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I'm trying to design a MOSFET based switch which allows a sinewave through, however I noticed that when I was simulating it in LTSpice, whenever I try to turn off the FET the negative half of the sinewave still passes through.

Why is this and how do I prevent this from happening?

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    \$\begingroup\$ Are you aware that FETs contain an internal body diode? \$\endgroup\$
    – Hearth
    May 6 '20 at 20:55
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Note that the source and body of your MOSFET are internally connected together. When you apply a negative voltage to the drain you will forward-bias the internal PN junction between the MOSFET body (p-type) and the drain (n-type).

You might want to just use an analog switch that is designed for this purpose rather than build your own.

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