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I'm trying to design a circuit with an operational amplifier (OPA625). The input signal is amplified and sent to an ADC. In order to estimate the input noise, I'm using the following equation from an Analog Devices tutorial:

$$ v_{n,\text{rms}} (F_L, F_C) = v_{\text{nw}} \cdot \sqrt{F_C} \cdot \sqrt{\displaystyle\int_{F_L}^{F_C} \frac{1}{f} \mathrm{d} f} $$

$$ v_{n,\text{rms}} (F_L, F_C) = v_{\text{nw}} \cdot \sqrt{F_C \ln{\dfrac{F_C}{F_L}}} $$

\$v_{\text{n,rms}}\$ — input noise RMS

\$F_L, F_H\$ — frequency bandwidth

\$v_{\text{nw}}\$ — voltage noise density in the white noise area

It's quite easy to calculate the noise for the specified bandwidth. But what happens when \$F_L\$ is close to 0? In the Analog Devices' tutorial I mentioned earlier, \$0.1\text{ Hz}\$ is used as a lower frequency limit, but how close it should be to 0? How do I estimate the noise for DC input?

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TI's Analog Applications Journal includes an article about noise analysis for an op amp driving an ADC as in your application. The author uses \$F_{\text{L}} = 0.1\text{Hz}\$ with the following rationale:

When we think about noise at these low frequencies, we may jump to the conclusion that we should take this formula down to a very low frequency, such as 0.0001 Hz (0.0001 Hz = 1 cycle per 2.8 hours). However, at frequencies lower than 0.1 Hz, which is one cycle every 10 seconds, it is very possible that other things such as temperature, aging, or component life are changing in the circuit. Realistically, low-frequency noise from the amplifier will probably not appear at this sample speed; but changes in the circuit, such as temperature or power supply voltage, may.

Additionally, the OPA625 datasheet specifies the input noise voltage starting at \$f = 0.1\text{Hz}\$.

\$F_{\text{L}} = 0.1\text{Hz}\$ seems like a good choice since all three documents use it.

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Although you might think that the 1/f noise is getting more important near DC / F = 0 it is not because the bandwidth (over which you integrate) is also getting very small. So taking the noise below 0.1 Hz into account will not increase the noise voltage in a significant way.

And like Null mentions, offset, temperture and drift effects will be more significant below 0.1 Hz.

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