Consoles 887Loop filters, such as described in Fig. 25-65, have a
number of inherent problems that are usually glossed
over for the sake of the operational simplicity and
elegance of the design.
25.11.20 Stability and Noise Characteristics
Each amplifier within the loop has a finite time delay,
which together add up to significant phase shifts within
the open loop bandwidths of the amplifiers. Some
simply add to the delay imparted by the integrators, but
the total time discontinuity around the summing amp
can promote instability in the multimegahertz region.
Compensation for this around the summing amplifier
can introduce further phase shifts, upsetting the filter
performance at high frequencies.
Two major problems are due to the nature of the inte-
grator arrangement itself. They come to light at the
extremes of the feedback capacitive reactance (i.e., at
very low and very high frequencies where, respectively,
the reactances are virtually open circuit and short
circuit).
Open circuit at low frequencies means the op-amp is
infinitely amplifying external resistor noise and inter-
nally generated thermal and (mostly) low-frequency 1/F
noise, plus any low-frequency noise presented to the
input along with the signal. There is a lot of generated
and circulating low-frequency noise.
At high frequencies, the reactance approaches a short
circuit, connecting the output back around to the
inverting input. This arrangement, zero closed loop
gain, is about as critical in terms of device instability as
it can get. It is directly analogous to a grounded-input
follower (see Section 25.7 for inherent problems), since
there is no possible way of further externally defining
the closed loop characteristics beyond those of the inte-
grating capacitor itself. For typical audio frequency EQ
the integration capacitor value can be quite sizable, up
to 1μF. Two further aggravations:
- Current limiting. Is the current output capability of
the op-amps sufficient to charge such a size capac-
itor instantaneously? If not, this will result in low
maxima of signal frequency and signal level before
op-amp slew-rate limitation sets in. The amplifier
just might not be able to deliver enough current
quickly enough. - Finite device output impedance. There will almost
certainly be another foible related to the open loop
output impedance of the op-amp; this corresponds to
a resistor in series with the device output that forms
a time constant and a filter with the integrator
capacitor, in addition to the intended one. Another
time constant means more time delay in the loop,
causing a seriously degraded (maybe already crit-
ical) stability phase margin. At best it adds a zero to
the integrator, reducing the integrator’s effective-
ness at high frequencies.Integrators ask a lot of device outputs; not only do
they have to cope with a vicious reactive load (with
which many op-amps are ill equipped to cope) but they
also have to drive other circuitry, such as the next stage.
A mad drive to bring circuit impedances down for noise
considerations can soon outstrip even the best op-amp’s
capabilities.
As tame as it may superficially seem, the state vari-
able is not an unconditionally or reliably stable arrange-
ment, with out-of-band dynamic problems potentially
degrading its sonic performance. It is an amazement
that these filters work as well as they do in many
commercial designs.
With the exception of inevitable loop effects (usually
time related), most of the undesirable things about the
state variable can be eliminated or mitigated by replacing
the integrators with constant amplitude, phase-shift
elements, Fig. 25-65D. This results in what could best be
known as a CAPS-variable filter. Here, all the constit-
uent elements are basically stable, and there are provi-
sions for independent device compensation. There is no
undefined gain for any of the spectrum. This seems to be
a far healthier format to start making filters around.
There is another way of looking at the state vari-
able/CAPS-variable filters that will suddenly resolve
the previous discussions on gyrators, L and C filters,
series-tuned circuits, and so on with the seemingly
at-odds approach of active filters.
Resonance depends on the reaction of the two reac-
tances of opposite sense, 180° apart in phase effect.
Rather than achieve this in a differential manner, one
element +90° with the other 90° at a given frequency,
these active filters achieve the total difference by
summing same-sense phase shifts (90° + 90°)–i.e.,
still 180° apart. Two reactive networks are still
involved; it is still a second-order effect. At the end of
the day, the principal difference is that such loop-type
active filters have their median resonance phase
displaced by 90° from their input as a result of both
reactive effects being in the same sense, as opposed to
the nil phase shift at resonance of a real LC network.