By Gordon S. Kino
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Extra info for Acoustic Waves: Devices, Imaging, and Analog Signal Processing (Prentice-Hall Signal Processing Series)
The function tan x has poles at x = (2n + 1)7r/2. 43) The coupling coefficients to the higher-order modes of the resonator keH,n fall off with n. The value of JFmE dz falls off with n for a given maximum value of E, because the negative contributions to the integral tend to cancel out the positive contributions. This implies that it is possible to excite a resonator at an odd harmonic of its fundamental resonant frequency, although the effective coupling coefficient for this higher-order mode is smaller than for the fundamental mode.
48). The results of Eqs. 5. on matching to an external electrical source and to bandwidth throughout this section. We can also use Eq. 46), or the Mason equivalent circuit of Fig. 4, to derive an alternative parallel equivalent circuit for the admittance Y3 = 1/Z3. 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.
What proportion of the power is reflected and transmitted at the sapphire-water interface? Despite the mismatch, this combination of materials is convenient to use in an acoustic microscope. Suppose that you wanted to improve the efficiency by using a quarter-wavelength matching section of impedance 2 = (ZolZm)”*,where Z,, is the impedance of the sapphire and Z,, is that of water. What would the impedance of this matching material have to be? As you will see from the tables in Appendix B, very few, if any, materials with this impedance exist.