Jawaharlal Nehru Technological University Hyderabad B.Tech IV Year ANALOG CMOS IC DESIGN Previous Question Paper (September - 2022 - R16)

The small-signal model of a MOSFET represents the device's behavior for small deviations around a stable DC operating point (bias point). It is derived by linearizing the non-linear current-voltage characteristics of the transistor.

The standard small-signal model, often referred to as the hybrid-pi model, consists of the following components:

• Gate-Source Capacitance (Cgs): Represents the capacitance between the gate and source terminals, primarily due to the overlap capacitance and the channel charge.
• Gate-Drain Capacitance (Cgd): Represents the overlap capacitance between the gate and drain regions.
• Transconductance (gm): This is a voltage-controlled current source that models the dependence of the drain current on the gate-source voltage. It is defined as the change in drain current for a small change in gate-source voltage.
gm = ∂Id / ∂Vgs
• Output Resistance (ro): This models the finite output impedance of the MOSFET due to channel length modulation. It represents the slope of the Id versus Vds curve in the saturation region.
ro = 1 / λId
• Body Transconductance (gmb): Also known as the back-gate transconductance, it accounts for the effect of the body-source voltage on the drain current, often referred to as the body effect.
gmb = ηgm
• Drain-Bulk and Source-Bulk Capacitances (Cdb, Csb): These represent the parasitic junction capacitances formed by the reverse-biased depletion regions between the drain/source diffusions and the substrate.

In a typical small-signal circuit diagram, the gate is connected to the source through Cgs and to the drain through Cgd. The current source gmVgs is placed between the drain and source, in parallel with the output resistance ro and the drain-bulk capacitance Cdb.