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    Inductor Inductivity.md
    Inductivity value
    


      

    • Todo formular
      • 

    • Lower inductivity -> higher ripple -> more loss in other components
      • 

    • Lower inductivity needs faster OC response
      • 

    


    Finding the coil
    


    Designing the coil is a multi-target optimization between size, cost, efficiency.
    


    <![CDATA[]]>TI AN-1197<![CDATA[]]> gives an overview of inductor current waveform
characteristics and how to estimate L for given converter requirements. It covers inductor energy handling capabilities
and power loss.
    


    Micrometals has a
good <![CDATA[]]>primer to inductor design<![CDATA[]]>.
    


    Design Approach
    


      

    • Choose switching frequency


        

      • if space and weight don't matter its good to start low at a 40 kHz
        • 

      • going below 20 kHz increases risk of audible coin whine
        • 

      • higher frequencies increase switching loss. placing another transistor in parallel
usually does not decrease switching loss, since slight production variances will cause one switch to take the full
transient (it always decreases conduction loss)
        • 

      • if you can't find a coil design that fits weight, cost (copper+core) or space constraints: increase switching
frequency
        • 

      • 

    • With input voltage, output voltage and output current requirements and the switching frequency compute the minimum
inductivity for a given ripple current. A good design has a coil ripple current in the range 0.25 - 0.5 at full load.


        

      • Effects of higher ripple current:


          

        • causes higher voltage ripple at the output
          • 

        • increases inductor core loss
          • 

        • emits increased EMI
          • 

        • increases control fet turn-off switching stress
          • 

        • 

      • 

    • With the computed inductivity and current requirement, you can try to find off-the-shelve inductors. if you don't find
any, its time to roll your own. Micrometals has an excellent designer to help you find the core material, core
geometry and winding. <![CDATA[]]>DC guide<![CDATA[]]>


        

      • consider ID window area. for 2 strands the designer appears to estimate the window usage too low, so the wires
would not fit in reality
        • 

      • if you only find inductors too big or too heavy, increase the switching frequency
        • 

      • 

    


    Materials
    


    Material selection is a trade-off between core loss, price and saturation robustness.
Care must be taken about temperature dependency of A_l and core saturation.
    


    


    
  
  micrometals
  KDM
  mag-inc
  

    
    


    
  Sendust
  MS
  KS
  KoolMµ
  

    

    
  Optimized Loss
  OC
  KAH Nanodust
  79
  

    

    
  Optimized Eco
  OE
  KNF Neu Flux
  
  

    

    
  High Flux
  
  
  
  

    
    

    


    MPP: low core loss
high flux: slightly lower loss than sendust. applications with high DC-bias current. limited choices
    




    Sendust
    




    choosing µi
    


    Notice that µi is the initial permeability. Effective permeability might be much lower, depending on DC bias current
(DC magnetization force) and the material's characteristic DC bias curve.
    


      

    • A_L ~ µ so higher µ needs less turns, less copper loss (or smaller core, less space) for same inductivity value
      • 

    • Bpk does not depend on µ
      • 

    • higher µ increases /or decreases Ipp (same core geometry and number of turns)
      • 

    • a core with a smaller µ can have a higher Ldc at high DC bias current
      • 

    • higher µ reduces core loss (although Ipp increases) TODO or increases
      • 

    • higher µ cores saturate earlier
      • 

    • lower Ipp means lower core loss and lower copper loss (P~I2R)
      • 

    • a higher µ usually means lower light-load efficiency (and higher eff at high-load)
      • 

    • a higher µ with same winding does usually not increase Ldc
      • 

    • if you have a core with hight µi and you are not satisfied with the dc bias performance, stack cores
      • 

    • big cores with ⁄
      • 

    


    for an application with Idc=30A, 75V/30V µ <= 125 appears to be a good choice.
    


    Off-the-shelf inductors
    


    many off-the-shelf inductors have flat wire winding for decreased ESR. with optimal copper/air ratio manufactureres
can make coils with different inductance values but the ESR and package size.
despite the heavy price tag, it might be useful to take a look what coils are available on digikey.
this way you can learn about whats physically possible, the data-sheet contain useful information
and might even give a clue about expected core loss.
    


    <![CDATA[]]>https://content.kemet.com/datasheets/KEM_LF0051_SHBC.pdf<![CDATA[]]>
    


      

    • SHBC Series (Fe-Si-Al)
SHBC24N-2R1B0039V 30 39 21.2 6.8 50 2.1 x 2 Parallel 135
SHBC24W-2R1B0065V 30 65 40.7 6.2 50 2.1 x 2 Parallel 217
      • 

    • why does the 65uH parts has a lower ESR?
      • 

    • price100: $12
      • 

    


    


    
  MFR
  MPN
  px100
  L
  DCR
  Isat10/20/30
  DC bias 30A

    
    


    
  würth
  7443763540470
  
  
  
  
  

    

    
  codaca
  CPEX4141L-500MC
  $25
  
  
  ?/?/44A
  90% <![CDATA[]]>https://www.codaca.com/Private/pdf/CPEX4141L.pdf<![CDATA[]]>

    

    
  coilcraft
  AGP4233-223ME
  
  
  
  
  

    

    
  itg
  L201316Q-470MHF
  
  
  
  
  

    

    
  KDM
  KS184125A
  
  
  
  
  <![CDATA[]]>https://www.kdm-mag.com/uploads/file/20200930/1601429594941622.pdf<![CDATA[]]>

    
    

    


    <![CDATA[]]>digikey<![CDATA[]]>
    


    core size vs ripple <![CDATA[]]>https://www.richtek.com/Design%20Support/Technical%20Document/AN009#Ripp...<![CDATA[]]>
img_5.webp
    


    Tools
    


    MicroMetals Inductors 66Vin/27V/33A
    


    Iripple=8.76A
    


    2stacked:
OC-157090-2 <![CDATA[]]>https://www.micrometals.com/design-and-applications/design-tools/inducto...<![CDATA[]]>
    


    Toroid Cores
    


    


    
  
  µ
  Al
  OD
  Height
  
  

    
    


    
  OC-134090-2
  90
  153
  33mm
  18mm
  50µH: 15N,5xAWG#14(d=1.6mm)
  <![CDATA[]]>https://datasheets.micrometals.com/OC-134090-2-DataSheet.pdf<![CDATA[]]>

    

    
  OC-132060-2
  60
  65
  33
  12
  
  <![CDATA[]]>https://datasheets.micrometals.com/OC-132060-2-DataSheet.pdf<![CDATA[]]>

    

    
  Ljf T132-AM-090A GK
  90
  97
  33
  12
  
  <![CDATA[]]>https://www.semic.info/ljf-t132-am-090a-gk-en/<![CDATA[]]>

    

    
  OC-199090-2
  
  
  
  
  
  

    

    
  OC-184125-2
  
  
  
  
  
  

    

    
  OC-184090-2
  90
  184
  
  
  3.4W loss @ 50uH, 30Adc, V=45/30, 50khz
  <![CDATA[]]>https://www.micrometals.com/design-and-applications/design-tools/inducto...<![CDATA[]]>

    

    
  
  
  
  
  
  
  

    
    

    


    MS-250147-2
T184-S-075A BK (MS-184-S-07A)
T184-AH-125A BU
    


    2s MS-184-S-125
    


    <![CDATA[]]>https://www.micrometals.com/design-and-applications/design-tools/inducto...<![CDATA[]]>
    


    T184 Designs
    


    DC-DC operating point: 26Adc, 45/30Von/off, 60khz
    




    2stack T132 Designs
    


      

    • MS-132090-2: 4.6W (1.8 + 2.7W) N=15
      • 

    • MS-132125-2: 4.6W
      • 

    • OC-132090-2: 3.6W (1.1 + 2.5W) N=17
      • 

    • OC-132125-2: 3.7W (1.5+2.2)(KDM: KAH130-125A , 5.5€)
      • 

    


    T134 Designs
    


    26Adc, 45/30Von/off, 60khz
    




    T199
    


    *
    


    MS-199125-2 <![CDATA[]]>https://www.micrometals.com/design-and-applications/design-tools/inducto...<![CDATA[]]>
    


      

    • OC-199090-2, 2.3W
      • 

    


    T250
    




    SP-226090-2H305
1.8W <![CDATA[]]>https://www.micrometals.com/design-and-applications/design-tools/inducto...<![CDATA[]]>
    


    SP-292090-2
1.5W <![CDATA[]]>https://www.micrometals.com/design-and-applications/design-tools/inducto...<![CDATA[]]>
    


    References
    




    Coils
    


    Choosing the inductor is a trade-off between size and power loss. Larger cores have a larger A_L value, requiring
less copper wire (turns) for the same inductivity (note: L = A_L * N^2) and reducing i2r loss.
Core loss is ~ f^a * B^b * Ve  (Steinmetz equation)
(f = frequency, B = peak flux density in gauss, Ve = eff. core volume, a = const. b = const)
    


    with B = Vt/A (V = voltage per turn, t = pulse width, A = core area)
and f = 1 / (2t), V = Vl/n, keeping non-inductor parameters const.:
Pcore ~ Ve/(n*A)^b x
    


    <![CDATA[]]>https://www.cwsbytemark.com/CatalogSheets/MPP%20PDF%20files/13.pdf<![CDATA[]]>
    


    A well designed inductor has a core/copper loss ratio of
20/80 (<![CDATA[]]>micrometals<![CDATA[]]>).
    


    If we design under this assumption, a bigger core is always better, because it reduces copper wire length.
    


    <![CDATA[]]>https://www.mouser.com/pdfDocs/Coilcraft_inductorlosses.pdf<![CDATA[]]>
<![CDATA[]]>https://www.psma.com/sites/default/files/uploads/tech-forums-magnetics/p...<![CDATA[]]>
<![CDATA[]]>https://www.cwsbytemark.com/CatalogSheets/MPP%20PDF%20files/13.pdf<![CDATA[]]>
<![CDATA[]]>https://www.mag-inc.com/design/design-guides/powder-core-loss-calculation<![CDATA[]]>
"Transformer and Inductor Design Handbook"
    


    Higher switching frequency reduces turn-on time, so we can use a smaller inductivity while maintaining an inductor peak
current below core saturation.
    


    For the 30A MPPT application, a switching frequency of 40-60 kHz turns out to be practible.
With higher frequency, switch loss increases, so we would need to decrease switching times, which often requires a very
dense,
integrated design. PCB with more than 2 layers is common. Hardware becomes less maintainable.
And we don't have a tight space and weight requirements. With 40 kHz and the given voltage and current requirements
an inductor with at least 50uH is needed.
    


    Off-the-shelve inductors exists for 30A output current, but mostly with inductivity < 20uH and they are
pricy.
    


    So we opt to build our own induutor.
    


    Inductivity
    


      

    • Choose inductivity L (link TODO)


        

      • lower inductivity, higher ripple current
        • 

      • higher voltage -> steeper current slope -> need higher inductivity
        • 

      • consider max flux density and prevent core saturation
        • 

      • 

    


    Core Geometry
    


      

    • toroids have low stray inductance but a hard to wind.
      • 

    • PQ-Core
      • 

    


    Core Size
    


      

    • Depends on the power needs and switching frequency
      • 

    • The Bigger the better


        

      • reduces flux density and core loss (but higher copper loss)
        • 

      • less thermal issues
        • 

      • but: more expensive, need more space
        • 

      • 

    • toroid sizes that make sense: T130, T184, T225/T226
      • 

    • You can easily stack toroidss
      • 

    


    Geometry
    


      

    • Choose core geometry and size (depends on power needs). Choose core materials.
Sendust aka KoolMu is a good choice. It is an alloy powder, composite of metal and plastic, distributed air gap.
      


        

      • sendust has high saturation current, so T130 works. however, wire diameter is limited because it just doesn't fit
through
        • 

      • smaller cores have smaller A_l value, so need more turns => more copper loss
        • 

      • 

    • Choose wire gauge and strands (consider DC loss and skin effect)
      • 

    • Compute num windings with A_L value and target L
      • 

    • Designers: <![CDATA[]]>micrometals<![CDATA[]]>
      • 

    • The bigger the better (usually)
      • 

    • Wire easier to cool than core. Power loss ratio core/wire:
20/80 <![CDATA[]]>micrometals core design considerations<![CDATA[]]>
      • 

    • Higher initial permeability increases A_L, reduces num windings, moves loss from wire to core
      • 

    • Sendust Toroid 60u - 125u
      • 

    • T184 (OD=1.84in/46.7mm) 125u A_l=281 <![CDATA[]]>https://www.semic-shop.de/ljf-t184-s-125a-bk-de/<![CDATA[]]>
      • 

    • 17-20 turns of 5xAWG15 (1.45mm)
      • 

    • T225 / T226 (OD=2.25in/57.15mm)
      • 

    


    T130
    


      

    • a single T130 with A_l=61 needs a lot of windings
      • 

    • stack 2 cores to reduce windings by 2^.5. for same inductivity
      • 

    • using 2 strands of 1.8mm wire (140cm length each) works
      • 

    • TODO test cores:


        

      • Ljf T130-S-125A BK
        • 

      • Ljf T130-S-075A BK
        • 

      • Ljf T130-NF-125A BR
        • 

      • 

    


    Materials
    


    three opt spots: saturation vs loss vs costs
    


      

    • Sendust (black, power supply, 10,5kGauss)
      • 

    • Super Sendust (PV inverter, 12kGauss
      • 

    • Sendust Plus
      • 

    • Neu FLUX
      • 

    


    Advantages of bigger cores
    


      

    • bigger volume => less magnetic flux density (TODO: replace volume with Ae?)
      • 

    • more surface => better cooling
      • 

    • usually higher A_l => need less windings


        

      • less copper loss due to reduced length and thicker wires
        • 

      • 

    • can fit thicker wires and/or more strands
      • 

    


    disadvantages
    


      

    • more loss, scales proportional to core size (TODO source)
      • 

    • cost, size, weight
      • 

    


    <![CDATA[]]>https://www.micrometals.com/design-and-applications/material-selection-a...<![CDATA[]]>
    


    Coil designs
    


      

    • T184 sendust (u_i=125, A_L=281)
      • 

    • N=17
      • 

    • 5xAWG15 (d=1.45mm) or 3x (d=1.9mm)
      • 

    • 130cm wire length for 17 turns on T184 (17 * 65mm)
      • 

    


    Strands Formular: d_b = (d_a2 * n_a/n_b).5 # d_b = diameter, n_b = num strands
    


    FEMM
    


    60 Khz
    


      

    • MS-184125-2, N17, AWG14, 1stack, 5strands (30A, 45/30V: Ipp=9A, Ploss=3.8W)
      • 

    • MS-184090-2 N22
      • 

    


    Core Suppliers
    




    Soldering Litz wires
    


    


    <![CDATA[]]>https://www.e-magnetica.pl/doku.php/litz_wire<![CDATA[]]>
    


    Specific Cores
    


    


    
  
  Al
  OD
  ID
  HT
  mat
  µi
  Micrometals
  KDM
  Mag-Inc
  
  

    
    


    
  T184
  139 nH
  46.7mm
  
  
  KoolMu Ultra
  60
  
  
  <![CDATA[]]>DK<![CDATA[]]>
  
  

    
    

    


    CSC Winding Table
t184-winding.webp
from <![CDATA[]]>https://mrccomponents.com/images/downloads_csc/pdf/OD467.pdf<![CDATA[]]>
    


    CSC Shapes
<![CDATA[]]>https://mrccomponents.com/en/products/material-core-materials-csc/toroid...<![CDATA[]]>
    


    Wire
    


    To eliminate (reduce) ac resistance loss, choose a copper wire with d=1.2mm and multiple strands.
This decreases the resistance rise due to skin and proximity effects. It is also easier to wind than a thick 2.5mm
single
strand coils.
    


    Make sure the copper you buy is made for electrical coils or motors. This is commonly referred as W210 (Grade 2),
DIN EN 60317-13, V180 or IEC 60317-51  and has a typical conductivity of 58.5 MS/m.
Another commonly traded copper wire material is CW024A, 2.0090, C12200, Cu-DHP or C106.
This copper is intended for use with low demands on electrical conductivity, e.g. water/gas pipes. Expect this to
have an increased resistivity by 28% as compared to the W210 copper.
    


    Core Material
    


    Chose sendust with initial permeability 60µ, 75µ, 90µ or 125µ.
Materials with higher permeability tend to suffer from increased dc bias saturation (i.e. inductivity drop) and
increased light-load loss. Use micrometals designer to find the right core for a given load condition.
    


    <![CDATA[]]>Overview<![CDATA[]]>
<![CDATA[]]>http://shindokogyo.com/products/toroidalCore<![CDATA[]]>
<![CDATA[]]>https://www.cwsbytemark.com/mfg/sendust.php<![CDATA[]]>
<![CDATA[]]>https://mhw-intl.com/products/magnetics/csc-powder-cores/<![CDATA[]]>
    


    


    
  
  apps
  Alloy
  Bsat/Gs
  loss
  µi
  Micrometals
  KDM
  mag-inc
  
  

    
    


    
  Sendust  Cost eff. low loss
  
  Fe-Si-Al
  10000
  1
  25~125
  MS (14~160µi)
  <![CDATA[]]>KS<![CDATA[]]>
  KoolMµ
  
  

    

    
  Fe-Si, Mega Fluximproved DC bias perf.
  buck/boost, solar, high-end
  Fe-Si
  16000
  
  14~90
  FS FluxScan
  <![CDATA[]]>KSF<![CDATA[]]>
  78 Series XFLUX (X)
  
  

    

    
  High Fluxbest DC bias perf.
  
  Fe-Ni
  15000
  <1
  
  HF, GX
  KH
  58 Series High Flux (H)
  
  

    

    
  Neu Flux, Optimized EconomyLowest Cost, half loss than Fe-Si. Cheap replacement for High Flux
  
  
  16000
  ~.5
  26~xx90
  OE
  KNF
  
  
  

    

    
  Nanodust, SenMaxaudibly quiet, MHz operation
  
  
  13000
  
  
  SM
  KAM
  
  
  

    

    
  Nanodust
  
  
  
  
  
  OC
  KAH
  
  
  

    

    
  MPP  lowest loss, highest temp. stability
  high Q, aero, mil, med, high temp
  Ni-Fe-Mo
  8000
  
  26~550
  
  
  
  
  

    
    

    


    Core Shape
    


    Toroids have least leakage flux and are good choice.
Use two stacked T132 cores (1 core is only suitable for power below ~400W).
    


    


    
  T184
  OD
  ID
  HT
  A_e
  l_e
  Wa
  V
  CSC
  
  
  

    
    


    
  T184
  46.7mm
  24.1mm
  18mm
  1.99cm2
  10.7cm
  4.27cm2
  21.4cm3
  <![CDATA[]]>OD467<![CDATA[]]>
  
  
  

    

    
  
  
  
  
  
  
  
  
  
  
  
  

    
    

    


    Use T184 for currents up to 30A. Micrometals: MS-184090-2, KDM: ???.
    


    


    
  Core
  Wire
  Num Strands
  Turns
  L0
  Rdc
  Rac@50kHz
  notesl

    
    


    
  2 stack MS-184125-2
  AWG17 (⌀1.2mm)
  10
  12
  
  
  
  up to 35A

    

    
  MS-184125-2
  
  12 AWG 16?
  10
  
  
  
  

    

    
  MS-184090
  
  40
  15
  
  
  
  

    

    
  2 stack MS-130060-2
  
  20?
  21
  55µH
  
  
  

    
    

    


    Fugu1 T134 20A Inductor
- 25 turns, 3x1.45mm, MS-134075-2
<![CDATA[]]>https://www.micrometals.com/design-and-applications/design-tools/inducto...<![CDATA[]]>
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