Lecture 9B: Large Signal Analysis of a MOSFET Amplifier

What this lecture covers

Building on the previous lecture's MOSFET amplifier, this lecture introduces "large signal analysis": the two-step process of finding a circuit's transfer function (output versus input) and then finding the range of input values for which the circuit actually satisfies the saturation discipline. The MOSFET amplifier from the last two lectures serves as the running example, but the lecture stresses that the same method applies to any device, including the bipolar junction transistor discussed in the course notes.

After watching, you can derive the valid input operating range for a MOSFET amplifier both algebraically (solving where the transfer function meets the triode boundary) and graphically (using the transfer curve or the load-line diagram), and you can explain why a DC offset is needed to keep a real input signal inside that valid range.

Key ideas

• Large signal analysis: a two-step process — (1) derive the transfer function relating output to input, (2) find the valid input range for which the assumed operating region (e.g., saturation) actually holds.
• Transfer function: for the MOSFET amplifier, vO = VS while vI < VT, and vO = VS - (K/2)(vI - VT)^2 * RL once the MOSFET turns on and stays in saturation.
• Valid input range: bounded below by vI = VT (MOSFET turns on) and above by the point where vO drops to exactly vI - VT (MOSFET enters the triode region).
• Graphical intuition: overlaying the line vO = vI - VT (the vO = vI line shifted right by VT) on the transfer curve locates the upper boundary of valid operation.
• Load-line view: the same boundary can be found by intersecting the saturation-region device curves with the load line iDS = VS/RL - vO/RL, giving the same operating point as the transfer-function method.
• Why graphical methods matter: many real devices (like the lab's MOSFET) are characterized only by measured data-sheet curves, not a clean equation, so graphical analysis is sometimes the only option.
• DC offset (boosting): a small-amplitude input signal must be shifted upward by a DC offset so all its excursions fall inside the valid operating range; too little or too much offset drives the MOSFET out of saturation and ruins the amplification.

Walkthrough

What "large signal analysis" means (1:38)

The lecture defines large signal analysis as figuring out, for a circuit built from a device like a MOSFET, how to set circuit parameters so the device stays in its intended operating region (here, saturation). It notes this generalizes beyond the MOSFET; the course notes work through the same kind of analysis for a bipolar junction transistor.

Reviewing the amplifier's equivalent circuit (4:40)

The lecture recaps the MOSFET amplifier and its saturation equivalent circuit, where the MOSFET is replaced by a dependent current source with iDS = (K/2)(vI - VT)^2. It restates the two saturation conditions: vGS >= VT and vDS >= vGS - VT (equivalently vI >= VT and vO >= vI - VT in this circuit), and frames the engineer's task as choosing VS, RL, and the input so these hold.

The two steps of large signal analysis (8:30)

The lecture lays out the method concretely: first write the transfer function vO versus vI under the saturation discipline (reusing the square-law result from the prior lecture), then find the valid input range that keeps the circuit within that discipline for given VS, RL, and MOSFET parameters. It notes the transfer function need not always be voltage-to-voltage; other circuits might relate an output current to an input voltage or current.

Building the graphical intuition for the valid range (16:18)

Using the plotted transfer curve of vO versus vI, the lecture identifies the lower bound of valid input (vI = VT, where the MOSFET turns on) and argues that the upper bound occurs where the output falls to exactly one threshold below the input. Drawing the vO = vI line and shifting it right by VT produces the line vO = vI - VT; above this line the MOSFET is in saturation, below it the MOSFET has entered the triode region. The intersection of this line with the transfer curve marks the valid range's upper edge.

Solving for the boundary point analytically (24:09)

The lecture solves for this boundary point (labeled point X) by substituting vO = vI - VT into the transfer function, producing a quadratic in vO. Using the quadratic formula and taking the positive root gives vO at the boundary in terms of VS, RL, and K, and back-substituting gives the corresponding vI. This yields the full valid input range, from VT up to VT plus an expression involving VS, RL, and K, with the corresponding valid output range running from VS down to that same boundary value.

The load-line alternative view (33:44)

As a second, equivalent approach, the lecture plots iDS versus vDS (the load-line graph used earlier), showing the saturation-region device curves for a family of vGS values together with the load line iDS = VS/RL - vO/RL derived from KVL around the output loop. The valid operating range corresponds to the segment of the load line lying in the saturation region, bounded by the point where vGS = VT (output at VS, current zero) and the point where the load line crosses into the triode region. The lecture notes this gives the same numerical answer as the transfer-function method, and that some people find one view more intuitive than the other.

Boosting a real input signal into range (45:28)

Finally, the lecture addresses how to actually keep an amplifier in its valid range: apply a DC offset to a small input signal so its full excursion stays inside the valid input window. A live demo drives the amplifier with a triangular wave at several offsets. With little or no offset the output is distorted because the MOSFET drops out of saturation; with too large an offset the amplifier is overdriven into the triode region and gain collapses; with the correct offset, the triangular wave is amplified cleanly, though still not perfectly linearly. The lecture closes by noting that achieving a genuinely linear response is the subject of small signal analysis, covered next.

Before you watch

• Review the MOSFET amplifier and its saturation equivalent circuit from the previous lecture (Lec 9), including the vO-versus-vI square-law transfer function.
• Be comfortable with the saturation conditions vGS >= VT and vDS >= vGS - VT.
• Recall the load-line construction from earlier nonlinear-circuit analysis.

Check your understanding

1. What are the two steps of large signal analysis, and why is the second step necessary even after finding the transfer function?
2. How does shifting the vO = vI line to the right by VT help locate the boundary of the valid input range?
3. Why might an engineer need the graphical (load-line or transfer-curve) method instead of an analytical equation when characterizing a real device?
4. What happens to the amplifier's output when the DC offset applied to the input is too small, and why?
5. What happens when the offset is too large, and why does the output shrink in that case?