$6.($a$)$ Consider isolated lossless $\backslash (($R$=0)\backslash )$ interconnect of length $\backslash ($ l $\backslash ),$ inductance per unitlength $\backslash ($ L $\backslash )$ and capacitance per unit$-$length $\backslash ($ C $\backslash ).$ Let the driver resistance of the source, and load impedance both be equal to the characteristic impedance of the interconnect. $($i$)$ What will be the transfer function of this interconnect. $($ii$)$ If a unit$-$step signal is fed to the input, what will be the output signal? Write the expression and plot $\backslash$& label the output signal. $($iii$)$ Will there be back reflection from the load in this case?

$($b$)$ Now two such identical interconnects are placed close together, along with their driver resistance and load resistance mentioned above. The capacitive coupling per unit$-$length, between these identical interconnects, is $\backslash ($ C$\_\{$c$\}\backslash ),$ and the mutual inductance is $\backslash ($ M $\backslash ).$ Derive the cross$-$talk transfer function of the coupled interconnects considering the source and load impedance. $\backslash \{$Use the $[$ABCD$]$ parameters and the matrix formulation. Since the interconnects are identical, you may assume $\backslash (\backslash$left$[$T$\_\{$V$\}\backslash$right$]=\backslash$left$[$T$\_\{$I$\}\backslash$right$]\backslash ).\backslash \}.$ Clearly write all the steps..

$($c$)$ Will there be back reflections from the load in this case? Justify your answer. Compare with your answer to Part$($a$-$iii$)$ above.