*3.1. Energy Transfer Period (0* − *T1)*

The starting values of the magnetizing current, *iLm*, and resonant tank current, *iLs*, are identical. The currents have distinct wave patterns and deviate because the series resonant capacitor, *C<sup>s</sup>* , and inductor, *L<sup>s</sup>* , are in resonance, and the magnetizing inductor is restrained to the output voltage. The magnetizing current, *iLm*, increases linearly when the clamped output voltage (+*Vo*)/n is applied. *iLs* starts out with a negative value, crosses the zero line, and then equals *iLm* at time *t*1. According to KCL, the output rectifier is responsible for

supplying any leftover current to the load. This period lasts until *t*<sup>1</sup> = *t<sup>d</sup> Tsw*/2, where *t<sup>d</sup>* is the diode to switch conduction ratio. The differential equations that represent this mode are as follows:

$$V\_i - \frac{V\_0}{n} = L\_s \frac{di\_{Ls}(t)}{dt} + v\_{Cs}(t) \tag{7}$$

$$\dot{\mathbf{u}}\_{Ls}(t) = \mathbf{C}\_s \frac{dv\_{\rm Cs}(t)}{dt} \tag{8}$$

$$i\_{Lm}(t) = \frac{1}{L\_m} \int\_0^t \frac{V\_0}{n} dt + i\_{Lm}(0) \tag{9}$$

Solving (7)–(9),

$$\dot{i}\_{\rm Ls}(t) = \dot{i}\_{\rm Ls}(0)\cos(\omega\_{\rm r}t) + \left[\frac{V\_i - \frac{V\_0}{n} - v\_{\rm Cs}(0)}{Z\_0}\right]\sin(\omega\_{\rm r}t) \tag{10}$$

$$i\_{Lm}(t) = \frac{\frac{V\_0}{n}}{L\_m}t + i\_{Lm}(0) \tag{11}$$

$$v\_{\rm Cs}(t) = Z\_0 i\_{\rm LS}(0) \sin(\omega\_r t) + v\_{\rm Cs}(0) \cos(\omega\_r t) + \left[V\_i - \frac{V\_0}{n}\right] \left[1 - \cos(\omega\_r t)\right] \tag{12}$$

$$i\_0(t) = i\_{Ls}(t) - i\_{Lm}(t) \tag{13}$$
