g$)$ Consider an $15$ mm $-$long, $\backslash (10\backslash$lambda $\backslash )$ wide metal wire in a $0\mathrm{.}6$ um process. The sheet resistance of the metal is $0\mathrm{.}08$ ohm per square and the capacitance of a $\backslash (4\backslash$lambda $\backslash )$ wide wire is $0\mathrm{.}2$ fF per um$.$ Construct a $5-$segment $\backslash (\backslash$pi $\backslash )-$model for the wire. $(2$ marks$)$

h$)$ Assume one end of the wire is attached to the input of a $\backslash (10$ x $\backslash )$ unit$-$sized inverter and a $2$ x unit$-$sized inverter drives the other end of the wire. Also assume both the gate and diffusion capacitance of a minimum width transistor is $2$ fF $,$ the diffusion resistance of a minimum width nmos transistor is $2\mathrm{.}5$ k ohms and the diffusion resistance of a minimum width pmos transistor is $5$ k ohms, and a unit$-$sized inverter consists of a $1$x nmos transistor and a $2$ x pmos transistor. Use the $\backslash (\backslash$pi $\backslash )$ model constructed in part g$)$ to calculate the propagation delay from the $\backslash (2$ x $\backslash )$ inverter to the $10$ x inverter. $(3$ marks$)$

i$)$ If a $\backslash (2$ x $\backslash )$ inverter is inserted to drive the $\backslash (2^\{\backslash$text $\{$nd $\}\},3^\{\backslash$text $\{$rd $\}\},4^\{\backslash$text $\{$th $\}\}\backslash ),$ and $\backslash (5^\{\backslash$text $\{$th $\}\}\backslash )$ segment, what will be the new propagation delay from the $\backslash (2$ x $\backslash )$ inverter to the $10$ x inverter. $(3$ marks$)$