# MOSFET transconductance

Discussion in 'Electronic Basics' started by Walter Harley, Dec 27, 2005.

1. ### Walter HarleyGuest

I'm trying to analyze a trivial common-source amplifier based on an IRFP9240
power P-channel MOSFET (datasheet at
http://www.irf.com/product-info/datasheets/data/irfp9240.pdf).

The circuit is simply this:

-24V
|
|
.-.
| | 100R
'-'
|
|
||-+
||-> IRFP9240
Vin ---||-+
|
|
===
GND

Now, I know that voltage gain = gm * Rd. But how do I find gm? I'm
interested in the condition where the MOSFET will be operating in its linear
region, with Vgs close to Vt; Vds around 1V, Id around 200mA.

The datasheet specifies forward transconductance of 4.2S, but that's at 7.2A
and 50V, in the saturation region. The transfer characteristic curves only
go down to 400mA, and anyway they're at 50V also. Similarly, the output
characteristic curves don't show the region I'm interested in.

Given the available data, how can I determine the transconductance at the
operating point of interest?

Thanks for any help!

2. ### Kevin AylwardGuest

The simplest way, is to run spice. The work has already been done for
you. Don't reinvent the wheel. If you want the equations, again, check
in the documentation of one of many spices out there.

I had a quick check on the irf site. They have the spice model in a
..subckt. The main model in the subckt is:

..MODEL MM PMOS(LEVEL=1 IS=1e-32
+VTO=-3.73073 LAMBDA=0.0109168 KP=7.97276
+CGSO=1.08608e-05 CGDO=1e-11)

This is enough information for you to either, put the device in a spice
circuit and let spice compute the gm from this data, or secondly, enable
*you* to *look* up the equations, with this data and manually calculate
the gm. If we tell you everything, you wont learn anything.

I know of one spice that will trivially plot this gm as a function of
Id

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

3. ### Paul BurridgeGuest

Presumably parameter variation. It wouldn't have much relevance to the
next one in the batch.

4. ### John LarkinGuest

Why not measure it?

John

5. ### Paul BurridgeGuest

It probably wouldn't be, in the unlikely event that you're using
KevSpice. I'll wager he still hasn't got that parameter-spread
algorithm sorted out properly. ;-)

6. ### John LarkinGuest

Well, that's a problem, but how would a Spice model be any better? In
fact, I'd not trust any Spice model of such a fet operating at such
low current and drain voltage.

If Id were forced somehow, I'd imagine Gm would be pretty consistant
across devices. Gate threshold voltages will be all over the place, of
course... been there, done that, got scars.

John

7. ### Walter HarleyGuest

Indeed I could. Or I could use a simulator.

But it seemed I should be able to analyze such a simple circuit by hand,
based on information available in the datasheet. I guess not!

8. ### Kevin AylwardGuest

Yes you can. I already pointed out where the basic equations can be
found. For the simple model, the device is either in linear (ron) region
or constant current (saturation) region. The formula for the gm in these
regions are available. Have you tried google?

In saturation the gm varies as sqrt(I). If you know it at one current,
then it is known at all currents. Do we need to hold you hand as well?

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

9. ### Kevin AylwardGuest

Ahmmmm...the default variations are actually pretty reasonable. The
issue with typical powerfet vendor models are that they are usually just
a simple level 1 model. This misses a lot of detail, especially
subthreshold. It can be better to fake a Bsim3.

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

10. ### Winfield HillGuest

Paul Burridge wrote...
Actually, parameters like g_m vs Id often don't change
much from part-to-part and batch-to-batch, for a given
manufacturer's MOSFET type, in my experience. It's well
worth the time to take measurements and analyze them in
a spreadsheet. Going from one manufacturer to another,
that's another matter. But you can explore that as well.

11. ### Walter HarleyGuest

Hi, Kevin. Yes, some handholding would be welcome; that's why I posted to
s.e.b., rather than s.e.d.

The model you cited earlier was:

..MODEL MM PMOS(LEVEL=1 IS=1e-32
+VTO=-3.73073 LAMBDA=0.0109168 KP=7.97276
+CGSO=1.08608e-05 CGDO=1e-11)

With some Googling I find many references to a 1968 paper by Shichman and
Hodges, in IEEE J. Solid State Circuits. But I can't seem to find the
actual formula itself. (I don't happen to have access to a technical
library, so I don't have the journal itself at hand.) Would you be able to
point me to an online reference that shows the formula that Spice is using
for this model?

And, should I believe that this "Level 1" model (which does not include the
subthreshold region) will be a good fit to the relatively low Id and Vds in
my scenario? After all, the whole reason for the question is that the
region I'm interested in is outside of the range shown in the datasheet.

Thanks,
-walter

12. ### John LarkinGuest

His specified Vds of 1 volt may change things a little. I'd just try a
part to be sure.

John

13. ### Kevin AylwardGuest

I was trying to avoid that. I am on holiday.
Yes. The subthreshold region is not accounted for at all in the Level 1
model. The level 1 model is "not bad" for the two main regions, that is
satuation (constant current with Vds)and ohmic (linear with Vds).

Satuation region:

Id = W/L . (Kp/2) . (1 + lambda.Vds).(Vgs-Vt)^2

Linear region:

Id = W/L . (Kp/2) . (1 + lambda.Vds).Vds.(2(Vgs-Vt) - Vds))

From gm = dI/dVgs

Satuation region gm:

let K = W/L . (Kp/2) . (1 + lambda.Vds)

then:

gm_satuation = 2.sqrt(K.I)

Linear region gm:

let K = W/L . (Kp/2) . (1 + lambda.Vds).Vds

then:

gm_linear = 2K

Note 1: Most spices will assume a default W=L=100u if not specified,
i.e. 1 for the ratio.
Note 2: I just had to redo the sums myself, so any errors in the above
are mine alone

In the subthreshold region, the relevent formular is:

Id = Io.exp(Vgs/Vc)

i.e. the same form as a bipolar, with Vc, a constant.

The gm is therefore = I/Vc.

For the bipolar Vc is Vt=KT/q, or 25mV (gm=40.I). The gm of a mosfet is
*always* less than that of a bipolar in subthreshold, say 4 times less,
i.e. a Vc of say, 100mv.

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

14. ### Pooh BearGuest

Do you mean " The gm of a mosfet in subthreshold is *always* less than that
of a bipolar, say 4 times less " ?

Graham

15. ### Kevin AylwardGuest

Indeed. I see your on the ball over the holidays Graham.

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

16. ### Walter HarleyGuest

Thanks, Kevin! I'm on holiday too - that's why I've got time to be thinking