Page 61 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Fundamental Noise Basics and Calculations

54 Chapter Three

be calculated at the temperature extremes. It may be that a conventional or
“super-b” bipolar design has smaller bias currents at high temperature than
does an FET device.
The equivalent voltage noise is usually due to thermal noise in resistive com-
ponents, for example the base/emitter resistors of input stage transistors. They
are often similar for bipolar and FET opamps, of the order of 5 to 50nV/ Hz .
However, specialist discrete and integrated devices are available with noise
densities down to about 0.75nV/ Hz .
Not all noise sources are “white.” The current noise and voltage noise param-
eters which are so necessary to photodetector analysis are therefore not scalar
quantities. Inspection of most opamp data sheets indicates that below a certain
frequency, called the lower corner frequency f L, both these noise parameters
increase. The frequency variation of noise density is different for FET and
bipolar opamps. This is especially marked in the case of the equivalent voltage
noise generator. For example, the data sheets for the LMC7101 give
37nV/ Hz at 10kHz, increasing to 80nV/ Hz at 100Hz, 200nV/ Hz at 10Hz,
and 600nV/ Hz at 1Hz. This is assumed to be an instance of so-called 1/f noise.
Current noise densities also show some 1/f character, but usually this is less
pronounced and starts at a lower frequency. The 1/f character means that the
noise power per decade is proportional to the reciprocal of the frequency. The
noise varies as:
2 Ê
i n = i no 1 + f L ˆ ¯ (3.12)
2
Ë
f
2
Here i no is the “white” contribution to total noise. It is unclear what is the cause
of this universal 1/f character, which can be found in an enormous variety of
sources and processes; it has been demonstrated in some opamps down to a fre-
-7
quency of 10 Hz, an equivalent period of 1 year. The high noise power density
at low frequencies strongly suggests that measurements should be carried out
at a higher frequency, preferably at audio frequencies or higher. Light sources
should therefore be modulated. The advantages of doing this are large, as we
will see in Chap. 5.
Either taking only the high-frequency noise spectral densities, or including
the full variation with frequency, system noise calculations are “simply” down
to determining the output noise contributions from these two noise generators,
modified if necessary by any connected circuitry. In practice, this process is
sometimes far from simple.

3.8 Discrete Active Component
Equivalent Noise Sources
Discrete active components such as bipolar and field effect transistors can be
2
2
characterized by voltage and current noise spectral densities i n and e n in the
same way as opamps. The input-equivalent noise sources of bipolar junction
transistors are the shot noise of the base current and the thermal noise of the
effective base and emitter resistance. These are given by:
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