of Microprocessors

404 MUSICAL ApPLICATIONS OF MICROPROCESSORS
and stopband attenuations of 50 to 90 dB are given. These should covet the
range of application for audio filters from minimum cost experimental units
to very sharp professional application units. The element values are given in
henties and farads for a cutoff frequency of 0.159 Hz and impedance level of 1
ohm. To compute actual practical component values, use the formulas below:
L' = 0.159RL
F
c' = 0.159C
RF
where L' and C' are the practical component values, Land C are from the
table, R is the source and termination impedance, and F is the cutoff
frequency. Figure 12-25C shows a practical seventh order parallel resonant
filter design having 0.28 dB ripple, 60 dB attenuation, a cutofffrequency of
10 kHz (25 ks/s sample rate), and an impedance of 5,000 ohms. Figure
12-25D shows a fifth order series resonant filter with 1.25 dB ripple, 40 dB
attenuation, 5,180 Hz cutoff (12.5 ks/s sample rate), and lK impedance.
Even considering the advantages of small size, inexpensive components,
etc., of active implementation, actual passive implementation of the
filter, just as shown in Fig. 12-25, does have some advantages. For one, there
are only two amplifiers in the signal path to contribute noise and distortion,
and these can often be part of surrounding circuitry and not specifically
"charged" to the filter. The L-C networks can be easy to tune, which may be
necessary with the higher-order filters. Finally, the component values tend to
be similar in magnitude unlike the active Chebyshev filter described earlier.
On the minus side, the inductors are susceptible to hum pickup from stray
magnetic fields and therefore should be of torroid or pot core construction
and kept away from power transformers. Also, it is conceivable that
nonlinearities in the magnetic core could contribute a slight amount of
distortion, so relatively wide air gaps within the core should be used.
lnductor size and Q are not much of a problem because the section resonant
frequencies will be in the high audio range.
In actually building such a filter, accurate element values are crucial;
2.5% for fifth order, 1% for seventh order, and O. 5% or better for ninth
order. This is normally accomplished with an impedance bridge, a bunch of
polystyrene capacitors, and a supply offerrite pot cores and magnet wire. The
pot cores usually have tuning slugs that simplify the task of getting exactly
the right inductance, and appropriate parallel combinations of two or three
capacitors can usually be determined easily. Typically, the parallel resonant
form will be preferred since it has fewer inductors.
An active implementation of the filter using only op-amps, resistors,
and capacitors is also possible and straightforward to derive from the passive
L-C circuit. Whereas the Sallen and Key circuit studied earlier is a contrived
form that just happens to have the same response as a resonant R-L-C low-