MOSFET Transconductance vs Drain Current

Well, of course, I forgot to post the spice list:

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The voltage gain equals the transconductance times the parallel combination of the drain load resistance and the drain resistance, which is 1/(partial dI_D / dV_DS) with V_GS held constant.

And MOSFETs don't have the simple device physics of BJTs, so it's harder to make good models, especially over a wide range of conditions.

I don't use many of them as linear amplifiers, so I don't think I've ever SPICEd one that way, but at least some of the circuits-course and AoE tricks that work with JFETs don't with MOSFETs--specifically, adding half of V_DS to V_GS. That linearizes a JFET variable resistor reasonably well, but getting the same effect with a 2N7002 requires adding 2*V_GS rather than 0.5*V_GS. (I posted some measurements of that a year or so ago in this august forum.)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

If you replace the drain load with a 6 ma current source, and bump up the feedback resistors, the gain increases to 3200. Which makes me suspect the fet model.

Get a real fet and try it.

John

Most Spice MOSFET models don't work properly in the subthreshold region. (Note, for power MOSFETs, this region continues up to fairly-high currents, because the current density is still quite low, given the high currents the parts are meant to handle.) However, if the Spice models did work properly in the subthreshold region, they'd show high gain, approaching or maybe exceeding that of a BJT.

For a BJT, g_m is proportional to current, g_m = Ic/V_T, until some internal resistances dominate at high current densities. V_T = kT/q = 25mV at room temp.

A MOSFET's g_m in the subthreshold region is also usually proportional to current: g_m = Ic/ n V_T, where n ranges from 2 to 5, etc. (At higher currents, g_m ~ sqrt Id.)

Assuming high load resistances, e.g., a current source, we can derive Gmax = g_m / g_os. That 2nd term is the output conductance = 1 / output-resistance. Most MOSFETs have remarkably-low output conductance, even much better than most BJTs (Another way of saying this is that they have very high Early voltages, V_A.) For many parts, Gmax doesn't change much with current, so it's a more useful parameter to evaluate this scene than g_os.

All this said, I suspect your value of G=690 wouldn't hold up with bench measurements. Another point I make all the time is, validate your Spice models with bench measurements before you give them any credence.

--
 Thanks,
    - Win

Nah, for a given drain current its transconductance can approach but not exceed the BJT's, because the fundamental limit of transconductance is set by the thermal spreading of the Fermi level, and BJTs achieve that limit.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

Absolutely, I didn't mean to imply otherwise, that's why I said n = 2 or higher. However, for a MOSFET with a fairly high g_m, close to a BJT, and a much better g_os than the BJT, as most have, I'm theorizing that it could have a higher Gmax.

--
 Thanks,
    - Win

I suppose that's conceivable, if you get to pick both the FET and the BJT. I'd like to know about it, if so!

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

Thanks, Win, I would have done so (without posting) if I had one of the devices that LTSpice has. I thought asking was faster than ordering devices.

Your input is very much appreciated.

Cheers, John S

A year or so ago I evaluated several brands for good modeling sub-threshold. It's likely still on my website. I'll try to remember what I called it ;-) ...Jim Thompson

[On the Road, in New York]

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| James E.Thompson, CTO                            |    mens     |
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Il Wed, 10 Aug 2011 18:00:26 -0400, Phil Hobbs ha scritto:

There should be a way to pull the area factor in as well..I don't have the theory fresh in mind but you can write a mos' gm as

gm = 2*Id/(Vgs-Vth)

which implies that you can make your W/L bigger to have Vgs -> Vth and increase gm arbitrarily. Surely below you can get Vgs-Vth below 50mV. This doesn't worry me too much anyways, because increasing the area you also slow down the transistor, which reminds you that the old GBW product should be the testbench.

M

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Here you go...

...Jim Thompson

[On the Road, in New York]

--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon at http://www.analog-innovations.com |    1962     |
             
I love to cook with wine.     Sometimes I even put it in the food.

Thanks, Jim.

It will take my old brain some time to digest this, but I appreciate your input very much.

Cheers, John S

Wow! It looks like the closer to zero Id it gets, the greater is dId/dVgs (Gm).

Yes?

John S

Is SPICE capabable of producing these quantities?

John S

I guess that was an ill-formed question.

I understand what you are saying. What I really want to know is, can I trust any of the results that you mention at those low drain currents?

John S

Yes, that is the ultimate answer. However, I do not have the devices available to LTSpice and I thought I could get the answer here without waiting for delivery. Poor excuse, perhaps. But I thought it worthwhile asking.

John S

Actually, I don't want to replace the drain load with a current source. Will you then no longer suspect the FET model?

John S

I was careful to say, "for a given drain current", because that's what governs the theoretical limit.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

Very possibly not. MOSFETs, by and large, are used for switching applications, and as such the SPICE models really only need to work when the thing is on or off, and sorta-kinda get things right in that swipe in the middle where things are transitioning.

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www.wescottdesign.com