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MOSFET transconductance

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

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  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!
     
  2. 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. Presumably parameter variation. It wouldn't have much relevance to the
    next one in the batch.
     
  4. John Larkin

    John Larkin Guest

    Why not measure it?

    John
     
  5. 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 Larkin

    John Larkin Guest

    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. 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. 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. 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. 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. 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 Larkin

    John Larkin Guest

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

    John
     
  13. 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 Bear

    Pooh Bear Guest

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

    Graham
     
  15. 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. 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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