Common Emitter π & T- Model Equivalents

COMMON EMITTER HYBRID – π MODEL

                           

The model obviously yields

ic=g_mV_be

i_b=V_be/r_π

    Emitter current

    I_e= (V_be/r_π) + g_mV_be

         =V_be/r_π( 1+ g_m r_π)

         =V_be/r_π( 1+ β)

         =V_be/r_e

T-Model equivalent of CE amplifier

                  

This model obviously yields

V_be=i_er_e

i_c =g_mv_be

Base current

 i_b =i_e -g_mv_be

=(v_{be /}r_e)- g_mv_be

=( v_{be /}r_e) (1-(β/1+β))

=v_be /(1+β)*r_e

= v_be /r_π

Sometimes we use

g_mv_{be ­}= g_m(i_er_e)

=( g_mr_e) i_e

=αi_e

IMPORTANT FORMULAES

Transconductance g_m=I_C/V_T

Input resistance r_π= ß/g_m = h_fe/g_m

Emitter resistance r_e=V_T/I_E

I_C = ß I_b

I_E = (1+ß)I_b

α = g_mr_e