$(30$ pts$)5.$ Consider the following circuit. $($For the BJT$,=100$&$r_o=)$

$(5)($a$)$ Find $R_E$ to have DC emitter current of $0\mathrm{.}6$ mA

$(5)($b$)$ Find $R_C$ to have DC collector voltage of $5$ V

$(10)($c$)$ Draw the small signal model of above circuit. $($Clearly specify the value of $r_e,$ and $g_m)$

$(10)($d$)$ Find $\frac{v_o}{v_S}$