Question $1$

$($i$)$ A power electronics converter is required for a smartphone charger application to charge the battery from the rectified AC mains supply. The charger must supply an output of power of $15$ W at $5$ V $.$

$-$ What type of converter could be used for this application?

$-$ Give reasons for your choice with reference to the main design $[15\backslash \%]$ considerations for this application.

$($ii$)$ A diode data sheet specifies that for a rate of fall of diode current, $\backslash ($ d i $/$ d t$=200\backslash$mathrm$\{$~A$\}/\backslash$mu $\backslash$mathrm$\{$s$\}\backslash ),$ the associated reverse recovery time is $40$ ns with $\backslash ($ t$\_\{$a$\}=30\backslash$mathrm$\{$~ns$\}\backslash ).$

$-$ Briefly explain what is meant by diode reverse recovery and why it may be a problem in a power electronics converter.

$-$ Calculate the expected value of peak reverse recovery current for the conditions given.

$-$ If the diode is used in a Buck converter with an input voltage of $24$ V $,$ an output voltage of $5$ V $,$ and a switching frequency of $200$ kHz $,$ calculate the losses in the diode due to the reverse recovery current.

$($iii$)$ A Boost converter delivers an output of $12$ V and $2$ A from an input voltage of $5$ V with an efficiency of $\backslash (90\backslash \%\backslash ).$ The converter operates in continuous conduction mode at a switching frequency of $500$ kHz and requires an inductor of value $\backslash (6\backslash$mu $\backslash$mathrm$\{$H$\}\backslash ).$ The inductor must be designed using one of the ferromagnetic cores from Table $1.$

$-$ Choose the best core to use for the inductor and justify your

$[25\backslash \%]$ choice.

Table $1.$

$($iv$)-$ Explain with the aid of a diagram how peak current mode control $[20\backslash \%]$ is implemented in a DC$-$DC converter.

$-$ What advantages does current mode control have compared to $[5\backslash \%]$ voltage mode control?