Question

2. Using an RLC circuit to design a band-reject filter, with the two cut off frequencies 40k and 90k Hz. Design the values of R, L, C, quality factor Q, and find the output terminals on the circuit. (20%)

Answer 1

Answer:

C = 59.17 nF

Q = 2.6

Explanation:

given data

frequencies = 40k Hz

frequencies  = 90k Hz

solution

we take here R, L C take in series

so cut off frequency is express as

Wc1 = $-\frac{R}{2L}+ \sqrt{(\frac{R}{2L})^2+\frac{1}{LC}}$   =  40000

wc2 = $\frac{R}{2L}+ \sqrt{(\frac{R}{2L})^2+\frac{1}{LC}}$    =  90000

so here

wc2 - wc1 will be

wc2 - wc1 = 90000 - 40000 = 50000

so

$\frac{R}{L}$ =  50000

we consider here R is 500

so  L = $\frac{500}{50000}$  

L = 10 m H

and here total cut off frequency is

total cut off frequency = 40000 + 90000 = 130000

so capacitance will be

capacitance  C is =  $\frac{1}{10\times 10^{-3}\times 130000^2}$  

so C = 59.17 nF

quality factor Q will be

Q = $\frac{130000}{50000}$  

Q = 2.6