6.2.4. Converter Gain

The output voltage and the input voltage relationship is found by assuming ˆ *dj* = 0 , *j* = 1, 2, ... , *n*, summing Equations in (99), and substituting (95), (97), (102)–(104) in the added equation.

$$\frac{D\_{eff}}{K} \sum\_{j=1}^{n} \mathfrak{d}\_{cdij} + \frac{V\_{in}}{\mathcal{\mathcal{H}}} \left( \sum\_{j=1}^{n} -\frac{\mathfrak{P} \mathcal{K} \mathcal{R}\_d}{V\_{in}} \hat{\mathfrak{i}}\_{Lj} + \sum\_{j=1}^{n} \frac{\mathfrak{P} b \mathcal{R}\_d D\_{eff}}{a \mathcal{R} V\_{in}} \mathfrak{d}\_{cdij} \right) = \mathrm{s} \mathrm{L} \sum\_{j=1}^{n} \hat{\mathfrak{i}}\_{Lj} + \sum\_{j=1}^{n} \mathfrak{d}\_{outj} \tag{118}$$

$$\frac{D\_{eff}}{K}\mathbf{y}\left(1+\frac{bR\_d}{aR}\right)\mathbf{\hat{o}}\_{in} = (s\mathbf{L}+R\_d)\left(\mathbf{\hat{o}}\_{out}\left(\frac{s\mathbf{R}\mathbf{C}+sbR\_c\mathbf{C}+b}{R\left(1+sR\_c\mathbf{C}\right)}\right)\right) + c\mathbf{\hat{o}}\_{out}\tag{119}$$

Rearranging (119) would result in (120).

$$G\_{v\overline{\chi}} = \frac{\vartheta\_{out}}{\vartheta\_{in}} = \frac{\frac{D\_{eff}}{K}\varphi\left(1 + \frac{bR\_d}{aR}\right)(1 + sR\_c\mathcal{C})}{s^2LC\left(1 + \frac{bR\_c}{R}\right) + s\left(\frac{bL}{R} + R\_d\mathcal{C}\left(1 + \frac{bR\_c}{R}\right) + cR\_c\mathcal{C}\right) + \frac{bR\_d}{R} + c} \tag{120}$$
