*4.2. Time-Domain Approximation Models*

For the time-domain model, the loss separation method is used in the frequency domain, using Fast Fourier Transform (FFT) [13].

Time-domain approximation (TDA) can be used for sinusoidal and non-sinusoidal magnetic flux density; however, it is only valid for linear systems [98]. The losses are calculated considering each frequency, separately, and adding them later [85,98].

$$P\_{\mathcal{L}} = \sum\_{n=1}^{\infty} \pi(fn) B\_n H\_n \sin \phi\_n. \tag{7}$$

According to Equation (7), time-domain approximation is a function of the fundamental frequency *f* , the peak values of the *n*th harmonic of the magnetic field *H* and magnetic flux density *B*, and *φ<sup>n</sup>* the angle between *B<sup>n</sup>* and *Hn*.

When a pulse width modulation (PWM) is induced in a magnetic component made with non-linear material, a non-sinusoidal ripple is generated [93]. Fourier's core loss decomposition accuracy is not acceptable for non-sinusoidal flux densities and it is limited for frequencies > 400 Hz, as it was reported in [99].
