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Design CE voltage divider bias, beta 200

Short answer

Design: VE=1.2V, VCE=6V, RE=597Ω, RC=2.4kΩ, R1=168kΩ, R2=38kΩ. RE unbypassed yields Rin≈24.7kΩ, Av≈-3.9, ensuring high input impedance with moderate gain.

Design common emitter BJT voltage divider bias circuit with high input impedance. Given: β= 200, IC = 2 mA, and VCC = +12 V.

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 that R1 || R2 is as large as possible (high input impedance) while the base voltage stays fixed and the bias remains independent of β.
  4. VB = VE + 0.7 V.
  5. For a high input impedance, RE is left unbypassed, so that (β+1)RE appears in the input resistance.

Design

IC  = 2 mA        IB = IC/β = 2 mA/200 = 10 µA
IE  = IC + IB = 2.01 mA
VE  = VCC/10 = 1.2 V     RE = VE/IE = 1.2/2.01 mA = 597 Ω
VCE = VCC/2  = 6 V
RC  = (VCC - VE - VCE)/IC = (12 - 1.2 - 6)/2 mA = 2.4 kΩ
VB  = VE + 0.7 = 1.9 V
I2  = 5 IB = 50 µA
R2  = VB/I2 = 1.9/50 µA = 38 kΩ
R1  = (VCC - VB)/(I2 + IB) = 10.1/60 µA = 168 kΩ

Calculated values: R1 ≈ 168 kΩ, R2 ≈ 38 kΩ, RE ≈ 597 Ω, RC ≈ 2.4 kΩ (in practice, use the nearest standard resistor values). C1 and C2 are the coupling capacitors.

Check and small-signal results (RE unbypassed)

re  = VT/IE = 25 mV/2.01 mA = 12.4 Ω
R1 || R2 = 31 kΩ
Rib = (β+1)(re + RE) = 201 × (12.4 + 597) = 122.5 kΩ
Rin = R1 || R2 || Rib = 31 k || 122.5 k = 24.7 kΩ
Av  = -RC/(re + RE) = -2400/609.4 = -3.9

Ro ≈ RC = 2.4 kΩ.

Because the base current is small (β = 200), a divider current of only 5 IB (50 µA) still keeps VB stiff and gives R1 || R2 ≈ 31 kΩ, so the amplifier's input resistance is high (≈ 24.7 kΩ). If RE were bypassed by a capacitor, the gain would rise to -gm RC = -80 mA/V × 2.4 kΩ = -192, but Rin would drop to R1 || R2 || rπ = 31 k || 2.49 k ≈ 2.3 kΩ (rπ = β re = 2488 Ω).

✓ Answer checked by Claude Opus 5.5 (high effort)

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