of Microprocessors

392
MUSICAL ApPLICATIONS OF MICROPROCESSORS
GAIN (dB)
0l--------~__---- __
-5
-10
-20
-30
-40
-50
- 60
-70
- 80 L----------::,-----=-----::"-,-----:"c:----::-:~~::_:__c:::..,_.:_.,.,._J'_::__U..:_""":""':......,..,~::'_t_
0.1 0.12 0.15 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.91.0 1.1 1.2 1.4 1.6 1.8 2.0
NORMALIZED fREQUENCY
Fig. 12-20. Seventh order, 1.25-dB-ripple, 60-dB-attenuation elliptical filter
amplitude response
Such filters are called elliptical (also Cauer) filters after the mathematical
functions that describe them. Three parameters are necessary to
specify an elliptical filter: the order, which is related to the number ofreactive
components, the allowable passband ripple, and the minimum allowable
stopband attenuation, also called stopband ripple. The latter figure is needed
in order to determine how closely the notches must be spaced. With such a
large number of variables, design tables for elliptical filters are almost
impossible to find and their design procedure is quite complex. Later in this
chapter, however, an abbreviated design table will be given along with
sample circuits.
Although an elliptical filter provides the sharpest cutoff with the fewest
number of reactive elements, these elements all interact with each other (there
are no discrete "sections" with isolating amplifiers between them) making
precise (1 % or better) element values mandatory. In contrast, the sections of
Butterworth and Chebyshev filters are independent because of isolating
amplifiers and, when necessary, can be tuned independently. Therefore, it is
probably better for the individual experimenter/designer to stick with the
latter types, at least, initially.
Phase Shift
So far in this discussion the phase response of the low-pass filters has
been ignored. Regretfully, it is a fact of life that the sharper a filter cuts off,