Page 316 - Mechatronics with Experiments

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f

w r

(a)

f

w
r
(b)

Low pass High pass
filter filter

w
r
(c)

Low pass
filter
V o
High pass
filter
w r
(d)

FIGURE 5.36: Some op-amp filter circuits: (a) low pass, (b) high pass, (c) band pass, (d) band
reject (notch) filters.

which the transition from low to high frequency occurs is defined by the filter parameters.
In addition, the rate of transition and the phase lag are determined by the filter order. The
frequency domain input–output voltage relationship of a low pass op-amp filter is
V (jw)
o 1
= (5.273)
V (jw) 1 + ⋅ jw
in
1
where the time constant of the first-order filter = RC.
1
The input–output voltage relationship for the low pass filter can be derived as follows.
The current into the op-amp is zero. Hence, the voltage at the (−) and (+) terminals of the