For a third order cascaded low pass filter consisting of thr

For a third order cascaded low- pass filter consisting of three identical first order filters, find the required value of the resistors (The maximum gain is 0 dB, the cutoff frequency for the entire filter is 1000 Hz and capacitors are all 0.47uF

Solution

The task is to design a third-order unity-gain Bessel high-pass filter with the corner fre-

quency fc= 1 kHz. Obtain the coefficients for a third-order Bessel filter

filter1 => a1= 0.756 b1= 0

filter2 =>a2 = 0.9996   b2= 0.4772

and compute each partial filter by specifying the capacitor values and calculating the

required resistor values.for C1= 0.47microF

first filter : R1= 1/(2*pi*fc*a1*C1) = 1/(2*pi*1000*0.756*0.47*10^-6) =447.92ohms

second filter:

R1= 1/(pi*fc*a1*C1) = 677.5ohms

R2 = a1/(4*pi*fc*C1*b1) = 354.66ohms