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MOSFET transconductance

W

Walter Harley

Jan 1, 1970
0
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
|
|
.-.
| | Load
| | 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!
 
K

Kevin Aylward

Jan 1, 1970
0
Walter said:
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
|
|
.-.
| | Load
| | 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!

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

Paul Burridge

Jan 1, 1970
0
Why not measure it?

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

John Larkin

Jan 1, 1970
0
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
|
|
.-.
| | Load
| | 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!

Why not measure it?

John
 
P

Paul Burridge

Jan 1, 1970
0
Well, that's a problem, but how would a Spice model be any better?

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. ;-)
 
J

John Larkin

Jan 1, 1970
0
Presumably parameter variation. It wouldn't have much relevance to the
next one in the batch.

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
 
W

Walter Harley

Jan 1, 1970
0
John Larkin said:
[...]
Why not measure it?

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!
 
K

Kevin Aylward

Jan 1, 1970
0
Walter said:
John Larkin said:
[...]
Why not measure it?

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!

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

Kevin Aylward

Jan 1, 1970
0
Paul said:
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. ;-)


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

Winfield Hill

Jan 1, 1970
0
Paul Burridge wrote...
Presumably parameter variation. It wouldn't have much
relevance to the next one in the batch.

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.
 
W

Walter Harley

Jan 1, 1970
0
Kevin Aylward said:
Walter said:
John Larkin said:
[...]
Why not measure it?

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!

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?

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
 
J

John Larkin

Jan 1, 1970
0
Walter said:
John Larkin said:
[...]
Why not measure it?

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!

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?

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

John
 
K

Kevin Aylward

Jan 1, 1970
0
Walter said:
Kevin Aylward said:
Walter said:
message [...]
Why not measure it?

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!

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?

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

I was trying to avoid that. I am on holiday.
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.

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

Pooh Bear

Jan 1, 1970
0
Kevin said:
The gm of a mosfet is *always* less than that of a bipolar in
subthreshold, say 4 times less

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

Graham
 
K

Kevin Aylward

Jan 1, 1970
0
Pooh said:
Do you mean " The gm of a mosfet in subthreshold is *always* less
than that of a bipolar, say 4 times less " ?

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

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

Walter Harley

Jan 1, 1970
0
Kevin Aylward said:
[...]

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.


Thanks, Kevin! I'm on holiday too - that's why I've got time to be thinking
about this stuff. I appreciate the handholding.

Over in s.e.d, Tony Williams posted a link to an online text
(http://ece.colorado.edu/~bart/book/book/contents.htm) that gives a
derivation of the Vc term in subthreshold region.

-walter
 
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