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**METHODS OF TRANSISTOR BIASING:**

1) Fixed bias (base bias)

This form of biasing is also called *base bias*. In the fig 4.3 shown, the single power source (for example, a battery) is used for both collector and base of a transistor, although separate batteries can also be used.

In the given circuit,

V_{cc} = I_{B}R_{B} + V_{be}

Therefore, I_{B} = (V_{cc} - V_{be})/R_{B}

Since the equation is independent of current I_{C}R, dI_{B/}/dI_{C}R =0 and the stability factor is **given by the equationâ€¦.. reduces to**

S=1+Î²

Since Î² is a large quantity, this is very poor biasing circuit. Therefore in practice the circuit is not used for biasing.

For a given transistor, V_{be} does not vary significantly during use. As V_{CC} is of fixed value, on selection of R_{B}, the base current I_{B} is fixed. Therefore this type is called *fixed bias* type of circuit.

Also for given circuit, V_{CC} = I_{C}R_{C} + V_{ce}

Therefore, V_{ce} = V_{CC} - I_{C}R_{C}

**Merits:**

It is simple to shift the operating point anywhere in the active region by merely changing the base resistor (R

_{B}).A very small number of components are required.

**Demerits:**

The collector current does not remain constant with variation in temperature or power supply voltage. Therefore the operating point is unstable.

Changes in V

_{be}will change I_{B}and thus cause R_{E}to change. This in turn will alter the gain of the stage.When the transistor is replaced with another one, considerable change in the value of Î² can be expected. Due to this change the operating point will shift.

**2) EMITTER-FEEDBACK BIAS:**

The emitter feedback bias circuit is shown in the fig 4.4. The fixed bias circuit is modified by attaching an external resistor to the emitter. This resistor introduces negative feedback that stabilizes the Q-point. From Kirchhoff's voltage law, the voltage across the base resistor is

*V _{RB} = V_{CC} - I_{E}R_{E} - V*

From Ohm's law, the base current is

I_{B} = V_{RB} / R_{B}.

The way feedback controls the bias point is as follows. If V_{be} is held constant and temperature increases, emitter current increases. However, a larger I_{E} increases the emitter voltage V_{E} = I_{E}R_{E}, which in turn reduces the voltage V_{RB} across the base resistor. A lower base-resistor voltage drop reduces the base current, which results in less collector current because I_{c} = Î²I_{B}. Collector current and emitter current are related by I_{C} = Î± I_{E} with Î± â‰ˆ 1, so increase in emitter current with temperature is opposed, and operating point is kept stable.

Similarly, if the transistor is replaced by another, there may be a change in I_{C} (corresponding to change in Î²-value, for example). By similar process as above, the change is neglected and operating point kept stable.

For the given circuit,

I_{B} = (V_{CC} - V_{be})/(R_{B} + (Î²+1)R_{E}).

**Merits:**

The circuit has the tendency to stabilize operating point against changes in temperature and Î²-value.

**Demerits:**

In this circuit, to keep I

_{C}independent of Î² the following condition must be met:

which is approximately the case if ( Î² + 1 )R_{E} >> R_{B}.

As Î²-value is fixed for a given transistor, this relation can be satisfied either by keeping R

_{E}very large, or making R_{B}very low.If R

_{E}is of large value, high V_{CC}is necessary. This increases cost as well as precautions necessary while handling.If R

_{B}is low, a separate low voltage supply should be used in the base circuit. Using two supplies of different voltages is impractical.In addition to the above, R

_{E}causes ac feedback which reduces the voltage gain of the amplifier.

**COLLECTOR TO BASE BIAS OR COLLECTOR FEED-BACK BIAS**

This configuration shown in fig 4.5 employs negative feedback to prevent thermal runaway and stabilize the operating point. In this form of biasing, the base resistor *R*_{b} is connected to the collector instead of connecting it to the DC source *V*_{CC}. So any thermal runaway will induce a voltage drop across the *R*_{C} resistor that will throttle the transistor's base current.

From Kirchhoff's voltage law, the voltage across the base resistor *R*_{b} is

By the Ebersâ€“Moll model, *I*_{c} = Î²*I*_{b}, and so

From Ohm's law, the base current and so

Hence, the base current *I*_{b} is

If *V*_{be} is held constant and temperature increases, then the collector current *I*_{c} increases. However, a larger *I*_{c} causes the voltage drop across resistor *R*_{c} to increase, which in turn reduces the voltage across the base resistor *R*_{b}. A lower base-resistor voltage drop reduces the base current *I*_{b}, which results in less collector current *I*_{c}. Since, **Because** increase in collector current with temperature is opposed, the operating point is kept stable.

**Merits:**

- Circuit stabilizes the operating point against variations in temperature and Î² (i.e. replacement of transistor)

**Demerits:**

- In this circuit, to keep
*I*_{c}independent of Î², the following condition must be met:

which is the case when

- As Î²-value is fixed (and generally unknown) for a given transistor, this relation can be satisfied either by keeping
*R*_{c}fairly large or making*R*_{b}very low. - If
*R*_{c}is large, a high*V*_{cc}is necessary, which increases cost as well as precautions necessary while handling. - If
*R*_{b}is low, the reverse bias of the collectorâ€“base region is small, which limits the range of collector voltage swing that leaves the transistor in active mode. - The resistor
*R*_{b}causes an AC feedback, reducing the__voltage gain__of the amplifier. This undesirable effect is a trade-off for greater__Q-point__stability.

**Usage:** The feedback also decreases the input impedance of the amplifier as seen from the base, which can be advantageous. Due to the gain reduction from feedback, this biasing form is used only when the trade-off for stability is warranted.

**COLLECTOR â€“****EMITTER FEEDBACK BIAS:**

The above fig 4.6 shows the collector â€“emitter feedback bias circuit that can be obtained by applying both the collector feedback and emitter feedback. Here the collector feedback is provided by connecting a resistance R_{B} from the collector to the base and emitter feedback is provided by connecting an emitter R_{E} from emitter to ground. Both feed backs are used to control collector current and base current I_{B} in the opposite direction to increase the stability as compared to the previous biasing circuits.

**VOLTAGE DIVIDER BIAS OR SELF BIAS OR EMITTER BIAS:**

The voltage divider as shown in the fig 4.7 is formed using external resistors R_{1} and R_{2}. The voltage across R_{2} forward biases the emitter junction. By proper selection of resistors R_{1} and R_{2}, the operating point of the transistor can be made independent of Î². In this circuit, the voltage divider holds the base voltage fixed independent of base current provided the divider current is large compared to the base current. However, even with a fixed base voltage, collector current varies with temperature (for example) so an emitter resistor is added to stabilize the Q-point, similar to the above circuits with emitter resistor.

**In this circuit the base voltage is given by:**

**V _{B = }voltage across **

**Provided **

**Also **

**For the given circuit,**

Let the current in resistor R1 is I1 and this is divided into two parts â€“ current through base and resistor R2. Since the base current is very small, so for all practical purposes it is assumed that I1 also flows through R2, so we have

Applying KVL in the circuit, we have

It is apparent from above expression that the collector current is independent of transistor parameters thus the stability is excellent. In all practical cases the value of V_{be} is quite small in comparison to the V_{2}, so it can be ignored in the above expression. Hence, the collector current is almost independent of the transistor parameters thus this arrangement provides excellent stability.

The resistor R_{E} provides stability to the circuit. If the current through the collector rises, the voltage across the resistor R_{E} also rises. This will cause V_{CE} to increase as the voltage V_{2} is independent of collector current. This decreases the base current, thus collector current increases to its former value.

Stability factor for such circuit arrangement is given by:

If R_{eq}/R_{E} is very small as compared to 1, it can be ignored in the above expression thus we have

which is excellent since it is the smallest possible value for the stability. In actual practice the value of stability factor is around 8-10, since R_{eq}/R_{E} cannot be ignored as compared to 1.

**Merits:**

- Unlike above circuits, only one dc supply is necessary.
- Operating point is almost independent of Î² variation.
- Operating point stabilized against shift in temperature.

**Demerits:**

- In this circuit, to keep I
_{C}independent of Î² the following condition must be met:

which is approximately the case if

where R_{1} || R_{2} denotes the equivalent resistance of R_{1} and R_{2} connected in parallel.

- As Î²-value is fixed for a given transistor, this relation can be satisfied either by keeping R
_{E}fairly large, or making R_{1}||R_{2}very low. - If R
_{E}is of large value, high V_{CC}is necessary. This increases cost as well as precautions necessary while handling. - If R
_{1}|| R_{2}is low, either R_{1}is low, or R_{2}is low, or both are low. A low R_{1}raises V_{B}closer to V_{C}, reducing the available swing in collector voltage, and limiting how large R_{C}can be made without driving the transistor out of active mode. A low R_{2}lowers V_{be}, reducing the allowed collector current. Lowering both resistor values draws more current from the power supply and lowers the input resistance of the amplifier as seen from the base. - AC as well as DC feedback is caused by R
_{E}, which reduces the AC voltage gain of the amplifier.

**Usage: **The circuit's stability and merits as above make it widely used for linear circuits.

The** **various biasing circuits considered use some type of negative feedback to stabilize the operation point. Also, diodes, thermistors and sensistors can be used to compensate for variations in current.

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