Fig. 3, shows the diode curve relating IE and VBE. In the absence of ac signal, the transistor operates at Q point (point of intersection of load line and input characteristic). When the ac signal is applied, the emitter current and voltage also change. If the signal is small, the operating point swings sinusoidally about Q point (A to B).
If the ac signal is small, the points A and B are close to Q, and arc A B can be approximated by a straight line and diode appears to be a resistance given by
If the input signal is small, input voltage and current will be sinusoidal but if the input voltage is large then current will no longer be sinusoidal because of the non linearity of diode curve. The emitter current is elongated on the positive half cycle and compressed on negative half cycle. Therefore the output will also be distorted.
r'e is the ratio of ΔVBE and Δ IE and its value depends upon the location of Q. Higher up the Q point small will be the value of r' e because the same change in VBE produces large change in IE. The slope of the curve at Q determines the value of r'e. From calculation it can be proved that.