In a message dated 27/05/00 20:57:35 GMT Daylight Time, sean@........... 
writes:

>  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.
 
>  This consideration of "by passing" high value resistors should be used
>  in variable gain stages as well as any offset adjustment arrangements
>  Every effort is needed to eliminate any gain at 60 Hz and above, 
>  especially where such noise will be amplified by later gain stages.
  
    Large signals that you do not want are also liable to produce some 
intermodulation products / distortion / drift. Ordinary low noise OP-AMPs 
still produce excess noise at the low frequencies that we are interested in - 
called 1/f noise because the amplitude increases as the frequency decreases.  

    The CAZ or commutating auto zero OP-AMPS (MAX422, MAX430, LTC1050, 
ICL7650, etc.) check and reset the zero continuously. They are still wide 
bandwidth devices, but the 1/f noise is greatly reduced. They do produce 
excess noise at the 'chopping frequency' which may be several hundred to 
several thousand Hz. You select the chopping frequency by your choice of 
device. It is particularly important for seismograph applications that the 
gain setting resistor should have a capacitor in parallel to give a roll off 
well below this frequency.

    Chopper amplifiers have a chopping frequency well above the roll off 
frequency and the total bandwidth is limited by this roll off. They are a bit 
more complicated to build, but may give noise levels 1/100 that of CAZ 
amplifiers. 0.1 to 10 Hz noise may be < 40 nV pk / pk.  Two are described in 
AN-45 'Measurement and Control Circuit Collection' by Jim Williams, Linear 
Applications Handbook, Vol. II by Linear Technology Inc. 
http://www.linear-tech.com/ . This is an interesting collection of circuits.

> 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. 
 
    This is particularly important if a correct roll off is to be achieved. 
Filters are normally designed to give a 3 dB reduction at the roll off 
frequency Fc. If you cascade 6 single stage sections, you will get 18 dB roll 
off at Fc. If you cascade three two pole filters you will get 9 dB roll off 
at Fc. 

    Another good book is 'Electronic Filter Design' + Disk by Arthur B. 
Williams, McGraw Hill 1995, ISBN 0070704414, but at $90, it is definitely 
'borrow from your library'.
    
>  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 cut-off (-3db down) frequency. 

    Since Bessel Filters are often not even mentioned in Filter Handbooks, it 
would be very helpful if you could give the constants for low pass Bessel 
Filters up to 6th order please?  I have been trying to get details through my 
library, so far without success.

    Regards,

    Chris Chapman
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