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Low-Pass Filter Design
C 1
R 1 R 2
V IN
V OUT
Figure 16–13.
First-Order Inverting Low-Pass Filter
The transfer functions of the circuits are:
A(s)
1 R 2
R 3
1 c R 1
C 1
s
and
A(s)
R 2
R 1
1 c R 2
C 1
s
The negative sign indicates that the inverting amplifier generates a 180° phase shift from
the filter input to the output.
The coefficient comparison between the two transfer functions and Equation 16–3 yields:
A 0
1 R 2
and A
R 0
R 2
3
a 1
c R 1
C
and
1
a 1
c R 2
C 1
To dimension the circuit, specify the corner frequency (f C ), the dc gain (A 0 ), and capacitor
C 1 , and then solve for resistors R 1 and R 2 :
R 1
a 1
and R
2f c C 2
a 1
1
2f c C 1
R 2
R 3
A0 1 and R 1
R 2
A 0
The coefficient a 1 is taken from one of the coefficient tables, Tables 16–4 through 16–10
in Section 16.9.
Note, that all filter types are identical in their first order and a 1 = 1. For higher filter orders,
however, a 1 ≠1 because the corner frequency of the first-order stage is different from the
corner frequency of the overall filter.
R 1
Active Filter Design Techniques
16-13