ina163u
Hello,
I would explain somewhat different, although input open crcuit is actually a keyword. The other keyword is current noise. INA163 has input stages optimzed for low source impedance (noise matching is for 200 Ω). As a result it has considerably current noise at the input, requiring low impedance termination of both input and also Rg terminals.
With microphone disconnected, some extra noise can't be avoided, unless not shorting the input with a switching connector. Depending on the microphone's specification, I would choose an appropriate low resistance parallel termination, may be a few 100 ohms to 1 or 2k.
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Regards,
Frank