In this article we are going to study **Current Gain in Transistor of Common Base Transistor** and ** Common Emitter Transistor**. Along with the formula of current gain in transistor.

Table of Contents

**Current gain in Common Base Transistor**

- Large signal current gain (
**α**) - D.C. current gain
**(α**)_{dc} - Small signal current gain (
**α**^{‘}or h_{fb}).

**Large signal current gain (α)**

We know

**α** is known as large signal** current gain of a common base transistor**. Since** I _{C}** and

**I**have opposite signs, so

_{E}**α**is a positive quantity. The value of

**α**lies between 0.90 to 0.995.

**Note**. **α** is not constant. It varies with the emitter current **I _{E}**

**and collector base voltage V**.

_{CB}**D.C. current gain (α**_{dc})

_{dc})

Since **I _{C} >> I_{CO}**,hence eqn. (1) can be written as

which is known as **d.c. current gain**. **α**_{dc} is a positive quantity. Its value is less than 1 as** I _{C} < I_{E}**.

**Small signal current gain (α**^{‘}or h_{fb}).

^{‘}or h

_{fb}).

Small signal current gain is defined as the negative ratio of the small change in collector current (ΔI_{C}) to small change in emitter current (ΔI_{E}). That is,

**α**^{‘ }is a positive quantity as I_{C} and I_{E} have positive signs.

**Current gain in a Common Emitter Transistor**

- D.C. current gain
**(β or h**_{FE}) - Small signal current gain
**(β**^{‘ }or h_{fe}).

**D.C. current gain (β or h**_{FE}) or Forward current transfer ratio

_{FE}) or Forward current transfer ratio

D.C. current gain of common emitter transistor is defined as the ratio of collector current (I_{C}) to the base current ( I_{B}. That is,

The value of β lies between 20 to 200.

**Small signal current gain (β**^{‘ }or h_{fe}).

^{‘ }or h

_{fe}).

It is defined as the ratio of small change in collector** (ΔI _{C})** to the small change in base current

**(ΔI**at constant Collector Emitter voltage

_{B})**(V**

_{CE}).β^{‘ } can be determine from the output characteristics of **Common Emitter Configuration**.

## Relation between Current Gain in Common Base Transistor and Common Emitter Transistor

It is also known as the relation between **α and β**.

We know, emitter current I_{E} in term of base current I_{B} and collector current is given by

Put this value in eqn. (1), We get

Since in active region of transistor, I_{B} >> I_{CO}. Hence neglect the term containing I_{C0} in eqn. (2)

**Collector Current in term of β**

Using eqn. (3) in eqn. (2), we get

When base is open circuited (i.e. I_{B}=0) and junction is reverse biased, then I_{C }=I_{CEO}. Hence eqn. (4) becomes

Using eqn. (5) in eqn. (4), we get