QUESTION $3(20$ marks$)$

Use the Smith Chart to find the following quantities for the transmission line circuit shown in Figure $2($b$),$ with characteristic impedance is $Z_0=100,$ and the load impedance is $Z_L=20-j90$ and the length of the line is $l=0\mathrm{.}3.$ Show your steps clearly on the Smith Chart of the following parameters:

i$.$ The reflection coefficient at the load $(2$ m $)$

ii$.$ The SWR on the line $(2$m$)$

iii. The return loss on the line $(2$m$)$

iv$.$ The input impedance to the line $(4$m$)$

v$.$ The load admittance $(2$m$)$

vi$.$ The distance from the load to the first voltage minimum $(4$m$)$

vii. The distance from the load to the first voltage maximum $(4$m$)$

Help me find $($vi$)$ and $($vii$).$ I already got the rest but im confused on how to get lmax and lmin. for lmax, Since the ZL line touchjng the WTG scale is $0\mathrm{.}382$lambda, should i do $0\mathrm{.}5$lambda$-(0\mathrm{.}5-0\mathrm{.}382)$lambda or just$(0\mathrm{.}25-0\mathrm{.}382)$lambda $=-0\mathrm{.}132$lambda?

Please clarify how to het those two.

Here are my answers for the rest of the question:

i$)$TLdeg

ii$)$SWR$=9\mathrm{.}2$

iii$)$RL$=1\mathrm{.}9$dB

iv$)$zin$=(60+$j$220)$ohm

v$)$yL$=2\mathrm{.}4$m $+$j$0\mathrm{.}01$S

vi$)$lmin $($need help$)$

vii$)$lmax$($need help$)$