Determine the transfer function for the Butterworth bandpass filter? (At the Transfer Function Factoring and Sp Substitution stage) The Parameter
$$a_{pass} = - 1dB$$ $$a_{stop} = - 20dB$$ $$f_{pass1} = 10kHz$$ $$f_{pass2} = 30kHz$$ $$f_{stop1} = 5kHz$$ $$f_{stop2} = 60kHz$$
A. Approximate Low Pass Filter
Filter Ordo $$n_B = 4.29$$ $$n_B = 5 $$
Magnitude Response $$\epsilon = 0.51$$
Radius $$R = 1,144$$
Angles $$m = 1$$
While m = 0 $$\theta_0 = 108°$$
While m = 1 $$\theta_1 = 144°$$
- Find $$\sigma_m$$ Value and $$\omega_m$$ value
- While m = 0
$$\sigma_0 = -0.354 $$ $$\omega_0 = 1.089 $$
- While m = 1
$$\sigma_1 = -0.926 $$ $$\omega_1 = 0.673 $$
$$\sigma R = - 1.144$$
- Find Value B1m and B2m
$$B_{1,0} = 0.708$$
$$B_{1,1} = 1.852 $$
$$B_{2,0} = 1.311 $$
$$B_{2,1} = 1.310 $$
- Low Pass Filter Aproximation Transfer Function
$$H_{B,5}(S) = \frac{1.144}{S} \frac{(1.311)(1.310)}{(S^2 + 0.708S + 1.311)(S^2 + 1.852 + 1.310)}$$
B. Unnormalized Butterworth Band Pass Filter
- $$ \Omega_{rP} $$
$$ \Omega_{rP} = 2.75$$
- $$ \omega_0 $$
$$ \omega_0 = 108.827,96 rad/s$$
- $$BW$$
$$BW = 125.663,71 rad/s$$
$$Sp = \frac{s^2+108.827,96}{125.663,71s}$$
Factoring Transfer Function and Subtitute S.
I'm still confused about the step of factoring the transfer function and substituting specific values to determine the transfer function of a Butterworth bandpass filter. Can someone help me?
