Page 394 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

374 IDT MICROSENSORS

The two reflectors are located such that the time delay at room temperature TQ is

T\ = 1 us and T 2 = 1.1 us (13.37)

Then,
TO = 0.1 us (13.38)

th
The transmitted FM signal is pulse-modulated with a time duration of 1760 of a second.
The carrier frequency varies linearly from 905 MHz to 925 MHz during the period. The
parameters in Equation (13.22) for the FM signal are

= 905 MHz (13.39)
3
fi/2n = 1.2 x 10~ MHz/us (13.40)
In operation, the distance between the two antennas is 1 to 2 meters so that r e can be
neglected compared with x\ or 12- The temperature variation can be in the range 0 to
200 °C. The first and second terms in Equation (13.30) can now be calculated

6
= 2n x 905 x 10 - 1.2 x 10 -3 x 1.05/2 (13.41)
6
= 2n x 905 x 10

So, the approximation in Equation (13.30) is clearly justified. From Equations (13.34),
(13.36), and (13.38), the constant a is

a = 3.06 angular degrees/°C (13.42)

The resolution of the phase shift is 1° so that the resolution of the temperature reading is
given by Equation (13.35) as
= 0.33°C (13.43)

The experimental calibration is done in a temperature-controlled chamber called a Delta
9023, (Figure 13.14).
A digital hand-held thermometer (Keruco Instruments Co.) with an accuracy of ±0.2 °C
is taken as the temperature standard. The temperature range in the experiment is from
room temperature (near 20 °C) to a maximum of 140 °C. The straight line theory, as
shown in Figure 13.15, fits well the experimental points of phase against temperature.
The equation for the line in Figure 13.15 is obtained by the least mean square method
and is given by
?> = 2.897-49.1 (13.44)

The value of the slope coefficient a (2.89) is in good agreement with that (3.06) estimated
from Equation (13.42). The root mean square (rms) error of the phase difference is equal
to 0.78°, which corresponds to an rms error of 0.26 °C.