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Fundamentals of Low-Pass Filters
sive components is the application of LRC filters. However, these filters are mainly used
at high frequencies. In the lower frequency range (< 10 MHz) the inductor values become
very large and the filter becomes uneconomical to manufacture. In these cases active filters
are used.
Active filters are RC networks that include an active device, such as an operational amplifier
(op amp).
Section 16.3 shows that the products of the RC values and the corner frequency must
yield the predetermined filter coefficients a i and b i , to generate the desired transfer function.
The following paragraphs introduce the most commonly used filter optimizations.
16.2.1 Butterworth Low-Pass FIlters
The Butterworth low-pass filter provides maximum passband flatness. Therefore, a Butterworth
low-pass is often used as anti-aliasing filter in data converter applications where
precise signal levels are required across the entire passband.
Figure 16–5 plots the gain response of different orders of Butterworth low-pass filters versus
the normalized frequency axis, Ω (Ω = f / f C ); the higher the filter order, the longer the
passband flatness.
10
0
–10
|A| — Gain — dB
–20
–30
–40
–50
1st Order
2nd Order
4th Order
10th Order
–60
0.01 0.1 1 10
Frequency — Ω
100
Figure 16–5. Amplitude Responses of Butterworth Low-Pass Filters
16-6