Environmental Engineering Reference
In-Depth Information
Noise is random and its average value over a certain period of time
T
is
zero. Consequently, it is characterised and measured in the
mean-square
or
root-mean-square
(rms). If we denote with
x
(
t
) a generic time-dependent
noise variable that can either be a voltage or a current, its mean-square value
is symbolised by
and its rms value by
The rms definition is
based on the equivalent heating effect
For electronic circuits, rms noise voltages and currents are usually expressed
in the n and ranges, respectively.
The frequency spectrum of noise extends from nearly zero to frequencies
up to However, it is measured by instruments with limited
bandwidth. Therefore, it is often convenient to express noise and particularly
its mean square value in a 1-Hz unit of bandwidth
Since power is proportional to the square of voltage (current),
is called the
power spectral density
(PSD) of
x
and measured in
. Note that
the square root of
(symbolised by
is also a quantity of interest
and its unit is
Spectral density is a narrowband noise. In order to obtain the
total
wideband noise, (8.2) can be used only if
is constant with frequency.
Otherwise the general relation between
and
is
In evaluating the output noise due to a single noise source, the usual rules
used for networks in a sinusoidal steady state apply.
