Question 9.5: Choose values for the Sallen-Key high-pass filter in Figure ...
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.
Start by selecting a value for R_A and R_B (R_1 or R_2 can also be the same value as R_A and R_B for simplicity).
R=R_A=R_B=R_2=3.3 ~\mathrm{k} \Omega (an arbitrary selection)
Next, calculate the capacitance value from f_c=1 / 2 \pi R C.
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}
For a Butterworth response, the damping factor must be 1.414 and R_1 / R_2=0.586 = 0.586.
R_1=0.586 R_2=0.586(3.3 ~\mathrm{k} \Omega)=1.93 ~\mathrm{k} \Omega
If you had chosen R_1=3.3 ~\mathrm{k} \Omega, then
R_2=\frac{R_1}{0.586}=\frac{3.3~\mathrm{k} \Omega}{0.586}=5.63~ \mathrm{k} \Omega
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 f_c = 300 Hz. Use equal-value components and optimize for a Butterworth response.