Analogue Electronics/BJTs/Active Mode/ß dimensional Analysis

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This page will show that β, the common-emitter current gain of a BJT has no units.

β is given by:

where

  • 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.