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DC offset correction loop (DC servo loop). What's its advantage, compared to a high-pass RC filter?

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Once in a while in literature I see a DC offset subtraction loop.

instrumentation amplifier with a DC servo loop

Here are a few more examples. DC servo loop removes a DC offset after an op-amp. DC servo loop removes DC current from a photodiode.

What are the advantages of such DC offset removal loop, compared to an RC high-pass filter?
The RC filter would look like this.

instrumentation amplifier followed by an RC filter

For context, I work on one-off research devices for which a cost of an op-amp isn't a problem. I'm not trying to economize the cost of one op-amp. I'm asking this question out of curiosity.

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In addition to what Andy said, the DC servo method doesn't add impedance to the signal. Note that in your bottom circuit, the signal with the DC offset removed has an impedance of 1 MΩ at DC.

In your case it doesn't matter since the signal is only going into an opamp input. In other cases it might force the use of a buffer, or some other means of dealing with high impedance, when that would not otherwise be necessary. For example, if you didn't need that additional gain after the offset removal, it might be inconvenient to have the signal be high impedance.

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What are the advantages of such DC offset removal loop, compared to an RC high-pass filter?

The primary advantage is that it keeps the front-end amplifier output centred in its DC operating region. If you used an external RC filter after the front-end amplifier and, sufficient offsets developed at the front-end amplifier's input, eventually, the front-end amplifier's output would saturate due to excessive offsets. This would cause AC signal degradation.

The disadvantage is clearly cost and, the possibility of instability in the front-end output (if not designed correctly).

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