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A Transistor has 3 terminals, the emitter, the base and the collector. Using these 3 terminals the transistor can be connected in a circuit with one terminal common to both input and output in a 3 different possible configurations.

The three types of configurations are **Common Base, Common Emitter** and **Common Collector** configurations. In every configuration, the emitter junction is forward biased and the collector junction is reverse biased.

The name itself implies that the Base terminal is taken as common terminal for both input and output of the transistor. The common base connection for both NPN and PNP transistors is as shown in the following figure.

For the sake of understanding, let us consider NPN transistor in CB configuration. When the emitter voltage is applied, as it is forward biased, the electrons from the negative terminal repel the emitter electrons and current flows through the emitter and base to the collector to contribute collector current. The collector voltage **V _{CB}** is kept constant throughout this.

In the CB configuration, the input current is the emitter current **I _{E}** and the output current is the collector current

**Current Amplification Factor (α)**

The ratio of change in collector current ($\Delta I_{C}$) to the change in emitter current ($\Delta I_{E}$) when collector voltage **V _{CB}** is kept constant, is called as

$$\alpha\:=\:\frac{\Delta I_{C}}{\Delta I_{E}}\:\:at\:constant\:V_{CB}$$

With the idea above, let us try to draw some expression for collector current. Along with the emitter current flowing, there is some amount of base current IB which flows through the base terminal due to electron hole recombination. As collector-base junction is reverse biased, there is another current which is flown due to minority charge carriers. This is the leakage current which can be understood as **I _{leakage}**. This is due to minority charge carriers and hence very small.

The emitter current that reaches the collector terminal is

$$\mathbf{\mathit{\alpha I_{E}}}$$

Total collector current

$$I_{C}\:=\:\alpha I_{E}\:+\:I_{leakage}$$

If the emitter-base voltage V_{EB} = 0, even then, there flows a small leakage current, which can be termed as I_{CBO} (collector-base current with output open).

The collector current therefore can be expressed as

$$I_{C}\:=\:\alpha I_{E}\:+\:I_{CBO}$$

$$I_{E}\:=\:I_{C}\:+\:I_{B}$$

$$I_{C}\:=\:\alpha(I_{C}\:+\:I_{B})\:+\:I_{CBO}$$

$$I_{C}(1\:-\:\alpha)\:=\:\alpha I_{B}\:+\:I_{CBO}$$

$$I_{C}\:=\:(\frac{\alpha}{1\:-\:\alpha})\: I_{B}\:+\:(\frac{I_{CBO}}{1\:-\:\alpha})$$

$$I_{C}\:=\:(\frac{\alpha}{1\:-\:\alpha})\: I_{B}\:+\:(\frac{1}{1\:-\:\alpha})I_{CBO}$$

Hence the above derived is the expression for collector current. The value of collector current depends on base current and leakage current along with the current amplification factor of that transistor in use.

This configuration provides voltage gain but no current gain.

Being

**V**constant, with a small increase in the Emitter-base voltage V_{CB}_{EB}, Emitter current**I**gets increased._{E}Emitter Current

**I**is independent of Collector voltage_{E}**V**._{CB}Collector Voltage

**V**can affect the collector current_{CB}**I**only at low voltages, when V_{C}_{EB}is kept constant.The input resistance ri is the ratio of change in emitter-base voltage ($\Delta{V_{EB}}$) to the change in emitter current ($\Delta{I_{E}}$) at constant collector base voltage

**V**._{CB}$$\eta\:=\:\frac{\Delta{V_{EB}}}{\Delta{I_{E}}}\:\:at\:constant\:V_{CB}$$

As the input resistance is of very low value, a small value of V

_{EB}is enough to produce a large current flow of emitter current**I**._{E}The output resistance r

_{o}is the ratio of change in the collector base voltage ($\Delta{V_{CB}}$) to the change in collector current ($\Delta{I_{C}}$) at constant emitter current**I**._{E}$$r_{o}\:=\:\frac{\Delta{V_{CB}}}{\Delta{I_{C}}}\: at\: constant\:l_{E}$$

As the output resistance is of very high value, a large change in

**V**produces a very little change in collector current_{CB}**I**._{C}This Configuration provides good stability against increase in temperature.

The CB configuration is used for high frequency applications.

The name itself implies that the **Emitter** terminal is taken as common terminal for both input and output of the transistor. The common emitter connection for both NPN and PNP transistors is as shown in the following figure.

Just as in CB configuration, the emitter junction is forward biased and the collector junction is reverse biased. The flow of electrons is controlled in the same manner. The input current is the base current **I _{B}** and the output current is the collector current

**Base Current Amplification factor (β)**

The ratio of change in collector current ($\Delta{I_{C}}$) to the change in base current ($\Delta{I_{B}}$) is known as **Base Current Amplification Factor**. It is denoted by β

$$\beta\:=\:\frac{\Delta{I_{C}}}{\Delta{I_{B}}}$$

Let us try to derive the relation between base current amplification factor and emitter current amplification factor.

$$\beta\:=\:\frac{\Delta{I_{C}}}{\Delta{I_{B}}}$$

$$\alpha\:=\:\frac{\Delta{I_{C}}}{\Delta{I_{E}}}$$

$$I_{E}\:=\:I_{B}\:+\:I_{C}$$

$$\Delta I_{E}\:=\:\Delta I_{B}\:+\:\Delta I_{C}$$

$$\Delta I_{B}\:=\:\Delta I_{E}\:-\:\Delta I_{C}$$

We can write

$$\beta\:=\:\frac{\Delta{I_{C}}}{\Delta I_{E}\:-\:\Delta I_{C}}$$

Dividing by $$

$$\beta\:=\:\frac{\frac{\Delta I_{C}}{\Delta I_{E}}}{\frac{\Delta I_{E}}{\Delta I_{E}}\:-\:\frac{\Delta I_{C}}{\Delta I_{E}}}$$

$$\alpha\:=\:\frac{\Delta I_{C}}{\Delta I_{E}}$$

We have

$$\alpha\:=\:\frac{\Delta I_{C}}{\Delta I_{E}}$$

Therefore,

$$\beta\:=\:\frac{\alpha}{1-\alpha}$$

From the above equation, it is evident that, as α approaches 1, β reaches infinity.

Hence, **the current gain in Common Emitter connection is very high**. This is the reason this circuit connection is mostly used in all transistor applications.

In the Common Emitter configuration, **I _{B}** is the input current and

We know

$$I_{E}\:=\:I_{B}\:+\:I_{C}$$

And

$$I_{C}\:=\:\alpha I_{E}\:+\:I_{CBO}$$

$$=\:\alpha (I_{B}\:+\:I_{C})\:+\:I_{CBO}$$

$$I_{C}(1\:-\:\alpha)\:=\:\alpha I_{B}\:+\:I_{CBO}$$

$$I_{C}\:=\:\frac{\alpha}{1-\alpha}I_{B}\:+\:\frac{1}{1-\alpha}\:I_{CBO}$$

If base circuit is open, i.e. if **I _{B}** = 0,

The collector emitter current with base open is I_{CEO}

$$I_{CEO}\:=\:\frac{1}{1-\alpha}\:I_{CBO}$$

Substituting the value of this in the previous equation, we get

$$I_{C}\:=\:\frac{\alpha}{1-\alpha}I_{B}\:+\:I_{CEO}$$

$$I_{C}\:=\:\beta I_{B}\:+\:I_{CEO}$$

Hence the equation for collector current is obtained.

In CE configuration, by keeping the base current **I _{B}** constant, if

This configuration provides good current gain and voltage gain.

Keeping

**V**constant, with a small increase in_{CE}**V**the base current_{BE}**I**increases rapidly than in CB configurations._{B}For any value of

**V**above knee voltage,_{CE}**I**is approximately equal to β_{C}**I**._{B}The input resistance

**r**is the ratio of change in base emitter voltage ($\Delta{V_{BE}}$) to the change in base current ($\Delta{I_{B}}$) at constant collector emitter voltage_{i}**V**._{CE}$$r_{i}\:=\:\frac{\Delta{V_{BE}}}{\Delta{I_{B}}}\:at\:constant\:V_{CE}$$

As the input resistance is of very low value, a small value of

**V**is enough to produce a large current flow of base current_{BE}**I**._{B}The output resistance

**r**is the ratio of change in collector emitter voltage ($\Delta{V_{CE}}$) to the change in collector current ($\Delta{I_{C}}$) at constant_{o}**I**._{B}$$r_{o}\:=\:\frac{\Delta{V_{CE}}}{\Delta{I_{C}}}\:at\:constant\:I_{B}$$

As the output resistance of CE circuit is less than that of CB circuit.

This configuration is usually used for bias stabilization methods and audio frequency applications.

The name itself implies that the **Collector** terminal is taken as common terminal for both input and output of the transistor. The common collector connection for both NPN and PNP transistors is as shown in the following figure.

Just as in CB and CE configurations, the emitter junction is forward biased and the collector junction is reverse biased. The flow of electrons is controlled in the same manner. The input current is the base current **I _{B}** and the output current is the emitter current

**Current Amplification Factor (γ)**

The ratio of change in emitter current ($\Delta{I_{E}}$) to the change in base current ($\Delta{I_{B}}$) is known as **Current Amplification factor** in common collector (CC) configuration. It is denoted by **γ**.

$$\gamma\:=\:\frac{\Delta{I_{E}}}{\Delta{I_{B}}}$$

The current gain in CC configuration is same as in CE configuration.

The voltage gain in CC configuration is always less than 1.

Let us try to draw some relation between γ and α

$$\gamma\:=\:\frac{\Delta{I_{E}}}{\Delta{I_{B}}}$$

$$\alpha\:=\:\frac{\Delta{I_{C}}}{\Delta{I_{E}}}$$

$$I_{E}\:=\:I_{B}\:+\:I_{C}$$

$$\Delta I_{E}\:=\:\Delta I_{B}\:+\:\Delta I_{C}$$

$$\Delta I_{B}\:=\:\Delta I_{E}\:-\:\Delta I_{C}$$

Substituting the value of I_{B}, we get

$$\gamma\:=\:\frac{\Delta{I_{E}}}{\Delta{I_{E}}\:-\:\Delta I_{C}}$$

Dividing by $\Delta I_{E}$

$$\gamma\:=\:\frac{\frac{\Delta I_{E}}{\Delta I_{E}}}{\frac{\Delta I_{E}}{\Delta I_{E}}\:-\:\frac{\Delta I_{C}}{\Delta I_{E}}}$$

$$\frac{1}{1\:-\:\alpha}$$

$$\gamma\:=\:\frac{1}{1\:-\:\alpha}$$

We know

$$I_{C}\:=\:\alpha I_{E}\:+\:I_{CBO}$$

$$I_{E}\:=\:I_{B}\:+\:I_{C}\:=\:I_{B}\:+\:(\alpha I_{E}\:+\:I_{CBO})$$

$$I_{E}(1\:-\:\alpha)\:=\:I_{B}\:+\:I_{CBO}$$

$$I_{E}\:=\:\frac{I_{B}}{1\:-\:\alpha}\:+\:\frac{I_{CBO}}{1\:-\:\alpha}$$

$$I_{C}\:\cong\:I_{E}\:=\:(\beta\:+\:1)I_{B}\:+\:(\beta\:+\:1)I_{CBO}$$

The above is the expression for collector current.

This configuration provides current gain but no voltage gain.

In CC configuration, the input resistance is high and the output resistance is low.

The voltage gain provided by this circuit is less than 1.

The sum of collector current and base current equals emitter current.

The input and output signals are in phase.

This configuration works as non-inverting amplifier output.

This circuit is mostly used for impedance matching. That means, to drive a low impedance load from a high impedance source.

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