The design of a linear ac inductor depends upon five related factors:
1 . Desired inductance
2. Applied voltage, (across inductor)
4. Operating Flux density
5. Temperature Rise
With these requirements established, the designer must determine the maximum values for, Bac, which will not produce magnetic saturation, and make trade-offs that will yield the highest inductance for a given volume. The core material selected determines the maximum flux density that can be tolerated for a given design.
The ac inductor, must support the applied voltage, Vac. The number of turns is calculated from Faraday's Law, which states:
The inductance of an iron-core inductor, with an air gap, may be expressed as:
Inductance is seen to be inversely dependent on the effective Magnetic Path Length, MPL, which is the sum of the air gap length, lg, and the ratio of the Magnetic Path Length, MPL, to material permeability, um.
When the core air gap, lg, is larger compared to the ratio, MPL/iim, because of the high material permeability, um, variations in, |tim, do not substantially affect the total effective Magnetic Path Length, MPL, or the inductance, L. The inductance equation then reduces to:
AC Inductor Design Example
Step No. 1 Design a linear ac inductor with the following specifications.
1. Applied voltage, VL = 120 volts
2. Line current, IL = 1.0 amps
3. Line frequency = 60 hertz.
4. Current density, J = 300 amp/cm2
5. Efficiency goal, μ(100) = 90%
6. Magnetic material = Silicon
7. Magnetic material permeability, μm = 1500
8. Flux density, Bac = 1.4 tesla
9. Window utilization, Ku = 0.4
10. Waveform factor, Kf = 4.44
11. Temperature rise goal, Tr = 50°C
Step No. 2 Calculate the apparent power, Pt or VA of the inductor, L.
Step No. 3 Calculate the area product, Ap.
Step No. 4 Select an suitable core frame ( e.g. EI lamination). The closest lamination to the calculated area product, Ap, is the El-100 with following charcteristics.
1. Core Number = EI-100
2. Magnetic Path Length, MPL = 15.2 cm
3. Core Weight, Wtfe = 676 grams
4. Mean Length Turn, MLT = 14.8 cm
5. Iron Area, Ac = 6.13 cm2
6. Window Area, Wa = 4.84 cm2
7. Area Product, Ap = 29.7 cm4
8. Core Geometry, Kg = 4.93 cm5
9. Surface Area, A, = 213 cm2
10. Winding length, G = 3.81 cm
11. Lamination tongue, E = 2.54 cm
Step No. 5 Calculate the number of inductor turns, NL.
1. Ruben, L., and Stephens, D. Gap Loss in Current-Limiting Transformer. Electromechanical Design,
April 1973, pp. 24-126.