Inductor design/Magnetics introduction

General relations:
μ0 = 4π⋅10^-7
μe = (le⋅μr)/(le+g⋅μr)
AL = (Ae⋅μe⋅μ0)/le
Imax = Φmax⋅N/L
Φmax = Bmax⋅Ae

Special considerations specific to the described application:
μr ≈ μi (Justification: owing to the relatively low flux densities involved).
Bsat ≈ Bmax (Justification: owing to modest ΔI/ΔT transitions inherent to the described application).

Where:

Ae=Core cross-section area (effective) [square meters]
AL=Inductance Factor [Henrys per N^2]
Bmax=Maximum flux density [Teslas]
Bsat=Saturation flux density [Teslas]
g=Reluctance gap length (effective) [Meters]
Imax=Saturation current [Amperes]
L=Inductance [Henrys]
le=Magnetic path length (effective) [Meters]
N=Integral turn count [Turns]
μe=Effective permeability [H/m]
μi=initial permeability [H/m]
μ0='Magnetic Constant' (i.e. permeability of free space) [H/m]
μr=Relative permeability [H/m]
Φmax=Maximum flux [Webers]


-----Requirements-----
The 'decoupling inductor' will be comprised of four series-connected non-interacting devices exhibiting the following parameters:

L≈120μH,
Imax (saturation threshold current) ≥ 18A
Winding resistance ≤ 40mΩ

Hence (Re: Each constituent inductor)
L≥3ouH
Saturation current (Imax) > 18A.
Winding resistance ≤ 10mΩ.

-----Stipulated parameters-----
⇒Core selection = PC-3019-77 (Ferroxcube: 3C8).
Rationale
: Optimal 'balance' of Ae, le, winding accommodation and magnetic properties (Re: material 77); Common NOS/surplus and salvage availability...

/////////////////////////
Data in regard to pc-3019-xx cores:

Ae=136 mm^2 -- [136E-6 m^2]
le=45mm -- [0.045m]

Data in regard to ferrite material 77
μi=2000 [H/m]
Bmax = 460mT -- [0.46T]
ur=2000[H/m]
////////////////////////

⇒Effective reluctance gap length (g) = 500μm (implying gap spacer thickness = 250um ≈ 0.01")
Rationale: Optimal compromise of Bsat, AL; Ready availability of 0.01" PTFE sheet stock.

⇒Winding conductor = 16 AWG solid Cu enameled conductor stock.
Rationale:
Optimal compromise of current handling, winding resistance and space restrictions.

Inasmuch as L=30uH corresponds to a turn-count (N) ≈ 9.6; N = 10 will be used.
Rationale Integral N preferred.

-----Parameters corollary to the above cited stipulations-----
AL=327nH/N^2
Imax=19.1A

//////////
AL Calculation (Exposition):
AL=
(Ae⋅μe⋅μ0)/le =
Ae⋅(le⋅μr/(le+g⋅μr))⋅4π⋅1E-7/le=
Ae⋅μr⋅π/(2.5E6*(g⋅μr+le))=
136E-6[Square Meters]⋅2000[Henry per meter]⋅π/(2.5E6⋅(500e-6[Meters]⋅2000[Henry per meter]+45E-3[meters]))≈
327nH/N^2

Imax calculation (exposition):
Imax=
ΦMax⋅N/L=
Bmax⋅Ae⋅N/L =
460mT⋅136mm^2⋅10/32uH =
460E-3[Tesla]⋅136E-6[Square meters]⋅10[Turns] /32.7 E-6[Henry]
19.1A
//////////

Calculated inductor characteristics following 'adjustments'
L≈32.7μH
Imax≈19.1A
Winding resistance ≈ 6mΩ (449mm [Len] 16AWG solid Cu conductor)



μr≈μi (via application specific approximation)
Bsat≈Bmax (via application specific approximation)

Anticipated FAQs:

Q) Most of the parameters are non-linearly interactive. Where do I begin?:confused:

A) Many find the the process 'intuitive' following assignment of the 'non-discretionary' parameters (i.e. requirements/stipulations based upon design goals, component availability, etc) -- FWIW Some find a 'spread-sheet' implementation of the formulae to be a highly useful aid to 'trade-off' evaluation...
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Q) Why is the recommended device (i.e. a chain of four series-connected pot-core inductors) so large/complicated? I've seen many Royer and Mazilli circuits 'around the web' wherein the choke is implemented via winding a small toroid salvaged from a PC SMPSU?

A) Optimal operation requires that the core is, as much as practical, kept out of saturation secondary to the relatively high DC/PDC currents ### --- You may be surprised at the greatly improved performance attending use of this application appropriate design!:cool:
/////

Q) Even so isn't ≈ 20A current handling capability overkill for a low power Royer test oscillator?

A) Well indeed it is! But then said device will be used in the high-power driver projects as well:cool:
/////

Q) Can I use toroids instead of pot core forms?

A) Inasmuch as toroidal forms are, as a practical matter, 'un-gappable' such are poorly suited to this application.
/////

Q) How about other form styles/magnetic materials?

A) Of commonly available magnetic materials; Ferrite (Mix '77') and Ferrite (Mix 'F') are best suited to this application. As regards forms; 'E-cores' are likewise quite acceptable where space economy is not a significant factor...
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Q) Couldn't I attain twice the Imax capability at the same inductance and resistance....

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