Theory

The circuit in Fig. 2.4 is a Common Emitter (CE) Amplifier.

  

Figure 2.4: Common Emitter Amplifier

As discussed above, with the CE amplifier, we first use R₁, R₂, C₁, and C₂ to set up a DC operating point with v_in=0. The purpose of C₁ and C₂ is to isolate the DC operating point currents and voltages from the rest of the world, i.e, the signal source and the load. After establishing a DC operating point, an input signal is applied to the base coupling capacitor C₁. For large enough frequencies, the signal will pass through the coupling capacitor and enter the base. This will result in variations in the bias conditions in accordance with the input signal. The variation of bias conditions at the collector is then passed through the capacitor C₂, which is taken to be v_out. The small signal voltage gain is then considered to be $\frac{v_{out}}{v_{in}}$.

For simple CE amplifiers, we have to first establish a DC bias condition which means that we have to choose bias resistors R₁ and R₂ that give us appropriate values for V_C, V_B and V_E. The DC bias point is usually established to allow for a large variation or swing in v_out. To provide this large swing in v_out, a bias network is chosen so that $V_C \approx \frac{V_{CC}}{2}$. In addition, V_B and V_E are chosen to be relatively small to make sure that V_C > V_B and the BJT does not enter the saturation region. (Saturation occurs when both the base-emitter and the base-collector junction are forward biased.)

If the values of R₁,R₂,R_E,R_C and V_CC are already known, (which is the situation for analyzing existing circuits) the DC bias conditions can be determined by first replacing the voltage divider with its Thevenin equivalent, and then by directly applying loop equations to the circuit while v_in=0. To see this consider the circuit in Fig. 2.5.

  

Figure 2.5: Determining DC Bias

Using KVL on the base emitter loop, we obtain

 

V_BB = I_BR_B+I_E R_E + V_BE (22)

where R_B=R₁||R₂ and $V_{BB}=\frac{V_{CC}R_2}{R_1+R_2}$.

The B-E loop gives one equation and three unknowns. We can easily reduce the number of unknowns by making the very good approximations $I_C \approx I_E$, and V_BE=0.7V. Using these approximations and recalling that $\beta I_B=I_C$,we can obtain the following equation for I_C in terms of known parameters.

$$I_C=\frac{V_{BB}-0.7}{\frac{R_B}{\beta}+R_E}$$ (23)

With I_C determined, V_C and V_E are readily obtained by observing that:

V_C=V_CC-I_CR_C

V_E=I_ER_E

V_B=V_E+0.7