b$)$ Given below are the characteristics for a uniform transmission line:

Resistance, $R=12m\frac{}{m},$

Inductance, $L=1\mathrm{.}6\frac{H}{m},$

Conductance, G $=1\mathrm{.}5mh\frac{o}{m},$

Capacitance, $C=1\mathrm{.}5n\frac{F}{m}.$

Hence, solve:

i$)$ the characteristic impedance $(Z_0)$ and the propagation constant $(Y)$ of the line when the operating signal frequency is $4$ kHz $,$

ii$)$ the characteristic impedance of the transmission line if the higher frequency is used and

iii$)$ the attenuation coefficient and the phase shift coefficient of the line if the signal travels $10$ m $.$

$(8$ marks$)$

c$)$ A $50$ transmission line is terminated by a load of $(30-j55).$ With the aid of Smith chart, determine the:

i$)$ actual admittance of the load,

ii$)$ standing wave ratio $($SWR$),$

iii$)$ reflection coefficient and it phase angle,

iv$)$ nearest distance from the load, a quarter$-$wave transformer must be placed to match the line,

v$)$ characteristic impedance of a quarter$-$wave transformer, $Z_o^{\text{'}}$ and

vi$)$ the nearest distance from the load and the shortest length of shunt stub to be placed to match the line.

$(16$ marks$)$