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This circuit is being called a constant current source, how can this be? Since the gate and the source are both connected together their isn't a potential difference between them. Doesn't' this mean that the transistor should be off? Or do I have this confused with a BJT?

enter image description here

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    \$\begingroup\$ That's not a MOSFET. See how the gate touches the channel? It's a JFET. \$\endgroup\$ – Ignacio Vazquez-Abrams Sep 26 '15 at 23:09
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    \$\begingroup\$ ... and with an N-channel JFET, you need several volts negative on the grid (cough) gate to turn it off. \$\endgroup\$ – Brian Drummond Sep 26 '15 at 23:22
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As others have said, it's a JFET, which behaves similarly to a depletion mode MOSFET.

For a voltage across the device that is much bigger than than the cutoff voltage (about 2V) the current is fairly constant. Here is a typical curve from the Onsemi datasheet:

enter image description here

So, at Vgs = 0, the current for voltages of more than a few volts only varies from about 3.5 to 4.0mA (+/- 7% or so). However the actual current is poorly controlled- it might be as low as 3mA or as high as 7mA (parameter IDSS on the datasheet).

Since it needs so much forward voltage it isn't all that useful a circuit compared to alternatives. You can buy more tightly specified devices in a two-lead package- they are called current regulator diodes, but they also require a lot of forward voltage to regulate well and have never been very popular so they are expensive.

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