Help with common collector formula

Hi,

Just learning about common collector transistor format.

Everything was going great till i got to this formula

AI = Iemitter / Ibase
AI = Ibase + Icollector / Ibase
AI = Icollector / Ibase + 1
AI = Hfe + 1

Can someone please explain what the 1 represents?

Simple terms please

Thanks

Mark S.

In all real situations you can ignore the 1 as it is so much smaller than the Hfe, and the Hfe isn't constant anyhow. It varies quite a lot with the collector voltage, the temperature and between transistors. Hfe is a useful concept, because the collector current varies in response to the base current, but you can't design circuits that rely on a linear relationship over a range of conditions.

Typical Hfe values could be around 100 - 200, and could vary that much, so the odd +1 on those values doesn't matter.

Back to the formulae. Hfe is a measure of the ratio of collector current to base current. If it is 120, that could mean that 1 mA flows into the base, and 120 mA flows into the collector. Both of those currents flow out of the emitter, so the emitter current would be 121 mA

In a common collector format, the emitter is the output, so the output current is 121 mA and the base current is 1 mA, so the gain is 121. In other words the base current becomes part of the output current.

Unless the gain is small, that makes no difference in practice.