How stable is the MOSFET Id=K(Vgs)^a function?

[jolshefsky]

I'm working on a project where I want to control the brightness of several LEDs to be proportional to a voltage. I realized that MOSFETs (well, FETs in general), when operated in saturation mode, act as a constant-current device that is proportional to the gate voltage, and since LED brightness is proportional to the current, I figure I've got a match!

Reading a bit, I found the PDF of a lecture on "Transistor Basics - MOSFETs" by Bob York. In it, he says that if Vds ? Vgs-Vt and Vgs>Vt, then Id = Kn ( Vgs-Vt )^2 where Kn is a device property with the units A/V^2.

But what isn't clear is whether Kn is dependent on any other factors (such as temperature), and how much it varies between devices of the same family (since it's not called out on the datasheet for the little PMV20XN I'd like to use.)

So that's my question: does Kn depend on temperature, and if so how much? And does Kn vary between devices of the same part number, and if so how much?

The project I'm making doesn't have to be too precise, so even varying Kn by 10% or more would be okay. But if it varies by 2x between devices, or is similarly affected by temperature, then I'll need to finagle a way to include the current sensing in some kind of feedback loop.

[wraper]

Your idea doesn't cope with the real life. Yes it is temperature dependent but it is not the biggest of your issues. Tolerance from MOSFET to MOSFET will be huge and you would need to fine tune for each of them. Also the voltage range where you can actually regulate will be very shallow and on top of that nonlinear.
If you need linear regulation, then put a current sense resistor between the source and the GND and control the current using an opamp. Just like in electronic load https://coolcapengineer.wordpress.com/2014/09/15/tutorials-simple-electronic-load-circuit/ Though for best efficiency better to use PWM controlled DC/DC converter.

[jolshefsky]

If you need linear regulation, then put a current sense resistor between the source and the GND and control the current using an opamp. Just like in electronic load https://coolcapengineer.wordpress.com/2014/09/15/tutorials-simple-electronic-load-circuit/

Thanks—that looks like a solid concept to start from and solves the inconsistency issue.

[T3sl4co1l]

At low currents, it reverts to "subthreshold" behavior, exponential like any transistor.  (Vacuum tubes do this, too; the useful exponential range is only a few decades though.  MOSFETs have more like 5 decades, and BJTs 7 or 8.)

Actually using parameters in circuit, with discrete transistors, is typically unfeasible.

They can get away with stuff like this in monolithic circuits, however, because basically all the transistors on one IC have identical parameters, in various ratios of size and length.

Tim

[jolshefsky]

At low currents, it reverts to "subthreshold" behavior, exponential like any transistor.  (Vacuum tubes do this, too; the useful exponential range is only a few decades though.  MOSFETs have more like 5 decades, and BJTs 7 or 8.)

Hmm ... if I'm understanding this correctly, I'm likely to tear my hair out over instability right around Vgs threshold voltage?

For what it's worth, the PMV20XN has a threshold voltage of 1 volt nominal. The datasheet Id/Vds curve shows the lowest trace with Vgs at 1.4V, saturating Id at (very) roughly 150mA when Vds is (very) roughly >0.3V. Am I to understand the curves between Vgs=1V and Vgs=1.4V will not run parallel-ish to the Vgs=1.4V? Or does it just get really weird when the currents are in the <1mA range (sub-threshhold?)?

In any case I'm going to do some experiments when I get a chance to see if the feedback loop current sense circuit will work at all.

[T3sl4co1l]

You're looking at the wrong curve: parallelism (or the lack thereof) on this graph is a matter of channel length modulation (lambda) or Rds(on) (the steep region on the left), not Id(Vgs).  The transfer curve gives Id vs. Vgs, and shows a quadratic dependency for larger values.  It may not show the exponential region:
http://www.ece.utah.edu/~harrison/ece5720/Subthreshold.pdf
(blah, try to ignore the Comic Sans)

Note the Id used in the measurement of Vgs(th).  It's too small to see on either graph in the datasheet.

Vgs is offset by a variable voltage, which depends on manufacture and temperature.  This is encapsulated in the min/max range on the datasheet: for so-and-so drain current Id and drain voltage Vds, the gate voltage might be anywhere in this region.  The current will still vary as usual (which is why Vgs - Vgs(th) gets into the formula) but the absolute voltage is all over the place.

BJTs are subject to the same limitation, but Vbe variation is much smaller, in the 10s of mV.  Still enough to change Ic by a large factor, but manageable to the extent that useful current mirrors, multipliers and whatnot can be built with discrete transistors (if drifty and inaccurate!).  The same cannot be done with any kind of FETs, straight out of the bag -- they have to be matched manually first, or Vgs(th) measured in circuit and adjusted out.

Tim

[SteveyG]

I did a basic video on linear LED regulators on my channel. Maybe it can be of help?

[jolshefsky]

It may not show the exponential region:
http://www.ece.utah.edu/~harrison/ece5720/Subthreshold.pdf
(blah, try to ignore the Comic Sans)

Thanks, Tim. This stuff is going way over my head right now ... I might revisit it when my brain is at its sharpest.

I did a basic video on linear LED regulators on my channel. Maybe it can be of help?

Thanks Stevey—that's also helpful, particularly the op-amp circuit. I'll likely be using that. Again, time for testing!

[jolshefsky]

If you need linear regulation, then put a current sense resistor between the source and the GND and control the current using an opamp. Just like in electronic load https://coolcapengineer.wordpress.com/2014/09/15/tutorials-simple-electronic-load-circuit/

Thanks—that looks like a solid concept to start from and solves the inconsistency issue.

I did a test design and got great results. Spot on what I'm looking for. It's even able to work in the barely-on low-current range!

[Audioguru]

The graphs on a datasheet are for a "typical" device that you cannot buy. You might get a minimum one or a maximum one. Maybe their last production run produced mostly minimum or maximum ones?
The PMV20XN tiny Mosfet has a Vgs(th) of from 0.5V to 1.5V for it to conduct only 0.25mA when its is at 25 degrees C but its graph shows a typical current of about 1A when its Vgs is 1.4V. The difference between 0.25mA and 1A is 4000 times.