On Tue, 18 Oct 2016 14:52:15 +0200, you wrote:

>Hoi David,
>On Tue, 18 Oct 2016 05:25:35 -0500
>David <davidwh...@gmail.com> wrote:
>> thermal EMF becomes a large if not the largest contributor.
>Ah.. good to know. Thanks!
>Any guess what the other big factors are?

Over time scales of 100s of milliseconds to seconds, the self heating
and temperature coefficient of the feedback network resistors causes
errors which extend settling time and look like low frequency noise.
At this level, self heating also contributes to non-linearity.

Intermodulation between frequency components of the signal close to
the chopping frequency can result in low frequency noise.  Modern
integrated chopper amplifiers do various things to prevent this so I
do not think it is a problem now.

External thermal effects are the big problem though.  Jim Williams
discusses this in Linear Technology application note 9 and includes
measurements showing noise down below 0.01 Hz.  He also discusses
other sources of noise:


>> When I did it, I extended the single ended design to a fully
>> differential gain of 1000 amplifier using a pair of LT1028s with a
>> pair of LTC1150s for correction.  I used the noise curves to estimate
>> what the integrator gain should be and after adjusting it for minimum
>> noise from about 0.1 to 10 Hz, it was very close to the actual
>> crossover point in the datasheet specifications.  RMS noise was
>> measured by taking the standard deviation of the DC values from a
>> Fluke 8505A over 10 seconds.
>You wouldn't have the schematics and the measurments available somewhere?
>It would be interesting to have a look at them.

I may have them and my notes from more than 10 years ago but I could
redraw the schematic from memory and describe it well enough to
duplicate; the design is not complicated.  I got the basic idea from
figure 14 on page 10 Linear Technology application note 21:


Mirror the standard high input impedance non-inverting amplifier
configuration top to bottom to produce a 2 operational amplifier (4 in
this case) differential amplifier.  The symmetry in the circuit helps
balance noise sources like thermocouples.  I do not remember if
synchronizing the clocks of the chopper stabilized amplifiers improved
performance but if it did, the difference was not large at least with
LTC1050s and LT1028s.

The part I found amazing when I worked with this circuit is everything
worked just as theory predicted; the calculated integrated noise level
was just about right and the crossover frequency between the
amplifiers matched the datasheet specifications.  The low frequency
noise was so low that I could measure resistance just from its low
frequency Johnson noise which scared me.

>BTW: Should this discussion be moved over to volt-nuts?
>I kind of feel we are getting too off-topic for time-nuts.
>(though my interest comes from long term time measurment)
>                       Attila Kinali

The original non-inverting circuit would be suitable for use in the
signal chain driving the voltage control input of a crystal oscillator
preserving low noise and low drift from the DAC.  Replace the low
noise precision bipolar operational amplifier with a low noise low
input bias current operational amplifier and it might be useful for
implementing long time constant filters in an analog GPSDO design
although I suspect sacrificing input bias current (the chopper input
bias current is relatively high) for this level of precision and low
frequency noise may not be a worthwhile trade off.
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