"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10

High-Pass Filter Design
16-26
Through coefficient comparison with Equation 16–5, obtain the following relations:
A C
C 2
a 1 2C C 2
cR 1 CC 2
b 1 2C C 2
cR 1 CC 2
Given capacitors C and C 2, and solving for resistors R 1 and R 2:
1 2A
R1
R 2
2fc·C·a 1
a 1
2fc·b 1 C 2 (1 2A)
The passband gain (A ∞) of a MFB high-pass filter can vary significantly due to the wide
tolerances of the two capacitors C and C 2. To keep the gain variation at a minimum, it is
necessary to use capacitors with tight tolerance values.
16.4.3 Higher-Order High-Pass Filter
Likewise, as with the low-pass filters, higher-order high-pass filters are designed by cascading
first-order and second-order filter stages. The filter coefficients are the same ones
used for the low-pass filter design, and are listed in the coefficient tables (Tables 16–4
through 16–10 in Section 16.9).
Example 16–4. Third-Order High-Pass Filter with f C = 1 kHz
First Filter
The task is to design a third-order unity-gain Bessel high-pass filter with the corner frequency
f C = 1 kHz. Obtain the coefficients for a third-order Bessel filter from Table 16–4,
Section 16.9:
ai Filter 1 a1 = 0.756
bi b1 = 0
Filter 2 a 2 = 0.9996 b 2 = 0.4772
and compute each partial filter by specifying the capacitor values and calculating the required
resistor values.
With C 1 = 100 nF,