A $100-$V switch$-$mode power supply contains two power semiconductor devices:

$-$ A MOSFET switch, which diasipates $1\mathrm{.}0$ W $.$

$-$ A diode, which desipaces $20$ W $.$

Both are in TO$220$ packages, which have Junction$-$Case thermal resistance $0$fc $\backslash (=3^\{\backslash$circ$\}\backslash$mathrm$\{$CW$\}^\{-1\}\backslash )$ and Case$-$Ambience thermal reziatance $\backslash (\backslash$theta $\backslash$mathrm$\{$ca$\}=60^\{2\}\backslash$mathrm$\{$CW$\}^\{-1\}\backslash ).$ The temperature of their junctions should not exceed $\backslash (125^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and the ambient temperature is $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Civen this and a $10-$Q load application current is shown in the below Fiqure.

a$)$ If used without a heatsink, what is the total thermal resistance fromjunction to ambient? $[$Please state the value in $\backslash (\{\}^\{2\}\backslash$mathrm$\{$CW$\}^\{1\}\backslash )][[2$ marked$]$

b$)$ What temperature difference muat not be eaceeded between the junction and ambient? $[$Please state the volue in $\backslash (\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )][2$ marks$]$

c$)$ For the MOSFET, what would be the temperature at the junction?$\text{'}[$Please state the value in $"$C$][2$ marks$]$

d$)$ What would be the junction temperature of the diode? $[$Please atabe the value in $\backslash (\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )][2$ marke$]$

e$)$ Calculate the switching duty cycle D of the MOSFET. $[2$ marks$]$ marke$]$

g$)$ Calculate the RMS value of the current: $[$Please atate the value in A$.][2$ marks$]$

h$)$ Calculate the average power consumption of the load. $[$Please state the value in W$][2$ marke$]$

i$)$ Calculate the average conduction loas of the MOSFET, taking the channel resiatance to be $\backslash ($ R$\_\{\backslash$text $\{$bs $\}|$o n$|\}=50\backslash$mathrm$\{$~m$\}\backslash$Omega $\backslash ).[$Please state the value in W$][2$ marks$]$

j$)$ Calculate the average switching loss of the MOSFET, taling both the switching$-$on and switching$-$off times to be $25$ ns and $30$ ns $,$ respectively. $[$Please state the value in W$],[2$ marke$]$

k$)$ Calculate the total power switching loas of the same MOSFET. $[$Please stabe the value in W$.][2$marks$]$