Question

Define α and β parameter of a transistor. Derive the relation between the two.

Answer 1

The terms Alpha and Beta refer to BJTs, Bipolar Junction Transistors. In these devices current leaves the emitter and crosses to the base and most is diverted towards the collector. The remainder leaves the base terminal.

Using a convenient notation, Ie = Ic + Ib

So Ib = Ie - Ic

Alpha is the proportion of Ie that flows to the collector,

ɑ = Ic/Ie ————— Definition

So Ic = ɑ Ie

Also Ib = Ie - ɑ Ie = Ie(1 - ɑ)

Beta is the current gain, the ratio of Ic to Ib.

β = Ic/Ib ————— Definition

Substituting in this definition for Ib and Ic

β = (ɑ Ie)/ Ie(1 - ɑ)

Cancelling Ie leaves:

β = ɑ/(1 - ɑ) ——————Q.E.F.

Answer 2

Plz refer to attachment also

As the load resistance ( RL ) is connected in series with the collector, the current gain of the common emitter transistor configuration is quite large as it is the ratio of Ic/Ib. A transistors current gain is given the Greek symbol of Beta, ( β ).

As the emitter current for a common emitter configuration is defined as Ie = Ic + Ib, the ratio of Ic/Ie is called Alpha, given the Greek symbol of α. Note: that the value of Alpha will always be less than unity.

Since the electrical relationship between these three currents, Ib, Ic and Ie is determined by the physical construction of the transistor itself, any small change in the base current ( Ib ), will result in a much larger change in the collector current ( Ic ).

Hope it helps

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