The electrical engineering handbook
Rogers, P.H. “Electroacoustic Devices” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000 © 2000 by CRC Press LLC 46 1 Electroacoustic Devices 46.1Introduction 46.2Transduction Mechanisms Piezoelectricity•Magnetostriction•Electrodynamic• Electrostatic• Magnetic•Hydraulic•Fiber Optic•Parametric Transducers•Carbon Microphones 46.3Sensitivity and Source Level 46.4Reciprocity 46.5Canonical Equations and Electroacoustic Coupling 46.6Radiation Impedance 46.7Directivity 46.1 Introduction Electroacoustics is concerned with the transduction of acoustical to electrical energy and vice versa. Devices which convert acoustical signals into electrical signals are referred to as “ microphones ” or “hydrophones” depending on whether the acoustic medium is air or water. Devices which convert electrical signals into acoustical waves are referred to as “loudspeakers” (or earphones) in air and “projectors” in water. 46.2 Transduction Mechanisms Piezoelectricity Certain crystals produce charge on their surfaces when strained or conversely become strained when placed in an electric field. Important piezoelectric crystals include quartz, ADP, lithium sulphate, rochelle salt, and tourmaline. Lithium sulphate and tourmaline are “volume expanders,” that is, their volume changes when subjected to an electric field in the proper direction. Such crystals can detect hydrostatic pressure directly. Crystals which are not volume expanders must have one or more surfaces shielded from the pressure field in order to convert the pressure to a uniaxial strain which can be detected. Tourmaline is relatively insensitive and used primarily in blast gauges, while quartz is used principally in high Q ultrasonic transducers. Certain ceramics such as lead zirconate titanate (PZT), barium titanate, and lead metaniobate become piezoelectric when polarized. They exhibit relatively high electromechanical coupling, are capable of producing very large forces, and are used extensively as sources and receivers for underwater sound. PZT and barium titanate have only a small volume sensitivity; hence they must have one or more surfaces shielded in order to detect sound efficiently. Piezoelectric ceramics have extraordinarily high dielectric coefficients and hence high capacitance, and they are thus capable of driving long cables without preamplifiers. 1 This chapter is adapted from R. M. Besançon, Encyclopedia of Physics , 3rd ed., New York: Chapman & Hall, 1985, pp. 337–341. With permission. Peter H. Rogers Georgia Institute of Technology © 2000 by CRC Press LLC Recently, it has been discovered that certain polymers, notably polyvinylidene fluoride, are piezoelectric when stretched. Such piezoelectric polymers are finding use in directional microphones and ultrasonic hydrophones. Magnetostriction Some ferromagnetic materials become strained when subjected to a magnetic field. The effect is quadratic in the field, so a bias field or dc current is required for linear operation. Important magnetostrictive metals and alloys include nickel and permendur. At one time, magnetostrictive transducers were used extensively in active sonars but have now been largely replaced by ceramic transducers. Magnetostrictive transducers are rugged and reliable but inefficient and configurationally awkward. Recently, it has been discovered that certain rare earth iron alloys such as terbium-dysprosium-iron possess extremely large magnetostrictions (as much as 100 times that of nickel). They have relatively low eddy current losses but require large bias fields, are fragile, and have yet to find significant applications. Metallic glasses have also recently been considered for magneto- strictive transducers. Electrodynamic Electrodynamic transducers exploit the forces produced on a current-carrying conductor in a magnetic field and, conversely, the currents produced by a conductor moving in a magnetic field. Direct radiation moving coil transducers dominate the loudspeaker field. Prototypes of high-power underwater projectors have been constructed using superconducting magnets. Electrodynamic microphones, particularly the directional ribbon microphones, are also common. Electrostatic Electrostatic sources utilize the force of attraction between charged capacitor plates. The force is independent of the sign of the voltage, so a bias voltage is necessary for linear operation. Because the forces are relatively weak, a large area is needed to obtain significant acoustic output. The effect is reciprocal, with the change in the separation of the plates (i.e., the capacitance) produced by an incident acoustic pressure generating a voltage. The impedance of a condenser microphone, however, is high, so a preamplifier located close to the sensor is required. Condenser microphones are very flat and extremely sensitive. The change in capacitance induced by an acoustic field can also be detected by making the capacitor a part of a bridge circuit or, alternatively, a part of an oscillator circuit. The acoustic signal will then appear as either an amplitude or frequency modulation of some ac carrier. The charge storage properties of electrets have been exploited to produce electrostatic microphones which do not require a bias voltage. Magnetic Magnetic transducers utilize the force of attraction between magnetic poles and, reciprocally, the voltages produced when the reluctance of a magnetic circuit is changed. Magnetic speakers are used extensively in telephone receivers. Hydraulic Nonreversible, low-frequency, high-power underwater projectors can be constructed utilizing hydraulic forces acting to move large pistons. Electroacoustic transduction is achieved by modulating the hydraulic pressure with a spool valve actuated by an electrostrictive (PZT) stack. Fiber Optic An acoustic field acting on an optical fiber will change the optical path length by changing the length and index of refraction of the fiber. Extremely sensitive hydrophones and microphones can be made by using a fiber exposed to an acoustic field as one leg of an optical interferometer. Path length changes of the order of 10 –6 optical wavelengths can be detected. The principal advantages of such sensors are their configurational flexibility, © 2000 by CRC Press LLC their sensitivity, and their suitability for use with fiber optic cables. Fiber optic sensors which utilize amplitude modulation of the light (microbend transducers) are also being developed. Parametric Transducers The nonlinear interaction of sound waves can be used to produce highly directional sound sources with no side lobes and small physical apertures. In spite of their inherent inefficiency, substantial source levels can be achieved and such “parametric sonars” have found a number of underwater applications. Parametric receivers have also been investigated but practical applications have yet to be found. Carbon Microphones Carbon microphones utilize a change in electrical resistance with pressure and are used extensively in telephones. 46.3 Sensitivity and Source Level A microphone or hydrophone is characterized by its free-field voltage sensitivity, M , which is defined as the ratio of the output voltage, E , to the free-field amplitude of an incident plane acoustic wave. That is, for an incident wave which in the absence of the transducer is given by P = P 0 cos( k · R – w t ) (46.1) M is defined by M = E / P 0 (46.2) In general, M will be a function of frequency and the orientation of the transducer with respect to the wave vector k (i.e., the direction of incidence of the wave). Thus, for a given frequency, M is proportional to the directivity of the transducer. It is usually desirable for a microphone or hydrophone to have a flat (i.e., frequency independent) free-field voltage sensitivity over the broadest possible range of frequencies to assure fidelity of the output electrical signal. A loudspeaker or projector is characterized in a similar manner by its transmitting current response, S , which is defined as the ratio of the acoustic source level to the driving current, I . In the farfield of a transducer the acoustic pressure is a spherical wave which can be expressed as P ( R ) = P s ( q , f )( R 0 / R ) cos( kR – w t ) (46.3) where q and f are elevation and azimuth angles and R 0 an arbitrary reference distance (usually 1 meter). P s ( q , f ) is defined as the source level. Thus S is given by S = P s ( q , f )/ I (46.4) which is a function of q and f and the frequency w . For high-fidelity sound reproduction S should be as flat as possible over the broadest possible bandwidth. For some purposes, however, such as ultrasonic cleaning or long-range underwater acoustic propagation, fidelity is unnecessary and high Q resonant transducers are employed to produce high-intensity sound over a narrow bandwidth. 46.4 Reciprocity Most conventional transducers are reversible , that is, they can be used as either sources or receivers of sound (a carbon microphone and a fiber optic hydrophone are examples of transducers which are not reversible). A transducer is said to be linear if the input and output variables are linearly proportional (hot-wire microphones © 2000 by CRC Press LLC and unbiased magnetostrictive transducers are examples of nonlinear transducers). A transducer is said to be passive if the only source of energy is the input electrical or acoustical signal (a microphone with a built-in preamplifier and a parametric projector are examples of nonpassive transducers). Most transducers which are linear, passive, and reversible exhibit a remarkable property called reciprocity . For a reciprocal transducer of any kind (moving coil, piezoelectric, magnetostrictive, electrostatic, magnetic, etc.) the ratio of the free-field voltage sensitivity to the transmitting current response is equal to the reciprocity factor J which is independent of the geometry and construction of the transducer. That is: (46.5) where r 0 is the density of the medium and R 0 is the reference distance used in defining the source level. Equation (46.5) has a number of useful consequences: (1) the receiving and transmitting beam patterns of a reciprocal transducer are identical, (2) a transducer cannot be simultaneously flat as a receiver and transmitter since S has an additional factor of w , and (3) Eq. (46.5) provides the basis for the three-transducer reciprocity calibration technique whereby an absolute calibration of a hydrophone or microphone can be obtained from purely electrical measurements. 46.5 Canonical Equations and Electroacoustic Coupling Simple acoustic transducers can be characterized by the following canonical equations: E = Z e I + T em V (46.6) F = T me I + Z m V (46.7) where V is the velocity of the radiating or receiving surface, F is the total force acting on the surface (including acoustic reaction forces), Z e is the blocked ( V = 0) electrical impedance, Z m is the open-circuit mechanical impedance, and T em and T me are the electromechanical coupling coefficients. For reciprocal transducers T em = ± T me . For example, for a moving coil transducer where the “motor” is coil in a radial magnetic field, B , T em = – T me = BL (46.8) where L is the length of the wire in the coil and the electrical impedance Z e is largely inductive. For a piston transducer with a piezoelectric “motor” T me = T em = –id 33 /(⑀ T sw) (46.9) where d 33 is the piezoelectric strain coefficient, s is the compliance, ⑀ T is the permittivity at constant stress, and the electrical impedance Z e is largely capacitive. If a piston transducer is placed in an acoustic field such that the average pressure over the surface of the piston is P B , then F = P B A, where A is the area of the piston, and for a receiver I = 0, so E = (T em A /Z m )P B (46.10) If the transducer is small compared with an acoustic wavelength P E » P 0 (in general P B = DP 0 where D is the diffraction constant) and the free-field voltage sensitivity is given by mM = T em A/Z m (46.11) M S J R(,, (,, ) () wqf wqf w p rw ) == 4 0 0 © 2000 by CRC Press LLC From Eq. (46.5) the transmitting current response is (46.12) From these simple considerations a number of principles of practical transducer design can be deduced. The mechanical impedance Z m is in general given by (46.13) where K m is an effective spring constant, M the mass, and R m the mechanical resistance. For a piezoelectric transducer [Eq. (46.9)] T em is inversely proportional to frequency; hence from Eqs. (46.10) and (46.11) we see that a piezoelectric transducer will have a flat receiving sensitivity below resonance (i.e., where its behavior is controlled by stiffness). On the other hand, a moving coil microphone must have a resistive mechanical impedance to have a flat response. From Eq. (46.12) we derive the fundamental tenet of loudspeaker design, that a moving coil loudspeaker will have a flat transmitting current response above resonance (i.e., where it is mass controlled). Accordingly, moving coil loudspeakers are designed to have the lowest possible resonant frequency (by means of a high compliance since the output is inversely proportional to the mass) and piezo- electric hydrophones are designed to have the highest possible resonant frequency. An interesting and important consequence of electromechanical coupling is the effect of the motion of the transducer on the electrical impedance. In the absence of external forces (including radiation reactance) from Eqs. (46.6) and (46.7) (46.14) That is, the electrical impedance has a “motional” component given by T em T me /Z m . The motional component can be quite significant near resonance where Z m is small. This effect is the basis of crystal-controlled oscillators. 46.6 Radiation Impedance An oscillating surface produces a reaction force F R on its surface given by F R = –Z R V (46.15) where Z R is the radiation impedance. We can thus rewrite Eq. (46.7) as F ext = T em I + (Z R + Z m )V (46.16) where F ext now includes only external forces. For an acoustically small baffled circular piston of radius a, Z R = pa 4 r 0 w 2 /2c – i(8/3)w r 0 a 3 (46.17) The radiation impedance thus has a mass-like reactance with an equivalent “radiation mass” of (8/3) r 0 a 3 and a small resistive component proportional to w 2 responsible for the radiated power. A transducer will thus have a lower resonant frequency when operated underwater than when operated in air or vacuum. The total radiated power of the piston transducer is given by S TA RZ em m = rw p 0 0 4 Z K i iM R m m m =+ + w w EZ TT Z I e em me m = æ è ç ö ø ÷ – © 2000 by CRC Press LLC p = ReZ r ΈVΈ 2 = (pa 4 r 0 w 2 /2c)V 2 (46.18) Most transducers are displacement limited, so for a direct-radiating transducer V in Eq. (46.18) is limited. To obtain the most output power the piston should have the largest possible surface area consistent with keeping the transducer omnidirectional (the transducer will become directional when a ³ l). This is easy to do in air but difficult in water since it is hard to make pistons which are both lightweight and stiff enough to hold their shape in water. Alternatively, the driver can be placed at the apex of a horn. For a conical horn, the fluid velocity at the end of the horn (where the radius is a e ) will be reduced to V(a/a e ) but the radiating piston will now have an effective radius of a e so the radiated power will increase by a factor of (a e /a) 2 . For high-power operation at a single frequency, the driver can be placed at the end of a quarter wave resonator. 46.7 Directivity It is often desirable for transducers to be directional. Directional sound sources are needed in diagnostic and therapeutic medical ultrasonics, for acoustic depth sounders; and to reduce the power requirements and reverberation in active sonars, etc. Directional microphones are useful to reduce unwanted noise (e.g., to pick up the voice of a speaker and not the audience); directional hydrophones or hydrophone arrays increase signal- to-noise and aid in target localization. One way to achieve directionality is to make the radiating surface large. A baffled circular piston has a directivity given by D e = 2J 1 (ka sinq)/ka sin q (46.19) D e equals unity for q = 0 and 1/2 when ka sin q = 2.2. For small values of ka, D e is near unity for all angles. Some transducers respond to the gradient of the acoustic pressure rather than pressure, for example, the ribbon microphone which works by detecting the motion of a thin conducting strip orthogonal to a magnetic field. Such transducers have a directivity which is dipole in nature, i.e., D e = cos q (46.20) Note that since the force in this case is proportional not to P 0 but to kP 0 , a ribbon microphone (which like a moving coil microphone is electrodynamic) will have flat receiving sensitivity when its impedance is mass controlled. By combining a dipole receiver with a monopole receiver one obtains a unidirectional cardioid receiver with D e = (1 + cos q) (46.21) Defining Terms Electroacoustics: Concerned with the transduction of acoustical to electrical energy and vice versa. Microphones: Devices which convert acoustical signals into electrical signals. Related Topic 49.1 Introduction References J.A. Bucaro, H.D. Dardy, and E.F. Carome, “Fiber optic hydrophone,” J. Acoust. Soc. Am., vol. 62, p. 1302, 1977. R.J. Bobber, “New types of transducer,” in Underwater Acoustics and Signal Processing, L. Bjorno (Ed.), Dor- drecht, Holland: D. Riedel, 1981. R.J. Bobber, Underwater Electroacoustic Measurements, Washington, D.C.: Government Printing Office, 1969. © 2000 by CRC Press LLC J.V. Bouyoucos, “Hydroacoustic transduction,” J. Acoust. Soc. Am., vol. 57, p. 1341, 1975. F.V. Hunt, Electroacoustics, Cambridge: Harvard University Press, and New York: Wiley, 1954. S.W. Meeks and R.W. Timme, “Rare earth iron magnetostrictive underwater sound transducer,” J. Acoust. Soc. Am., vol. 62, p. 1158, 1977. M.B. Moffett and R.M. Mellon, “Model for parametric acoustic sources,” J. Acoust. Soc. Am., vol. 61, p. 325, 1977. D. Ricketts, “Electroacoustic sensitivity of piezoelectric polymer cylinders,” J. Acoust. Soc. Am., vol. 68, p. 1025, 1980. G.M. Sessler and J.E. West, “Applications,” in Electrets, G.M. Sessler (Ed.), New York: Springer-Verlag, 1980. Further Information IEEE Transactions on Acoustics, Speech, and Signal Processing. . transducer where the “motor” is coil in a radial magnetic field, B , T em = – T me = BL (46.8) where L is the length of the wire in the coil and the electrical. an acoustic field such that the average pressure over the surface of the piston is P B , then F = P B A, where A is the area of the piston, and for a receiver