Electronic – BJT and signal source

As Olin said, circuit shown in #1 and #3 are completely open loop. So the bias stability of the circuit is less and it can even lead to thermal runaway. The bias stability can be improved by including a negative feedback mechanism in these circuits. Circuits #2 and #4 does that.

Negative feedback in circuit #2: Assume that the collector current increases. This leads to increase in voltage across \$R_E\$. So the voltage at emitter increases. Since \$V_{BE}\$ remains almost constant, the voltage at base also increases. This leads to decrease in base current as an effect the collector current also reduces. So there exists a negative feedback to stabilize the operating point.

$$I_C\uparrow I_ER_E\uparrow V_E\uparrow V_B\uparrow I_B\downarrow I_C\downarrow $$

Negative feedback in circuit #4: Assume that the collector current increases. This leads to increase in voltage across \$R_C\$. So the voltage at collector decreases. This leads to decrease in base current as an effect the collector current also reduces. So here also there is a negative feedback to stabilize the operating point.

$$I_C\uparrow (I_C+I_B)R_C\uparrow V_C\downarrow I_B\downarrow I_C\downarrow $$

PS: The negative feedback affects the ac signal also which will reduce the gain of the amplifier. To avoid that a bypass capacitor is usually connected in parallel to \$R_E\$ in circuit #2.

It is an approximation.

You typically work around the approximation by setting the current flow the two bias divider resistors be 10X what the maximum expected base current would be. Some folks like to use a higher ratio than 10X.