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Circuits, electronics and noise
BJT base current with divider bias and emitter resistor
Base current of an NPN transistor in forward-active bias, after replacing the base divider by its Thevenin voltage and resistance.
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- ELN-16
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- v1
- Field
- Circuits, electronics and noise
- Result
- IB [A]
Replace the base divider with its Thevenin voltage Vth and resistance Rth. Then Kirchhoff’s voltage law around the base–emitter loop gives Vth = Ib Rth + Vbe + (β + 1) Ib Re, because the emitter carries (β + 1) times the base current. The emitter resistor appears in the base circuit multiplied by β + 1, which is what makes the bias stable against changes in β.
Base current of an NPN transistor in forward-active bias, after replacing the base divider by its Thevenin voltage and resistance. The emitter resistor appears multiplied by β + 1.
Calculator
- Collector current, β Ib0.0018 A
- Emitter current, (β + 1) Ib0.001818 A
- Emitter voltage, (β + 1) Ib Re1.818 V
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The base current is 1.818×10−5 A (18.18 µA), giving a collector current of 0.0018 A for β = 99.
- Because the loop resistance is dominated by (β + 1)Re = 100,000 Ω, the emitter current is nearly (Vth − Vbe)/Re, whatever the exact value of β.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (A) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Re Emitter resistor | 100 to 10,000 Ω | 1.98e-6 | 1e-4 | 9.802e-5 | +10% | −8.33 % |
| Vth Thevenin voltage of the base divider | 1 to 10 V | 2.727e-6 | 8.455e-5 | 8.182e-5 | +10% | +13.5 % |
| β DC current gain | 20 to 500 | 3.914e-6 | 6.452e-5 | 6.06e-5 | +10% | −8.26 % |
| Rth Thevenin resistance of the base divider | 100 to 100,000 Ω | 1e-5 | 1.998e-5 | 9.98e-6 | +10% | −0.901 % |
| Vbe Base–emitter drop | 0.5 to 0.9 V | 1.636e-5 | 2e-5 | 3.636e-6 | +10% | −3.5 % |
Sweep of DC current gain
| DC current gain | Base current (A) |
|---|---|
| 20 | 6.452e-5 |
| 80 | 2.198e-5 |
| 140 | 1.325e-5 |
| 200 | 9.479e-6 |
| 260 | 7.38e-6 |
| 320 | 6.042e-6 |
| 380 | 5.115e-6 |
| 440 | 4.435e-6 |
| 500 | 3.914e-6 |
Sweep one variable
Variables and how each one contributes
Base current
What the equation gives you. Everything else feeds it.
Thevenin voltage of the base divider
The Thevenin voltage of the base divider, in V. Raises the base current: it is the voltage available above the base–emitter drop. Raising it by 10 % (to 2.97) moves the result by +13.5 %, from 1.818×10−5 to 2.064×10−5 A.
Base–emitter drop
The base–emitter voltage drop, in V, about 0.7 V for silicon. A larger drop leaves less voltage to drive the base current, so Ib falls. Raising it by 10 % (to 0.77) moves the result by −3.5 %, from 1.818×10−5 to 1.755×10−5 A.
Thevenin resistance of the base divider
The Thevenin resistance of the base divider, in Ω. A larger Rth adds to the resistance in the base loop and lowers Ib. Raising it by 10 % (to 11,000) moves the result by −0.901 %, from 1.818×10−5 to 1.802×10−5 A.
DC current gain
The DC current gain β of the transistor. A larger β makes the emitter resistor look bigger from the base, so Ib falls. Raising it by 10 % (to 108.9) moves the result by −8.26 %, from 1.818×10−5 to 1.668×10−5 A.
Emitter resistor
The emitter resistor, in Ω. A larger Re adds (β + 1)Re to the base loop and lowers Ib. Raising it by 10 % (to 1,100) moves the result by −8.33 %, from 1.818×10−5 to 1.667×10−5 A.
Worked example with the values above
- Drive voltage: Vth − Vbe = 2.7 − 0.7 = 2 V.
- Loop resistance: Rth + (β + 1)Re = 10,000 + 100 × 1,000 = 110,000 Ω.
- Ib = 2 / 110,000 = 1.8182×10−5 A.
Assumptions and limits
- An NPN transistor in the forward-active region, with a fixed base–emitter drop of about 0.7 V.
- Midband small signals, an AC-grounded supply and negligible transistor output conductance.
Common mistakes
- Forgetting to check that the collector–base junction is still reverse biased.
- Using the DC current gain where the small-signal gain is needed, or the reverse.
- Forgetting that an unbypassed emitter resistor adds (β + 1) times its value to the input resistance.
Statistics and uncertainty
Transistor current gain β varies by a factor of two or more between parts and with temperature, so a stable design depends on emitter feedback, not on β. Thermal voltage changes by about 0.33 % per kelvin.
Where it is used
- Setting the operating point of transistor amplifiers and switches.
- Estimating small-signal gain, input resistance and the effect of emitter degeneration.
Maths you need
- Thevenin equivalent: a source and a resistance in series
- Transistor current gain: β = Ic / Ib
- Thermal voltage: kT/q, about 25 mV at room temperature