Rogers, P.H. Electroacoustic Devices The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Rogers, P.H. “Electroacoustic Devices” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
46 Electroacoustic Devices 46.1 Introduction 46.2 Transduction Mechanisms ctricity· Magnetostriction· Electrodynamic Electrostatic· Magnetic. Hydraulic· Fiber Optic· Parametric Transducers. Carbon Microphones 46.3 Sensitivity and Source Level 46.5 Canonical Equations and Electroacoustic Coupling Peter H. Rogers 46.6 Radiation Impedance Georgia Institute of Technology 16.7 Directivity 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 lezoelectricity Certain crystals produce charge on their surfaces when strained or conversely become strained when placed 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 objected 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 hig capacitance, and they are thus capable of driving long cables without preamplifier This chapter is adapted from R. M. Besancon, Encyclopedia of Physics, 3rd ed, New York: Chapman Hall, 1985 pp 337-341. With permission. c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 46 Electroacoustic Devices1 46.1 Introduction 46.2 Transduction Mechanisms Piezoelectricity • Magnetostriction • Electrodynamic • Electrostatic • Magnetic • Hydraulic • Fiber Optic • Parametric Transducers • Carbon Microphones 46.3 Sensitivity and Source Level 46.4 Reciprocity 46.5 Canonical Equations and Electroacoustic Coupling 46.6 Radiation Impedance 46.7 Directivity 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
ecently, 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 magnetostriction(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 ectrodynamic 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, c 2000 by CRC Press LLC
© 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 magnetostrictive 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
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 transd 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=P0cos(k·R-ot) (46.1) Mis defined by M=E/Po (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 dependent)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, whic 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(0, O)(Ro/R)cos(kR-ot (46.3) where e and o are elevation and azimuth angles and Ro an arbitrary reference distance(usually 1 meter ). Pi (e, o)is defined as the source level. Thus S is given by S=P6,@)I (46.4) which is a function of 8 and o and the frequency a 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 c 2000 by CRC Press LLC
© 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 = P0 cos(k · R – wt) (46.1) M is defined by M = E /P0 (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) = Ps (q, f)(R0/R) cos(kR – wt) (46.3) where q and f are elevation and azimuth angles and R0 an arbitrary reference distance (usually 1 meter). Ps (q, f) is defined as the source level. Thus S is given by S = Ps (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
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 ensitivity to the transmitting current response is equal to the reciprocity factor which is independent of the geometry and construction of the transducer. That is: (o) S(O,6,@) where Po is the density of the medium and R, 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 @, 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=ZI+t. (46.6) F=TI+zv (46.7) where V is the velocity of the radiating or receiving surface, Fis the total force acting on the surface(including acoustic reaction forces), Ze is the blocked(V=0) electrical impedance, Zm is the open-circuit mechanical impedance, and Tem and Tme are the electromechanical coupling coefficients. For reciprocal transducers Tem +Tme For example, for a moving coil transducer where the "motor"is coil in a radial magnetic field, B, T= BL (468) where L is the length of the wire in the coil and the electrical impedance Ze is largely inductive. For a piston e=Tm=-id3/(∈so) where da is the piezoelectric strain coefficient, s is the compliance, E is the permittivity at constant stress, and If a piston transducer is placed in an acoustic field such that the average pressure over the surface of the piston is PB, then F=Ps A, where A is the area of the piston, and for a receiver I=0,so E=(TemA/ZmPa (46.10) If the transducer is small compared with an acoustic wavelength Pe Po(in general Ps= DPo where D is the diffraction constant)and the free-field voltage sensitivity is given by c 2000 by CRC Press LLC
© 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 r0 is the density of the medium and R0 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 = Ze I + TemV (46.6) F = Tm e I + ZmV (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), Ze is the blocked (V = 0) electrical impedance, Zm is the open-circuit mechanical impedance, and Tem and Tme are the electromechanical coupling coefficients. For reciprocal transducers Tem = ±Tme. For example, for a moving coil transducer where the “motor” is coil in a radial magnetic field, B, Tem = –Tme = BL (46.8) where L is the length of the wire in the coil and the electrical impedance Ze is largely inductive. For a piston transducer with a piezoelectric “motor” Tme = Tem = –id33 /(eT sw) (46.9) where d33 is the piezoelectric strain coefficient, s is the compliance, eT is the permittivity at constant stress, and the electrical impedance Ze 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 PB , then F = PB A, where A is the area of the piston, and for a receiver I = 0, so E = (Te mA/Zm)PB (46.10) If the transducer is small compared with an acoustic wavelength PE ª P0 (in general PB = DP0 where D is the diffraction constant) and the free-field voltage sensitivity is given by mM = Tem A/Zm (46.11) M S J (,, R (,,) ( ) wqf wqf w p r w ) = = 4 0 0