Analogue Electronics/BJTs/Active Mode/ß dimensional Analysis
This page will show that β, the common-emitter current gain of a BJT has no units.
β is given by:
- Dp and Dn are the hole and electron diffusivity, in cm2 s−1
- ND and NA are the donor and acceptor doping concentrations, in cm−3
- W is the base width, in cm
- Lp is the hole diffusion length in the emitter, in cm
- τb is the minority carrier lifetime in the base, in s
So we have:
Notice that the first term in the addition is a ratio of two quantities with identical dimensions. This leaves us with:
We now have the reciprocal of a ratio of identically dimensioned quantities. Therefore, β is dimensionless.