Recently I have been asked to look at a few designs of seismic
amplifiers and filters used by PSN members. Two points that I
have not previously noticed are worth considering.

re: not amplifying all the noise:

The first point is that even when an amplifier is not specifically being 
used as a low pass filter, but only for signal gain, the frequency
response should still be limited to the low frequencies generally 
used in seismic work. There is no point amplifying all the noise,
especially 60 hz noise. This may be strong enough that after a 
gain of 1000 it might even saturate a later amplifier stage. 

The solution is to always use a capacitor in parallel with the high
value feedback resistor that sets the amplifier gain. For example,
for a gain of 40 db or x 100, the feedback R would be 990k ohm to the
inverting input, with 10k ohm to ground. If the 990k is paralleled
with a 0.005 uf capacitor, the frequency response would begin to decrease
by 6 db per octave at f=/2*pi*R*C or 32 hz. Otherwise it would only be
limited by the gain-bandwidth figure of the amplifier.

This frequency is usually selected to be well away from the response
shaping multi-pole filters that are used, so it could be ignored in
the circuit analysis. In the seismic amplifier I have posted, the
first stage has a 0.001uf, which when in parallel with the highest
gain resistor of 1.4 megohms (where less noise amplification is needed 
most), has a frequency of 114 hz. Only three gains are selectable for
the second stage, so a capacitor is used for each, with a corner at
about 25 hz. The following four-pole unity-gain filter has an effective 
corner at 19.5 hz.

This consideration of "by passing" high value resistors should be used
in variable gain stages as well as any offset adjustment arrangements 
(although I prefer to use the relatively low power LM308 amplifiers 
because they have little appreciable offset problems and produce little
heat). Every effort is needed to eliminate any gain at 60 hz and above, 
especially where such noise will be amplified by later gain stages.

If radio telemetry is used, further care in by-passing any vestige
of it from the power supply rails, the input circuitry, etc, is needed.
For RF suppression, low inductance ceramic capacitors should be used.
Often low value (100 ohm) wire-wound (= inductive) resistors are used
in series with the DC supplies at the inputs to a circuit card, which
are then by-passed to common with both ceramic AND large electrolytic
capacitors.

Re: multi-pole filters

The other observation is that simply cascading identical 2-pole filters
is not the way to achieve multi-pole performance. The individual response
curves don't stack up as one would expect because of interaction between
the stages. In fact, different effective frequencies and/or damping are
selected for each stage, depending on the total number of poles, to
achieve the overall result of total attenuation and the shape of the
rolloff (Buttworth, Chebyshev. Bessel, etc). "Stacking" identical
filters with any appreciable gain often results in oscillation. Even
multi-pole Butterworth filters have the same frequency but radically
different damping (and gain) per stage. But Bessel filters are preferred
in seismic amplifiers because of their uniform phase delay. 

For an example of the range of values, a 6-pole low pass Bessel filter 
will have three second-order sections with frequencies of 1.609f, 1.694f,
1.910f, and damping per section of 1.96, 1.64, 0.98, where "f" is the
overall cutoff (-3db down) frequency.  The "compromise" filter, also
called a Thompson-Butterworth, has frequencies of 1.268f, 1.301f, 1.382f,
and damping of 1.95, 1.52, 0.71. Even the flattest response Butterworth
filter, where the frequencies are all 1.000f, has damping values of 
1.93, 1.41, and 0.52 per section.

Among the references I use, two give very workable designs and tables
for multi-pole filters. The NASA publication, "An RC Active Filter
Design Handbook", NASA SP-5104, 1977, gives standard designs for up 
to 8 poles, and uses a constant resistance algorithm for unity gain 
1 khz filters that unfortunately results in very uncommon capacitor 
values. The designs are impedance and frequency scaled by multiplying/
dividing the R and C values. I have found that the odd capacitor values
can usually be made up with two common values. The unity gain design
is stable and simplifies inclusion in precision amplifier designs.

The other reference is the Sams publication "Active-Filter Cookbook" by 
Don Lancster; Howard W. Sams & co, 1975, Indianapolis; ISBN 0-672-21168-8;
Library of Congress 74-33839. He uses an algorithm that gives equal
values for all the capacitors, with the frequency and damping changed
by the filter and feedback resistors. The designs are also scaleable
from 1 khz. Since the damping of each stage is controlled by the feedback
resistance, this results in gain variability depending on the response
selected and number of poles. There are excellent tables for filters
of 7 different characteristics and up through sixth order (or poles) 
with all the resistance values, gains, and component tolerances
calculated and graphs for frequency scaling the capacitor values.

I prefer the NASA filters because they are all unity gain and often use
a constant resistance for all the stages, which helps quantity buying
of 1% values. The capacitor values are usually made up with a larger
value, like 0.47, which can be purchased in quantity, and smaller parallel
values, which cost much less and can be selected for value with a meter.

So if your filter design involves several identical stages but doesn't
realize the multi-pole performance you want, or even oscillates, you
might want to look at these references.

Regards,
Sean-Thomas
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