Page 393 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

APPLICATIONS 373

excitation and the SAW device. To eliminate the error from the variation of , a second
r e
reflector is put on the wafer. The corresponding time delay is 12- Similar to the first
reflector, we have the IF corresponding to the second reflector as

h(t} = B 2 cos[0(f) - 02(01 = B 2 cos[+^t 2t + co 0t 2 - ^ 2t/2] (13.27)

where
= r e + and T 2 = 2d 2/v (13.28)
t 2 T 2
and d 2 is the distance between the IDT and the second reflector. The difference between
the two phase shifts can now be written as

<Pd = (<P2 - <p\) = No - M/2fe + ti)](t2 -t1) = Kr (13.29)

where
K = a>o - fJL/2(t 2 + t\)**a) 0 (13.30)

Since O>Q ^> pL/2(t 2 + 1\ ) as can be seen from the values calculated and

(13.31)

where TO is the total travel time of the surface wave from the first reflector to the second
and back. This time being inversely proportional to the surface wave speed is very sensi-
tive to the temperature in the vicinity of the SAW device and we propose the following
relationship between the travel time t and the temperature T

T = T 0[l+a(T -To)] (13.32)

where a is the temperature coefficient of the time delay of the SAW device and TO is the
ambient temperature.
From Equation (13.29),

+ KT O(! - T 0) (13.33)

= aT +b

a = KaiQ and b = KT Q(\ - 7b) (13.34)

If the resolution of phase shift difference in degrees is A<p, then the resolution of the
temperature reading will be
AT = A<p/a (13.35)

The wafer is made of YZ-cut lithium niobate with

6
a = 94xlO~ /°C (13.36)