[47]
`[31]
`[44]
`[50] 1
`[50] 2
`[51] 1
`[51] 2
`[51] 3
`[45]
`[52]
`[53]
`
`Li et al., 2010
`Li et al., 2010
`Li et al., 2010
`Rylko et al., 2010
`Rylko et al., 2010
`Fukunaga et al., 1990
`Fukunaga et al., 1990
`Yanai et al., 2008
`Long et al., 2008
`Rylko et al., 2009
`Fukunaga et al., 2002
`Yoshida et al., 2000
`Yoshida et al., 2000
`Endo et al., 2000
`Endo et al., 2000
`Endo et al., 2000
`Yoshizawa et al., 2003
`Kolano-Burian et al., 2008
`Martis and Rogers, 1994
`
`MnZn ferrocube 3F51
`NiZn ferrocube 4F1
`Cool Mu
`METGLAS 2605SA1
`JFE 10JNHF600
`FINEMET FT-1M cut core
`Ferrite TDK H3ST cut core
`Stress annealed FINEMET
`Cut core FeCo HTX-002
`MPP 26 powder
`Stress annealed FINEMET
`Amorphous Fe70Al5Ga2P9:65C5:75B4:6Si3 powder
`Mo-permalloy powder
`Mn-Zn ferrite
`ðFe0:97Cr0:03Þ76ðSi0:5B0:5Þ22C2 amorphous powder
`Sendust
`Field annealed Fe8:8Co70Cu0:6Nb2:6Si9B9 nanocomposite
`Field annealed Fe14:7Co58:8Cu1Nb3Si13:5B9 nanocomposite
`METGLAS 2705M
`
`Ex.1024 / IPR2022-00117 / Page 7 of 10
`APPLE INC. v. SCRAMOGE TECHNOLOGY, LTD.
`
`

`

`200 kHz. A 25-kW converter with a FeCo nanocom-
`posite core was 39% lighter than a Finemet-based
`design.47 Inoue shows a 6% efficiency improvement
`for a Finemet core compared with a previous ferrite
`design and predicts improved efficiencies with SiC
`switching.48
`
`FUTURE PROCESSING OPPORTUNITIES
`
`Low resistivities of electrical steels and thermal
`conductivity of ferrites limit their high-frequency
`power applications. Of the various bulk materials,
`amorphous alloys and nanocrystalline/amorphous
`nanocomposites are best suited for high-frequency
`and high-power applications because of the combi-
`nation of high resistivity, saturation induction, and
`thermal conductivity. Nanocomposites can be engi-
`neered with distinct advantages over amorphous
`alloys in terms of high-temperature stability making
`them superior candidates for long-term operation.
`The high Curie temperature of the amorphous phase
`in FeCo compositions54,55 allows for reduced cooling
`requirements and expands the allowable design
`space from Fig. 5. Conde et al.56,57 explore composi-
`tion modifications to FeCo nanocomposites to opti-
`mize microstructures. Processing considerations for
`nanocomposites are focused primarily on achieving
`thin and consistent ribbon cross sections through
`melt spinning or planar flow casting techniques as
`discussed in Ref. 58. Thin, high-quality ribbons al-
`low for a reduction in eddy current losses and an
`improved packing factor that will enable designers
`to take advantage of the higher induction levels in
`these materials and reduce component size. Two
`additional areas where high-frequency losses and
`the power ratio of Eq. 10 can be improved for nano-
`composite materials involve tuning permeability
`through advanced thermomechanical or thermomag-
`netic processing techniques and increasing resistivity
`through careful alloy selection.
`Because of the important role of the permeability
`in optimizing the performance of a magnetic core, a
`number of processing techniques has been devised
`to control the permeability for a given magnetic
`material. Adjustments to the annealing conditions
`produce hysteresis loops with constant permeability
`as a function of applied field up to core saturation.
`The two typical methods are magnetic field pro-
`cessing, where an external field is applied in either
`a parallel or circumferential direction with respect
`to the core axis, and stress annealing in which the
`sample is placed under tension during crystalliza-
`tion. In both cases, a controlled anisotropy induces
`permeability changes while maintaining random
`anisotropy and low coercivity. Induced anisotropy
`transverse to the field direction restricts domain
`wall movement and promotes low-loss rotational
`magnetization changes. For high-frequency and high-
`power applications, transverse induced anisotropy
`is desirable for minimizing anomalous eddy current
`losses and increasing the maximum stored energy.
`
`Leary, Ohodnicki, and McHenry
`
`Stress-induced anisotropy presents a promising
`method to tune anisotropy59 by magnetoelastic
`effects. However, while hardness is improved in
`Fe-based nanocomposite materials,60
`they can
`become brittle after crystallization. Co-based com-
`positions show improved mechanical properties61
`and large responses to transverse field anneal-
`ing,62,63 but the cost of Co may preclude widespread
`use. It is important to point out, however, that high-
`frequency power converters require significantly
`less material and may justify the use of more
`expensive compositions and processing techniques.
`The stress annealed materials in Fig. 8 illustrate
`the advantages of low permeability, but permeabil-
`ities <100 are not practical due to winding consid-
`erations. Research that focuses on mechanisms to
`limit eddy current losses presents the greatest
`opportunity to improve material performance.
`Resistivity and thermal conductivity are related to
`the atomic structure and in amorphous materials
`the disorder leads to increased electron scattering
`and increases resistivity. Composition adjustments
`to nanocomposite materials can further effect resistiv-
`ity by impacting grain size.64 Very high resistivities
`are correlated with decreased thermal conductivities
`that limit ferrite materials from use in high-power
`applications. This thermal conductivity limitation
`may also apply to nanogranular-based material
`approaches where an insulating oxide phase is
`continuous.19
`The kinetics of nanocrystallization and the
`sequence of crystallization events impact the prop-
`erties of nanocomposite materials.65 Recent work
`has demonstrated that large isotropic pressures on
`the order of 1 GPa can have a pronounced impact on
`the kinetics of crystallization from amorphous pre-
`cursors. In some cases, a large applied pressure
`enhances crystallization kinetics,66,67,68 while in
`other cases, it tends to inhibit crystallization.69,70
`Crystallization at elevated pressures is relevant for
`compaction to form bulk parts of arbitrary shape
`from rapidly solidified ribbons of amorphous metals.
`As a result, most fundamental investigations of the
`effects of large isotropic pressure on crystallization
`have focused on Al-based compositions with attrac-
`tive mechanical properties. In Ref. 68, the effects of
`applied pressure on crystallization were described
`by using the specific nucleation work (W) shown in
`Eq. 12, which is the sum of the activation e