Using the circuit shown a Design a band reject notch filter

Using the circuit shown :

a) Design a band reject (notch) filter to have a center frequency of frequency of 25 kHz and a Bandwidth of 500 Hz.(Note the capacitor value is 0.5nF)

b) Determine the cut off frequencies in kHz.

c) Determine the Quality of the filter.

d) Assuming a load resistance of 165 ohms is placed across the output terminals, how do all the filter parameters change?(Recalculate all Parameters).

MS Word. Be sure to show the cut-off frequencies on th S. V1 Vo 0.5 nF Figure 1. Circuit configuration for notch filter.

Solution

AS PER THE EQUATION OF band reject (notch) filter ,

W₀ = 1 / SQRT( LC)

W₀²= 1 / ( LC)

L = 1 / W₀² C   

L = 1 / (2x pai x 25x10³ )²   * 0.5nF

= 1 / (2x pai x 25x10³ )²   * 0.5 x 10^-9 =    1 / 12.32 = 0.08113    =   81.13 mH

value of L=81.13 mH

Now to find resister :

B = 1/RC

B= 2 pai 500hz = 2* 3.14 * 500 = 3140

R =   1/ 3140 * 0.5nF

     = 1/ 3140 * 0.5 * 10 ^-9    

     = 636942.67 = 636.9 K ohm

R = 636.9 K ohm

Quality of the filter.

Q = W₀ R C =

     =  2x pai x 25x10³ ( 636.9 Kohm ) ( 0.5nF )

     =2X 3.14 X 25 X 10³ X 636.9 X 10³ X 0.5 X 10^-9

Q= 49.99

iF WE PUT LOAD RESSITOR ACROSS LOAD TERMINALS OF 165 OHM

tOTAL RESISTOR WILL BE

R_TOTAL    =   636.9 KOHM x 165 OHM /   636.9 KOHM x 165 OHM

               =   164.95 OHM

SO THERE WILL BE CHAGES AS PER THIS VALUE IN EACH VALCULATION

FOR EX =

Q WILL BE

Q = W₀ R C =

     =  2x pai x 25x10³ (  164.95) ( 0.5nF )

     =2X 3.14 X 25 X 10³ X 164.95 X 0.5 X 10^-9

Q= 0.012