current gain (beta)

Current gain is the answer to one question: how much bigger is the collector current than the base current that controls it? We call this ratio beta (the Greek letter), and on a datasheet it is usually printed as hFE. If beta is 150, then 1 microamp into the base produces 150 microamps at the collector. It is the multiplier in the tap analogy — how much the big flow grows for each unit of handle movement.

Formally, beta = Ic / Ib for the DC (steady) currents. A closely related number is alpha, the fraction of emitter current that reaches the collector: alpha = Ic / Ie, always just under 1 (like 0.99). The two are linked by beta = alpha / (1 - alpha); an alpha of 0.99 gives a beta of 99. Worked example: a transistor with beta = 100 driven by a 22 microamp base current should pass about 2.2 mA at the collector. Beta is a pure number with no units — it just counts how many collector electrons each base electron is worth.

Here is the honesty that good engineers live by: beta is unreliable. For the very same part number it can range from, say, 100 to 300 between two transistors out of the same bag, it grows as the device heats up, and it sags at very high or very low currents. So a design that depends on beta having an exact value is a bad design. The whole art of biasing (voltage-divider bias with an emitter resistor) is to arrange the circuit so the operating point barely cares what beta is, as long as it is reasonably large. Treat beta as "big, but I do not know exactly how big", and design accordingly.