Inductor Impedance

The inductor is a reactive component and its impedance is a complex number. Ideal inductor impedance is purely reactive impedance. The impedance of an inductor increase with frequency as shown below by the impedance formula for an inductor. At low frequencies, the impedance of the inductor is low and its acts similar to a close circuit. At low freqencies, current will flow through the inductor. At high frequencies, the impedance of the inductor is high and its acts similar to an open circuit.

Z_L (\Omega )=\mathrm{j}\omega L

\omega =2\pi f

where :

f is the frequency in Hertz, (Hz)

L is the inductance in Henry, (H)

The j indicates the phase. The voltage across an inductor leads the current by 90°. Figure 1 shows a visual representation of an AC voltage and current at the terminals of an inductor:

Figure 1 : Visual representation of voltage leads in an inductor. Voltage leads current by 90°

In figure 2, we have a Cartesian representation of impedance. In Cartesian form, the impedance is defined as:

Z (\Omega )= R + \mathrm{j}X

The real part (x-axis) of impedance is the resistance (R) and the imaginary part (y-axis) is the reactance (X).

Figure 2 : Cartesian representation of the complex impedance

For an ideal inductor :

R (\Omega )= 0

and

X (\Omega )=\omega L=2\pi f L

Inductor are not ideal component in real-life and the impedance formula above won’t give accurate result since the inductance will vary with current, frequency and temperature. In figure 3, you have the real-life model for an inductor. As you can see in figure 3, the inductor is far from ideal. Some model will also include a resistor in series with the capacitor. Most inductors manufacturer will provide 1 or multiples inductance curves for their inductor. Some manufacturer also provide curves for the DC and AC resistance. The DC and AC resistance will also be affected by the current, frequency and temperature.

Figure 3 : Real model of an inductor
   C = Inter-Winding\ Capacitance\\   R_{ac} = AC\ Resistance\\   R_{dc} = DC\ Resistance\\   L = Ideal\ Inductor\\