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A toroidal transformer is a doughnut‑shaped device that uses a circular iron core wrapped with insulated wire to store magnetic energy. The core and its windings are referred to as the "winding." When powered, the winding generates a magnetic field whose strength is measured in inductance, expressed in henries (H). Like most transformers, a toroidal transformer contains a primary winding (input) and a secondary winding (output) to step voltage up or down.
Identify the number of turns in the primary winding, denoted as N. This figure is typically listed in the transformer’s datasheet. For example, let’s assume N = 300 turns.
Determine the radius of the toroid, referred to as r. Again, refer to the specification sheet; in this illustration, we’ll use r = 0.030 m.
The area of the core’s cross‑section is calculated with the familiar formula:
A = π × r²
Using π ≈ 3.1415, we get:
A = 3.1415 × (0.030)² = 0.0028 m².
The inductance of the primary winding can be approximated by:
L = (μ₀ × N² × A) / (2 × π × r)
where μ₀ is the permeability of free space, equal to 4π × 10⁻⁷ T·m/A. Calculating μ₀ gives:
μ₀ = 4 × 3.1415 × 10⁻⁷ = 12.566 × 10⁻⁷ T·m/A.
Substituting the known values:
L = [(12.566 × 10⁻⁷) × (300)² × 0.0028] / [2 × 3.1415 × 0.030] = 0.000316 / 0.188 ≈ 0.00168 H, or 1.68 mH.
These calculations follow the standard formulas used by electrical engineers worldwide and provide a reliable estimate of a toroidal transformer’s inductance.
