Transistor Emitter follower operation

The transistor connected in the common -collector configuration, with input and output signal appearing at base and emitter terminals, respectively. This type of circuit often referred to as an Emitter follower circuit. Below circuit shows a transistor connected in a emitter follower configuration.

Although the collector terminal at + V_cc volts it is shorted to ground for ac signals,the transistor is connected as a common collector circuit element  

                                        Base current flows into the transistor of above circuit when a positive input signal rises above the base emitter turn on voltage level. The potential difference across the base and emitter terminals is equal to the value of  V_BE(ON).Thus the  output potential is slightly less positive than the input-voltage level and follows closely the voltage excursion of the positive-input signal.

Voltage gain of the circuit given by 

                               A_v=V_in-V_BE(ON)∕v_in

                         where Av = voltage gain of the emitter-follower circuit

                                    Vin = de level of input signal 

The above expression approaches unity for V_in≫V_BE(ON).The maximum positive-voltage level at the base terminal is limited by the value of V_cc and the turn-on voltage of the base-collector diode. If base-terminal voltage rises to a level which causes the base-collector diode to conduct, a clamp- ng action occurs which will not allow the base voltage to become significantly more positive. This clamped-voltage level is the sum of V_cc and the magnitude of base-collector diode drop. In order to prevent clamping of the input-signal level, V_cc should be at least as positive as the most positive  input-voltage level. 

Collector current of the non-saturated transistor is given by,

                               IC =h_FEI_B

Emitter current is expresse by,

                                        I_E=I_C+I_B

                                        I_E=I_B(h_FE+1)

Current gain is defined to be the ratio of input current to output current and from above equation can be expressed   A_I=I_E/I_B=h_FE+1