handbook of modern sensors

206 5 Interface Electronic Circuits
ment is made (in Hz). For practical purposes, noise density per √ Hz generated
by a resistor at room temperature may be estimated from a simplified formula:
e n ≈ 0.13 √ R in nV/ √ Hz. For example, if the noise bandwidth is 100 Hz and the
resistance of concern is 10 M (10 7 ), the average noise voltage is estimated as
e n ≈ 0.13 √ 10 7√ 100 = 4,111nV≈ 4µV.
Even a simple resistor is a source of noise. It behaves as a perpetual generator of
electric signal. Naturally, relatively small resistors generate extremely small noise;
however, in some sensors, Johnson noise must be taken into account. For instance, a
pyroelectric detector uses a bias resistor on the order of 50 G. If a sensor is used
at room temperature within a bandwidth of 100 Hz, one may expect the average
noise voltage across the resistor to be on the order of 0.3 mV—a very high value.
To keep noise at bay, bandwidths of the interface circuits must be maintained small,
just wide enough to pass the minimum required signal. It should be noted that noise
voltage is proportional to the square root of the bandwidth. It implies that if we reduce
the bandwidth 100 times, the noise voltage will be reduced by a factor of 10. The
Johnson noise magnitude is constant over a broad range of frequencies. Hence, it is
often called white noise because of the similarity to white light, which is composed
of all the frequencies in the visible spectrum.
Another type of noise results because of dc current flow in semiconductors. It is
called shot noise; the name was suggested by Schottky not in association with his own
name but rather because this noise sounded like “a hail of shot striking the target”
nevertheless, shot noise is often called Schottky noise. Shot noise is also white noise.
Its value becomes higher with the increase in the bias current. This is the reason why
in FET and CMOS semiconductors current noise is quite small. For a bias current of
50 pA, it is equal to about 4 fA/ √ Hz—an extremely small current which is equivalent
to the movement of about 6000 electrons per second. A convenient equation for shot
noise is
i sn = 5.7 × 10 −4√ If, (5.74)
where I is a semiconductor junction current in picoamperes and f is a bandwidth
of interest in hertz.
An additional ac noise mechanism exists at low frequencies (Fig. 5.44). Both the
noise voltage and noise current sources have a spectral density roughly proportional
to 1/f , which is called the pink noise, because of the higher noise contents at lower
frequencies (lower frequencies are also on the red side of the visible spectrum). This
Fig. 5.44. Spectral distribution of 1/f “pink”
noise.