Voltage divider bias circuit

Voltage divider bias circuit:

Figure shows the voltage divider bias circuit. In this, biasing is provided by three resistors R₁, R₂ and R_E. The resistors R₁& R₂ act as a potential divider giving a fixed voltage to base. If collector current increases due to change in temperature or change in β, emitter current I_E also increases and voltage drop across R_E increases thus reducing the voltage difference between base and emitter. Due to reduction in base emitter voltage, base current and collector current reduces. So we can say that negative feedback exists in emitter bias circuit. This reduction in collector current compensates for the original change in I_C.

Circuit analysis:

Base circuit:

Fig. Base circuit

Let us consider the base circuit as shown in above figure. Voltage across R₂ is base voltage V_B. Applying voltage divider rule to find V_B

Collector circuit:

Let us consider the collector circuit as shown in above figure. Voltage across R_E can be obtained as,

Simplified circuit of voltage divider bias

Fig.Thevenin’s equivalent circuit for voltage divider bias

From above figure, R₁ and R₂ are replaced by R_B and V_T.

Where R_B is the parallel combination of R=1 and R₂

V_T is the thevenin’s voltage

Problem 1: 

For the given circuit β=100 for silicon transistor. Calculate V_CE and I_C. 

Problem 2:

For the given figure find Q point with V_CC = 15V, V_BE = 0.7V and β = 100.

Stability factor for voltage divider bias:

Stability factor S:

For determining stability factor S for voltage divider bias, consider the equivalent circuit. Thevenin’s voltage is given by,

R₁, R₂ are replaced by R_B which is the parallel combination of R₁ and R₂.

Apply KVL to base circuit,

Differentiating with respect to I_C and considering V_BE to be independent of I_C,

From above equation, the following points are observed.

1. The ratio R_B /R_E controls value of stability factor S. If R_B/R_E<< 1 then it is reduced to S = (1+β). 1/ (1+β) = 1

Practically R_B/R_E not equal to zero. But to have better stability factor S , we have to keep ratio R_B/R_E as small as possible.

2.     To keep R_B/R_E small, it is necessary to keep R_B small. Due to small value of R₁ and R₂, potential divider circuit will draw more current from V_CC reducing the life of the battery. Another important aspect is that reducing R_B will reduce input impedance of the circuit, since R_B comes in parallel with the input. This reduction of input impedance in amplifier circuit is not desirable and hence R_B cannot be made very small.

3.     Emitter resistance R_E is another parameter, it is used to decrease the ratio R_B/R_E. Drop across R_C will reduce. This shifts the operating point Q which is not desirable and hence there is limit for increasing R_E.

While designing voltage divider bias circuit, the following conditions are to be satisfied,

S   – Small

RB    - Reasonably small

RE     - Not very large

4.     If ratio R_B/R_E  is fixed, S increases with β. So stability decreases with increasing β.

5.     Stability factor S is essentially independent of β for small value of S.

Substituting the differentiation value of I_B /I_C,

Problem 1:

For the given circuit, V_CC = 20V, R_C = 2KΩ, β = 50, V_BE = 0.2V, R₁ = 100KΩ, R_E = 100Ω. Calculate I_B, V_CE, I_C and stability factor S.