How to Calculate Toroidal Transformers

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A toroidal transformer is a transformer shaped like a doughnut. It has a round iron core with a coil of insulated wire wrapped around it. The iron core with the coil of wire is also called the "winding." Once powered, the winding generates a magnetic field and stores energy. The amount of energy is measured in units of inductance. As with most transformers, toroidal transformers have both a primary and secondary inductive winding, which is used to step down or step up the input voltage applied to the primary winding.

    Determine the number of turns in the primary winding of the transformer. Call this value "N." Refer to the transformer specifications. As an example, assume N is 300 turns.

    Find the radius of the transformer. Refer to transformer specifications. As an example, assume radius is 0.030 meters.

    Calculate the area using the formula A = π * r² where π is 3.1415. Continuing with the example:

    A = 3.1415 * (0.030)(0.030) = 0.0028 square meters

    Calculate the inductance of the primary winding using the formula L = (μ0 * N² * A) / 2 * π * r, where μ0 is the relative permeability of space with a value of 4 * π * 10^-7 T m/A. Continuing with the example:

    μ0 = 4 * π * 10^-7 = 4 * 3.1415 * 10^-7 = 12.56 * 10^-7.

    L = [(12.56 * 10^-7)(300^2)(0.0028)] / [(2)(3.1415)(0.030)] = 0.000316 / 0.188 = 0.00168 henries or 1.68 millihenries.

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