Most circuit designers use the following equations to describe the current of a MOSFET.

There is a discontinuity point in the equations located at

Question

Most circuit designers use the following equations to describe the current of a MOSFET.

There is a discontinuity point in the equations located at

BlackTom AI · Accepted Answer

Question restatement: The problem shows MOSFET drain current equations with a discontinuity point, and asks where that discontinuity occurs.

Option 1: V_G = 0 V. This would imply the gate-source voltage is zero. In that case, the transistor is off or at least not in conduction, but the discontinuity in the piecewise current model is not defined by VG = 0; the model transitions are tied to the operating region boundary, not to VG being zero. So this is not the location of the discontinuity between pieces of the Id model.

Option 2: V_G = V_T. Gate threshold being equal to the threshold voltage would indicate the point at which channel forms in some simplified views, but the standard piecewise MOSFET current model uses the region boundary involving V_DS and (V_GS − V_T), not VG = VT as a standalone discontinuity in the equations for Id. Therefore this is not the location of the discontinuity in the given model.

Option 3: V_D = 0 V. While V_DS = 0 is a special case (no drain-source voltage), the discontinuity in the standard piecewise current expressions occurs at the boundary between linear (triode) and saturation regions, which is defined by V_D = V_G − V_T, not by V_D = 0. Thus this is not the correct discontinuity point.

Option 4: V_D = (V_G − V_T). This matches the well-known boundary between the triode (linear) and saturation regions in MOSFET operation, where the drain current expression changes form. The given Id_lin expression is valid for V_D ≤ V_G − V_T, and Id_sat applies for V_D > V_G − V_T. Hence the discontinuity occurs at the exact condition V_D = V_G − V_T.

In summary, the discontinuity point is tied to the region boundary defined by the drain-source voltage reaching the effective overdrive voltage (V_G − V_T). The other options fail to identify this region boundary, either because they refer to gate bias alone or to a different voltage threshold not governing the piecewise transition in these equations.

EESM5200 (L2) Part II: Topic 5 - Classical MOSFET Turn-on Current

Most circuit designers use the following equations to describe the current of a MOSFET. There is a discontinuity point in the equations located at

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