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MOSFETs not properly driven OFF will not stay OFF?

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Hi,
In the attached Back-to-back NFET circuit, the NFETs are initially turned off by the minus 3v source…but then the switch opens and the gates are just left floating. Will the NFETs stay OFF?....or is there a chance that background electromagnetic fields could induce them to come ON?
LTspice sim and PDF schem attached
 

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first with the switch open.... and as you said they float.... you need to make sure they don't float for one, and by the way M1 is connected backwards.
the gates are capacitive, and so opening the switch leaves them with nowhere for the charge to go. as a matter of fact this is one method i have for testing MOSFETS out of circuit with a DVM. i measure between source an drain and should get an open circuit. then i disconnect the + lead from the drain, touch the gate lead with the meter lead, and then source to drain will conduct.... this doesn't work with all MOSFETS as some have thresholds higher than the open circuit voltage of my meter, but it usually works.

to answer your last two questions, yes, the FETS will stay off since the gates can't bleed off their charge.... background electromagnetic fields likely won't turn them on because there's no path for induced currents, but electrostatic fields might turn them on.
 
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Simply stated, put 10k or 4.7k resistors on the gates so they can drain their charge when the switch is open. The lower the resistance, the faster they will turn off, to a point...
 
Your two MOSFETs are arranged like a solid state relay but your V1 and V2 in series makes a 6.4VDC supply. Therefore, the MOSFET on the left (M1) is simply acting as a diode. M2 gate needs to be pulled down to its source pin with some value of resistor (depending on your target turn-off time and gate capacitance).
 
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