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

In order to obtain real values for R 2, C 2 must satisfy the following condition:
C 2 C 1
4b 1 1 A 0
16.3.3 Higher-Order Low-Pass Filters
a 1 2
Active Filter Design Techniques
Low-Pass Filter Design
Higher-order low-pass filters are required to sharpen a desired filter characteristic. For
that purpose, first-order and second-order filter stages are connected in series, so that
the product of the individual frequency responses results in the optimized frequency response
of the overall filter.
In order to simplify the design of the partial filters, the coefficients a i and b i for each filter
type are listed in the coefficient tables (Tables 16–4 through 16–10 in Section 16.9), with
each table providing sets of coefficients for the first 10 filter orders.
Example 16–3. Fifth-Order Filter
First Filter
The task is to design a fifth-order unity-gain Butterworth low-pass filter with the corner frequency
f C = 50 kHz.
First the coefficients for a fifth-order Butterworth filter are obtained from Table 16–5, Section
16.9:
ai bi Filter 1 a1 = 1 b1 = 0
Filter 2 a2 = 1.6180 b2 = 1
Filter 3 a3 = 0.6180 b3 = 1
Then dimension each partial filter by specifying the capacitor values and calculating the
required resistor values.
Figure 16–20. First-Order Unity-Gain Low-Pass
With C 1 = 1nF,
V IN
R 1
C 1
R1 a1
2fcC1 The closest 1% value is 3.16 kΩ.
V OUT
1
2·50·103Hz·1·109 3.18 k
F
16-19