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Any transistor has three 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 three 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

The ratio of change in collector current (ΔI_{C}) to the change in emitter current (ΔI_{E}) when collector voltage V_{CB} is kept constant, is called as **Current amplification factor**. It is denoted by **α**.

$\alpha = \frac{\Delta I_C}{\Delta I_E}$ at constant V_{CB}

With the above idea, let us try to draw some expression for collector current.

Along with the emitter current flowing, there is some amount of base current **I _{B}** 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

The emitter current that reaches the collector terminal is

$$\alpha I_E$$

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

$$I_C = \alpha I_E + I_{CBO}$$

$$I_E = I_C + I_B$$

$$I_C = \alpha (I_C + I_B) + I_{CBO}$$

$$I_C (1 - \alpha) = \alpha I_B + I_{CBO}$$

$$I_C = \frac{\alpha}{1 - \alpha}I_B + \frac{I_{CBO}}{1 - \alpha}$$

$$I_C = \left ( \frac{\alpha}{1 - \alpha} \right )I_B + \left ( \frac{1}{1 - \alpha} \right )I_{CBO}$$

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

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

_{E}is independent of Collector voltage V_{CB}.Collector Voltage V

_{CB}can affect the collector current I_{C}only at low voltages, when V_{EB}is kept constant.The input resistance

**R**is the ratio of change in emitter-base voltage (ΔV_{i}_{EB}) to the change in emitter current (ΔI_{E}) at constant collector base voltage V_{CB}.

$R_i = \frac{\Delta V_{EB}}{\Delta I_E}$ 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**is the ratio of change in the collector base voltage (ΔV_{o}_{CB}) to the change in collector current (ΔI_{C}) at constant emitter current IE.

$R_o = \frac{\Delta V_{CB}}{\Delta I_C}$ at constant I_{E}

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

_{CB}produces a very little change in collector current 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

The ratio of change in collector current (ΔI_{C}) to the change in base current (ΔI_{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 ΔI_{E}

$$\beta = \frac{\Delta I_C/\Delta I_E}{\frac{\Delta I_E}{\Delta I_E} - \frac{\Delta I_C}{\Delta I_E}}$$

We have

$$\alpha = \Delta I_C / \Delta I_E$$

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 I_{C} is the output current.

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 V_{CE} is varied, I_{C} increases nearly to 1v of V_{CE} and stays constant thereafter. This value of V_{CE} up to which collector current I_{C} changes with V_{CE} is called the **Knee Voltage**. The transistors while operating in CE configuration, they are operated above this knee voltage.

This configuration provides good current gain and voltage gain.

Keeping V

_{CE}constant, with a small increase in V_{BE}the base current I_{B}increases rapidly than in CB configurations.For any value of V

_{CE}above knee voltage, I_{C}is approximately equal to βI_{B}.The input resistance

**R**is the ratio of change in base emitter voltage (ΔV_{i}_{BE}) to the change in base current (ΔI_{B}) at constant collector emitter voltage 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

_{BE}is enough to produce a large current flow of base current I_{B}.The output resistance

**R**is the ratio of change in collector emitter voltage (ΔV_{o}_{CE}) to the change in collector current (ΔI_{C}) at constant 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

The ratio of change in emitter current (ΔI_{E}) to the change in base current (ΔI_{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 ΔI_{E}

$$\gamma = \frac{\Delta I_E / \Delta I_E}{\frac{\Delta I_E}{\Delta I_E} - \frac{\Delta I_C}{\Delta I_E}}$$

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

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

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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