BJT Bias Formulas: Voltage Divider Bias
Bipolar transistor voltage divider bias formulas: base voltage, emitter and collector current, collector voltage and VCE, with a worked example and a table.
The formulas
| To find | Formula |
|---|---|
| Base voltage (stiff divider) | VB = Vcc × R2 / (R1 + R2) |
| Emitter voltage | VE = VB − VBE |
| Emitter current | IE = VE / RE |
| Collector current | IC ≈ IE (for a high gain) |
| Collector voltage | VC = Vcc − IC × RC |
| Collector-emitter voltage | VCE = VC − VE = Vcc − IC × (RC + RE) |
VBE is about 0.7 V for a silicon transistor and falls by about 2 mV per °C. The method assumes the divider current is at least ten times the base current, so the base voltage is set by the divider and not by the transistor gain. This is why the circuit is stable against changes in β. For a mid-supply bias aim for VCE near half of Vcc, and check the result on the bench.
Worked example: 12 V supply
R1 = 47 kΩ, R2 = 10 kΩ, RC = 2.2 kΩ and RE = 1 kΩ.
- VB = 12 × 10 / (47 + 10) = 2.105 V
- VE = 2.105 − 0.7 = 1.405 V, so IE = 1.405 / 1000 = 1.405 mA
- VC = 12 − 1.405 mA × 2.2 kΩ = 8.908 V
- VCE = 8.908 − 1.405 = 7.503 V
Effect of VBE on the bias point
| VBE | IE | VCE |
|---|---|---|
| 0.6 V | 1.505 mA | 7.183 V |
| 0.7 V | 1.405 mA | 7.503 V |
| 0.8 V | 1.305 mA | 7.823 V |
Frequently asked questions
Why is an emitter resistor used?
It gives negative feedback. If the current rises, the voltage across RE rises and reduces the base-emitter voltage, which holds the current steady against changes in β and temperature.
How stiff must the divider be?
The divider current should be about ten times the base current. A stiffer divider holds VB better but loads the signal source and wastes power.
Why aim for VCE near half of the supply?
It leaves equal room for the collector voltage to swing up and down before the signal clips.
What if the transistor gain is low?
Then the base current is not small and the base voltage drops. Use the Thévenin equivalent of the divider and include the base current in the calculation.
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