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Why gm is not zero even when iDS is a constant DC current?

BaaB

I am trying to plot transconductance gm of M0 in the picture below. However, what I am supprised here is why gm is not zero when iDS is a constant DC current (1uA).

gm = diDS/dvGS

So according to this, gm should be zero when iDS is a constant.

As seen from the picture below, gm is not zero.

Could anyone explain why and how gm is calculated by the simulator?

Thank you.

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  • BaaB

    Could you help me with this if you know about this and when you have time?

    From b4ld.c file of latest BSIM4 version this is the code section for calculating gm:

    Ids = Idsa * T0;  

    Gm = T0 * dIdsa_dVg - Idsa * (dVdseff_dVg + T9 * dVASCBE_dVg) / VASCBE;
    Gds = T0 * dIdsa_dVd + Idsa * (1.0 - dVdseff_dVd - T9 * dVASCBE_dVd) / VASCBE;
    Gmb = T0 * dIdsa_dVb - Idsa* (dVdseff_dVb + T9 * dVASCBE_dVb) / VASCBE;


    tmp1 = Gds + Gm * dVgsteff_dVd;
    tmp2 = Gmb + Gm * dVgsteff_dVb;
    tmp3 = Gm;

    Gm = (Ids * dVdseff_dVg + Vdseff * tmp3) * dVgsteff_dVg;

    The first yellow line is Gm that is equal to derivative of Ids with respect to Vgs. I already checked and understood how to derive this result.

    However, I couldn't follow why Gm is calculated as the second yellow line?

    Where does this equation come from?

    Also, if I am not mistaken the dimensions are inconsistent here.

    The left hand side of the equation Gm has unit of current over voltage while the right hand side has unit of current.

     

Reply
  • BaaB

    Could you help me with this if you know about this and when you have time?

    From b4ld.c file of latest BSIM4 version this is the code section for calculating gm:

    Ids = Idsa * T0;  

    Gm = T0 * dIdsa_dVg - Idsa * (dVdseff_dVg + T9 * dVASCBE_dVg) / VASCBE;
    Gds = T0 * dIdsa_dVd + Idsa * (1.0 - dVdseff_dVd - T9 * dVASCBE_dVd) / VASCBE;
    Gmb = T0 * dIdsa_dVb - Idsa* (dVdseff_dVb + T9 * dVASCBE_dVb) / VASCBE;


    tmp1 = Gds + Gm * dVgsteff_dVd;
    tmp2 = Gmb + Gm * dVgsteff_dVb;
    tmp3 = Gm;

    Gm = (Ids * dVdseff_dVg + Vdseff * tmp3) * dVgsteff_dVg;

    The first yellow line is Gm that is equal to derivative of Ids with respect to Vgs. I already checked and understood how to derive this result.

    However, I couldn't follow why Gm is calculated as the second yellow line?

    Where does this equation come from?

    Also, if I am not mistaken the dimensions are inconsistent here.

    The left hand side of the equation Gm has unit of current over voltage while the right hand side has unit of current.

     

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