D4 · MOSFET

The Common-Source Amplifier: Same Gain, Open Input

Fit the MOSFET small-signal model into a circuit to make a voltage gain. Grow the drain resistor yourself and see the output swell inverted, in the same form as the common-emitter, while the input takes no burden at all.

Grow the drain resistor to make gain

The faint curve is the gate input vin and the bold curve is the output vout. Grow the drain resistor Rd and the output gets larger, tracing a flipped shape that falls when the input rises. The gate draws no current, so the input signal is delivered intact.

Drain resistor RdRd = 2.0 kΩ

Voltage gain Av

Av = -gm Rd = -4

Rin ≈ ∞

Rd is small. The voltage the same drain current makes across a small resistor is small, so the output is not much larger.

Low gain

The gate signal wobbles the drain current

Couple the input signal onto the gate and a small vgs is added on top of the operating point. As seen in D3, this small voltage makes a drain signal current id = gm vgs. An important difference lives here: the gate is insulated and draws no current, so the signal source in front applies its voltage fully to the gate with no burden. This is the very opposite of the BJT base, which demanded a current.

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 wobbles by id Rd. The output is taken at the drain, whose voltage is the supply Vdd minus Id Rd. So when the signal current rises, the drain voltage instead falls. The output falls when the input rises: an inverted output, vout = -id Rd. What the collector did in the common-emitter (C4), the drain does identically here.

Av = -gm Rd, and the open input

Substituting id = gm vgs into vout = -id Rd gives the voltage gain Av = -gm Rd, exactly the same form as the common-emitter’s -gm Rc. But two things differ. First, the MOSFET’s gm grows only as the square root of current (D3), so at the same current the gain is usually lower than the BJT’s. Second, the gate is insulated, so the input impedance is nearly infinite, and this amplifier barely steals signal from the stage before it. Even if it yields raw gain to the BJT, this high input impedance, which burdens no preceding stage, is the great strength of the MOSFET amplifier.

Observevout = -id Rd

The output voltage is what the signal current makes across Rd, with opposite sign.

Chooseid = gm ?

The drain signal current is transconductance times gate voltage.

Fill inAv = voutvin = -gm ?

The gain is minus the product of transconductance and drain resistor.

On your ownRin ≈ ?

With an insulated gate, the input impedance is nearly infinite.

Back to the first screen

The more you grew the drain resistor, the larger the output became, falling each time the input rose to trace a flipped shape. The arithmetic was identical to the common-emitter. The small gate voltage became a drain signal current gm vgs, and that current, flowing through the drain resistor Rd, became a voltage that pulled the drain voltage down. Their product, -gm Rd, is the voltage gain. Two things differed: the MOSFET’s small gm gives lower raw gain, but thanks to the insulated gate the input draws no current and barely burdens the stage before. Large gain to the BJT, large input impedance to the MOSFET, the designer chooses between the two.

A common-source amplifier is the MOSFET small-signal model (D3) placed in a circuit. A small gate signal vgs makes a drain current id = gm vgs, and this current flows through the drain resistor Rd to make vout = -id Rd. Since rising current lowers the drain voltage, the output is inverted. The voltage gain Av = -gm Rd, the same form as the common-emitter (C4). The MOSFET’s gm is small, so the gain is usually lower, but the insulated gate gives a nearly infinite input impedance that burdens no preceding stage.

What comes next

So far we used the MOSFET for analog amplification. But the stage where the MOSFET changed the world is digital. The next unit pairs an NMOS and a PMOS top and bottom to build a CMOS inverter, where only one of the two turns on depending on whether the input is 0 or 1. The output flips completely, yet in the static state almost no current flows and it spends almost no power.