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I ran across an instrumentation amplifier datasheet from "THAT Corporation", and noticed the polarized capacitor in series with the gain resistor:

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It is a typical 3 op-amp in-amp, so the differential input will be seen across the gain resistor, and C1 is meant to avoid changes in dc output offset with gain.

Now, the input is typically a microphone, and the AC voltage can reach 100mV or even a bit more.

For a 2k gain resistor and 6.8uF cap, 10 Hz will be seen with -3dB across the cap: 70 mVAC.

So the question is, will an electrolytic survive and work properly during these small negative excursions?

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Yes, it appears that this is OK for such small voltages.

According to CDE's Application Guide, Aluminum Electrolytic Capacitors:

Aluminum electrolytic capacitors are polarized and must be connected in the correct polarity. They can withstand reverse voltages up to 1.5 V.

If you are uncomfortable with that (from the same application guide):

If two, same-value, aluminum electrolytic capacitors are connected in series, back-to-back with the positive terminals or the negative terminals connected, the resulting single capacitor is a non-polar capacitor with half the capacitance.

For solid Tantalum capacitors, from Vishay's Solid Tantalum Capacitors: Frequently Asked Questions (FAQs):

Tantalum capacitors are capable of withstanding peak voltages in the reverse direction equal to 10 % of the DC rating at + 25 °C and 5 % of the DC rating at + 85 °C.

Also, you may not want to consider a ceramic capacitor for this due to the piezoelectric effects: Ceramic vs. Film Capacitor: Which one is preferred in audio circuits?

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