Question $3$

$($i$)$ Design a Half$-$Bridge converter to meet the following specifications:

$-$ Input voltage is the full wave rectified Irish mains voltage $(230$ V rms $+/-10\backslash \%)$

$-$ Output voltage, $\backslash ($ V$\_\{\backslash$text $\{$out $\}\}=12\backslash$mathrm$\{$~V$\}\backslash )$

$-$ Maximum output current, $\backslash ($ I$\_\{\backslash$text $\{$out $\}\}=20\backslash$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 $2$ A $.$

The design should also:

$-$ Use a switching frequency of $200$ kHz

$-$ Assume an efficiency of $\backslash (85\backslash \%\backslash )$

$-$ Allow for a $\backslash (20\backslash \%\backslash )$ 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 $2$ below is to be used for the half bridge 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 $2$

$($iii$)$ The inductor used for the half$-$bridge converter in part $($i$)$ must be

designed using one of the ferromagnetic cores from Table $3.$ Choose the best core to use for the inductor and justify your choice. Calculate the worst case core loss for the inductor given that the coefficients for the Steinmetz core loss equation are:

$\backslash [$

C$=0\mathrm{.}01,\backslash$alpha$=1\mathrm{.}9,\backslash$beta$=2\mathrm{.}1$

$\backslash ]$

Table $3.$