Lab guide
Why transistor β (hFE) is not a constant
β, the Early effect and saturation, read off NPN transistor simulation results.
Textbooks write IC = β·IB and treat β as a constant. Even within one transistor, though, β moves quite a bit with current. These are base, collector and emitter currents from a PSpice NPN transistor model.
1. The three currents versus VBE
| VBE | IB | IC | |IE| | β = IC/IB | α = IC/IE |
|---|---|---|---|---|---|
| 0.65 V | 4.559 µA | 587 µA | 592 µA | 129 | 0.9916 |
| 0.70 V | 23.68 µA | 3.753 mA | 3.776 mA | 158 | 0.9939 |
| 0.73 V | 64.55 µA | 10.61 mA | 10.68 mA | 164 | 0.9939 |
| 0.76 V | 174.6 µA | 26.33 mA | 26.5 mA | 151 | 0.9934 |
- β ranges from 129 to 164: a 28% spread in one part just from the current. Between real parts, datasheets allow two to three times that.
- Kirchhoff's current law: IB + IC matches |IE| to within 0.07% in every row.
- The exponential law: a tenfold rise in collector current took 62 to 76 mV of VBE. The ideal figure is 59.5 mV; at higher current internal resistance adds more.
2. IC–VCE curves and the Early effect
| VBB | VCE 0.1 V | VCE 0.2 V | VCE 0.3 V | VCE 0.4 V | VCE 0.5 V | VCE 1 V | VCE 3 V | Early voltage |
|---|---|---|---|---|---|---|---|---|
| 1 V | 0.096 mA | 0.39 mA | 0.419 mA | 0.42 mA | 0.421 mA | 0.423 mA | 0.435 mA | ≈ 69 V |
| 2 V | 0.597 mA | 1.7 mA | 1.87 mA | 1.878 mA | 1.881 mA | 1.894 mA | 1.945 mA | ≈ 73 V |
| 4 V | 0.847 mA | 4.512 mA | 5.102 mA | 5.121 mA | 5.129 mA | 5.163 mA | 5.301 mA | ≈ 74 V |
Above about 0.3 V of VCE the current flattens out, but not completely. Extending the slope between 1 V and 3 V back to the VCE axis gives the Early voltage, about 69 to 74 V in all three cases. That sets the transistor's output resistance, ro ≈ VA / IC.
At VCE = 0.1 V the current fell to 16 to 32% of its active-region value: both junctions are forward biased, the saturation region.
3. When you design
- Amplifiers: set the gain with emitter degeneration or feedback rather than β, so a spread like this barely moves the operating point.
- Switches: assume a β far below even the datasheet minimum (typically 10 to 20) and give plenty of base current so the transistor saturates. The transistor base resistor calculator works this way.
Size load resistors such as LEDs with the LED resistor calculator and check base and collector currents with the Ohm's law calculator.