Voltage gain of a common-base (CB) amplifier: Given r_e = 6 Ω, R_L = 600 Ω and current gain α = 0.98, compute the midband voltage gain.

Introduction / Context:The CB amplifier is known for a high voltage gain and low input impedance. A quick estimation formula relates the voltage gain to the transconductance (1/r_e), the load resistance, and the current gain α.

Given Data / Assumptions:

• Small-signal emitter resistance r_e = 6 Ω.
• Collector load resistance R_L = 600 Ω.
• Common-base current gain α = 0.98.

Concept / Approach:

For a midband CB stage, the approximate magnitude of voltage gain is A_v ≈ α * (R_L / r_e). This comes from v_out ≈ i_c * R_L with i_c ≈ α * i_e and i_e ≈ v_in / r_e.

Step-by-Step Solution:

Verification / Alternative check:

Using a hybrid-π model: g_m ≈ 1/r_e; v_out ≈ −α * g_m * R_L * v_in. The magnitude equals α * (R_L/r_e), matching the quick formula.

Why Other Options Are Wrong:

• 100 ignores α < 1.
• 600 × 0.98 omits division by r_e.
• 6 and 0.98 are unrelated to the required composite expression.

Common Pitfalls:

• Confusing CB with CE gain expressions; CE uses −g_m * R_C when r_o is neglected.

Final Answer:

98.