TR (48.11) z02+Z0 When an acoustic wave meets a discontinuity or a mismatch, part of the wave is reflected. For an incident mode, an interface represents a lumped impedance. If the medium on the other side of the interface is infinitely leep, that lumped impedance is the characteristic impedance of the second medium. However, if the second medium is of finite depth h in the direction of propagation and it in turn is terminated by a lumped impedance Zu the impedance seen by the incident wave at the interface is given, as in transmission line theory, by ZL2 cos k,h+ jZoz sin k,h (48.12) Zoz cos k,h+ jZu sin k,h Thus, as with transmission lines, an intervening layer can be used to match from one transmitting medium to another. For example, if the medium following the layer is infinite and of characteristic impedance Zo3,i.e Zu= Zo, the interface will look like Zo to the incident wave if kh= m/2, quarter-wave thickness, and the layer characteristic impedance is Z02=Zo1Zo3. This matching, which provides complete power transfer from medium I to medium 3, is valid only at the frequency for which kh=T/2. For matching over a band of frequencies, multiple matchin 48.5 Transducers Electrical energy is converted to acoustic waves in ultrasonic applications by means of electro-acoustic trans ducers. Most transducers are reciprocal in that they will also convert the mechanical energy in acoustic waves into electrical energy. The form of the transducer is very application dependent. Categories of applications include imaging, wherein one transducer is used to create an acoustic beam, discontinuities in the propagating medium scatter this beam, and the scattered energy is captured by the same or another transducer [see Fig. 48. 4(b). From the changes of the scattered energy as the beam is moved, characteristics of the scatterer are determined. This is the process in the use of ultrasonics for nondestructive evaluation(NDE), flaw detection, for example, and in ultrasonic images for medical diagnosis. These are radar-like applications and are practical at reasonable frequencies because most solids and liquids support acoustic waves with tolerable losses and the avelength is short enough that the resolution is adequate for practical targets By recording both the amplitude and phase of the scattered signal as the transmitter-receiver combination is rotated about a target, one can generate tomographic-type images of the target A second category of transducer provides large acoustic standing waves at a particular frequency and, as a result, has a resonant electrical input impedance at this frequency and can be used as a narrowband filter in electrical circuits. In a third category of transducer, the object is to provide an acoustic beam that distorts the medium, as it passes through, in a manner periodic in space and time, and thus provides a dynamic diffraction grating that will deflect or modulate an optical beam that is passed through it[see Fig. 48.4(c). Such acousto- optic devices are used in broadband signal processing. Another category of transducer uses variation of the shape of the electrodes and the geometry of the electroacoustic coupling region so that the transfer function between a transmitting and a receiving transducer made to have a prescribed frequency response. Such geometries find wide application in filtering and pulse compression applications in the frequency range up to a few gigahertz. Because of the ease of fabrication of complicated electrode geometries, special forms of the solution of the wave equation, Eq (48.1), called surfac acoustic waves(SAW)are dominant in such applications. Because surface acoustic waves are discussed in another section of this handbook, here we will confine the discussion to transducers that generate or detect acoustic waves that are almost plane and usually single mode, the so-called bulk modes The prototype geometry for a bulk-mode transducer is shown in Fig. 48. 2. The active region is the portion of the piezoelectric slab between the thin metal electrodes, which can be assumed to be circular or rectangular c 2000 by CRC Press LLC© 2000 by CRC Press LLC (48.11) When an acoustic wave meets a discontinuity or a mismatch, part of the wave is reflected. For an incident mode, an interface represents a lumped impedance. If the medium on the other side of the interface is infinitely deep, that lumped impedance is the characteristic impedance of the second medium. However, if the second medium is of finite depth h in the direction of propagation and it in turn is terminated by a lumped impedance ZL2 the impedance seen by the incident wave at the interface is given, as in transmission line theory, by (48.12) Thus, as with transmission lines, an intervening layer can be used to match from one transmitting medium to another. For example, if the medium following the layer is infinite and of characteristic impedance Z03, i.e., ZL2 = Z03, the interface will look like Z01 to the incident wave if kh = p/2, quarter-wave thickness, and the layer characteristic impedance is Z2 02 = Z01Z03. This matching, which provides complete power transfer from medium 1 to medium 3, is valid only at the frequency for which kh = p/2. For matching over a band of frequencies, multiple matching layers are required. 48.5 Transducers Electrical energy is converted to acoustic waves in ultrasonic applications by means of electro-acoustic trans￾ducers. Most transducers are reciprocal in that they will also convert the mechanical energy in acoustic waves into electrical energy. The form of the transducer is very application dependent. Categories of applications include imaging, wherein one transducer is used to create an acoustic beam, discontinuities in the propagating medium scatter this beam, and the scattered energy is captured by the same or another transducer [see Fig. 48.4(b)]. From the changes of the scattered energy as the beam is moved, characteristics of the scatterer are determined. This is the process in the use of ultrasonics for nondestructive evaluation (NDE), flaw detection, for example, and in ultrasonic images for medical diagnosis. These are radar-like applications and are practical at reasonable frequencies because most solids and liquids support acoustic waves with tolerable losses and the wavelength is short enough that the resolution is adequate for practical targets. By recording both the amplitude and phase of the scattered signal as the transmitter-receiver combination is rotated about a target, one can generate tomographic-type images of the target. A second category of transducer provides large acoustic standing waves at a particular frequency and, as a result, has a resonant electrical input impedance at this frequency and can be used as a narrowband filter in electrical circuits. In a third category of transducer, the object is to provide an acoustic beam that distorts the medium, as it passes through, in a manner periodic in space and time, and thus provides a dynamic diffraction grating that will deflect or modulate an optical beam that is passed through it [see Fig. 48.4(c)]. Such acousto￾optic devices are used in broadband signal processing. Another category of transducer uses variation of the shape of the electrodes and the geometry of the electroacoustic coupling region so that the transfer function between a transmitting and a receiving transducer is made to have a prescribed frequency response. Such geometries find wide application in filtering and pulse compression applications in the frequency range up to a few gigahertz. Because of the ease of fabrication of complicated electrode geometries, special forms of the solution of the wave equation, Eq. (48.1), called surface acoustic waves (SAW) are dominant in such applications. Because surface acoustic waves are discussed in another section of this handbook, here we will confine the discussion to transducers that generate or detect acoustic waves that are almost plane and usually single mode, the so-called bulk modes. The prototype geometry for a bulk-mode transducer is shown in Fig. 48.2. The active region is the portion of the piezoelectric slab between the thin metal electrodes, which can be assumed to be circular or rectangular G G R T Z Z Z Z Z Z Z = + = + 02 01 02 01 02 02 01 – 2 and Z Z Z k h jZ k h Z k h jZ k h in L L = + + 02 2 2 02 2 2 2 2 2 cos sin 0 cos sin