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\begin{array}{l}i_{L}=i_{c}+i_{0} \\i_{c}=i_{L}-i_{0} \\\left(i_{c}\right)_{\text {AVg }}=0\end{array}v_{c}=\theta_{0}^{1}v_{c}=\frac{1}{c} \int j_{t} d tl linearParababa\begin{array}{l}\begin{array}{c}T_{O N} \\\left.c \Delta \psi \quad \Delta V_{C}=\Delta Q / c\right)= \\\Delta V_{C}=\frac{\Delta I_{L}}{8 f C} \quad\end{array} \\\begin{array}{l}A C-\text { Componen } \\\Delta I_{L}=\Delta \tilde{I}_{C}\end{array} \\\Delta L_{L}=\Delta I_{C} \\\end{array}\begin{array}{c}\rightarrow i_{L} \supset_{>C \text { - component }}-(i q)_{\text {Avg }}: I_{L} \approx I_{0} \\\Delta I_{L}=\Delta I_{C}\end{array}\begin{array}{l}\rightarrow t \\\left.=\frac{1}{2} \frac{1}{2} \times \frac{\Delta \pi}{2}\right\} \\x_{c}=\frac{1}{2} c \\x c-\operatorname{comp}=x_{c}^{T}=\infty \\A c-\text { comp }=x_{c}=0 \\(\text { high foq } \\\text { for low freq } \\x \neq 0\end{array}for low forq.\therefore x_{c} \neq 0Ac-com flows to loadboukdany \left(I_{L B}\right)=\frac{\Delta I_{L}}{2}=I_{0 B-1}(0 / p curoht at the Boundary)\alpha \approx \alpha   \begin{array}{l}I_{M X}=I_{L(A \cup g)}+\frac{\Delta I_{L}}{2} \\I_{M X}=I_{0}+\frac{\Delta I_{L}}{2} \\I_{M n}=I_{L(A v g)}-\frac{\Delta I_{L}}{2} \\I_{M n}=I_{0}-\frac{\Delta I_{L}}{2}\end{array}\rightarrow continugus conduction:Mode -1: 0 \leqslant t \leqslant T_{0} \cap\begin{array}{l}\mathrm{CH}-\mathrm{ON} \\\text { VUL }:-V_{S}+V_{L}+V_{O}=0 \\\int_{d}^{I_{N X}}=\frac{v_{S}-v_{0}}{L} \int_{0}^{T_{0} n} d t \\v_{L}=V_{S}-V_{0} \\L \frac{d_{c}^{-}}{d t}=v_{S}-\psi^{\prime} \\\Delta I_{L}=\frac{V_{s}-v_{0}}{L} T_{0 R} \\v_{0}=\alpha v_{S} \\\Delta I_{L}=\frac{v_{s}(1-\alpha)_{\alpha} \alpha}{\nu f} \\T_{0 r}=d T=\frac{\alpha}{f} \\\end{array}nople of capof \longleftrightarrow\left(\Delta \hat{S}_{L}\right)_{\operatorname{Max}}=\frac{V_{S}}{4 f L} \rightarrow a t \quad \alpha=0.5 Hit like if you are happy with this. Instead of hitting dislike, it's better to ask the requirements or doubts. Please comment below if you have any queries regarding this. Have a great day.   ...