handbook of modern sensors

5.9 Noise in Sensors and Circuits 205
5.9.1 Inherent Noise
A signal which is amplified and converted from a sensor into a digital form should be
regarded not just by its magnitude and spectral characteristics but also in terms of a
digital resolution. When a conversion system employs an increased digital resolution,
the value of the least significant bit (LSB) decreases. For example, the LSB of a 10-bit
system with a 5-V full scale is about 5 mV; the LSB of 16 bits is 77 µV. This by itself
poses a significant problem. It makes no sense to employ, say, a 16-bit resolution
system, if combined noise is, for example, 300 µV. In the real world, the situation is
usually much worse. There are almost no sensors which are capable of producing a 5-V
full-scale output signals. Most of them require amplification. For instance, if a sensor
produces a full-scale output of 5 mV, at a 16-bit conversion it would correspond to a
LSB of 77 nV—an extremely small signal which makes amplification an enormous
task by itself. Whenever a high resolution of a conversion is required, all sources
of noise must be seriously considered. In the circuits, noise can be produced by the
monolithic amplifiers and other components which are required for the feedback,
biasing, bandwidth limiting, and so forth.
Input offset voltages and bias currents may drift. In dc circuits, they are indistinguishable
from low-magnitude signals produced by a sensor. These drifts are usually
slow (within a bandwidth of tenths and hundredths of a hertz); therefore, they are often
called ultralow-frequency noise. They are equivalent to randomly (or predictable—
say, with temperature) changing voltage and current offsets and biases. To distinguish
them from the higher-frequency noise, the equivalent circuit (Fig. 5.3) contains two
additional generators. One is a voltage offset generator e 0 and the other is a current
bias generator i 0 . The noise signals (voltage and current) result from physical mechanisms
within the resistors and semiconductors that are used to fabricate the circuits.
There are several sources of noise whose combined effect is represented by the noise
voltage and current generators.
One cause for noise is a discrete nature of electric current because current flow
is made up of moving charges, and each charge carrier transports a definite value
of charge (the charge of an electron is 1.6 × 10 −19 C). At the atomic level, current
flow is very erratic. The motion of the current carriers resembles popcorn popping.
This was chosen as a good analogy for current flow and has nothing to do with the
“popcorn noise,” which we will discuss later. As popcorn, the electron movement
may be described in statistical terms. Therefore, one never can be sure about very
minute details of current flow. The movement of carriers are temperature related and
noise power, in turn, is also temperature related. In a resistor, these thermal motions
cause Johnson noise to result [12]. The mean-square value of noise voltage (which is
representative of noise power) can be calculated from
( V
2
)
en 2 = 4kT Rf , (5.73)
Hz
where k = 1.38 × 10 −23 J/K (Boltzmann constant), T is the temperature (in K),
R is the resistance (in ), and f is the bandwidth over which the measure-