For an Emitter Bias BJT configuration arrange stability factor S(Iw) in descending order if β = 50. RB is base resistance and RE is emitter resistance. (A) RE = 0.1 RB Choose the most appropriate answer from the options given below :
(B) RB = 60 RE
(C) RB = 100 RE
(D) RE = 10 RB
(E) RB = 30 RE
(C), (B), (E), (A), (D)
The stability factor for emitter bias depends on one ratio only, so the five cases can be ranked by that ratio alone.
\(S=\dfrac{\left(1+\beta\right)\left(1+\dfrac{R_{B}}{R_{E}}\right)}{1+\beta+\dfrac{R_{B}}{R_{E}}}\)
Step 1 — express every case as the ratio k = RB/RE. Note that (A) and (D) are stated the other way round and must be inverted:
| Case | Given | k = RB/RE |
|---|---|---|
| (A) | RE = 0.1 RB | 10 |
| (B) | RB = 60 RE | 60 |
| (C) | RB = 100 RE | 100 |
| (D) | RE = 10 RB | 0.1 |
| (E) | RB = 30 RE | 30 |
Step 2 — evaluate with β = 50, so 1 + β = 51.
\(S=\dfrac{51\left(1+k\right)}{51+k}\)
| Case | k | S |
|---|---|---|
| (C) | 100 | \(\dfrac{51\times101}{151}=34.1\) |
| (B) | 60 | \(\dfrac{51\times61}{111}=28.0\) |
| (E) | 30 | \(\dfrac{51\times31}{81}=19.5\) |
| (A) | 10 | \(\dfrac{51\times11}{61}=9.2\) |
| (D) | 0.1 | \(\dfrac{51\times1.1}{51.1}=1.10\) |
Descending order is (C), (B), (E), (A), (D) — option 2.
Since S rises monotonically with k, no arithmetic is strictly needed: ranking the ratios 100, 60, 30, 10, 0.1 gives the answer directly. The two inversions in (A) and (D) are the only real trap, and (D) — a large emitter resistance against a small base resistance — is the best-biased case of the five.
What S means, and why small is good. It is defined as
\(S=\dfrac{\partial I_{C}}{\partial I_{CO}}\)
— how much the collector current moves for a given change in leakage. The ideal is \(S=1\), and case (D) very nearly reaches it. The two limits of the formula show the whole story: as \(k\to\infty\), S tends to \(1+\beta=51\), which is fixed bias, the worst possible; as \(k\to0\), S tends to 1, the best.
The design rule follows immediately : make \(R_{E}\) large compared with the Thevenin base resistance. The emitter resistor senses the collector current and feeds a correction back to the base-emitter loop, and the larger it is relative to \(R_{B}\), the more completely that correction acts.
Hence, the descending order is (C), (B), (E), (A), (D).
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