Grasping the fundamentals
Apr 1, 1999 12:00 PM, Drew Daniels
Transducers are not magical or mystical, though one might think so after being exposed to sufficient loudspeaker marketing. The depth of understanding about transducers is shallow, owing in large part to the lack of exposure most Americans get to schooling in physics and other sciences. This leaves many people with inadequate defenses against those who use ignorance to prey upon consumers. Two examples are loudspeakers that lay on their sides with the woofers and tweeters horizontally spaced apart and loudspeaker wire priced at $1,000/ft. There are many more, but this article will focus on the narrower topic of what a typical loudspeaker transducer is and how it functions, so that after review, you will be able to disregard the marketing hype and see the essential quality of the transducer elements you purchase and use.
Loudspeakers are transducers that convert electrical energy to acoustic energy. Acoustic energy, in the strictest definition, is a mechanical vibratory motion of matter propagating through matter as waves. Acoustic energy may consist of one or two types of mechanical waves. Transverse waves have the motional characteristic of musical instrument strings, such as the slow, easily visible wave that propagates along a rope when one end is wagged or the ripples on the surface of a still pond when an object is dropped into the water. Longitudinal waves are those characterized by the end-to-end waves of the air column developed along the pipe of a horn. It is sometimes possible to see a longitudinal wave propagating along a floppy stretched spring, but longitudinal waves generally move too fast to be seen.
Sound that we hear is made by longitudinal waves moving through open air. These waves vary in air pressure, density and to a small extent, temperature. Waves begin at a source and spread out spherically; the natural shape of a large wave emanating from a small source is always a sphere. This natural tendency can be visualized if we imagine the air as a medium in which changes in air pressure are being evened out. Given no restraint, the pressure will flow in every direction equally where the density and pressure of the air is equal. A static analogy of this phenomenon is easily imagined using water poured into a pan already filled half way with water. Rather than forming a rising mound of water as new material is poured in, the surface pressure propagates throughout the pan equally until gravity has smoothed out the surface and brought the entire volume of material to equilibrium at dead-level.
Loudspeakers work by moving air, or more precisely, by disturbing the air from its normal static location. Airbornesound, as stated before, is vibrating air molecules, but this definition bears some examination. It is not necessary for air to blow or move to make sound, although blow it does, mostly near loudspeaker cones and loudspeaker vent ports. It is possible for waves to move through still air because of air's elasticity; you might picture each air molecule loosely attached to its neighbors in all directions by tiny springs. Thus, when a molecule is given a shove, it passes the energy on-through its springs-to the molecules around it. This is the essence of longitudinal soundwave motion, the phenomenon that makes it possible for a loudspeaker to shove air and produce a wave that travels outward from the cone and through the air medium in a longitudinal motion away from the cone.
Perception of sound starts with the vibration of air molecules pushing against our eardrums. It does not take much pushing for us to hear; in fact, at 4 kHz, most people can hear sound when the eardrum motion is about equal to the distance across the diameter of a hydrogen molecule (Figure 1). Displacement amplitude of air molecules depends on the frequency of the sound (Table 1).
Air-molecule motion in a spherically spreading wave decreases in amplitude as the square of the distance from the stimulus source (1/4 the amount of the motion as distance doubles). The motion itself gets pretty small by the time we get as far away as a typical listener. In unit terms, one acoustic milliwatt per square centimeter (0.001 W/cm2 or somewhere near the total area of both your eardrums) is enough to cause physical pain in the ears and some permanent hearing loss.
That may not sound like a lot of power, but it is approximately 130 dB or so, and loudspeakers are not terribly efficient. Loudspeaker transducer efficiency is a measure of the output of acoustical energy versus the input of electrical energy. When a specification tells us that a given loudspeaker device is 3% efficient, it means that if we feed the loudspeaker 100 W of electrical energy, it should produce 3 W of acoustical energy as output. The maximum efficiency achievable by a loudspeaker is half the electrical input power, or to put it another way, 1 W in, 0.5 W out.
Typical loudspeaker transducer efficiency ranges from 0.2% to 5% for cone-type transducers and 15% to 45% for compression driver-type transducers (horn driver). This is because of a trick nature plays on us called radiation resistance, which boils down to the inability of a loudspeaker cone or diaphragm made of a solid (hard substance) to transfer energy to a soft substance (gas). The energy transfer from solid to gas must take place through a gross mechanical impedance mismatch.
Magnetism, electromagnetism and motors Electromagnetism is the magnetism resulting from the application of electricity to wires or other electrical conductors. When electric current flows in a wire, a magnetic field is created around the wire. The nature of the magnetic field created follows the right-hand rule to label the direction of the current flow through the wire and the magnetic field geometric orientation. By making a fist with your right hand around the wire and pointing the thumb in the direction of current flow (pictured as positive flowing toward negative), the field twists around the wire in the direction that the fingers point. Magnetic-field orientation (N-S alignment) around the wire is perpendicular to the flow of current. The field also curls around the wire, revolving back onto itself. For a straight segment of wire, the magnetic field forms a cylinder; for a loop of wire, the field forms a toroid. In a coil of wire, the magnetic field strength is multiplied directly by the number of turns. Magnetic field variations near a wire cause currents to flow in the wire that are proportional to the rate of change of the magnetic field strength (flux).
Flux is the strength of a magnet or magnetic field-producing means. This definition applies to the total of the magnetism available in the magnet or magnetic field-producing device. Flux density, onthe other hand, is the local magnetic field intensity. This term applies to the magnetic field near the business end of the magnetic device, such as the air gap in a loudspeaker magnet where the loudspeaker's voice coil resides. The total flux and the flux density can appear to be quite independent from one another; for example, a ferrite loudspeaker magnet slab may measure only 0.2 T to 0.35 T (teslas, see SI definitions) on its surface, but with iron pole pieces to collect and concentrate the total flux in the slab, the flux density or field intensity in a small air gap between two pieces of iron can be focused to produce a field strength as high as 1.8 T-the maximum determined by the magnetic permeability (field-carrying ability) of iron.
Here are a few other relevant definitions. The pole is the end or terminus of a magnet defining its magnetic field maximum. The pole piece is a magnetic-conducting steel or iron plate or ring used to conduct and concentrate magnetism from a magnetic material to an air gap. Finally, a transducer is a device that converts energy from one form to another. Examples include the light bulb (electricity to heat and light), electric motor (electricity to rotational motion), mic (sound to electricity), battery (chemical reaction to electricity), car engine (chemical reaction to motion and heat) and solar cells (light to electricity).
Loudspeakers convert electricity to the alternating-direction linear motion of the voice coil, resulting in cone vibration and ultimately resulting in sound. Dynamic mics work in exactly the opposite way. In fact, many headphone transducers can demonstrate mic-like behavior when plugged into an audio mixer's input, and most dynamic mics could be used as (low-power) earphones in a pinch.
Loudspeakers are not limited to linear reciprocal motion by anything in their nature. In fact, a totally rotational loudspeaker exists wherein the rotational motion of an electric motor is used to wag a vane inside an axially ported cylinder to push air back and forth. From the standpoint of simplicity and economy, however, nothing has ever bested the familiar cone-style loudspeaker using a voice coil glued directly to the sound-producing cone. It needs no gears, slides or bearings, only some self-centering compliance rings to hold the cone so that the voice coil remains centered in the air gap.
In the cross-section shown in Figure 2, the magnetic field flux is concentrated in the air gap. The magnetic field crosses the air gap horizontally so that it is oriented parallel to the voice coil (all the way around the coil). Thus, when a current passes through the coil, the resulting magnetic field-at a right angle to the stationary field-pushes to repel or pulls to attract the stationary field, producing motion at a right angle to the permanent magnet's field direction. Given typically high field strength and a sufficient number of turns of wire in the air gap, push-pull force as high as 22 newtons per ampere is common in modern high-power loudspeakers. As you might imagine, this challenging set of conditions has created a large new market segment in adhesive compounds.
On Table 2, Table 3 and Table 4, you are given the units of measure and their definitions. The charts are not complete, but they do contain those units required to examine loudspeaker transducers. Once you have the units, you can calculate the expected results. Indeed, this is how transducer engineers design transducers-starting with a model and plugging in numbers to obtain an expected result.
In 1960, the international General Conference on Weights and Measures met in Paris and named the Metric System of units (based on the meter, kilogram, second, ampere, kelvin and candela) the "International System of Units." The international General Conference on Weights and Measures established the abbreviation "SI" as the official abbreviation, to be used in all languages (not S.I.). SI units are used to derive units of measurement for all physical quantities and phenomena. There are seven SI base units, from which mostother units are derived.
Definitaions of SI units The following list is provided to allow correspondence between magnetic and electrical quantities. The wording used by the Conference may seem stilted, but it is carefully chosen for semantic clarity to make the definitions unambiguous.
The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 m apart in a vacuum, would produce between these conductors a force equal to 2 x 10-7 N/m.
The coulomb is the quantity of electricity transported in 1 second by the current of 1 A.
The farad is the capacitance of a capacitor between the plates of which there appears a difference of potential of 1 V when it is charged by a quantity of electricity equal to 1 coulomb (C).
The henry is the inductance of a closed circuit in which an electromotive force of 1 V is produced when the electric current in the circuit varies uniformly at a rate of 1 ampere per second.
The joule is the work done when the point of application of 1 N is displaced a distance of 1 m in the direction of the force.
The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. The international prototype of the kilogram is a particular cylinder of platinum-iridium alloy preserved in a vault at Sevres, France, by the International Bureau of Weights and Measures.
The meter is the length equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton-86 atom.
The newton is that force which gives to a mass of 1 kg an acceleration of 1 meter/second2.
The ohm is the electric resistance between two points of a conductor when a constant difference of potential of 1 V, applied between these two points, produces in this conductor a current of 1 A, this conductor not being the source of any electromotive force.
The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.
The volt is the difference of electric potential between two points of a conducting wire carrying a constant current of 1 A, when the power dissipated between these points is equal to 1 W.
The watt is the power which gives rise to the production of energy at the rate of 1 joule per second.
The weber is the magnetic flux which, linking a circuit of one turn, produces in it an electromotive force of 1 V as it is reduced to zero at a uniform rate in 1 second.
Transducer theory, as it applies to loudspeakers, is not difficult to grasp. In taking that integral first step in understanding the physics of the loudspeaker, however, you will go a long way to improving the level of service you can provide your clients. A little knowledge is all that is needed to cut through the myths.
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