MIKE'S SIMPLIFIED CHOKE THEORY

The theory is similar to the transformer theory, but a choke only has 1 winding. The turns per volt (TPV) can be calculated in the same way, but the choke has a heavy DC current flowing through it so the core WILL saturate unless the flux density is reduced massively. This is done with a gap.

After the bobbin is wound with wire, the E laminations are inserted all on one side as sort of shown to the right. The I laminations are clamped together and stuck on the end of the E laminations with a gap created by a few sheets of paper. What follows is a discussion of the gap.

THE GAP

Without looking at all the hysteresis curves and permeability curves, suffice it to say that DC current through the core as in a choke or SET output transformer leads quickly to saturation of the core. So an air gap is placed to increase the reluctance. Air has a permeability of 1. The grueling calculations are below.

Reluctance (R) is the magnetic equivalent of electrical resistance. From equation (19) on the Brain Dead Transformer Theory page we can express the reluctance of the core and the reluctance of the gap and they are additive:
(1)   R_c = ℓ_MP/(μ_Rμ_OA_c)
(2)   R_g = g/μ_OA_g            where g = width of gap, μ_R=1 for air
Remembering the ohm's law analogy, total R = R_c + R_g

From (18), and remembering that MMF = NI
NI = Φ(R_g + R_c)
      = Φ[g/(μ_OA_g) + ℓ_MP/(μ_Rμ_OA_c) ]
      = Φ/A *[g/μ_O + ℓ_MP/(μ_Rμ_O)      this assumes A_c=A_g, which is not exactly correct because of fringing.
      = B*[g/μ_O + ℓ_MP/(μ_Rμ_O)      from equation (3)

Divide both sides by ℓ_MP and remember that H = NI/ℓ_MP you get:
H= B * [g/(μ_Oℓ_MP) + 1/(μ_Rμ_O)]

From equation (2) H = B * 1/μ, so......
H = B * 1/μ_EF, where
1/μ_EF = 1/[g/(μ_Oℓ_MP)+ 1/(μ_Rμ_O)]

Things get a little easier for chokes (or transformers) with a gap. A typical μ_Rμ_O for the core may be in the neighborhood of 10,000 while the μ for the gap is 1. For, say, EI66 laminations, a typical gap is .15mm and a typical ℓ_MP is maybe 12cm and A=6.8.
So, from equations (22) and (23),
R_c = 12/(10000*6.8) = 1.77x10^-4
R_g = .15/6.8 = 2.2x10^-3
So the reluctance R_g of the gap is 12 times the reluctance of the core, so is the overwhelming determinant of total reluctance.

EXAMPLE

Assume EI66 lamination with 31mm stack thickness. From chart a=22, so A = 3.1*2.2=6.8cm². The magnetic path length ℓ_MP, as calculated way above is 12.25cm. The core has μ = 10,000 and the gap g = .15mm.
From equation (17):
R_c = ℓ_MP/μA = 12.25/(10000*6.8) = .0001801
R_g = g/A = .15/6.8 = .002206

So R_g is 12X as large as R_c, meaning that the total reluctance is almost entirely determined by the gap, so the quality of the core is much less important in a choke with a gap.