Consoles 885There comes a breakpoint with increasing Q where
you are not so much listening to the effect of the filter as
to the filter itself. Resonant-tuned circuits are essentially
ac electrical storage mechanisms, where energy inside
the circuit shuffles backward and forward between the
two reactive elements until the circuit losses waste it
away. The greater the Q (and by definition the lower the
included losses), the more pronounced this signal
storage is.
Think of a high-Q circuit as a bell, which is just an
acoustic version of the same thing. If the bell gets
booted either physically or by being excited by audible
frequencies at its tuned pitch, it will ring until its natural
decay. It’s the same with a filter. A transient will set it
ringing with a decay time related to the filter Q. Music
containing energy at the filter frequency will set it off
just as well; a listener will hear the filter ringing long
after the original transient or stimulus has stopped.
Despite being good for a laugh, extremely high Qs and
the resultant pings trailing off into the sunset are of no
value whatsoever in a practical EQ. A transient hitting
such a filter fires off a virtually identical series of
decaying sine waves at the frequency of the filter.
Square waves sent through audio paths are good for
kicking resonant ringing off at almost any frequency.
It’s a convenient means of unearthing inadvertent
response bumps, phase problems, and instabilities. The
breakpoint—where filter ringing is as audible as
signal—is quite low, a Q of between five and ten
depending on the nature of the program material.
25.11.18 Push or Retard?
It is not too difficult now to appreciate that resonant
circuits and oscillators are very close cousins—often
indistinguishable, except for maybe an odd component
value here and there. There are two fundamental
approaches to achieving a resonant bandpass character-
istic using active-filter techniques.
The first is to start off with a tame, poorly
performing, passive network and then introduce positive
feedback to make it predictably (we hope) unstable. The
feedback exaggerates the filter character and increases
the Q to the desired extent. A perfect example of this is
the Wein Bridge development of Fig. 25-64. The major
disadvantage of such methods is that the Q is dispropor-
tionately critical with respect to the feedback adjust-
ments, especially if tight Qs are attempted.
The second approach is to start off with an oscillator
and then retard it until it’s tame enough. This is the
basis of the state variable, the biquad, and similar
related integrator-loop-type active filters.
25.11.19 The Two-Integrator Loop
This, for better or worse, and a variety of reasons, is by
far and away the most popular filter topology used in
parametric equalizers. Three inverting amplifiers
connected in a loop, as shown in Fig. 25-65, seem a
perfectly worthless circuit and, as such, it is. It’s there to
demonstrate (assuming perfect op-amps) that it is a
perfectly stable arrangement. Each stage inverts (180°
phase shift), so the first amplifier section receives a
perfectly out-of-phase (invert, revert, invert) feedback,
canceling any tendency within the loop to drift or
wobble. Removing 180° phase shift would result in
perfect in-phase positive feedback; the result is an oscil-
lator of unknown frequency determined predominantly
by the combined propagation times of the amplifiers.
Arranging for the 180° to be lost only at one specific
frequency results in the circuit being rendered unstable
at just that one frequency. In other words, it oscillates
controllably. Creating the 180° phase loss is left to two
of the inverting amps being made into integrators, Fig.
25-65B, so called because they behave as an electrical
analog of the mathematical function of integration.
The integrator you may recognize from a
single-order filter variation in Fig. 25-59. It’s not so
much the amplitude response that’s useful here as the
phase response, which at a given frequency (dictated by
the R and C values) reaches 90° with respect to its
input. Two successive ganged-value integrators create a
180° shift.
Retarding the loop to stop it from oscillating can be
achieved in a variety of ways:- Trimming the gain of the remaining inverter. This is
unduly critical like the Wein Bridge for Q determi-
nation. - Doping one of the integrator capacitors with a
resistor, Fig. 25-65C. This in essence is the biquad
filter (after biquadratic, its mathematical determina-
tion). The Q is largely dependent on the ratio of the
capacitive reactance to the parallel resistance;
consequently, it varies proportionally with
frequency. For fixed-frequency applications the
biquad is easy, docile, and predictable. - Phased negative feedback. This is not true negative
feedback but taken from the output of the first inte-
grator (90° phase shift). It provides an easily
managed Q variation, is constant, and is indepen-
dent of filter frequency, Fig. 25-65C. Forming the
basis of the state-variable filter, this has turned out
to be “the active filter most likely to succeed,” if the
majority of current commercial analog console
designs are to be believed.