5.2.5. 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 (71) and substituting (67), (69), and (74) in the added equation.

$$\frac{3D\_{eff}}{K} \left( 1 + \frac{3R\_d}{R} \right) \hat{v}\_{in} = \left( \frac{(sL + R\_d)(sRC + 3)}{R} + 1 \right) \hat{v}\_{out} \tag{92}$$

Simplifying (92) would result in (93):

$$G\_{\rm v\overline{\chi}} = \frac{\hat{v}\_{\rm out}}{\hat{v}\_{\rm in}} = \frac{\frac{3D\_{eff}}{K} \left(1 + \frac{3R\_d}{R}\right)}{s^2 LC + s\left(\frac{3L}{K} + R\_d C\right) + \frac{3R\_d}{R} + 1} \tag{93}$$
