Document created by analog-archivist on Feb 23, 2016
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### Q

In AD7712 data sheet, pages 11 and 12, noise is specified as total rms value. I
would like to know noise spectral density ( in particular for a 1kHz notch
frequency selection and in a 1 mHz to 1 Hz bandwidth ). Have you got some
specifications or estimations even if not garanted ?
If noise for a 10Hz notch frequency selection ( -3dB at 2.62 Hz ) is specified
at 1 uV  ( in datasheet for a  x1 gain ) can we assume a 1uV/sqrt(2.62Hz)=0.6
uV/sqrt(Hz) noise spectral density at low frequecies even if we are using a 1kHz
notch frequency selection ? Is noise increasing with a 1/f law at low frequncies
and how much would the "corner frquency" ?

### A

There is chopping internally on the front end integrator of the AD7712 which
will eliminate any 1/f noise from the integrator. I checked with our designers
and although we have not explicitly looked at noise spectral density at high
update rates, our low update rate tests would indicate that the noise at low
frequency is dominated only by thermal noise and therefore essentially flat.

The calculation you propose of dividing the rms noise by the square root of the
bandwidth assumes a “brick wall” bandwidth i.e. an infinitely sharp cutoff and
transition band. To get a close approximation of the noise spectral density you
will have to calculate the equivalent brick wall bandwidth of a (sin(x)/x)^3
filter.

The Noise spectral density at low frequency will not change with update date
rate but it will change with gain. This is because we use a mixture of
different size sample capacitors and different integration periods in order to
realize the different gain settings.

Also note: at low frequencies noise is dominated by the thermal (white) noise
of the silicon. At high frequencies the noise is dominated by the quantisation
noise. The cross over point where quantisation noise starts to dominate is
between 100 and 300Hz. At an update rate of 1kHz you are going to see a lot of
high frequency quantisation noise.

I presume from your query that you propose to do some external post filtering.
Post filtering will allow you to customise the response and settling time of
the decimating filter. However, any digital filter is periodic about the
sampling frequency and offers no attenuation at integer multiples of the
sampling frequency.