*3.4. DC-DC Boost Converter Equivalent Circuit*

The equivalent circuit of the DC-DC converter is shown in Figure 5. At the initial stage Switch, sw1 and sw2 are in closed and open positions, respectively, and the inductor current (IL) will be raised from zero. Consequently, switch sw1 and sw2 are in open and closed positions respectively; at that time, the inductor current will supply the load, and the charges will be stored in the capacitor. The voltage in proportion to the duty cycle of the input and output of a DC-DC converter is depicted in this equation.

$$\frac{V\_O'}{V\_{IN}'} = \frac{1}{1 - d\_{DITT}'} \tag{4}$$

$$\frac{V\_O'}{V\_{IN}'} = \frac{T\_{RISE}'}{T\_{FALL}'} + 1\tag{5}$$

$$d\_{DITT}^{\prime} = \frac{T\_{RISE}^{\prime}}{T\_{RISE}^{\prime} + T\_{FALL}^{\prime}} \tag{6}$$

where, *d DUTY* = duty cycle, *T RISE* = switch sw1 is in closed at the moment of raising the inductor current, *T FALL*= switch sw1 is open at the moment when the inductor current is falling.

**Figure 5.** DC-DC boost converter equivalent circuit.
