MOSFET transconductance

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

  1. 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!
    Walter Harley, Dec 27, 2005
    #1
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  2. 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
    > |
    > |
    > .-.
    > | | 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

    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
    #2
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  3. 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
    #3
  4. Walter Harley

    John Larkin Guest

    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
    > |
    > |
    > .-.
    > | | 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
    John Larkin, Dec 27, 2005
    #4
  5. 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
    #5
  6. Walter Harley

    John Larkin Guest

    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
    #6
  7. "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
    #7
  8. 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
    #8
  9. 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
    #9
  10. 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
    #10
  11. "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
    #11
  12. Walter Harley

    John Larkin Guest

    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
    #12
  13. 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
    #13
  14. Walter Harley

    Pooh Bear Guest

    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
    #14
  15. 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
    #15
  16. "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
    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
    Walter Harley, Dec 29, 2005
    #16
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