Calculate JFET resistance

Question

I'm exploring JFETs at the moment; I'd like to use them as a variable resistor and set the resistance with a control voltage. I'm using it to control a 1Vpp sine wave through ds. I'm using a J201 JFET.

What I am interested in: How to calculate the resistance of Rds with Vgs = 0 and Vgs = Vgs(off).

I read this (amongst a lot of other sites and vids) https://effectpedalkits.com/blog/electronics-tutorials-the-jfet-junction-field-effect-transistor-ii-circuit-analysis/

Based on this source, I know that when Vgs = 0, Id = Idss and Vp is fixed (1.5v for a J201) So the equation would be relatively easy:

Rmin= 1/slope = 1/(Idss/Vp) = 1/(0.005/1.5) = 1/0.008333 = 300 ohm

Question: Are my assumptions correct? And how do I calculate the resistance of the JFET when Vgs = Vgs(off). (Do I take Igss from the datasheet for Id then with the corresponding V? This gives me a 20000Million ohm R..)

Answer 1

You can't determine it solely based on the gate-source voltage.

Small signal JFET like the J201 have a strong dependence on the current (or drain-source voltage), too.

If you pass a small current, well below IDSS, then yes the resistance will be minimum. This resistance is shown by the red line below and is on the order of 1 kOhm for a J201. It varies with IDSS (more IDSS, less resistance). Reducing the gate voltage will increase the resistance from there.

But this simple picture only works for small drain-source voltage and currents well below IDSS. As you can see in the above graphic, if the drain-source is more than a few 100 mV, the resistance will strongly increase without bound. This latter property makes small-signal JFET actually nice current limiters.

How to measure Rmin ?

If your JFET has very low cut-off voltage like the J201, then even a small handheld multimeter might already start to saturate the JFET channel during measurement. If this happens, the measure resistance would be larger than Rmin for that JFET. Whether this is case, you can check by putting a 10-100 kOhm resistor in series with the channel and measure the difference in the multimeter reading with and without the channel. Or if you can, use a controlled probe current that is at least one order below IDSS.