## 3 Mathematical Modelling of Multi-Output Forward Converter with Weighted Control
The next stages, respectively, are to determine the wire diameter for each transformer winding based on the rms current, to determine the proper core and the number of turns for the output inductor, to define the wire diameter for each inductor winding based on the rms current, to determine the diode on the secondary side based on the voltage and current ratings, to determine the output capacitor by taking into consideration the voltage and current ripple, to design the reset circuit, and to design the feedback loop, which is essential [33]. Another step is to calculate the wire diameter for each transformer winding based on the rms of the current. This is obtained using Equations (10) and (11). The results are given in \[\mathrm{V_{ds}}^{\mathrm{max}}=\mathrm{V_{DC}}^{\mathrm{max}}\bigg{(}1+\frac{ \mathrm{N_{P}}}{\mathrm{N_{r}}}\bigg{)} \tag{1}\]1  
\[\mathrm{V_{ds}}^{\mathrm{max}}=\mathrm{V_{DC}}^{\mathrm{max}}\bigg{(}1+\frac{ \mathrm{N_{P}}}{\mathrm{N_{r}}}\bigg{)} \tag{1}\]2  
For copper cables longer than 1 m, the current density is typically 5 A/mm\({}^{2}\)[33]. However, the transformer windings were chosen to be less than 2 amperes so that they would not heat up. Additionally, we cannot neglect the skin effect in our copper cable selection. An ETD44 core was selected as the transformer and wrapped with copper wire. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Diameter** & **Parallel** & **I\({}_{\rm rms}\) (A)** & **A/mm\({}^{2}\)** & **Turn** \\ \hline Primary Winding & 0.445 mm & 9 & 1.89 & 1.29 & 22 T \\ Reset Winding & 0.445 mm & 1 & 0.07 & 0.42 & 11 T \\ Vcc Winding & 0.445 mm & 1 & 0.1 & 0.62 & 4 T \\ First Output Winding & 0.445 mm & 4 & 0.67 & 1.03 & 16 T \\ Second Output & 0.445 mm & 8 & 1.34 & 1.03 & 13 T \\ Winding & 0.445 mm & 8 & 1.34 & 1.03 & 4 T \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Diameter for each transformer winding based on the rms current for the first transformer. After this stage, it is necessary to determine the proper core and the number of turns for the output inductor. \[\frac{\text{N}_{\text{s(n)}}}{\text{N}_{\text{s1}}}=\frac{\text{N}_{\text{L(n)}}}{ \text{N}_{\text{L1}}} \tag{12}\]  
\[\text{L}_{1}=\frac{\text{V}_{\text{o1}}(\text{V}_{\text{o1}}+\text{V}_{\text{F1 }})}{2\text{f}_{\text{g}}\text{K}_{\text{RF}}\text{P}_{\text{o}}}\left(1-\text{ D}_{\text{min}}\right) \tag{13}\]  
\[\text{N}_{\text{L1}}^{\text{min}}=\frac{\text{L}_{\text{1}}\text{P}_{\text{O}} (1+\text{K}_{\text{RF}})10^{6}}{2\text{V}_{\text{o1}}\text{B}_{\text{sat}} \text{A}_{\text{e}}} \tag{14}\]  
\[\text{I}_{\text{L(n)}}^{\text{rms}}=\text{I}_{\text{O(n)}}\sqrt{\frac{\left(3+ \text{K}_{\text{RF}}^{2}\right)}{3}} \tag{15}\]  
ETD 44 cores were used in the circuit. The minimum windings that must be wound on the core are calculated as 15.8 turns by using Equations (13) and (14). L1 inductance has been selected as 24 windings. Table 2 was prepared using Equations (12) and (15). For saturation, the maximum magnetic field has been taken to be 0.3 tesla. The cross sectional area of the inductor core is 173 mm\({}^{2}\). Another next step is to determine the diode on the secondary side, based on the voltage and current ratings. The maximum voltage and the rms current of the rectifier diode of the n-th output are calculated as follows:  
\[\text{I}_{\text{D(n)}}^{\text{rms}}=\text{I}_{\text{o(n)}}\sqrt{\left(3+\text{ K}_{\text{RF}}^{2}\right)\frac{\text{D}_{\text{max}}}{3}} \tag{16}\]  
\[\text{V}_{\text{D(n)}}=\text{V}_{\text{DC}}^{\text{max}}\frac{\text{N}_{\text {s(n)}}}{\text{N}_{\text{P}}} \tag{17}\]  
The reverse voltage and rms current of the diodes are given in Table 3.  
Another next step is to determine the output capacitor, taking into consideration the voltage and current ripple.