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Transistor as an amplifier

Main utility of a transistor lies in its ability to amplify weak signals
An amplifier is a circuit which is capable of increasing the signals and a transistor can not accomplish this task.
Along with transistors an amplifying circuit consists of passive components like resistors and capacitor and a biasing battery
We generally use CE configuration of transistor for most of amplifier circuit as it has high current voltage and power gain. Also input and output impedance characterstics of CE type amplifier are suitable for many applications
Figure given below shows the basis CE amplifier circuit using an NPN transistor
The Battery V_BB forward biases the emitter junction and the collector junction is biased by battery V_CC relatively higher voltage battery then V_BB
Role of load resistance R_B is to limit the base current within certain specified limits and R_C is the load resistance in the collector circuit and amplified AC voltage appears across it.
The emitter terminal is common and grounded
In this common emitter circuit the input signal is applied to the base and output signal is obtained at the collector
We know that very small base current in a transistor corresponds to large collector current
Therefore with input signal applied to the base, a very small charge in I_B produces a much large change in I_C and thus a substantial current gain is obtained
The potential difference V_BE changes with time due to the alternating input signals and this leads to the change in base current
In the absence of ac signal a closed emitter base circuit results I_B,I_E and I_C as base ,emitter and collector currents .From Kirchhoff first law
I_E=I_B+I_C ----(7)
Due to collector current I_C a voltage drop develops across R_L which is equal to I_CR_L
Applying Kirchhoff�s law in output loop we get
V_CC=V_CE+I_CR_C ---(8)

and for input loop we get
V_BB=V_BE+I_BR_B ---(9)
when input signal v_i is not zero then
V_BB+ V_i=V_BE+I_BR_B +ΔI_B(R_B+r_i)
where r_i is the input dynamic resistance relating V_BE and I_B as given in equation (3).Hence
v_i=ΔI_B(R_B+r_i)=rΔI_B
The change in I_B causes a change in I_C. Thus AC current gain A_i (or Β_ac) is defined as
Β_ac=ΔI_C/ΔI_B=i_C/i_b ---(10)
Change in collector current I_C due to change in I_B causes a change in V_CE and the voltage drop across R_C as V_CC is fixed
Thus from equation (8)
V_CC=V_CE+I_CR_C
so ΔV_CC=ΔV_CE+ΔI_CR_C
as ΔV_CC=0
Or
ΔV_CE=-R_CΔI_C
This change in V_CE is the output voltage ,Thus
v₀=ΔV_CE=-R_CΔI_C
=-Β_acR_CΔI_B
Voltage gain for the amplifier is
A_v=v₀/v_i=ΔV_CE/rΔI_B=-Β_acR_C/r ---(11)
Here negative sign in equation (11) represents that the phase of the output voltage is opposite to that of input voltage
Power gain of the amplifier is given by
A_p=Β_acA_v=Β_ac²R_C/r ---(12)