On the noise figure of weak signal receivers

A signal transmission system can be modeled as a system terminated in a reactive load
C_{0}
driven by a source with an internal resistance
R_{0}
via an intermediate two-port network. If
H(s)
is the source-to-load voltage transfer function, a very simple expression for the maximum value of the integral
\frac{1}{2 \pi} \int_{-\infty}^{\infty} |H(j \omega)|^{2} d \omega
is given. Using this value and under the condition that an active device with low input conductance is used in the front stage of a receiver, the overall noise figure of the input stage is found to be
F = 1+4C_{0} R_{n} B
. Therefore, by using small
C_{0}
's we can manage to make the noise figure quite small at rather large wide bands
B
.