ripple voltage

$$ V_R = \frac{V_P - 2VD_{on}}{2RCf_{in}} \\ f_{in} :\text{input 주파수} \\ V_P : \text{peak 전압} \\ V_{D,on} : \text{diode on 전압} $$

buck converter

$$ V_L = V_i -V_o $$

$$ V_L = -V_o \\ V_L = L\frac{dI_L}{dt} \\ \therefore \Delta I_{t,on} = \int^{t_{on}}{0}\frac{v_L}{L}dt = \frac{V_i-V_o}{L}t{on} \\ \Delta I_{t,off} = \int^{T}{t{on}}\frac{v_L}{L}dt = \frac{-V_o}{L}t_{off} \\ \therefore \Delta I_{t,on} + \Delta I_{t,off}=0 \\ \therefore V_o = DV_i (0 \leq D\leq1) $$

buck boost converter

$$ V_L = V_i $$

$$ V_L = V_o $$

$$ V_L = L\frac{dI_L}{dt} \\ \therefore \Delta I_{t,on} = \int^{t_{on}}{0}\frac{V_L}{L}dt = \frac{V_i}{L}t{on} \\ \Delta I_{t,off} = \int^{T}{t{on}}\frac{V_L}{L}dt = \frac{V_o}{L}t_{off} \\ \therefore \Delta I_{t,on} + \Delta I_{t,off}=0 \\ \therefore V_o = -V_iD/(1-D) (0 \leq D\leq1) $$