Page 182 - Mechanical Engineers' Handbook (Volume 2)

6 Electron Noise Thermometers 171

(wide-band material). Narrow-band paints can be mixed; as long as the active bands do not
overlap, the calibration of each band is unaffected by the presence of the other materials. A
mixture of narrow-band materials painted on a surface will display a set of rainbow-colored
lines representing isotherms centered around each active band. A wide-band paint displays
a gradual shift in hue from one end of the range to the other. Digital image processing is
required for interpretation of the wide-band images, especially when the incident light may
54
change its spectrum over time, as discussed by Farina et al. Liquid crystal material can be
suspended in water and used to make visible the temperature distribution in the water. 55 If
a liquid crystal is painted on a surface with known heat release per unit area, then the surface
temperature distribution can be interpreted to learn the heat transfer coefficient distribution. 56
Rajendran et al. 57 described a novel optical temperature measurement sensing system
based on time-domain reflectometry. A long optical fiber was etched with 150 Bragg gratings
regularly spaced along the fiber. The fiber was then embedded in the stator windings of an
electric motor, along with a reference set of resistance–temperature detectors. The fiber was
then pulsed from one end and time-domain reflectometry, using the back-scattered light from
the gratings, was used to infer the temperature distribution along the fiber. The optical mea-
surements agreed with the RTD measurements within 3 C over the length of the fiber.
Many features of the distribution were evident in the optical measurements that were not
visible in the RTD measurements since only a few RTDs were installed. An acoustic coun-
terpart to this technique in described in Section 7.

6 ELECTRON NOISE THERMOMETERS

The electron noise method of temperature measurement uses for its signal the voltage de-
veloped by thermal agitation of the electrons in a resistor. The voltage is small (on the order
of microvolts) and at high frequencies (up to 1 GHz). But, of greatest importance, the signal
is linearly related to the absolute temperature (for frequencies less than kT/h, defined later)
by a known physical law. Furthermore, the voltage is independent of the resistor material.
The signal using multiple measurements can be made independent of the resistor value and
insensitive to background noise (electrical noise). The signal is broadband with a zero mean
and a high bandwidth. These characteristics allow rejection, by filtering, of environmental
noise without loss of measurement accuracy.
The theory is described by Decreton et al. 58
Electric noise due to thermal agitation was first described by Nyquist (1928) 59 and
Johnson (1928) 60 An unloaded passive network always presents at its ends a voltage V
n
fluctuating statistically around zero. This mean-squared noise voltage is given by
(hƒ)/(kT)
2
V 4kTR (18)
n
exp[(hƒ)/(kT)] 1
where h and k are Planck’s and Boltzmann’s constants respectively, T the absolute temper-
ature, ƒ the frequency, and R the resistance. For temperatures above 100 K and frequencies
below 1 GHz, Eq. (18) can be accurately approximated by
2
V 4kTR (19)
n
Equation (19) represents a frequency-independent white-noise signal. In a practical mea-
surement, a given frequency bandwidth (dƒ) is imposed, and the true rms voltage V is then
n
given by