2.1 Passive Filters
The filters used for the earlier examples were all made up of
passive components: resistors, capacitors, and inductors,
so they are referred to as passive filters. A passive filter is
simply a filter that uses no amplifying elements (transistors,
operational amplifiers, etc.). In this respect, it is the simplest
(in terms of the number of necessary components) implementation
of a given transfer function. Passive filters have
other advantages as well. Because they have no active
components, passive filters require no power supplies.
Since they are not restricted by the bandwidth limitations of
op amps, they can work well at very high frequencies. They
can be used in applications involving larger current or voltage
levels than can be handled by active devices. Passive
filters also generate little nosie when compared with circuits
using active gain elements. The noise that they produce is
simply the thermal noise from the resistive components,
and, with careful design, the amplitude of this noise can be
very low.
Passive filters have some important disadvantages in certain
applications, however. Since they use no active elements,
they cannot provide signal gain. Input impedances
can be lower than desirable, and output impedances can be
higher the optimum for some applications, so buffer amplifiers
may be needed. Inductors are necessary for the synthesis
of most useful passive filter characteristics, and these
can be prohibitively expensive if high accuracy (1% or 2%,
for example), small physical size, or large value are required.
Standard values of inductors are not very closely
spaced, and it is diffcult to find an off-the-shelf unit within
10% of any arbitrary value, so adjustable inductors are often
used. Tuning these to the required values is time-consuming
and expensive when producing large quantities of filters.
Futhermore, complex passive filters (higher than 2nd-order)
can be difficult and time-consuming to design.
2.2 Active Filters
Active filters use amplifying elements, especially op amps,
with resistors and capacitors in their feedback loops, to synthesize
the desired filter characteristics. Active filters can
have high input impedance, low output impedance, and virtually
any arbitrary gain. They are also usually easier to design
than passive filters. Possibly their most important attribute
is that they lack inductors, thereby reducing the problems
associated with those components. Still, the problems
of accuracy and value spacing also affect capacitors, although
to a lesser degree. Performance at high frequencies
is limited by the gain-bandwidth product of the amplifying
elements, but within the amplifier's operating frequency
range, the op amp-based active filter can achieve very good
accuracy, provided that low-tolerance resistors and capacitors
are used. Active filters will generate noise due to the
amplifying circuitry, but this can be minimized by the use of
low-noise amplifiers and careful circuit design.
Figure 32 shows a few common active filter configurations
(There are several other useful designs; these are intended
to serve as examples). The second-order Sallen-Key lowpass
filter in (a) can be used as a building block for higherorder
filters. By cascading two or more of these circuits,
filters with orders of four or greater can be built. The two
resistors and two capacitors connected to the op amp's
non-inverting input and to VIN determine the filter's cutoff
frequency and affect the Q; the two resistors connected to
the inverting input determine the gain of the filter and also
affect the Q. Since the components that determine gain and
cutoff frequency also affect Q, the gain and cutoff frequency
can't be independently changed.
Figures 32(b) and 32(c) are multiple-feedback filters using
one op amp for each second-order transfer function. Note
that each high-pass filter stage in Figure 32(b) requires
three capacitors to achieve a second-order response. As
with the Sallen-Key filter, each component value affects
more than one filter characteristic, so filter parameters can't
be independently adjusted.
The second-order state-variable filter circuit in Figure 32(d)
requires more op amps, but provides high-pass, low-pass,
and bandpass outputs from a single circuit. By combining
the signals from the three outputs, any second-order transfer
function can be realized.
When the center frequency is very low compared to the op
amp's gain-bandwidth product, the characteristics of active
RC filters are primarily dependent on external component
tolerances and temperature drifts. For predictable results in
critical filter circuits, external components with very good
absolute accuracy and very low sensitivity to temperature
variations must be used, and these can be expensive.
When the center frequency multiplied by the filter's Q is
more than a small fraction of the op amp's gain-bandwidth
product, the filter's response will deviate from the ideal
transfer function. The degree of deviation depends on the
filter topology; some topologies are designed to minimize
the effects of limited op amp bandwidth.
NATIONAL - APPLICATION NOTE 779
