Question 3.SP.15: Find the value of the emitter resistor RE that, when added t......

Schaum’s Outline of Electronic Devices and Circuits [1089587]

Find the value of the emitter resistor $R_E$ that, when added to the Si transistor circuit of Fig. 3-17, would bias for operation about $V_{CEQ} = 5 \text{V}$ . Let $I_{CEO} = 0, β = 80, R_F = 220 kΩ, R_C = 2 kΩ$ , and $V_{CC} = 12 \text{V}$ .

3.17

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Application of KVL around the transistor terminals yields
$I_{BQ} = \frac{V_{CEQ} – V_{BEQ}}{R_F} = \frac{5 – 0.7}{220 × 10^{3}} = 19.545 μ\text{A}$

Since leakage current is zero, (3.1) and (3.2) give $I_{EQ} = (β + 1)I_{CQ}$ ; thus KVL around the collector circuit gives
$α(≡ h_{FB}) ≡ \frac{I_C – I_{CBO}}{I_E}$ (3.1)
$β(≡ h_{FE}) ≡ \frac{α}{1 – α} ≡ \frac{I_C – I_{CEO}}{I_B}$ (3.2)
$(I_{BQ} + βI_{BQ})R_C + (β + 1)I_{BQ}R_E = V_{CC} – V_{CEQ}$

so $R_E = \frac{V_{CC} – V_{CEQ} – (β + 1)I_{BQ}R_C}{(β + 1)I_{BQ}} = \frac{12 – 5 – (80 + 1)(19.545 × 10^{-6})(2 × 10^{3})}{(80 + 1)(19.545 × 10^{-6})} = 2.42 kΩ$

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