$10$Questions $10-13$ involve the boost converter illustrated below.Schematic of boost converterIn the boost converter above, the diode has forward voltage drop Vd$.$ You may model this voltage drop as independent of current. All other elements should be modeled as ideal. In this problem, you will find how this voltage drop changes the equations of the discontinuous conduction mode of the boost converter. The transistor duty cycle is D$.$Question $10$Derive the conditions under which this converter operates in the discontinuous conduction mode. Express your result in the form K $<$ Kcrit with K $=2$L$/($RTs$).$ Kcrit is a function of D$,$ Vd$,$ and Vg$.$ Enter your expression for Kcrit.: $[$object Object$]111.11$Derivation of inductor volt$-$second balance equation: write the equation of the average inductor voltage in DCM$.$ Your expression should be written in terms of the input voltage Vg$,$ output voltage V$,$ diode forward voltage drop Vd$,$ interval $1$ duty cycle D$1,$ and interval $2$ duty cycle D$2.$ : $[$object Object$]112.12$Derivation of capacitor charge balance equation: write the equation of the average capacitor current in DCM$.$ Your expression should be written in terms of the input voltage Vg$,$ output voltage V$,$ inductance L$,$ load resistance R$,$ interval $1$ duty cycle D$1,$ interval $2$ duty cycle D$2,$ and switching period Ts$.$: $[$object Object$]113.13$Solve your equations to derive an expression for the voltage conversion ratio V$/$Vg in DCM$.$ Your result will involve a quadratic expression. You are given the following values:Vg $=12$Vd $=1$D $=0\mathrm{.}4$K $=0\mathrm{.}075$Compute the output voltage V$,$ and enter your value below.: $[$object Object$]1$