Question

The transfer function of a second order band-pass filter, having a centre frequency of 1000 rad/s, selectivity of 100 and a gain 0 dB at the centre frequency is

• A. $\frac{10s}{s^2+10s+{10}^6}$
• B. $\frac{s}{s^2+s+{10}^6}$
• C. $\frac{100s}{s^2+100s+{10}^7}$
• D. $\frac{100s}{s^2+100s+{10}^6}$

Answer 1

The correct option is A $\frac{10s}{s^2+10s+{10}^6}$

Transfer function of second order band-pass filter is

$A_v\left(s\right)=\frac{\left(\frac{{\omega }_0}{Q}{A}_{0}s\right)}{s^2+\left(\frac{{\omega }_0}{Q}\right)s+{\omega }_0^2}$
Given,

$Q=100$
$A_0=1$
${\omega }_0=1000rad/sec$
we get,

$A_v=\frac{\left(\frac{1000}{100}\right).1.s}{s^2+\left(\frac{1000}{100}\right)s+(1000{)}^2}$
$=\frac{10s}{s^2+10s+{10}^6}$