IDVds

IdVds refers to the drain current (Id) as a function of the drain-source voltage (Vds) in a field-effect transistor. The Id–Vds characteristic, typically plotted for several gate-source voltages (Vgs), is a fundamental descriptor of a transistor’s output behavior and is central to device modeling, circuit simulation, and analog design. It captures how the transistor conducts as Vds changes while the gate bias sets the operating point.

In a MOSFET, the Id–Vds curve reveals two main regions of operation. In the ohmic or triode region, when Vds is small (approximately Vds < Vgs − Vth), Id increases roughly linearly with Vds and the device behaves like a variable resistor with a finite conductance gds. In the saturation region, for Vds ≥ Vgs − Vth, Id is predominantly set by Vgs and remains nearly constant with further increases in Vds; in real devices, Id grows slightly with Vds due to channel-length modulation or velocity saturation in short-channel devices.

Mathematical models describe these regions. For long-channel MOSFETs in saturation: Id ≈ 1/2 μ Cox (W/L) (Vgs − Vth)^2 (1 + λVds). In the triode region: Id ≈ μ Cox (W/L) [(Vgs − Vth)Vds − Vds^2/2]. Short-channel devices exhibit deviations such as velocity saturation and mobility degradation, which modify these relationships.

Measurement and interpretation involve analyzing Id–Vds curves under different Vgs values. Key parameters include ro = ∂Id/∂Vds in saturation (the inverse of gds) and gds itself. Id–Vds behavior is influenced by temperature, body bias, threshold voltage, and device geometry (W/L). Applications include biasing, current-source and amplifier design, and validating transistor models in circuit simulations.