2.2.5. Converter Gain

The output voltage and the input voltage relationship is found by assuming ˆ *dj* = 0, *j* = 1, 2, and 3, summing the KVL Equations in (6), and substituting (2), (4), (9)–(11) in the added equation.

$$\frac{D\_{eff}}{K} \left( 1 + \frac{R\_d}{3R} \right) \mathfrak{b}\_{in} = \left( \frac{(sL + R\_d) \left( sRC + 1\right)}{R} + 3 \right) \mathfrak{d}\_{out} \tag{39}$$

Simplifying (39) would result in (40):

$$G\_{\text{v\S}} = \frac{\hat{v}\_{\text{out}}}{\hat{v}\_{\text{in}}} = \frac{\frac{D\_{eff}}{K} \left(1 + \frac{R\_d}{3R}\right)}{s^2 L \mathcal{C} + s \left(\frac{L}{R} + R\_d \mathcal{C}\right) + \frac{R\_d}{R} + 3} \tag{40}$$
