Important Formula : Transistor Biasing

 

( 1 ) Current amplification factor

β= I_C / I_B

( 2 ) Collector current for common emitter configuration

I_C = βI_B + I_CBO

Where

I_CBO = Collector – base current with emitter open

I_CEO = Collector cut off current ( Collector current when

           base is open circuited )

I_CEO >> I_CBO

( 3 ) Stability Factor

S = dI_C / dI_CO   at constant I_B and β

Where

dI_CO = Collector leakage current

        General equation of stability factor

S = ( β + 1 ) / 1 -  β ( dI_B / dI_C )

Base Resistor Method

( 1 ) Base resistor method

R_B = V_CC – V_BE / I_B

     = V_CC / I_B

         V_BE is very small so it is neglected

         Stability factor S = ( β + 1 ) / 1 -  β ( dI_B / dI_C )

• The base current I_B is independent of I_C in the fixed bias method so dI_B / dI_C = 0

Stability factor S = ( β + 1 )

( 2 ) The Q point is extremely depends on β in a base resistor method therefore the base bias circuit is unstable. It is not used in the linear operation.

Emitter Bias Circuit

 ( 1 ) Emitter bias circuit

• The emitter bias circuit requires one positive voltage source ( + V_CC ) and negative voltage source ( - V_EE ) and these two voltage sources are equal.

       V_CC = + 10 V DC

       V_EE = - 10 V DC

Collector current

      I_C = V_EE – V_BE / ( R_E + R_B / β )

      R_E >> R_B / β

Therefore I_C = V_EE – V_BE / ( R_E )

Similarly V_EE >> V_BE

      I_C = V_EE / R_E

• As I_C is independent of β and V_BE, the Q point is not affected so much.

Biasing with collector feedback resistor

 ( 2 ) Biasing with collector feedback resistor

The stability factor

S < ( β + 1 )

It provides better stability than fixed bias method.

V_CC = I_CR_C + I_BR_B + V_BE

Voltage divider Bias Method

( 1 ) Voltage divider bias method

Current I₁ passes through resistor R₁

       I₁ = V_CC / ( R₁ + R₂ )

Voltage across R₂ is

       V₂ = ( V_CC / R₁ + R₂ ) R₂

       V₂ = V_BE + V_E

            = V_BE + I_ER_E

        I_E = V₂ – V_BE / R_E

        As I_E ≈  I_C

        I_C = V₂ – V_BE / R_E

• The value of I_C does not depend on β. The value of IC independent of transistor parameters therefore good stabilization is provided.

Equation for collector side

     V_CC = I_CR_C + V_CE + I_CR_E

    Therefore V_CE = V_CC – I_CR_C – I_CR_E

    Stability factor S = ( β + 1 )( R₀ + R_E ) / R_O + R_E + β R_E

Where

    R_O = R₁ × R₂ / ( R₁ + R₂ )

    S = ( β + 1 ) [ 1 + ( R_O / R_E )] / ( β + 1 ) + R_O / R_E

• The ratio of R_O / R_E is very small therefore it is neglected.

    S = ( β + 1 ) / ( β + 1 )

       = 1

The smallest value of stability factor leads to thermal runaway.  The ratio of R₀ / R_E cannot be neglected.

The stability factor should be around 10 in this method.

( 1 ) Mid point Biasing

As the Q point lies at centre

I_C = ½ I_{C MAX}

V_CE = V_CC / 2

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