2.?Method Based on the Volterra SeriesMOSFETs are widely used in electric systems as ideal on-off switches, but some fail to take into account their actual equivalent circuit, which is shown in Figure 1. It has energy storage element distributed parameters such as inductor, capacitor, Seliciclib and resistance Inhibitors,Modulators,Libraries (i.e., CGE, CGE, LC, LE, RG, etc.), which have inherent nonlinear Inhibitors,Modulators,Libraries characteristics.Figure 1.The actual equivalent circuit of a MOSFET.From the topology structure of SMPS, which is represented in Figure 2, the MOSFET driven by PWM is a complex memory function and nonlinear dynamic system. Due to aging, environmental impacts and dynamic loading, the MOSFET will degrade over time. The failure mechanisms of MOSFETs include intrinsic mechanisms and transistor packaging.

Dielectric breakdowns, electro- migration, bond-wire lift, die-solder degradation and contacts can cause the failure of MOSFETs. All the failures lead to changes in their inherent characteristics. However, Inhibitors,Modulators,Libraries the distributed parameters are difficult to measure directly. All the above parameters changes can be equivalent to the change of the internal R, L, C. According to the system theory, given the constant input signal, the output signal will change when the system itself changes. When internal parameters are changing, the response signal will change too.Figure 2.The SMPS topology structure.Based on the nonlinear theory, the output signal y(t) is expressed by:y(t)=��n=0��yn(t)(1)in whichyn(t)=��?�ޡ�?��?�ޡ�hn(��1,��2,?,��n)��i=1nu(t?��i)d��i(2)where yn(t) is time domain response, u(t ? ��i) is input signal, and hn(��1, ��2, , ��n) are the Volterra kernel.

The hn(��1, ��2, , ��n) can be expressed by a multidimensional Fourier transform as follows:Hn(��1,��2,?,��n)=��?�ޡ�?��?�ޡ�hn(��1,��2,?,��n)exp??j(��1,��2,?,��n)?d��1d��2?d��n(3)where Hn(��1, ��2, ��n) is generalized frequency response function (GFRF).Given the excitation signal is a square wave signal, it Inhibitors,Modulators,Libraries can be expressed in the following form:u(t)=��i=1K|Ai|cos(��it+��i)=��i=?Ki��0KAi2exp(j��it)(4)Considering Dacomitinib the actual application, we only use the first three frequencies to replace the square wave signal. So, the u(t) can be given as follows:u(t)?|A1|cos(��1t+��1)+|A2|cos(��2t+��2)+|A3|cos(��3t+��3)(5)According to Equations (1), (2) and (5), it is clear that the output frequency depends on the inherent characteristics.

From the theory analysis, thorough we can know that when the health of a MOSFET changes, the output frequency will change accordingly, so the degradation of the MOSFET can be mapped to the changing amplitudes of different frequency. Here, we extract the amplitude of the third order nuclear frequency as the feature parameters for the degradation of the MOSFET.According to the experiments, the relationship between life state (LS) and degradation state can be expressed as follows:{LS=ak��i=1,j=1i=n,j=mBi,jAi,jk=m��ak=1(6)where Ai,j is the normal MOSFET amplitude of i-order nuclear and j-frequency.