running mode and lock the other one to the first one using an XOR gate and then use the output of the XOR gate as an output signal. However, we are wondering if any of you know a better idea. Maybe there is an off-the-shelf piece

Nearly any idea is better than the XOR gate you proposed. A simple double balanced diode mixer followed by an LT1028 preamp would easily meet your needs.

What about simply mixing two signals in a resistor network, sampling by ADC, and mixing purely in DSP domain on a non-linearity (e.g. f(x)=x^2)?

Regards,
Marek

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