of Microprocessors

214 MUSICAL ApPLICATIONS OF MICROPROCESSORS
required for any degree of sharpness. There exists, however, a very versatile
filter structure that not only simulates exactly an R-L-C filter in the resonant
(bandpass) mode but simultaneously simulates the other three possible filtering
functions that could be built with one resistor, one inductor, and one
capacitor as shownin Fig. 6-22. The family of amplitude response curves
represents low, medium, and high Q cases corresponding to high, medium,
and low values of RQ.
The circuit configuration in Fig. 6-23, which requires two integrators
and a summing amplifier, is well known to analog computer users but only
fairly recently has gained popularity as a cost-effective active filter circuit. This
is called a "two-pole filter" because two energy storage elements (capacitors)
are present in the signal path. The basic circuit is called a "state-variable" or
"integrator-loop" filter and provides simultaneous high-pass, bandpass, and
low-pass filtering functions of the same input. A band-reject output is obtained
by summing (they are 180 0
out of phase at resonance) the high-pass
and low-pass outputs with an additional op-amp. Figure 6-24 shows the
amplitude responses of each of the outputs for both low Q (1.5) and moderately
high Q (15). Note that the low-pass and high-pass functions have
cutoffs that are twice as sharp as the single-pole filters discussed earlier and
that they develop a prominent peak just before the cutoff point for high Q
settings.
Besides simultaneous filtering functions, the circuit has the advantage
that frequency and Qfactor (or bandwidth in hertz with a different configuration)
are independently variable. In other words, RQ only affects the Q factor
and RF only affects the center or cutoff frequency. Note that two resistors
affect frequency. Actually, the frequency is inversely proportional to the
square root of their product. If they are equal and varied together, however,
the square root drops out al}d the frequency-resistance relationship is linear.
R
HIGH-PASS
OUTPUT
C
BANDPASS
OUTPUT
C
INPUT
R
R
RF
RF
LOW-PASS
OUTPUT
R
R
R
R
F=_I­
2rrRFC
BAND-REJECT
OUTPUT
0= RO+R
R
Fig. 6-23. Two-pole tunable active filter