Operational Amplifier Circuits

78 OPERATIONAL AMPLIFIER CIRCUITS: ANALYSIS AND DESIGN

where

and

This unwieldy equation can be simplified by letting R

l

=R

2

= R and C

x

= C

2

= C;

hence,

This is of the general form

which is the response of a second-order band pass filter. Notice that A!# which

is the gain at the center frequency, is not equal to as was the case for the

low- and high-frequency gains of the low and high pass filters, respectively.

The damping coefficient a can be shown to be the reciprocal of the Q of

the filter. Therefore, from Equations (5.56) and (5.57) we have

(5.58)

(5.59)

Also,

(5.60)

(5.54)

(5.55)

(5.56)

(5.57)