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.
Electronics and Communication Engineering
Analog Electronics
Difficulty: Easy
Choose an option
-
A100
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B600 × 0.98
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C98
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D6
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E0.98
Answer
Correct Answer: 98
Explanation
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:
Compute the ratio R_L / r_e = 600 / 6 = 100.Multiply by α: A_v ≈ 0.98 * 100 = 98.Thus, the midband voltage gain is approximately 98 (in magnitude).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.