$3$

$3.$ This problem is on the Single Tone AM$-$DSB$.$ Let's assume message $m(t)$ and carrier $c(t)$ are respectively defined as$,m(t)=2$Cos$(210t)$ and $C(t)=10$Cos$(2100t).$

The general form of AM$-$DSB modulated signal is written as $S(t)=\frac{A_c}{t}+k_{a}m\frac{t}{C}os2fct.$

$($a$)$ Decide the maximum value of $K_g$ to avoid envelope distortion. $(3)$

$($b$)$ For modulation index of $0\mathrm{.}4,$ decide the value of $k_a.$

$(3)$

$($c$)$ Decide the portion of message related power among the total transmission powe across $1$ load in $[$Watt$]$ for $k_{{?}_{?}}(a)=0\mathrm{.}2.(4)$