Choose values for the Sallen-Key high-pass filter in Figure 9–15 to implement an equal-value second-order Butterworth response with a critical frequency of approximately 10 kHz.

Question

Accepted Answer

Start by selecting a value for [latex]R_A[/latex] and [latex]R_B[/latex] ([latex]R_1[/latex] or [latex]R_2[/latex] can also be the same value as [latex]R_A[/latex] and [latex]R_B[/latex] for simplicity).

[latex]R=R_A=R_B=R_2=3.3 ~\mathrm{k} \Omega[/latex] (an arbitrary selection)

Next, calculate the capacitance value from [latex]f_c=1 / 2 \pi R C[/latex].

[latex]C=C_A=C_B=\frac{1}{2 \pi R f_c}=\frac{1}{2 \pi(3.3~ \mathrm{k} \Omega)(10~ \mathrm{kHz})}=\mathbf{0 . 0 0 4 8} \boldsymbol{\mu} \mathbf{F}[/latex]

For a Butterworth response, the damping factor must be 1.414 and [latex]R_1 / R_2=0.586[/latex] = 0.586.

[latex]R_1=0.586 R_2=0.586(3.3 ~\mathrm{k} \Omega)=1.93 ~\mathrm{k} \Omega[/latex]

If you had chosen [latex]R_1=3.3 ~\mathrm{k} \Omega[/latex], then

[latex]R_2=\frac{R_1}{0.586}=\frac{3.3~\mathrm{k} \Omega}{0.586}=5.63~ \mathrm{k} \Omega[/latex]

Either way, an approximate Butterworth response is realized by choosing the nearest standard values.

PRACTICE EXERCISE

Select values for all the components in the high-pass filter of Figure 9–15 to obtain an [latex]f_c[/latex] = 300 Hz. Use equal-value components and optimize for a Butterworth response.

Question 9.5: Choose values for the Sallen-Key high-pass filter in Figure ...

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