Question 9.4: For the four-pole filter in Figure 9–12(b), determine the ca...

Both stages must have the same f_c. Assuming equal-value capacitors,

f_c=\frac{1}{2 \pi R C}

C=\frac{1}{2 \pi R f_c}=\frac{1}{2 \pi(1.8~ \mathrm{k} \Omega)(2680 \mathrm{~Hz})}=0.033~ \mu \mathrm{F}

C_{A 1}=C_{B 1}=C_{A 2}=C_{B 2}=\mathbf{0 . 0 3 3} ~\boldsymbol{\mu} \mathrm{F}

Also select R_2=R_4=1.8 ~\mathrm{k} \Omega for simplicity. Refer to Table 9–1. For a Butterworth response in the first stage, DF = 1.848 and R_1 / R_2=0.152. Therefore,

R_1=0.152 R_2=0.152(1800~ \Omega)=274~ \Omega

Choose R_1 = 270 Ω.

In the second stage, DF = 0.765 and R_3 / R_4=1.235. Therefore,

R_3=1.235 R_4=1.235(1800~ \Omega)=2.22~ \mathrm{k} \Omega

Choose R_3= 2.2 kΩ.

PRACTICE EXERCISE

For the filter in Figure 9–12(b), determine the capacitance values for f_c = 1 kHz if all the filter resistors are 680 Ω. Also specify the values for the feedback resistors to produce a Butterworth response.