The ADG1612 does not appear to transmit bipolar signals properly when operated with single supplies. When the signal goes below ground the signal is clipped. How can I avoid this situation?
If the analog inputs on the source or drain pins go below the substrate (Gnd) when the part operates from a single supply, internal ESD protection diodes will start to turn on. When this occurs you can expect to see distortion or clipping of the ON channel and current flow in the OFF channel. Also, the OFF switch may in fact be turning on. To turn OFF the switch, you need Vgs < Vtn ( ~ 0.7v). The lowest voltage is applied to gate (GND in this case). However if S/D goes below the gate voltage you now have a positive Vgs and the channel will start to conduct.
You can workaround above by applying a DC bias, to bias the negative signal above GND. Alternatively the ADG4612 can pass bipolar signals down to -5.5V with a single supply. Please see the ADG4612 datasheet for further details.
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