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.

Common Base (CB) Configuration

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 I_C.

Current Amplification Factor (α)

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

Expression for Collector current

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 I_leakage. This is due to minority charge carriers and hence very small.

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.

Characteristics of CB configuration

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_i is the ratio of change in emitter-base voltage (ΔV_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_o is the ratio of change in the collector base voltage (ΔV_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.

Common Emitter (CE) Configuration

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 I_C here.

Base Current Amplification factor (β)

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.

$$\beta = \frac{\Delta I_C}{\Delta I_B}$$

Relation between β and α

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.

Expression for Collector Current

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.

Knee Voltage

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.

Characteristics of CE Configuration

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_i is the ratio of change in base emitter voltage (ΔV_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_o is the ratio of change in collector emitter voltage (ΔV_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.

Common Collector (CC) Configuration

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 I_E here.

Current Amplification Factor (γ)

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.

Relation between γ and α

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

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

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

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

Expression for collector current

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.

Characteristics of CC Configuration

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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