4.2.5. Converter Gain

The output voltage and the input voltage relationship is found by assuming ˆ *dj* = 0, *j* = 1, 2, and 3, summing Equations in (46), and substituting (42), (44), and (48) in the added equation.

$$\frac{3D\_{eff}}{K} \left( 1 + \frac{R\_d}{3R} \right) \mathfrak{H}\_{\text{in}} = \left( \frac{(sL + R\_d)(sRC + 1)}{R} + 3 \right) \mathfrak{O}\_{\text{out}} \tag{64}$$

Simplifying (64) would result in (65):

$$G\_{\text{vg}} = \frac{\vartheta\_{\text{out}}}{\vartheta\_{\text{in}}} = \frac{\frac{3D\_{eff}}{K} \left(1 + \frac{R\_d}{3R}\right)}{s^2 LC + s\left(\frac{L}{R} + R\_d C\right) + \frac{R\_d}{R} + 3} \tag{65}$$
