Write down each current gain.

(b) Common base — the smallest.

\(\alpha=\dfrac{I_C}{I_E}\approx0.95\text{ to }0.99\ \ (\lt 1)\)

Since the emitter current splits into base and collector currents, the collector can never receive quite all of it. CB is therefore a current attenuator — it gives voltage gain, not current gain.

(a) Common emitter — next.

\(\beta=\dfrac{I_C}{I_B}=\dfrac{\alpha}{1-\alpha}\approx 50\text{ to }200\)

(c) Common collector — slightly higher than CE.

\(\gamma=\dfrac{I_E}{I_B}=1+\beta\)

Exactly one greater than β, because the emitter carries the base current as well as the collector current. This is the emitter follower: unity voltage gain but the highest current gain of the three transistor configurations, which is what makes it a buffer.

(d) Op-amp — the largest by far. An ideal op-amp draws zero input current (infinite input impedance) while its output can supply milliamps, so the ratio of output to input current is effectively infinite. Even a real device with picoamp bias currents gives a current gain of many millions.

Ascending order:

\(\alpha \lt \beta \lt (1+\beta) \ll \infty \Rightarrow (b), (a), (c), (d)\)

The relation worth remembering ties the first three together:

\(\gamma=1+\beta=\dfrac{1}{1-\alpha}\)

so all three configurations are described by a single parameter, and the ordering α < β < γ is automatic. Note also that CB and CC have current gains that differ by roughly β², which is why they sit at opposite ends of the list.

Hence, the ascending order of current gain is (b), (a), (c), (d).