Simplified Mode Design of Micro Inductors 2

You can refer to the design technical conditions for the application of step-down transformers and select: input voltage Uin, output voltage Uo, DC output peak to peak ripple current Idc, r=△ Ipp/Idc, switching frequency ω=2 π f.diode

According to equation (9), the power loss in the winding can be reduced by increasing the conductor height hc. However, this improvement ignores the fact that the conductor has a penetration depth greater than twice. When conducting approximate analysis, hc can choose approximately 1-2 penetration depths. When considering overlooked factors, hc can be optimized more accurately. For the power loss in the magnetic core, the increase in the number of layers N can be almost ignored. Considering manufacturing costs, N should be optimized, assuming a certain number of layers. In this way, the height of the magnetic core can be adjusted to the maximum power density, and an expression can be obtained (for example, for the application of this buck converter)

In the equation, A is the "effective" device region, ρ s and ρ c represent the resistivity of the magnetic core and conductor, D is the duty cycle of the transformer, Kcore is the factor for measuring harmonic losses in the magnetic core, and | a1 |=2sin (D π)/[π 2D (1-D)] is the first Fourier coefficient of the current waveform. The variable Bpk is half of the peak to peak value of the AC magnetic flux density. For the optimal design, the total peak magnetic flux density should be close to (or equal to) the saturation level Bsat. Therefore, Bpk=Bsat/(1+2/r) is chosen, so that Bdc+Bpr=Bsat, and the expression for maximum power density (1) is used as a function of the given coefficients.diode