Since seismologists need to measure very small signals, there are several 
sources of noise which may interfere with our measurements. 
    If a sensor such as a coil has a resistance R Ohms, it generates a noise 
voltage across it's output (due to the internal movements of the electrons) 
'en' where 
    en = SQRT(4xKxTxRxB) 
where K is a constant, T is the absolute temperature in Deg K (=293 at 20 Deg 
C) and B is the bandwidth (say 10 for a frequency range from 0 to 10 Hz).
    at room temperature en = 1.27x(10^ -10)xSQRT(RxB) 
    so for a 1000 ohm coil and a 10 Hz bandwidth the noise voltage will be
    en = 12.7 nano volts
    This doesn't sound much, but we then have to amplify our signals a lot 
and there are TWO additional types of noise in the amplifier itself. You may 
see a figure of 3.8 nano volts per root Hz quoted for an OP27 OP-AMP at 10 
Hz. This means that the average noise voltage for a 10 Hz bandwidth will be 
3.8xSQRT10 = 12 nano volts.  
    Unfortunately, most semiconductor amplifiers also generate additional 
noise at low frequencies called '1/f' noise. It is called this because the 
amplitude increases as the frequency decreases and it is the biggest 
interfering signal below about 10 Hz.
    There are two ways of controlling amplifier noise problems. You can fit a 
pair of low noise transistors on the OP-AMP input and get down to less than 1 
nano volt per root Hz. The best you can do this way, with a lot of effort, is 
about 0.3 nano volts per root Hz. You can use a 'chopper stabilised 
amplifier' like the MAX422 or the LTC1050 which, by the way that they work, 
eliminate the 1/f noise. They do add some high frequency noise above about 5 
KHz, but this is easily filtered out. This is good news in general for 
seismolgists, but the price tag is not such good news.
    You will notice that I have quoted the AVERAGE noise voltage. When you 
look at the amplifier output with an oscilloscope, you may wonder what has 
gone wrong. You soon realise that the maximum voltage, which is the one you 
tend to notice, is probably at least twice the average that you expected and 
quite 'lumpy' as well. That is the nature of averages. FET and CMOS 
amplifiers also have other types of noise which limit their performance. 
    The final noise output is the sum of the various components. If you do 
wind a huge coil, while the output may go up with the number of turns, so 
does the noise. To wind a larger number of turns in a given space, you need 
finer wire which has a higher resistance per turn and since it is more 
difficult to wind it evenly, the wasted space also increases. The likelyhood 
of picking up mains other types of electrical interferance also increase and 
screening may be difficult. 
    The 'rare earth' and 'neodymium' magnets have the strongest magnetic 
fields and enable you to get more volts out of your coil than a similar sized 
alnico magnet would give.  
    To estimate the total average noise voltage, you square the calculated / 
measured values from the various sources, add them together and then take the 
square root. You need to get the best signal to noise ratio that you can, so, 
if you have a high resistance coil, adding an expensive chopper amplifier 
will probably not do much good. Buying a samarium magnet might be much more 
cost effective.
    Chris     

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