A quick way to answer this question is to compare the common gate (CG) FET amplifier with its closest BJT counterpart, the common base (CB) amplifier, since both share the same topology: input at the low-impedance terminal (source or emitter), output at the high-impedance terminal (drain or collector), and the middle terminal (gate or base) held at AC ground.
- voltage controlled voltage source: This describes a follower stage, where the output voltage copies the input voltage with near-unity gain and low output impedance. The common drain (source follower) fits this description, not the common gate stage, since the CG stage has high output impedance at the drain, not low.
- current controlled current source: The CG stage is driven by a current at the source (low impedance point) and delivers essentially the same current at the drain (high impedance point), since almost all of the source current continues through the channel to the drain. A stage whose output current is set by its input current, with a low-impedance input port and a high-impedance output port, is exactly a current buffer, that is, a CCCS.
- voltage controlled current source: This is the defining behavior of the common source stage, where $i_d = g_m v_{gs}$ links the gate to source voltage directly to the drain current. The common gate stage is driven at the source terminal by a current, not by a high-impedance gate voltage, so this model does not apply here.
- current controlled voltage source: This is the behavior of a transimpedance amplifier, which needs a feedback network, such as an op-amp with a feedback resistor, to convert an input current into an output voltage. A basic single-transistor CG stage has no such feedback resistor converting current to voltage.
Since the CG stage passes its source current through to the drain with current gain near $1$ while offering a low input impedance and a high output impedance, exactly like a common base BJT stage, it is classified as a current buffer, that is, a current controlled current source.
Let's summarize:
- Common source = voltage controlled current source (transconductance amplifier).
- Common drain = voltage controlled voltage source (voltage buffer / follower).
- Common gate = current controlled current source (current buffer), the same role a common base stage plays for a BJT.
So the correct choice is option (B), current controlled current source.