Important Formula of Transistor

 ( 1 ) Relation between emitter current, base current and collector     current

                       I_E = I_B + I_C

            Where I_E = Emitter current

                       I_B = Base current

                       I_C = Collector current

( 2 ) The emitter is heavily doped, base is lightly doped and collector is moderately doped.

( 3 ) Configuration of Transistor : 

• Common Base ( CB ) 
• Common Emitter ( CE ) and 
• Common Collector ( CC )

( 4 ) Common Base Configuration

Current amplification factor

             α = dI_C / dI_E , V_CB Constant

           Where

             dI_C = Change in collector current

             dI_E = Change in emitter current

Collector current

              I_C = αI_E + I_Leakage

              I_C = αI_E + I_CBO

                  = α / ( 1 – α ) I_B + I_CBO / ( 1 – α )

                  = βI_B + I_CBO / ( 1 – α )

Therefore β = α / ( 1 – α )

Where I_CBO = Collector – base current with emitter open

                β = Current amplification factor for common emitter

                      configuration

Input resistance ( r_i )

                  r_i = dV_BE / dI_E at constant V_CB

Output resistance ( r_o )

                  r_o = dV_CB / dI_B

( 5 ) Common Emitter Configuration 

Current amplification factor

                β = dI_C / dI_B

                Where dI_C = Change in collector current

                           dI_B = Change in base current

Collector current

                I_C = βI_B + I_CEO

                Where

                β = α / ( 1 – α )

                 I_CEO = Collector current flows when base is open circuited

Relation between I_CEO and I_CBO

               I_CEO = 1 / ( 1 – α ) I_CBO

Input resistance ( r_i )

              r_i = dV_BE / dI_B at constant V_CE

Output resistance ( r_o )

             r_o = dV_CE / dI_C at constant I_B

( 6 ) Common Collector Configuration

Current amplification factor

                     γ = dI_E / dI_B

Relation between α and γ

                   γ = 1 / ( 1 – α )

Collector current

               I_C = α I_E + I_CBO

                   = ( β + 1 )I_B + ( β + 1 )I_CBO

( 7 ) Operating Point

The zero signal values of I_C and V_CE is known as operating point.

( 8 ) Transistor  As An Amplifier

The common emitter configuration is generally used in the transistor amplifier circuit

Current Gain 

                  β  = dI_C / dI_B

Voltage gain

              A_V = dV_CE / dV_BE

                   = β × ( R_AC / R_i )

Where R_AC =  R_C  ‖ R_i

                   = ( R_C ) ( R_i ) / ( R_C + R_i )

              R_i = Input resistance of next stage

             R_C = Collector current

( 9 ) Power Gain

                 A_P = A_V × A_i

     Where A_P = Power gain

                A_V = Voltage gain

                 A_i = Current gain

( 10 ) Cut off , active and saturation region

Cut off region

Emitter diode – OFF and Collector diode – OFF

Active region

Emitter diode – ON and Collector diode – OFF

Saturation region

Emitter diode – ON and Collector diode – ON

( 11 ) Permissible Power rating of transistor

        P = T_jmax – T_amb / θ

       Where

       P = Power dissipated in the transistor

      T_jmax = Maximum junction temperature

      T_amb = Ambient temperature

     θ = Thermal resistance in degree centigrade per watt

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