On the Excess Noise Factor $\Gamma$ of a FET Driven by a Capacitive Source

The excess noise factor
$\Gamma$
, also known as Ogawa's noise factor, is frequently used in the literature on optical receivers to calculate the noise and sensitivity of FET front-ends. After revisiting its definition and clarifying its applications and limitations, we derive an analytical expression for
$\Gamma$
in terms of the channel noise factor
$\gamma$
, the gate noise factor
$\delta$
, and the correlation coefficient
$c$
. We explain the difference between
$\Gamma$
and
$\gamma$
and discuss the dependence of
$\Gamma$
on the source (photodetector) capacitance. The latter dependence, which is weaker than previously thought, is verified by circuit simulations. Additional insight is obtained by complementing van der Ziel's noise model with Pospieszalski's noise model. Finally, we use the derived expression for
$\Gamma$
to calculate its value from measured noise data of a 0.18-
$\mu \hbox{m}$
CMOS technology.