Question

A lead compensator network includes a parallel combination of $R$ and $C$ in the feed-forward path. If the transfer function of the compensator is$G_c\left(s\right)=\frac{s+2}{s+4},$ the value of $RC$ is

• A. 0.5

Answer 1

The correct option is A 0.5

$G_c\left(s\right)=\frac{s+2}{s+4}$
For lead compensator,

$Transferfunction=\frac{1+s\tau }{1+\alpha s\tau }$
Where,
$\tau =Leadtimeconstant=R_{1}C$
$and\alpha =\frac{R_2}{R_1+R_2}$
Comparing equation (i) and (ii), we get
$\tau =\frac{1}{2}and\alpha \tau =\frac{1}{4}$
$or\alpha =\frac{1}{2}$
$\therefore$ RC time constant = 0.5