BJT Alpha–Beta Relationship

α = β/(β+1), β = α/(1−α)

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Result
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Formula

α = β / (β + 1), β = α / (1 − α)

Description

A bipolar transistor has two current gains: alpha (common-base, collector/emitter current) is just under 1, and beta (common-emitter, collector/base current) is large. They describe the same device and convert directly into one another. A small change in alpha near unity produces a large change in beta, which is why beta is poorly controlled in manufacturing.

Variables

  • α — Common-base current gain (Ic/Ie, < 1)
  • β — Common-emitter current gain (Ic/Ib)

Practical Notes

α = 0.99 gives β = 99; α = 0.995 gives β = 199. This sensitivity is why circuits are designed to be insensitive to β using emitter degeneration and feedback.

Related Concepts

All Discrete Amplifiers formulas →
Thermal Voltage Small-Signal Emitter Resistance Transistor Transconductance Diode Dynamic Resistance Common-Emitter Voltage Gain BJT Alpha–Beta Relationship Darlington Pair Current Gain Emitter-Follower Input Impedance

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