It is given that $V_d=400V,v_{ac}=340sin(377t)V,L=1mH$ and the switching frequency is $20$ kHz $.$ The converter uses unipolar PWM and is operating with $v_{CA}=-v_{cB}=0\mathrm{.}85sin(377t+3^0)V.$

$($a$)$ Calculate the expression for the CCA value of $i_L(t)$

$($b$)$ Draw the following four instantaneous waveforms over one switching period around $4$ ms $.$ You may neglect the high frequency ripple in the inductor current. Show all relevant information.

$(1)v_{AN}(t),(2)v_{BN}(t),(3)v_{AB}(t)$ and $(4)i_L(t)$N