Impedance calculation

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Impedance in AC magnetic analysis is a complex coefficient between complex values of current and voltage, V = Z / I. Its real part represents active resistance of the conductor, calculated with the skin effect taken into account. The imaginary part of the impedance is the inductance multiplied by the angular frequency ω (ω = 2πf).

Z = R + iωL

As values of voltage and current in any conductor are easily accessible in the postprocessor, you can determine the impedance by dividing voltage by current using complex arithmetic. Let V and I be peak values of voltage and current, and φ_V and φ_I be phases of those quantities. Then the active resistance could be calculated as

R = (V / I) · cos(φ_V - φ_I)

and the inductance as

L = (V / 2πf·I) · sin(φ_V - φ_I)

To get mutual inductance between two conductors, you can specify nonzero total current in one of them, make the ends of the other open (applying zero total current), and measure the voltage induced in the second conductor by the current in the first one.

Note. As in planar case voltage is applied and measured per unit length, the impedance is also calculated per unit length in z-direction.