Question

For the Bode plot shown below the transfer function is,

• A. $\frac{100s}{(s+4)(s+10{)}^2}$
• B. $\frac{100(s+4)}{s(s+10{)}^2}$
• C. $\frac{100}{(s+4)(s+10)}$
• D. $\frac{100}{s^2(s+4)(s+10)}$

Answer 1

The correct option is A $\frac{100s}{(s+4)(s+10{)}^2}$

Transfer function is,

$G\left(s\right)H\left(s\right)=\frac{Ks}{(\frac{s}{4}+1){(\frac{s}{10}+1)}^2}=\frac{400Ks}{(s+4)(s+10{)}^2}$

Magnitude of initial plot is given by,

$M=20log\omega +20logK$
and $M=0dBat\omega =4$
$0=20lo{g}_{10}4+20$ log K
(or) $20log\frac{1}{K}=20log4$

(or) $\frac{1}{K}=4$

(or) $K=\frac{1}{4}$

Hence, $G\left(s\right)H\left(s\right)=\frac{100s}{(s+4)(s+10{)}^2}$