**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:

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...

Rationale

**/////////////////////////**

Data in regard to pc-3019-xx cores:

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.

Rationale:

**⇒**Inasmuch as L=30uH corresponds to a turn-count (N) ≈ 9.6;

**N = 10 will be used.**

*Integral N preferred.*

**Rationale****-----Parameters corollary to the above cited stipulations-----**

AL=327nH/N^2

Imax=19.1A

//////////

**AL Calculation (Exposition):**

AL=(Ae⋅μe⋅μ0)/le

AL=

**=**

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=

Imax calculation (exposition):

Imax=

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?

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...

/////

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!

/////

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

/////

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....