The Common-Source Amplifier: Same Gain, Open Input
Grow the drain resistor and the inverted gain grows
The faint curve is the gate input vin, and the bold gold curve is the drain output vout. The red dashed lines above and below are the supply limits the output cannot cross. As you raise the drain resistor Rd, the output grows, and it falls whenever the input rises, so the two curves mirror each other. The voltage gain Av on the indicator also grows in proportion to the resistor.
The gate signal wobbles the drain current
Put the input signal on the gate and a small vgs rides on top of the DC operating point. As seen in D3, this small voltage creates a drain signal current id = gm vgs. Here the MOSFET parts ways with the BJT. A thin oxide layer sits under the gate, so no DC current flows in, and the signal source in front only has to supply a voltage, not a current. The BJT was the exact opposite: its base drew signal current from the source.
That current becomes a voltage across Rd and inverts
This drain signal current flows through the drain resistor Rd. By Ohm's law, the voltage across Rd swings by id Rd. The output is taken at the drain, and the drain voltage is the supply Vdd minus the resistor voltage Id Rd. When the signal current rises, the resistor takes more of the voltage and the drain voltage drops. The output falls as the input rises, an inversion written as vout = -id Rd. The role the collector played in the common emitter (C4) is played here by the drain.
Av = -gm Rd, and the open input
Substituting id = gm vgs into vout = -id Rd gives the voltage gain Av = -gm Rd, the same form as the common emitter's -gm Rc. Two things differ. The first is size. The MOSFET's gm grows only with the square root of the drain current (D3), so at the same current its gm is usually smaller than a BJT's and the gain is lower. The second is the input. The gate is insulated, so the device's own input impedance is nearly infinite, and in a real circuit the input resistance is set by the bias resistors that hold the gate at its DC voltage. The amplifier therefore takes almost no signal from the stage before it. Even if it gives up raw gain to the BJT, this high input impedance, which does not load the previous stage, is the strength of the MOSFET amplifier.
Back to the first screen
As you raised the drain resistor, the output grew, and every time the input rose it fell, tracing an upside-down shape. The math matched the common emitter. The small gate voltage became a drain signal current gm vgs, and that current flowed through the drain resistor Rd, turned into a voltage, and pulled the drain voltage down. Their product, -gm Rd, is the voltage gain. You also saw why the resistor cannot grow forever. The output clipped at the supply limits, and in a real device the output resistance created by channel-length modulation sits in parallel with the drain resistor and caps the gain. Two things set it apart from the BJT. The MOSFET's smaller gm means lower raw gain, but the insulated gate takes no current, so it barely loads the stage before it. High gain lives with the BJT, high input impedance with the MOSFET, and designers choose between them.
What comes next
So far the MOSFET has served analog amplification. Yet the stage where the MOSFET changed the world is digital. In the next unit, you stack an NMOS and a PMOS to build a CMOS inverter, in which only one of the two turns on depending on whether the input is 0 or 1. The output flips completely, yet in either resting state there is no direct path from the supply to ground, so almost no current flows while it sits still.