## 3 Mathematical Modelling of Multi-Output Forward Converter with Weighted Control
\[\text{I}_{\text{C(n)}}^{\text{rms}}=\frac{\text{I}_{\text{o(n)}}\text{K}_{ \text{RF}}}{\sqrt{3}} \tag{18}\]  
\[\text{\Delta V}_{\text{o(n)}}=\frac{\text{I}_{\text{o(n)}}\text{K}_{\text{RF} }}{4\text{C}_{\text{o(n)}}\text{f}_{\text{s}}}+2\text{K}_{\text{RF}}\text{I}_ {\text{o(n)}}\text{R}_{\text{c(n)}} \tag{19}\] \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameters** & **Diameter** & **Parallel** & **Irms (A)** & **A/mm\({}^{2}\)** & **Turn** \\ \hline Winding for L1 & 0.445 mm & 5 & 1 & 1.23 & 24 \\ Winding for L2 & 0.445 mm & 10 & 2 & 1.23 & 19.5 \\ Winding for L3 & 0.445 mm & 10 & 2 & 1.23 & 6 \\ \hline \end{tabular}
\end{table} 
Table 2: Diameter for each transformer winding based on the rms current for output inductances (second transformer). \begin{table}
\begin{tabular}{c c c} \hline
**Parameters** & **Reverse Voltage (V)** & **Rms Current (A)** \\ \hline Vcc Diode & 31 & 0.1 \\ First Output Diode & 43 & 0.67 \\ Second Output Diode & 35 & 1.34 \\ Third Output Diode & 11 & 1.34 \\ \hline \end{tabular}
\end{table} 
Table 3: Reverse voltage and rms current for diode selection. where Rc(n) is the effective series resistance (ESR) for n-th output capacitor, and Co(n) is the capacitance of the n-th output capacitor. The ripple voltages and current ripples for the output capacitors are given in Table 4. The electrolytic capacitors' ESRs are around 40 m\(\Omega\). In some cases, it is impossible to meet the voltage ripple with a single output capacitor, because of the high ESR of the electrolytic capacitors. Thus, an additional LC filter (post-filter) can be utilized. If using this LC filter, for the stability of the circuit, the corner frequency of the filter should be between 1/5 and 1/10 of the switching frequency. SRP6050 CA-1R2M model inductances have been used as the output inductances in the filter design for the 12 V and 15 V outputs. The filter output capacitors have been selected as electrolyte 330 uF/25 V capacitors for the 12 V and 15 V outputs. By using these values in the design, we have already equalized a very small voltage ripple to a value so low that it cannot be taken into consideration. We can mention that the output voltages are full dc voltages, which are completely non-ripple. The first key power stage parameters of the forward converter with a weighted control are given in Table 5.  
An FS7M0880 integrated circuit has been used in the design, and it has its own control design. In addition, it contains a power MOSFET. Furthermore, it is a control IC that is compatible with the existing forward converter, which has features such as overload protection, over-voltage protection (OVP) and over-current protection (OCP). After determining the power stage parameters of the forward converter with weighted control, it is necessary to design a suitable output that can control the power stage. Figure 4 shows a multi-output forward converter closed-loop control system. A voltage divider, compensator and optocoupler constitute the main structure of the circuit, which is called output-to-control. The remaining structure is regarded as the power stage, or control-to-output. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Esr (m\(\Omega\))** & **Current Ripple (A)** & **Voltage Ripple (V)** \\ \hline First Output Capacitor & 40 & 0.1 & 0.01 \\ Second Output Capacitor & 40 & 0.1 & 0.02 \\ Third Output Capacitor & 40 & 0.1 & 0.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Ripple voltages and current ripples for output capacitors.