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

Active Filter Design Techniques
Low-Pass Filter Design
The multiplication of the denominator terms with each other yields an n th order polynomial
of S, with n being the filter order.
While n determines the gain rolloff above f C with n·20 dBdecade, a i and b i determine
the gain behavior in the passband.
In addition, the ratio b i
ai more a filter inclines to instability.
16.3 Low-Pass Filter Design
Q is defined as the pole quality. The higher the Q value, the
Equation 16–1 represents a cascade of second-order low-pass filters. The transfer function
of a single stage is:
A i (s)
A 0
1 a i s b i s 2
For a first-order filter, the coefficient b is always zero (b 1=0), thus yielding:
A(s) A 0
1 a 1 s
(16–2)
(16–3)
The first-order and second-order filter stages are the building blocks for higher-order filters.
Often the filters operate at unity gain (A 0=1) to lessen the stringent demands on the op
amp’s open-loop gain.
Figure 16–11 shows the cascading of filter stages up to the sixth order. A filter with an even
order number consists of second-order stages only, while filters with an odd order number
include an additional first-order stage at the beginning.
16-11