handbook of modern sensors

5.9 Noise in Sensors and Circuits 207
1/f noise occurs in all conductive materials; therefore, it is also associated with resistors.
At extremely low frequencies, it is impossible to separate the 1/f noise from
dc drift effects. The 1/f noise is sometimes called a flicker noise. Mostly, it is pronounced
at frequencies below 100 Hz, where many sensors operate. It may dominate
Johnson and Schottky noises and becomes a chief source of errors at these frequencies.
The magnitude of pink noise depends on current passing through the resistive or
semiconductive material. Currently, progress in semiconductor technology resulted
in significant reduction of 1/f noise in semiconductors; however, when designing a
circuit, it is a good engineering practice to use a metal film or wire-wound resistors
in sensors and the front stages of interface circuits wherever significant currents flow
through the resistor and low noise at low frequencies is a definite requirement.
A peculiar ac noise mechanism is sometimes seen on the screen of an oscilloscope
when observing the output of an operational amplifier—a principal building block
of many sensor interface circuits. It looks like a digital signal transmitted from outer
space; noise has a shape of square pulses having variable duration of many milliseconds.
This abrupt type of noise is called popcorn noise because of the sound it makes
coming over a loudspeaker. Popcorn noise is caused by defects that are dependent on
the integrated-circuit manufacturing techniques. Thanks to advances fabricating technologies,
this type of noise is drastically reduced in modern semiconductor devices.
A combined noise from all voltage and current sources is given by the sum of
squares of individual noise voltages:
√
e = en1 2 + e2 n2 +···+(R 1i n1 ) 2 + (R 1 i n2 ) 2 +···. (5.75)
A combined random noise may be presented by its root mean square (r.m.s) value,
which is
√
∫
1 T
E rms = e
T
2 dt, (5.76)
0
where T is the time of observation, e is the noise voltage, and t is time.
Also, noise may be characterized in terms of the peak values which are the differences
between the largest positive and negative peak excursions observed during
an arbitrary interval. For some applications, in which peak-to-peak (p-p) noise may
limit the overall performance (in a threshold-type devices), p-p measurement may
be essential. Yet, due to a generally Gaussian distribution of noise signal, p-p magnitude
is very difficult to measure in practice. Because r.m.s. values are so much
easier to measure repeatedly and they are the most usual form for presenting noise
data noncontroversially, Table 5.3 should be useful for estimating the probabilities of
exceeding various peak values given by the r.m.s. values. The casually observed p-p
noise varies between three times the r.m.s. and eight times the r.m.s., depending on
the patience of observer and amount of data available.
5.9.2 Transmitted Noise
A large portion of environmental stability is attributed to the resistance of a sensor
and an interface circuit to noise which originated in external sources. Figure 5.45 is