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Fundamentals of Low-Pass Filters
V IN
R
C
R
C
R
C
R
C
V OUT
Figure 16–3. Fourth-Order Passive RC Low-Pass with Decoupling Amplifiers
The resulting transfer function is:
A(s)
1
1 1 s 1 2 s (1 n s)
In the case that all filters have the same cut-off frequency, f C , the coefficients become
1 2 n n 2 1, and f C of each partial filter is 1/α times higher than f C
of the overall filter.
Figure 16–4 shows the results of a fourth-order RC low-pass filter. The rolloff of each partial
filter (Curve 1) is –20 dB/decade, increasing the roll-off of the overall filter (Curve 2)
to 80 dB/decade.
Note:
Filter response graphs plot gain versus the normalized frequency axis
Ω (Ω = f/f C ).
Active Filter Design Techniques
16-3