Question $3$

$($i$)$ Design a Forward converter to meet the following specifications:Input voltage, $\backslash ($ V$\_\{\backslash$text $\{$in $\}\}=50\backslash$mathrm$\{$~V$\}+/-10\backslash$mathrm$\{$~V$\}\backslash )$Output voltage, $\backslash ($ V$\_\{\backslash$text $\{$out $\}\}=12\backslash$mathrm$\{$~V$\}\backslash )$Maximum output current, $\backslash ($ l$\_\{\backslash$text $\{$out $\}\}=10\backslash$mathrm$\{$~A$\}\backslash )$Maximum output voltage ripple

The design should ensure that the converter remains in continuous conduction mode $($CCM$)$ for output currents greater than $0\mathrm{.}5$ A $.$

The design should also:Use a switching frequency of $500$ kHzAssume an efficiency of $\backslash (90\backslash \%\backslash )$Allow for a $20\backslash \%$ tolerance on the inductor and capacitor values

Comment on all of your design steps and on all of the design choices and assumptions made.

$($ii$)$ A MOSFET with the parameters given in Table $3$ below is to be used for the Forward converter. The MOSFETs will be driven by a gate source voltage of $10$ V $.$

$-$ Calculate all of the losses associated with the MOSFETs when

used in the Forward converter at nominal input voltage and full load.

Table $3$

$($iii$)$ An important application of the Boost converter is in active power factor correction $($PFC$).$

$-$ Describe briefly, with the aid of diagrams, why there is a need for power factor correction in equipment supplied by the rectified

mains voltage.

$-$ Describe how the Boost converter is used to achieve active

power factor correction.