Homework #$4$ Problem Design a transformer for a forward converter with these specifications: $$ Switching frequency: fs $=100$kHz $$ V$1=$ V$2=$ V$3=30$V $$ The RMS current in each winding is $2\mathrm{.}5$A Assume: $$ Peak flux density: Bmax $=0\mathrm{.}25$T $$ Maximum allowed current density: Jmax $=5$A$/$mm$2$ Window fill factor: kw $=0\mathrm{.}5$ Forward converter factor kconv $=0\mathrm{.}5(=$ duty cycle$)$ Determine: $$ Determine the area product Ap $$ Select an appropriate magnetic core: o Provide its part number o Provide its core area Acore o Provide its window Area: Awindow $$ Calculate the wire cross$-$sectional area $$ Determine the wire gauge $($and its cross$-$sectional area$)$ to use and indicate if you$$re using a single wire for each winding or if you$$re using multiple strands $($in this case, indicate how many strands, wire gauge, cross$-$sectional area$)$ Calculate the number of turns for each winding.