$[$C$,$ None, $4\mathrm{.}2]$ Consider the circuit of Figure $6\mathrm{.}11.$ Let $C_x=50fF,M_r$ has $\frac{W}{L}=\frac{0\mathrm{.}375}{0\mathrm{.}375},M_n$ has $\frac{W}{L_{\text{e}\text{f}\text{f}}}=\frac{0\mathrm{.}375}{0\mathrm{.}25}.$ Assume the output inverter doesn't switch until its input equals $\frac{V_{DD}}{2}.$

a$.$ How long will it take $M_n$ to pull down node $x$ from $2\mathrm{.}5$ V to $1\mathrm{.}25$ V if $In$ is at $0$ V and $B$ is at $2\mathrm{.}5$ V $?$

b$.$ How long will it take $M_n$ to pull up node $x$ from $0$ V to $1\mathrm{.}25$ V if $V_{In}$ is $2\mathrm{.}5$ V and $V_B$ is $2\mathrm{.}5$ V $?$

c$.$ What is the minimum value of $V_B$ necessary to pull down $V_x$ to $1\mathrm{.}25$ V when $V_{In}=0V?$

Chapter $6$ Problem Set

Figure $6\mathrm{.}11$ Level restorer. SOLVE on paper please with each equation and steps. TIA