**Self Bias or Potential Divider Bias Circuit:**

This is the most commonly used biasing arrangement. The arrangement of Self Bias or Potential Divider Bias Circuit is shown in Fig. 12.17 (a). The name voltage divider is derived due to the fact that the voltage divider is formed by the resistors R_{1} and R_{2} across V_{CC}. The emitter resistor R_{E} provides stabilization. The resistor R_{E} causes a voltage drop in a direction so as to reverse bias the emitter junction. Since the emitter-base junction is to be forward biased, the base voltage is obtained from supply V_{CC} through R_{1}Â – R_{2}Â network.

For forward biasing the emitter-base junction R_{1} and R_{2} are so adjusted that the base terminal becomes more positive than emitter. The net forward bias across the emitter-base junction, V_{BE} is equal to V_{B} minus dc voltage drop across R_{E}. The dc bias circuit is independent of transistor current gain factor Î². In case of amplifiers, to avoid the loss of ac signal (because of feedback caused by R_{E}) a capacitor of large capacitance is connected across R_{E}. The capacitor offers a very small reactance to the ac signal and so it passes through the capacitor.

**Approximate Circuit Analysis:**

Voltage divider bias circuits are usually designed to have the voltage divider current very much larger than the transistor base current I_{B} and in this circumstance, base voltage V_{B} is largely unaffected by base current I_{B} and therefore, V_{B} can be assumed to remain constant.

Assuming the current flowing through the resistor R_{1} to be equal to I_{1} and neglecting base current I_{B}, being much smaller than voltage divider current, current flowing through resistance R_{2} can also be assumed to be equal to I_{1}

Voltage across resistance R_{2},

Applying Kirchhoff’s second (or voltage) law to the base-emitter loop [Fig. 12.17(a)] we have

and collector current,

Applying Kirchhoff’s second (or voltage) law to the collector-emitter loop we have

From Eqs. (12.24) and (12.25) the values of I_{C} and V_{CE} can be determined and the quiescent point Q is established.

It is clear from Eq. (12.24) that I_{C} does not at all depend upon Î². Though collector current l_{C} depends upon V_{BE} but in practice V_{BE} is very small in comparison to V_{B} and so collector current I_{C} is practically independent of V_{BE}. Thus collector current I_{C} in this biasing circuit is almost independent of transistor parameters and hence good stabilization is ensured.

In this Potential Divider Bias Circuit the emitter resistance R_{E} provides excellent stabilisation. This is explained as below :

Now let the temperature of transistor junction rise when it is loaded. This causes increase in leakage currents and so increase in the value of Î². Hence collector current I_{C} tends to increase. With the increase in the value of l_{C}, voltage drop across emitter resistance R_{E} increases. Since voltage drop across R_{2} (i.e. V_{B}) is independent of collector current, therefore, V_{BE} decreases and so I_{B}, I_{E} and I_{c}.

Thus we see that the Potential Divider Bias Circuit has tendency to hold the Q point (I_{C}) stable automatically. This is due to feedback action. The increase in I_{C} has immediately a reaction change of feedback so as to correct the situation.

**Precise Circuit Analysis:**

For exact analysis of a self bias or Potential Divider Bias Circuit, the voltage divider (the circuit to the left of the base terminal) is replaced by its Thevenin’s equivalent circuit, as shown in Fig. 12.17 (b).

Open-circuit voltage across base and ground terminals,

Resistance seen into the base and ground terminals with V_{CC} short circuited,

Applying Kirchhoff’s voltage law around the closed base circuit [Fig. 12.17 (b)] yields

or Base current,

Once the base current has been determined, l_{C} can be computed using appropriate value of Î², and the transistor terminal voltages can then be computed.

**Stability Factor:**

Differentiating Eq. (12.28) w.r.t. I_{C} (considering V_{BE}Â to be independent of l_{C}) we have

From Eq. (12.5) stability factor S is given as

Substituting the value of dI_{B}/dI_{C} from Eq. (12.29) in above equation we have

Stability factor,

The above equation shows that stability factor S varies between 1 for small values of R_{Th}/R_{E} and (1 + Î²) for larger values of R_{Th}/R_{E}. For proper operation both R_{E} and V_{CC} should be largerÂ and R_{Th} small. Typical practical value of S for this type of biasing circuit is about 10.

Equation (12.28) may be written as

Differentiating above equation w.r.t. V_{BE},Â we have