P$\mathrm{.}8-1$ Consider lossless stripline designs for a given characteristic impedance.

a$)$ How should the dielectric thickness, $d,$ be changed for a given plate width, $w,$ if the dielectric constant, $lo{n}_r,$ is doubled?

b$)$ How should $w$ be changed for a given $d$ if $lo{n}_r$ is doubled?

c$)$ How should $w$ be changed for a given $lo{n}_r$ if $d$ is doubled?

d$)$ Will the velocity of propagation remain the same as that for the original line after the changes specified in parts $($a$),($b$),$ and $($c$)?$ Explain.