## Q. 14.11

If the bandstop filter in Fig. 14.37 is to reject a 200-Hz sinusoid while passing other frequencies, calculate the values of L and C. Take R = 150 Ω and the bandwidth as 100 Hz.

## Verified Solution

We use the formulas for a series resonant circuit in Section 14.5.

B =  2π (100) =  200π  rad/s

But

$B = \frac{R}{L } ⇒ L = \frac{R}{B} = \frac{150}{200π} = 0.2387 H$

Rejection of the 200-Hz sinusoid means that  $f_{0}$ is  200 Hz, so that $ω_{0}$  in Fig. 14.38 is

$ω_{0} = 2π f_{0} = 2π (200) = 400 π$

Since $ω_{0} = 1/ \sqrt{LC} ,$

$C = \frac{1}{ω^{2}_{0}L} = \frac{1}{(400π)^{2}(0.2387)} = 2.653 μF$