# A Novel Secondary Side Series LCD Forward Converter with High Efficiency and Magnetic Reset
## 1 Introduction
### Analysis of the Working Mode and Energy Transfer Process of the Converter
Phase III [\(t_{2}\)-\(t_{3}\)]: At \(t_{2}\), S was turned off, D\({}_{3}\) was forward biased, and D\({}_{4}\) was reverse biased. The secondary winding \(W_{2}\) delivered the excitation energy to the capacitor \(C_{2}\) and the voltage across \(C_{2}\) increased from zero. D\({}_{1}\) conducted a freewheeling loop for \(L_{1}\) and its current \(i_{L1}\) decreased linearly from the maximum value. \(L_{2}\) was short-circuited due to the conduction of D\({}_{1}\) and D\({}_{3}\), and \(i_{L2}\) continued to remain unchanged until \(i_{L1}\) decreased to be equal to \(i_{L2}\). This mode ended at \(t_{3}\) when \(i_{Lm}\) reached zero and the transformer core was reset. Phase IV [\(t_{3}\)-\(t_{4}\)]: This mode began when the voltage across \(C_{2}\) reached the maximum value, the energy stored in the capacitor \(C_{2}\) was released to W\({}_{2}\) via D\({}_{3}\), and the current \(i_{L1}\) continued to decrease linearly until \(i_{L1}\) decreased to be equal to \(i_{L2}\). Hence, D\({}_{1}\) was turned off at the end of this mode. Phase V [\(t_{4}\)-\(t_{5}\)]: At \(t_{4}\), \(L_{1}\) and \(L_{2}\) were connected in a continuous series to supply energy to the load through D\({}_{3}\), and \(i_{L1}\) and \(i_{L2}\) decreased linearly. At the end of this mode, the currents flowing through inductors \(L_{1}\) and \(L_{2}\) were equal to the current flowing through \(C_{2}\). Phase VI [\(t_{5}\)-\(t_{6}\)]: At \(t_{5}\), D\({}_{3}\) was turned off, the energy stored in capacitor \(C_{2}\) was released to \(L_{1}\), \(L_{2}\), and W\({}_{2}\), and \(i_{L1}\) and \(i_{L2}\) gradually increased. During this mode, if the voltage across \(C_{2}\) equaled the output voltage \(V_{o}\) and the voltage polarity across the secondary side was changed to the positive direction, \(C_{2}\), \(L_{1}\), \(L_{2}\), and W\({}_{2}\) delivered energy to the load simultaneously. At the end of this interval, the voltage stress on the power switch was lower than the input voltage \(V_{i}\); that is, the switch achieved a low-voltage turn-on. Selection and Analysis of the Additional Capacitance Parameters When the Excitation Inductor Works in the DCM  
During the switch-off period, the magnetizing current coupled to the secondary winding charged \(C_{2}\) through \(D_{3}\), and the voltage across \(C_{2}\) increased from zero. Its equivalent circuit is shown in Figure 3.  
Figure 2: Key waveforms of the proposed converter. According to Figure 3, we can obtain the following equation. \[u_{\rm C2}(t)-u_{\rm W2}(t)=0 \tag{1}\]  
The currents flowing through the capacitor \(C_{2}\) and the secondary excitation winding \(W_{2}\) can we written as the following. \[i_{\rm C2}=i_{W2}=C_{2}\frac{du_{\rm C2}(t)}{dt} \tag{2}\]  
The voltage across the secondary side can be obtained from Equation (2). \[u_{W2}(t)=-L_{W2}C_{2}\cdot\frac{d^{2}u_{\rm C2}(t)}{dt^{2}} \tag{3}\]  
Substituting Equation (3) into Equation (1), we can derive the following equation. \[u_{\rm C2}(t)+L_{W2}C_{2}\cdot\frac{d^{2}u_{\rm C2}(t)}{dt^{2}}=0 \tag{4}\]  
At the moment when the switch is turned off, the current flowing through the secondary winding \(W_{2}\) is \(nl_{\rm Lm,max^{\prime}}\) and the voltage across \(C_{2}\) is equal to zero. Therefore, the initial conditions of \(u_{\rm C2}(0)=0\) and \(u_{\rm C2}^{\prime}(0)=nl_{\rm Lm,max^{\prime}}/C_{2}\) can be obtained. According to these initial conditions, we can obtain the following by solving Equation (4). \[u_{\rm C2}(t)=nI_{\rm Lm,max^{\prime}}\sqrt{\frac{L_{W2}}{C_{2}}}\cdot\sin \left(\frac{t}{\sqrt{L_{W2}C_{2}}}\right) \tag{5}\]  
where \(n=N_{1}\):\(N_{2}\) represents the turn ratio of the transformer. By solving Equation (5), the current flowing through \(C_{2}\) can be obtained as follows. \[i_{\rm C2}(t)=nI_{\rm Lm,max^{\prime}}\cos\left(\frac{t}{\sqrt{L_{W2}C_{2}}}\right) \tag{6}\]  
From Equation (6), the time for the excitation current to decreased from the maximum value to zero can be obtained as follows.