:
The base internal current is mainly by diffusion and
:
Where
- is the emitter current
- is the collector current
- is the common base forward short circuit current gain (0.98 to 0.998)
- is the reverse saturation current of the base-emitter diode (on the order of 10−15 to 10−12 amperes)
- is the Thermal Voltage (approximately 26 mV at room temperature ≈ 300 K).
- is the base-emitter voltage
- ''W'' is the base width
The collector current is slightly less than the emitter current, since the value of is very close to 1.0. In the BJT a small amount of base-emitter current causes a larger amount of collector-emitter current. The ratio of the allowed collector-emitter current to the base-emitter current is called ''current gain'', β or . A β value of 100 is typical for small bipolar transistors. In a typical configuration, a very small signal current flows through the base-emitter junction to control the emitter-collector current. β is related to α through the following relations:
:
:
:
Emitter Efficiency:
Another set of equations used to describe the three currents in the any operating region are given below. These equations are based on the transport model for a Bipolar Junction Transistor.
Where
- is the collector current
- is the base current
- is the emitter current
- is the forward common emitter current gain (20 to 50)
- is the reverse common emitter current gain (0 to 20)
- is the reverse saturation current (on the order of 10−15 to 10−12 amperes)
- is the Thermal Voltage (approximately 26 mV at room temperature ≈ 300 K).
- is the base-emitter voltage
- is the base-collector voltage
As the applied base-collector voltage () varies, the base-collector depletion region varies in size. This variation causes the gain of the device to change, since the gain is related to the width of the effective base region. This is often called the "Early Effect".
In the forward active region the Early Effect modifies the collector current () and the forward common emitter current gain () to the following equations.
Where
- is the collector-emitter voltage
- is the Early voltage (15 V to 150 V)
- is forward common emitter current gain at zero bias
When the base-collector voltage reaches a certain (device specific) value, the base-collector depletion region boundary meets the base-emitter depletion region boundary. When in this state the transistor effectively has no base. The device thus loses all gain when in this state.
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