By Gordon S. Kino
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Extra resources for Acoustic Waves: Devices, Imaging, and Analog Signal Processing (Prentice-Hall Signal Processing Series)
This circuit is convenient for cases where we need to operate near the series resonance into a real input impedance that is relatively small compared to the impedance at shunt resonance. The result obtained is shown in Fig. 11(a). The series and parallel resonances are at frequencies wy and U,, respectively, as we might expect. A similar derivation from the Mason equivalent circuit, which takes account of the loads Z1and Z,, can be used to derive the equivalent circuit shown in Fig. 11(b). Here the direct use of the Mason equivalent circuit is the most convenient approach (see Prob.
It is convenient because it expresses the acoustic parameters in terms of an equivalent transmission line, regarding the stress T as equivalent to a voltage -V, and the velocity v as equivalent to a current 1. This makes it easier to design multiple matching layers [lo]. On the other hand, the electrical terminal parameters are expressed in terms of an equivalent lumped circuit, which is convenient for the design of electrical matching networks at com= (cD/pm0)”*, 2, = monly used frequencies. Using the relations E, = dv,, (cDpm0)lD,2, = AZO,and Z3 = joAD and substituting Eq.
In this case, D may be finite and we can define an effective dielectric constant of the medium. We have seen that if the strain is zero, the ratio DIE is E ~ the , strain-free dielectric constant. In the same way, we define an effective permittivity under stress-free conditions E T. Putting T = 0 in Eq. 18) CE Thus, on substituting Eq. 18) into Eq. 20) Thus the stress-free dielectric constant is larger than the strain-free dielectric constant. The definitions given here can and must be generalized to define E * correctly.