# 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!

Walter Harley, Dec 27, 2005

2. ### Kevin AylwardGuest

Walter Harley wrote:
> 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!

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.

Kevin Aylward, Dec 27, 2005

3. ### Paul BurridgeGuest

On Tue, 27 Dec 2005 15:26:26 -0800, John Larkin
<> wrote:

>Why not measure it?

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

"What is now proved was once only imagin'd" - William Blake

Paul Burridge, Dec 27, 2005
4. ### John LarkinGuest

On Tue, 27 Dec 2005 00:46:29 -0800, "Walter Harley"
<> wrote:

>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!
>

Why not measure it?

John

John Larkin, Dec 27, 2005
5. ### Paul BurridgeGuest

On Tue, 27 Dec 2005 16:18:03 -0800, John Larkin
<> wrote:

>On Wed, 28 Dec 2005 00:01:58 +0100, Paul Burridge
><> wrote:
>
>>On Tue, 27 Dec 2005 15:26:26 -0800, John Larkin
>><> wrote:
>>
>>
>>>Why not measure it?

>>
>>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?

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. ;-)
--

"What is now proved was once only imagin'd" - William Blake

Paul Burridge, Dec 27, 2005
6. ### John LarkinGuest

On Wed, 28 Dec 2005 00:01:58 +0100, Paul Burridge
<> wrote:

>On Tue, 27 Dec 2005 15:26:26 -0800, John Larkin
><> wrote:
>
>
>>Why not measure it?

>
>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

John Larkin, Dec 28, 2005
7. ### Walter HarleyGuest

"John Larkin" <> wrote in message
news:...
> [...]
> 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!

Walter Harley, Dec 28, 2005
8. ### Kevin AylwardGuest

Walter Harley wrote:
> "John Larkin" <> wrote in
> message news:...
>> [...]
>> 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

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

Kevin Aylward, Dec 28, 2005
9. ### Kevin AylwardGuest

Paul Burridge wrote:
> On Tue, 27 Dec 2005 16:18:03 -0800, John Larkin
> <> wrote:
>
>> On Wed, 28 Dec 2005 00:01:58 +0100, Paul Burridge
>> <> wrote:
>>
>>> On Tue, 27 Dec 2005 15:26:26 -0800, John Larkin
>>> <> wrote:
>>>
>>>
>>>> Why not measure it?
>>>
>>> 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?

>
> 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

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

Kevin Aylward, Dec 28, 2005
10. ### Winfield HillGuest

Paul Burridge wrote...
>
> John Larkin wrote:
>
>> Why not measure it?

>
> 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.

--
Thanks,
- Win

Winfield Hill, Dec 28, 2005
11. ### Walter HarleyGuest

"Kevin Aylward" <> wrote in message
news:z7ssf.32418\$...
> Walter Harley wrote:
>> "John Larkin" <> wrote in
>> message news:...
>>> [...]
>>> 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

Walter Harley, Dec 28, 2005
12. ### John LarkinGuest

On Wed, 28 Dec 2005 08:35:43 GMT, "Kevin Aylward"
<> wrote:

>Walter Harley wrote:
>> "John Larkin" <> wrote in
>> message news:...
>>> [...]
>>> 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

John Larkin, Dec 28, 2005
13. ### Kevin AylwardGuest

Walter Harley wrote:
> "Kevin Aylward" <> wrote in message
> news:z7ssf.32418\$...
>> Walter Harley wrote:
>>> "John Larkin" <> wrote in
>>> message news:...
>>>> [...]
>>>> 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

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

Kevin Aylward, Dec 29, 2005
14. ### Pooh BearGuest

Kevin Aylward wrote:

> 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

Pooh Bear, Dec 29, 2005
15. ### Kevin AylwardGuest

Pooh Bear wrote:
> Kevin Aylward wrote:
>
>> 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 " ?
>

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.

Kevin Aylward, Dec 29, 2005
16. ### Walter HarleyGuest

"Kevin Aylward" <> wrote in message
news:FDPsf.32503\$...
> [...]
>
> 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