DYNAMIC CURRENT AMPLIFICATION

Another way of specifying current amplification is as the ratio of a difference in I_C to a small incremental difference in I_B that produces it. This is the dynamic current amplification, also known as current gain. It is customary to abbreviate the words the difference in by the uppercase Greek letter delta (Δ) in mathematical expressions. Then, according to this definition,

Current gain = ΔI_C/ΔI_B
The ratio ΔI_C/ΔI_B is greatest where the slope of the characteristic curve is steepest. Geometrically, ΔI_C/ΔI_B at any given point on the curve is the slope of a line tangent to the curve at that point. When the operating point of a transistor is on the steep part of the characteristic curve, the device has the largest possible current gain, as long as the input signal is small. This value is close to H_FE. Because the characteristic curve is a straight line in this region, the transistor can serve as a linear amplifier if the input signal is not too strong. This means that the output signal waveform is a faithful reproduction of the input signal waveform, except that the output amplitude is greater than the input amplitude.
As the operating point is shifted into the part of the characteristic curve where the graph is not straight, the current gain decreases, and the amplifier becomes nonlinear. The same thing can happen if the input signal is strong enough to drive the transistor into the nonlinear part of the curve during any portion of the signal cycle.