For the four-pole filter in Figure 9–12(b), determine the capacitance values required to produce a critical frequency of 2680 Hz if all the resistors in the RC low-pass networks are 1.8 Ω. Also select values for the feedback resistors to get a Butterworth response.

Question

Accepted Answer

Both stages must have the same [latex]f_c[/latex]. Assuming equal-value capacitors,

[latex]f_c=\frac{1}{2 \pi R C}[/latex]

[latex]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}[/latex]

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

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

[latex]R_1=0.152 R_2=0.152(1800~ \Omega)=274~ \Omega[/latex]

Choose [latex]R_1[/latex] = 270 Ω.

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

[latex]R_3=1.235 R_4=1.235(1800~ \Omega)=2.22~ \mathrm{k} \Omega[/latex]

Choose [latex]R_3[/latex]= 2.2 kΩ.

PRACTICE EXERCISE

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

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

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