Transistor Operation

A transistor in a circuit will be in one of three conditions
  1. Cut off (no collector current), useful for switch operation.
  2. In the active region (some collector current, more than a few tenths of a volt above the emitter), useful for amplifier applications
  3. In saturation (collector a few tenths of a volt above emitter), large current useful for "switch on" applications.
Transistor load lineCharacteristic curves
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Collector Current Determination

The base-emitter voltage can be considered to be the controlling variable in determining transistor action. The collector current is related to this voltage by the Ebers-Moll relationship (sometimes labeled the Shockley equation):

where
The saturation current is characteristic of the particular transistor (a parameter which itself has a temperature dependence). This relationship is stable over a wide range of voltages and currents. A further useful relationship is
where can be called the current gain. The value of is not highly dependable since it depends on , and the temperature.
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References
Horowitz & Hill
Sec. 2.10

Floyd
Electronic Devices, Appendix B
 
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Base-Emitter Junction Details

Some useful "rules of thumb" which help in understanding transistor action are (from Horowitz & Hill):
  1. A base emitter voltage of about 0.6 v will "turn on" the base-emitter diode and that voltage changes very little, < +/- 0.1v throughout the active range of the transistor which may change base current by a factor of 10 or more.
  2. An increase in base-emitter voltage by about 60 mV will increase the collector current by about a factor of 10.
  3. The effective AC series resistance of the emitter is about 25/ ohms.
  4. The base-emitter voltage is temperature dependent, decreasing about 2.1 mV/C
  5. The base-emitter voltage varies slightly with the collector-emitter voltage at constant collector current : .
Base-emitter Voltage Curve
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Reference
Horowitz & Hill
Sec 2.10

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Transistor Action

More on transistor regions
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Reference
Simpson
Ch 5
 
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More about transistor regions

Transistor action
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Collector Current

Normal transistor action results in a collector-to-emitter current which is about 99% of the total current. The usual symbols used to express the transistor current relationships are shown.

The proportionality β can take values in the range 20 to 200 and is not a constant even for a given transistor. It increases for larger emitter currents because the larger number of electrons injected into the base exceeds the available holes for recombination so the fraction which recombine to produce base current delines even further.

Use of the current gain beta.
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Use of the Current Gain

Any circuit that depends on a specific value of the current gain β is a bad circuit because that value varies for a given transistor as well as between different transistors of the same type.

The current gain is useful for:
Design of the biasing circuitsCommon EmitterCommon Collector
Calculation of impedancesCommon EmitterCommon Collector
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