Relation between α , β and γ

Deriving the Relationship Between Alpha, Beta, and Gamma

Understanding Amplification Factors

• The lecture introduces the amplification factors in transistor configurations: alpha (α), beta (β), and gamma (γ).

• Alpha (α) has two types:

• Alpha DC: Ratio of collector current to emitter current.

• Alpha AC: Ratio of change in collector current to change in emitter current when output voltage is constant.

Exploring Beta

• Beta (β) also has two types:

• Beta DC: Defined as the ratio of collector current to base current.

• Beta AC: Defined as the ratio of change in collector current to change in base current when output voltage is constant.

Introduction to Gamma

• Gamma (γ) is defined for common collector configuration with two types:

• Gamma DC: Ratio of emitter current to base current.

• Gamma AC: Ratio of change in emitter current to change in base current when output voltage is constant.

Deriving Relationships Among Alpha, Beta, and Gamma

• The relationship between these amplification factors can be derived using the equation I_E = I_C + I_B .

• Dividing both sides by I_B :

• This leads to I_E/I_B = I_C/I_B + 1 .

• Here, I_E/I_B = γ_DC and I_C/I_B = β_DC .

Final Relationships Established

• The final relationship derived shows that:

• γ = β + 1

• Additionally, substituting for beta gives:

• γ = α/1 - α + 1

• Simplifying this results in: