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Design divider-bias CE amplifier (24 V, 2 mA, beta 90)

Short answer

Using VE = VCC/10 = 2.4 V, VCE = VCC/2 = 12 V, and I2 = 5IB yields RE ≈ 1.19 kΩ, RC = 4.8 kΩ, R1 ≈ 157 kΩ, R2 ≈ 27.9 kΩ. With bypassed RE, Av = -gmRC = -384, Rin = R1||R2||rπ ≈ 1.06 kΩ.

Design β independent type DC biased common emitter amplifier with emitter resistance bypassed and find its voltage gain and input resistance. Given parameters Vcc = 24, Ic = 2 mA, β = 90. Use appropriate guideline to have high input resistance.

Design guidelines used

  1. Emitter voltage VE ≈ VCC/10 (large enough for thermal and bias stability, small enough to leave room for the output swing).
  2. Collector-emitter voltage VCE ≈ VCC/2, so the output can swing equally up and down (Q-point at the centre of the load line).
  3. Divider current I2 = 5 IB (the lower end of the 5 to 10 IB range, so R1 || R2 is as large as possible for a high input resistance), which still fixes the base voltage and keeps the bias independent of β.
  4. VB = VE + 0.7 V.

Design

IC  = 2 mA        IB = IC/β = 2 mA/90 = 22.2 µA
IE  = IC + IB = 2.022 mA
VE  = VCC/10 = 2.4 V     RE = VE/IE = 2.4/2.022 mA = 1.19 kΩ
VCE = VCC/2  = 12 V
RC  = (VCC - VE - VCE)/IC = (24 - 2.4 - 12)/2 mA = 4.8 kΩ
VB  = VE + 0.7 = 3.1 V
I2  = 5 IB = 111.1 µA
R2  = VB/I2 = 3.1/111.1 µA = 27.9 kΩ
R1  = (VCC - VB)/(I2 + IB) = 20.9/133.3 µA = 157 kΩ

Calculated values: R1 ≈ 157 kΩ, R2 ≈ 27.9 kΩ, RE ≈ 1.19 kΩ, RC ≈ 4.8 kΩ (in practice, use the nearest standard resistor values). The emitter resistor RE is bypassed by a large capacitor CE; C1 and C2 are the coupling capacitors.

Check and small-signal results (RE bypassed)

re  = VT/IE = 25 mV/2.022 mA = 12.4 Ω
rπ  = β re = 1113 Ω         gm = IC/VT = 80 mA/V
R1 || R2 = 23.7 kΩ
Rin = R1 || R2 || rπ = 1.06 kΩ
Av  = -gm RC = -80 mA/V × 4.8 kΩ = -384

Ro ≈ RC = 4.8 kΩ.

Answer: R1 ≈ 157 kΩ, R2 ≈ 27.9 kΩ, RE ≈ 1.19 kΩ, RC = 4.8 kΩ; voltage gain Av ≈ -384; input resistance Rin ≈ 1.06 kΩ (limited by rπ, since RE is bypassed).

✓ Answer checked by Claude Opus 5.5 (high effort)

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