TLH8694 – 19

FIGURE 11 Eighth-Order multiple-feedback bandpass filter using two MF8s The circuit shown

accepts a TTL-level clock signal and has a clock-to-center-frequency ratio of 1001

15 TRACKING AND CASCADED SECOND-ORDER

BANDPASS FILTERS

The individual second-order bandpass stages may be used

as ‘‘stand-alone’’ filters without adding external feedback

resistors The clock frequency and Q logic voltages set the

center frequency and bandwidth of both second-order

bandpass filters so the two filters will have equivalent re-

sponses Thus they may be used as separate ‘‘tracking’’

filters for two different signal sources as in

Figure 2a or

cascaded as in

Figure 2b For individual or cascaded sec-

amplitude response are given by the following two equa-

tions

Q

(1)

%

Q

s

Q

–

N

(2)

where

TLH8694 – 20

FIGURE 12 H(s) For second-order bandpass filters with

TLH8694 – 21

FIGURE 13 Design Nomograph for Cascaded

Identical Second-Order Bandpass Filters

Q

e

the Q of each second order bandpass stage

e

the center frequency of the filter in Hertz

per second

N

e

n

2

H(s) for a second order bandpass filter is plotted in

Figure

12 Curves are shown for several different values of Q Cen-

ter frequency is normalized to 1 Hz and center-frequency

gain is normalized to 0 dB

To find the necessary order n for cascaded second-order

bandpass filters using the nomograph in

Figure 13 first de-

just above the point of intersection of the two lines Remem-

ber that each second-order filter section will have a center

frequency gain of 2 so the overall gain of a cascaded filter

Cascading filters in this way may provide acceptable per-

formance when minimum external parts count is very impor-

16