handbook of modern sensors

460 16 Temperature Sensors
(A)
(B)
Fig. 16.2. Temperature changes of a sensing element: (A) the element is ideally coupled with
the object (no heat loss); (B) the element has heat loss to its surroundings.
One time constant τ T is equal to the time required for temperature T to reach 63.2% of
the initial gradient T . The smaller the time constant, the faster the sensor responds
to a change in temperature.
If, in Eq. (16.8), t →∞, then the temperature of the sensor becomes equal to
the temperature of the object: T = T 1 . Theoretically, it takes an infinite amount of
time to reach a perfect equilibrium between T 1 and T . However, because only a
finite accuracy is usually required, for most practical cases a quasiequilibrium state
may be considered after 5–10 time constants. For instance, after t = 5τ, the sensor’s
temperature will differ from that of the object by 0.7% of the initial gradient T 0 ,
whereas after 10 time constants, it will be within 0.005%.
Now, if r 2 ̸=∞, the thermal time constant should be determined from
τ T =
mc
r 1
= mc
(16.9)
α 1 + α 2 1 + r 1 /r 2
and the sensor’s response is shown in Fig. 16.2B. Note that the sensor’s temperature
never reaches exactly that of the object, no matter how long you wait.
A typical contact temperature sensor consists of the following components (Fig.
16.3A):
1. A sensing element: a material which is responsive to the change in its own temperature.
A good element should have low specific heat, small mass, high thermal
conductivity, and strong and predictable temperature sensitivity.
(A)
(B)
Fig. 16.3. General structures of temperature sensors: (A) contact sensor and (B) thermal radiation
sensor (noncontact).