Library / Circuits, electronics and noise / ELN-17
Circuits, electronics and noise
BJT collector-emitter bias voltage
Voltage across the transistor from collector to emitter, found from the supply minus the drops across the collector and emitter resistors.
- Ref
- ELN-17
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- Vce [V]
Going round the collector side of an NPN stage, the supply is shared between the collector resistor, the transistor and the emitter resistor. Vce = Vcc − Ic Rc − Ie Re, where the emitter current is Ic + Ib. For linear operation Vce should stay above about 0.2 V, and ideally leave half the supply for the signal swing. Below that the transistor saturates and the formulas for gain no longer apply.
Voltage across the transistor from collector to emitter, found from the supply minus the drops across the collector and emitter resistors. Use it to check headroom in the forward-active region.
Calculator
- Drop across the collector resistor4 V
- Drop across the emitter resistor2.02 V
- Headroom above saturation (Vce − 0.2 V)5.78 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 transistor has 5.98 V from collector to emitter, so it is in the active region with 5.78 V of headroom.
- The stage is best biased with Vce near half the supply, here 6 V, so the output can swing equally up and down.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (V) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Rc Collector resistor | 100 to 100,000 Ω | −190 | 9.78 | 199.8 | +10% | −6.69 % |
| Ic Collector current | 1e-4 to 0.02 A | −48.02 | 11.68 | 59.7 | +10% | −10 % |
| Vcc Supply voltage | 5 to 30 V | −1.02 | 23.98 | 25 | +10% | +20.1 % |
| Re Emitter resistor | 100 to 10,000 Ω | −12.2 | 7.798 | 20 | +10% | −3.38 % |
| Ib Base current | 1e-6 to 0.001 A | 5 | 5.999 | 0.999 | +10% | −0.0334 % |
Sweep of Collector resistor
| Collector resistor (Ω) | Collector–emitter voltage (V) |
|---|---|
| 100 | 9.78 |
| 237.1 | 9.506 |
| 562.3 | 8.855 |
| 1,334 | 7.313 |
| 3,162 | 3.655 |
| 7,499 | −5.018 |
| 17,780 | −25.59 |
| 42,170 | −74.36 |
| 100,000 | −190 |
Sweep one variable
Variables and how each one contributes
Collector–emitter voltage
What the equation gives you. Everything else feeds it.
Supply voltage
The supply voltage, in V. Raises Vce one for one, as every other quantity is held fixed. Raising it by 10 % (to 13.2) moves the result by +20.1 %, from 5.98 to 7.18 V.
Collector current
The collector current, in A. More current increases the drops over Rc and Re, so Vce falls. Raising it by 10 % (to 0.0022) moves the result by −10 %, from 5.98 to 5.38 V.
Base current
The base current, in A. Adds to the emitter current, so the drop across Re rises slightly and Vce falls. Raising it by 10 % (to 2.2×10−5) moves the result by −0.0334 %, from 5.98 to 5.978 V.
Collector resistor
The collector resistor, in Ω. A larger Rc drops more voltage and lowers Vce. Raising it by 10 % (to 2,200) moves the result by −6.69 %, from 5.98 to 5.58 V.
Emitter resistor
The emitter resistor, in Ω. A larger Re drops more voltage and lowers Vce. Raising it by 10 % (to 1,100) moves the result by −3.38 %, from 5.98 to 5.778 V.
Worked example with the values above
- Collector drop: Ic Rc = 0.002 × 2,000 = 4 V.
- Emitter drop: (Ic + Ib) Re = 0.00202 × 1,000 = 2.02 V.
- Vce = 12 − 4 − 2.02 = 5.98 V.
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
The result is a small difference between large numbers, so it is sensitive to the tolerances of the supply and of the resistors. Check the worst case with the supply high and the resistors at their extremes.
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