Lecture 9: The MOSFET as a Dependent Source

What this lecture covers

The previous lecture built an amplifier out of an idealized dependent current source. This lecture asks what real device can play that role, and shows that a MOSFET does it once you look past the simple on/off switch model used for digital circuits. The lecture works out the MOSFET's full drain-current behavior across both small and large drain-to-source voltages, and pins down exactly when the device acts like a resistor and when it acts like a current source.

By the end, you can explain the difference between the triode (SR) and saturation (SCS) regions of a MOSFET, state the saturation discipline used for analog design in this course, and set up the node equation for a MOSFET amplifier using both the analytical and graphical methods. This is the second lecture in a five-lecture sequence on amplifiers and leads directly into the next lecture's discussion of the valid operating range.

Key ideas

• Control port: the implicit terminal pair of a dependent source at which a voltage or current sets the value of the dependent current or voltage.
• Superposition with dependent sources: dependent sources are never turned off during superposition; only independent sources are toggled, while dependent sources stay in the circuit and are analyzed normally.
• SR model: for small vDS, a MOSFET with vGS above the threshold VT behaves approximately like a resistor between drain and source (used for digital circuit analysis).
• SCS model: once vDS is greater than or equal to vGS - VT, the MOSFET current saturates and the device behaves like a current source, with iDS = K/2 * (vGS - VT)^2.
• Triode vs. saturation region: the resistive region (vDS < vGS - VT) is the triode region; the current-source region (vDS >= vGS - VT) is the saturation region.
• Saturation discipline: for analog (amplifier) design in this course, MOSFETs are deliberately constrained to operate in saturation so the current-source model applies and amplification is possible.
• Load line: the straight-line relationship from the output loop equation, superimposed on the device's iDS vs. vDS curves, whose intersection gives the operating point.

Walkthrough

Review: superposition with dependent sources (1:30)

The lecture opens by revisiting the amplifier built from an idealized dependent current source in the prior class, where iD depended on an input voltage vI. It then addresses a subtlety in the superposition technique: dependent sources must never be turned off during superposition, only independent sources are switched on and off one at a time while dependent sources remain in the circuit throughout. Applying KVL to the earlier example recovers the relationship vO = VS - iD*RL, with iD substituted as a function of vI, matching what was derived previously.

The full MOSFET characteristic: triode and saturation (22:00)

The lecture reframes the three-terminal MOSFET as a two-port device by treating the source as a common terminal, giving a vGS-controlled port and a vDS/iDS output port. A live demonstration sweeps vDS upward and shows that the current, which looked resistive for small vDS, tails off and saturates at higher vDS. This saturated region is where vDS >= vGS - VT, and there the current is given by iDS = K/2 * (vGS - VT)^2, independent of vDS — the switch current source (SCS) model. Below that boundary, the device follows the resistor-like SR model from earlier lectures (the triode region). The lecture plots the full family of curves for different vGS values, showing the square-law increase in saturation current as vGS rises, and explains that digital circuits use the SR model (since pull-down transistors keep vDS small) while analog amplifier design in 6.002 restricts itself to the saturation region.

Building the MOSFET amplifier (33:50)

The lecture replaces the current source in the earlier amplifier circuit with a MOSFET: drain and gate/source wired so that vI drives the gate-source port and vO is taken across the drain-source port through a load resistor RL to a supply VS. This circuit is identical in topology to the digital inverter seen earlier, but its use differs: for digital logic the MOSFET swings between cutoff and the resistive SR region, while for amplification the circuit is deliberately operated where vDS stays large enough for saturation, since only the current-source behavior produces the gain seen in the previous lecture's vO-versus-vI plot. Operating the device in the resistive region instead does not produce amplification.

The saturation discipline and equivalent circuit (39:40)

The lecture formalizes the constraint: whenever a circuit is stated to have its MOSFETs "in saturation," this means vGS >= VT and vDS >= vGS - VT, letting you replace the MOSFET with its SCS current-source model with iDS = K/2*(vGS - VT)^2. In this specific amplifier, vDS is identical to vO and vGS is identical to vI, since the source is grounded, so the two pairs of labels can be used interchangeably in this circuit (though not in circuits with multiple MOSFETs).

Solving the amplifier: analytical and graphical methods (42:22)

With the MOSFET replaced by its saturation current source, the circuit is a nonlinear circuit, so the lecture applies the node method. Setting the current out of the output node equal to the current into it gives iDS = (VS - vO)/RL. Substituting the saturation expression for iDS and multiplying through by RL yields vO = VS - (K/2)*(vI - VT)^2*RL, valid only while the saturation constraints hold; otherwise (vGS < VT) the device is off and vO = VS. The same problem is then solved graphically by plotting the family of iDS-vs-vDS saturation curves and overlaying the straight "load line" iDS = VS/RL - vO/RL from the output loop equation; the intersection of a given vGS curve with the load line gives the operating point. The lecture ends by noting that the next lecture will determine the range of inputs for which the MOSFET stays in saturation.

Before you watch

• Review the dependent-source amplifier and the vO-versus-vI derivation from the previous lecture.
• Be comfortable with the MOSFET's basic on/off and SR (resistive) models from earlier digital-circuits lectures.
• Recall the node method and the graphical (load-line) method for nonlinear circuits.

Check your understanding

1. Why must dependent sources stay active (never turned off) during superposition, unlike independent sources?
2. What condition on vDS relative to vGS - VT separates the triode region from the saturation region?
3. Why does operating a MOSFET amplifier in the resistive (triode) region fail to produce amplification, according to the lecture?
4. In the amplifier circuit analyzed here, why are vDS and vO (and vGS and vI) treated as identical quantities?
5. How does the load line in the graphical method relate to the output-loop equation iDS = VS/RL - vO/RL?