BJT Common-Emitter Voltage Divider Bias Calculator

BJT CE voltage-divider bias: Vb = Vcc × R2/(R1+R2). Ve = Vb − 0.7 V. Ic ≈ Ve/Re. Vce = Vcc − Ic(Rc + Re). Also checks if bias is stable (R1∥R2 ≤ β×Re/10).

BJT Common-Emitter — Voltage Divider Bias

ParameterValue
VB (base)--
VE (emitter)--
IC (collector)--
VC (collector)--
VCE--
Bias Stability--

Formula & Theory

  • Base voltage: VB = VCC × R2 / (R1 + R2)
  • Emitter voltage: VE = VB − 0.7 V (Vbe approximation)
  • Collector current: IC ≈ VE / RE (assuming β×Re >> R1∥R2)
  • Collector voltage: VC = VCC − IC × RC
  • Collector-emitter voltage: VCE = VC − VE
  • Stability condition: R1∥R2 ≤ β × RE / 10

Worked Example

Design a CE amplifier biased at Ic = 5 mA, Vce ≈ 6 V, Vcc = 12 V, β = 100:

  • Choose Re = 470 Ω, then Ve = Ic × Re = 5 mA × 470 = 2.35 V
  • Vb = Ve + 0.7 = 3.05 V
  • Rc = (Vcc − Vce − Ve) / Ic = (12 − 6 − 2.35) / 0.005 = 730 Ω → use 680 Ω
  • Divider: Vb/Vcc = 3.05/12 = 0.254. Set R2 = 10 kΩ, R1 = R2 × (Vcc/Vb − 1) = 10 × (12/3.05 − 1) = 29.3 kΩ → use 27 kΩ
  • Stability: R1∥R2 = 27∥10 = 7.3 kΩ vs β×Re/10 = 100×470/10 = 4700 Ω → UNSTABLE — reduce R1, R2 by 2×

Assumptions & Limitations

  • Vbe = 0.7 V (silicon BJT at room temperature, moderate Ic)
  • β is constant — in reality β varies with Ic, temperature, and device-to-device
  • The β×Re/10 stability rule assumes strong temperature/device-to-device independence is required
  • DC analysis only — AC gain requires bypass capacitor on Re and coupling capacitors

Common Mistakes

  • Choosing Vce too low: Keep VCE ≥ 1–2 V minimum to maintain the transistor in the active region and provide headroom for signal swing. VCE < 0.2 V means saturation — the BJT is no longer amplifying.
  • Ignoring Ic vs β variation: Even with a "stable" design, replacing the BJT with one of different β shifts the Q-point slightly. Test the design with β at its minimum datasheet value.
  • No bypass capacitor on Re: Without a bypass capacitor across Re, Re provides negative feedback that reduces AC gain to approximately Rc/Re. Add a capacitor across Re (value: 1/(2π × f_low × Re)) for full AC gain.
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Frequently Asked Questions

What does the bias stability check mean?

Bias stability requires that R1∥R2 (the Thevenin resistance of the voltage divider) is less than β×Re/10. If this condition is met, the bias point is relatively insensitive to transistor beta (hFE). If it fails, Vce will shift significantly if you replace the BJT with one that has a different beta — a common problem in production.

Why is Vbe assumed to be 0.7 V?

For silicon BJTs at room temperature with moderate collector currents (1–100 mA), Vbe is typically 0.6–0.7 V. This calculator uses 0.7 V as a standard approximation. At low collector currents (<1 mA), Vbe may be closer to 0.55–0.60 V; at high currents it can reach 0.75–0.80 V.

How do I choose the Q-point for a linear amplifier?

For maximum symmetric output voltage swing, set Vce ≈ Vcc/2 and Ic such that the load line passes through the center of the active region. A starting point: Ic ≈ (Vcc/2) / (Rc + Re), then adjust R1 and R2 to set Vb = Ve + 0.7 V = Ic × Re + 0.7 V.