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Emitter-bias BJT Q point and load line

Short answer

Base loop KVL: I_B = (VCC−V_BE)/[R_B+(β+1)R_E] = 19.3/481k = 40.1 µA. I_C = βI_B = 2.01 mA, V_CE = VCC−I_C R_C−I_E R_E ≈ 13.94 V. Q point: I_CQ = 2.01 mA, V_CEQ = 13.94 V. DC load line: cut‑off (20 V, 0 mA), saturation (0 V, 6.67 mA). Active region.

For the given Emitter-bias BJT network, find Q point. Draw dc load line and find region of operation. [Figure: npn BJT with β = 50; VCC = +20 V; base resistor RB = 430 kΩ from VCC to base; collector resistor RC = 2 kΩ from VCC to collector; emitter resistor RE = 1 kΩ to ground bypassed by CE = 40 µF; input vi coupled to base through 10 µF and output vo taken from collector through 10 µF.]

For DC analysis the capacitors are open circuits; the bypass capacitor CE does not affect the DC values, so RE = 1 kΩ is in the emitter circuit. Take V_BE = 0.7 V (Si).

Q point

Base loop (KVL): VCC − I_B RB − V_BE − I_E RE = 0 with I_E = (β + 1) I_B:

I_B = (VCC − V_BE)/(RB + (β + 1) RE)
    = (20 − 0.7)/(430 k + 51 × 1 k)
    = 19.3/481 k
    = 40.12 µA
I_C = β I_B = 50 × 40.12 µA = 2.006 mA
I_E = (β + 1) I_B = 2.046 mA

Collector loop:

V_CE = VCC − I_C RC − I_E RE
     = 20 − 2.006 × 2 − 2.046 × 1
     = 13.94 V

(Taking I_E ≈ I_C: V_CE ≈ 20 − 2.006 × 3 ≈ 13.98 V.)

Q point: I_CQ ≈ 2.01 mA, V_CEQ ≈ 13.94 V (I_BQ ≈ 40.1 µA).

DC load line

Equation (I_E ≈ I_C): V_CE = VCC − I_C (RC + RE)

I_C = 0       → V_CE(cutoff) = VCC = 20 V
V_CE = 0      → I_C(sat) = 20/(2 k + 1 k) = 6.67 mA

 I_C (mA)
 6.67 *
      | \
      |   \
 2.01 |- - -Q
      |      : \
      |      :   \
    0 +------:-----*----- V_CE (V)
      0    13.94   20

Region of operation

V_CE = 13.94 V is well above V_CE(sat) ≈ 0.2 V and I_C = 2.01 mA is well below I_C(sat) = 6.67 mA. The base-emitter junction is forward biased and the base-collector junction is reverse biased (V_C = 20 − 2.006 × 2 = 15.99 V > V_B = 2.75 V).

Answer: the transistor operates in the active region, near the middle of the load line, suitable for amplification.

✓ Answer checked by Claude Opus 5.5 (high effort)

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