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    Small Signal Operation and Model: Assignment-3

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    Keshavamurthy L
    This document discusses small signal operation and modeling of an analog MOSFET circuit. It contains the following key points: 1. It defines the DC bias point and derives an expression for the signal current in the drain as a function of the input signal vgs. 2. It derives an expression for the voltage gain of the MOSFET as the transconductance gm multiplied by the drain resistance RD. 3. It presents the small signal equivalent circuit model of the MOSFET, modeling it as a voltage controlled current source with output resistance ro in parallel with RD.

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    Small Signal Operation and Model: Assignment-3

    Uploaded by

    Keshavamurthy L
    21 views15 pages
    This document discusses small signal operation and modeling of an analog MOSFET circuit. It contains the following key points: 1. It defines the DC bias point and derives an expression for the signal current in the drain as a function of the input signal vgs. 2. It derives an expression for the voltage gain of the MOSFET as the transconductance gm multiplied by the drain resistance RD. 3. It presents the small signal equivalent circuit model of the MOSFET, modeling it as a voltage controlled current source with output resistance ro in parallel with RD.

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    Analog circuit

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    This document discusses small signal operation and modeling of an analog MOSFET circuit. It contains the following key points: 1. It defines the DC bias point and derives an expression for the signal current in the drain as a function of the input signal vgs. 2. It derives an expression for the voltage gain of the MOSFET as the transconductance gm multiplied by the drain resistance RD. 3. It presents the small signal equivalent circuit model of the MOSFET, modeling it as a voltage controlled current source with output resistance ro in parallel with RD.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    21 views15 pages

    Small Signal Operation and Model: Assignment-3

    Uploaded by

    Keshavamurthy L
    This document discusses small signal operation and modeling of an analog MOSFET circuit. It contains the following key points: 1. It defines the DC bias point and derives an expression for the signal current in the drain as a function of the input signal vgs. 2. It derives an expression for the voltage gain of the MOSFET as the transconductance gm multiplied by the drain resistance RD. 3. It presents the small signal equivalent circuit model of the MOSFET, modeling it as a voltage controlled current source with output resistance ro in parallel with RD.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 15

    ANALOG CIRCUIT -18EC42

    ASSIGNMENT-3

    SMALL SIGNAL OPERATION AND MODEL


    Topics

    Dc bias point
    Signal current in the drain thermal
    Voltage gain
    Small signal equivalent
    transconductance
     DC BIAS POINT
    •The
      Dc bias current ID can be found by setting the signal Vgs to
    zero
    Thus
    ID= K’n
    The dc voltage at drain VD is given by
    VD= VDD – IDRD

    To ensure saturation region operation,we must Have

    VD >VGS –Vt
     THE SIGNAL CURRENT IN THE DRAIN
    TERMINAL

    •   the input signal vgs is applied , the total instantaneous gate tyo source voltage is
    When
    given by
    VGS = VGS + vgs ->(1)
    The total current ID Is given by
    ID = K ’ n -> (2)
    Substituting equation in equation 2
    ID = K ’ n
    •   WE KNOW,
     (a + b - c)2 = a2 + b2 + c2 + 2ab - 2bc - 2ca

    ID = K’n (V2GS + V2gs + V2t +2VGS vgs -2 Vgs vt - 2 VGS Vt)


    = K’n + K’n 2(VGS - Vt) Vgs + K’n V2gs
    First term represents dc bias current ID
    Second term represents a current component i.e directly propotional to input
    signal Vgs
    Third term represents a current component i,.e directly propotional to the
    square of the input signal.
    •The
      last term is undesirable because ot represents non linear distortion. To
    reduce the non linear distortion introduced ,the input signal should be kept
    small ,so that
    K’n v2gs << K’n (VGS -vt) vgs
    vgs << 2( VGS - Vt)

    or vgs << 2 Vov where vov is over drive voltage at which transistor is
    operating
    If the above condition is satisfied then third time can be neglected
    •Then
     
    i d ~ ID + i d

    Whee id = K’n (VGS -vt) vgs -> 3

    The MOSFET transcoundance is given by


    Gm = K’n vov

    fig below represents interpretation of small signall enhancement MOSFET


    amplifier
    •

    • Small signal operation of MOSFET amplifier


     THE VOLTAGE GAIN
    The total instantaneous voltage vd is given by

    Vd = vDD – IDRD

    Under the small signal condition we have


    Id = I D + i d

    Thus,
    Vd = vDD –(ID + id)RD

    Vd = vDD –IDRD + idRD

    Vd = vD– idRD

    Vd = vD– vd
    •  Where vd = -id RD is signal component of drain voltage
    • vd = -id RD=-gmvgsRD

    • Voltage gain AV=


    • AV = -gm RD
     SMALL –SIGNAL EQUIVALENT CIRCUIT MODELS
    Form the signal point of view. The MOSFET behaves as a voltage controlled
    current source. It accepts a signal vgs between gate and source and provides a
    current gm vgs at the drain therminal.
    The input resistance of this controlled source is very high ideally infinite. The
    resistance i.e. the resistance looking into the drain is also high.
    Assuming output resistance is infinite, in the analysis of MOSFET amplifier
    circuit , the transistor can be replaced by the equivalent model as shown in
    below fig (a)
    For small signal analysis , ideal constant dc voltage sources are replaced by
    short circuits.
    • Since the siganal current of an ideal constant dc current source will always be
    Zero , an ideal constant dc current source can be replaced by an open circuit
    in the small signal circuit of the amplifier.
    •  It is assumed that drain current in saturation is independent of drain voltage.
    However , the drain current does depend on vds.
    • Considering the output resistance ro , the small signal equivalent circuit is
    shown in fig (b)
    The value of ro is given by
    ro = =
    Where VA is called MOSFET parameter.

    Considering ro , the voltage gain expression is modified as


    AV = = -gm (rd || ro)
    Since the finite output resistance ro and the resistance ro and the resistance RD
    are in parallel ,then the effect is reduction in the magnitude of voltage gain.
    •
     
    THE TRANSCONDUCTANCE g m
    The MOSFET transconductance is given by

    gm= K’n (VGS – Vt)


    gm= K’n vov ->1
    Above eqn indicates , gm is propotional to transconductance parameter K’n aspect ratio and
    over drive voltage vov
    Drain current ID is given by
    ID= ½ K’n
    ID= ½ K’n

    VOV= ->2
    •Substituting
      eqn 2 in eqn 1
    gm=
    gm=
    =
    =

    gm=
    From,
    Nithin L
    USN: 4AD19EC418
    C SECTION

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