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I have a sensor which outputs a normally distributed baseband signal with cut-off frequency of 100Hz, whose mean is ~1mV and variance is (0.1mV)2. I want to amplify it about x1000 times by using TL084 opamp (other three opamps the TL084 contains are already occupied for different functions).

schematic

simulate this circuit – Schematic created using CircuitLab

I have a practical consideration on this circuit. The input signal is smaller than the input off-set voltage of the opamp which is given to be 3mV. Will this opamp successfully and precisely amplify my signal? If not, how do I increase precision of this circuit?

And how does the input offset voltage appear at the output (suppose that the input offset voltage s 3mV, the input signal is x(t) and the opamp output is y(t))?
a) 1000 times amplified along with the input signal. (i.e.; y(t) = 3V + 1000x(t))
b) Added at the output stage. (i.e.; y(t) = 3mV + 1000x(t))

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  • \$\begingroup\$ The output signal will include 1000 x input offset plus all the self-induced op-amp noise x 1000 too! \$\endgroup\$ – Andy aka Sep 4 '13 at 13:48
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Other answers have already made the main point: TL084 is not a good op-amp for your application. I'll answer one of your specific questions:

And how does the input offset voltage appear at the output (suppose that the input offset voltage s 3mV, the input signal is x(t) and the opamp output is y(t))?

The input offset appears as if it were a voltage source in front of one of the input pins (doesn't really matter which one).

This typically means it appears as an error in your input signal, and sees the same gain as the input signal.

a) 1000 times amplified along with the input signal. (i.e.; y(t) = 3V + 1000x(t))

Yes, though it might be more clear to say \$ y(t) = 100 \left( x(t) + V_{os}(t) \right)\$.

If you look you will be able to find an op-amp with Vos in the 10 uV range, which might be acceptable for your application.

You might also consider that 1000x is a very high gain to achieve with a single op-amp stage. You might want to consider doing this with two stages instead of one.

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Only the TL084BC has a worst-case input offset of 3mV, and that's only at 25C. (It's 5mV over the full range, and the non-BC versions can go as high as 20mV). Also, the TL084 doesn't have input offset nulling inputs.

Since your signal is swamped by the input offset range of the part, I wouldn't expect good results without some attempt at nulling. There are some methods of external nulling by injecting current, which can introduce noise but may make the opamp useable with such a small input signal.

It would be best to use a chopper-stabilized or precision low offset opamp for such a small signal instead of external nulling, since offset nulling often has a temperature coefficient (depending on the method used).

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    \$\begingroup\$ Also, a relatively low-cost option besides chopper-stabilized opamps is to use a current sense opamp. \$\endgroup\$ – user36129 Sep 4 '13 at 13:20
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I'd change the quad op-amp to something that is going to be more practical for your requirement. The offset drift for the TL084 is 18\$\mu V\$ per ºC and this is going to be a showstopper - a 10ºC shift in temperature is starting to ruin your performance expectations.

Something else that you may not have considered is this. Although your signal bandwidth is 100Hz, the op-amp doesn't understand this and with a gain of 1000, the self-induced noise of the TL084 will, over an untamed spectrum (of say 1MHz) be: -

\$ 18nV / \sqrt{Hz} \times \sqrt{1,000,000} \times\$ amp-gain (1000) \$ = 18mV_{RMS}\$

As a peak to peak value this is approximately 108mV (sigma of 6) and may render your signal unusable. To be able to use it, you might need significant filtering but this depends on what your circuit feeds. There are better op-amps around i.e. quieter but you may still have the basic problem of having to have a 2nd or 4th order low pass filter stage incorporated into the design just to make the real output usable.

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