This biasing arrangement worked for my FET (2N3819), as I tried to turn it off by applying a negative voltage. Since it's a depletion mode fet, it needs to be biased in a different manner than our everyday transistors. I found that I had to obtain -1.7v relative to 0v ground. A simple way to do this was to put 2 AA batteries in series, and then dial to the correct value via 1 Mohm potentiometer.
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If you don't wish to do the job with batteries, it is possible to derive a negative polarity supply from a positive, by using a charge pump circuit.
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Similarly to turn off the P type fet requires 1.7v above the supply voltage. It would likewise require a pair of batteries, or a charge pump, or a boost converter.