SPEAKERS [Hi-Fi Stereo Handbook (1974)]

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The speaker system constitutes several links in the overall high fidelity equipment chain. These links are illustrated in the block dia gram of Fig. 6-1. Each link must be considered not as a separate entity but in its relationship to the links which precede and follow it.

The amplifier output stage may be considered the energy source which supplies the driving power to the speaker system. Because most speaker electrical input circuits have a low impedance ( 2 to 20 ohms), most systems must employ an output transformer to convert this low impedance to the value into which the output amplifier should work, ordinarily about 1500 to 6000 ohms. As will be explained, the transformer works both ways. The load on the speaker system is reflected back to the amplifier stage and influences its operation, and the amplifier impedance is reflected forward to contribute to the load on the speaker driver and radiator.

The speaker system itself can be divided into three functional parts:

1. The electromagnetic part, consisting of the voice coil and field magnet. Audio-frequency electric current in the coil causes mechanical motion of the cone or diaphragm on which it is mounted. This part is often referred to as the driver or motor of the system.

2. The mechanical part, on which the driving coil is usually mounted and which is set into mechanical motion by the audio-frequency electric current in the driving coil.

3. The acoustic part, which transmits the sound energy developed by the mechanical part to the room or other area served by the system, in the most efficient and faithful manner possible.

This takes the form of a baffle or enclosure, with a horn being a form of enclosure.

A complete understanding of the operation of speaker systems requires a sufficient view of the whole flow of sound energy from the output amplifier stage to the listener, as depicted in Fig. 6-1.


This section will cover the definitions and types of drivers. The speaker driver is that portion which converts electrical energy from the output transformer to mechanical energy in the diaphragm or cone radiator. The driver is also sometimes called the motor because, like electric motors, its input is electrical and its output mechanical.

A number of different types of speaker drivers have been tried during the history of sound-system development. Those sufficiently successful to be commercially available include the following:

1. Moving-coil dynamic driver

2. Crystal drivers

3. Capacitor drivers

Of these, by far the most popular and useful in high-fidelity applications is the dynamic moving-coil type, so our discussion will be primarily about that type. Capacitor and crystal drivers are sometimes employed in high-frequency (tweeter) portions of dual systems, and these are also given brief mention.

It should be mentioned here that the performance of direct radiator speakers is very importantly influenced by the type of baffle or enclosure used. Since baffles and enclosures are a subject in them selves and must be discussed after speakers, the explanation of these factors must await a later Section. All comparative data in this section will assume that direct-radiator speakers are employed with an infinite baffle. A definition of an infinite baffle is given in the Section on baffles and enclosures.

Moving-Coil Dynamic Drivers

The principle of the dynamic speaker driver is based on the inter action of two magnetic fields. One field is relatively strong and steady; the other, developed by the passage of an audio-frequency signal current through the voice coil, varies with the instantaneous amplitude of the sound to be reproduced.

Fig. 6-1.

Electrodynamic Type---The basic construction features of an electrodynamic moving-coil type of driver are shown in Fig. 6-2. The strong, steady magnetic field is generated by a large field coil wrapped around the core. This core is mounted in a frame of magnetic material. The shape of the core and frame is such that magnetic flux is concentrated in the annular gap in the front of the structure. The voice coil, which is wound on a cylinder of fiber or aluminum, fits into the annular air gap in the core and frame structure. The AF electrical signal output from the output transformer is applied across the voice coil. The AF current in the voice coil generates a varying magnetic field which works against the strong static field of the field coil, and the resultant motor force produces mechanical motion of the voice coil. The voice coil is mounted to the cone-type radiator; hence the cone also moves with it and radiates the sound.


Fig. 6-2. Construction of a moving-coil dynamic speaker.

For minimum distortion and maximum frequency range, it is important that the voice coil and radiator or diaphragm have a mini mum mechanical mass. Excessive mass in this structure would result in inertial effects that become worse at high frequencies, and the cone or diaphragm would have a tendency to distort physically in an attempt to follow the rapid variations of high-frequency sound components. For this reason, the voice coil is made as small and light as possible. It usually consists of a single layer of fine enameled wire about ½ to 2 inches long wound along the outside surface of the voice-coil form. Because the voice coil must be so compact and light, its impedance is necessarily low; this is why output trans formers must be used to couple efficiently between the relatively high-impedance output-amplifier tubes and the dynamic speaker.

Leads from the voice coil are usually cemented to the middle portion of the cone surface, then brought out to terminals mounted on the basket of the speaker structure.

The impedance rating of the voice coil, in commercially available units, may be any value from 2 to 16 ohms. This impedance is not that of the voice coil alone but includes the effect of acoustic loading on the cone or diaphragm and mechanical effects in the structure.

These factors tend to resist motion of the voice coil and thus raise the impedance "looking into" the voice-coil terminals. These latter effects are the largest part of the rated impedance, and the effects of the self-inductance and resistance of the voice coil are relatively small. The impedance rating is also specified for some standard frequency, usually either 400 or 1000 Hz. For the foregoing reasons, a simple resistance test of the voice coil will show a relatively low resistance, compared with the impedance rating of the speaker as a whole. Further details about the acoustic and other loading effects which help make up the impedance looking into the voice coil are discussed later, under "Enclosures and Baffles."

Permanent-Magnet Type---The foregoing discussion was devoted to the dynamic driver which employs a field coil, as shown in Fig. 6-2, to derive the strong steady flux required in the gap containing the voice coil. This type of driver is referred to as the electro dynamic type. The magnetic-field flux is provided by a permanent magnet instead of a coil in what is known as the permanent-magnet dynamic speaker. The constructional features of this type of speaker are illustrated in Fig. 6-3.

Fig. 6-3. Construction of a permanent-magnet speaker.

Practical permanent-magnet dynamic speakers were made possible by the development of high-grade magnetic materials, particularly alnico. Very powerful magnets, which hold their magnetic proper ties indefinitely with little loss, can be made from this material.

A round piece of this magnetized material is mounted between the core and the frame of the magnet structure in the dynamic-driver unit, as shown in Fig. 6-3. It is thus effectively in series with the other iron in the magnetic circuit, producing flux in the same way as the many turns in the field coil of the electrodynamic type. The obvious advantage of such an arrangement is that no field-coil supply is required. Also, because the permanent magnet is lighter than a field coil providing the same amount of field, the overall weight of the speaker is reduced below that of an equivalent electrodynamic unit.

Since the permanent magnet supplies the fixed field for operation of the driver, the output power of the speaker is limited by the avail able flux and the size of the permanent magnet. In addition to power-handling capability, the size of the magnet also affects frequency response because the lower-frequency components contain most of the power in the audio signal, and they are attenuated in driver units with small magnets. Permanent-magnet speakers in general contain magnets weighing from 2 to more than 20 ounces.

Types desirable from a high-fidelity standpoint are those with 6 ounce or heavier magnets, depending on the power requirements for the speaker.

The use of the dynamic driver is by no means limited to cone radiators. It is also frequently employed with horn-type radiators, as illustrated in Fig. 6-4.

Fig. 6-4. Cross-sectional view of a horn-type reproducer.

Magnetic-Armature Type

At one time, magnetic-armature speakers were the most popular type in use, but they have now been almost completely superseded by the more efficient and better-quality dynamic type. In the magnetic type, the coil is fixed and consists of many turns of wire around a soft-iron core. The armature, which is either the radiator or a diaphragm fastened to the radiator, is also of soft iron and is mounted in a gap in the iron-core magnetic circuit around which the coil is wound. One of the prime advantages of this arrangement is the fact that the coil, being fixed, can be large enough to match the impedance of the output tube or tubes without an output trans former. Inertial and mechanical-motion limitations and nonlinearity of flux distribution have all but made this type obsolete, and it is mentioned here only for the purpose of completeness and perspective.

Crystal Drivers

Rochelle-salt crystals have the property of becoming physically distorted when a voltage is applied across two of their surfaces.

This property is the basis of the crystal type of speaker driver. The crystal-driver type of speaker is illustrated schematically in Fig. 6-5. The crystal is clamped between two electrodes across which the audio-frequency output voltage is applied. The crystal is also mechanically connected to a diaphragm. The deformations of the crystal caused by the audio-frequency signal across the electrodes cause the diaphragm to vibrate and thus to produce sound output.

Fig. 6-5. Schematic representation of a crystal-type speaker.

In general, crystal speakers have been impractical for reproduction of the full audio-frequency range because the input impedance is almost completely capacitive. Thus it is difficult to couple power into them. At high audio frequencies, the reactance becomes lower and the relative amount of power smaller. Consequently, crystal units have found some use in tweeters ( the high-frequency portion of dual-speaker units to be discussed later). Even as such, they offer no obvious or outstanding advantages over moving-coil dynamic types, and thus they are rarely encountered.

Capacitor Drivers

Another principle which has been applied to speaker drivers is that of electrostatic force. When a potential is applied between two metal plates, the resulting electrostatic field produces a force that tends to pull the plates together ( because opposite charges attract) . If like charges are applied to the plates, a force which tends to push the plates apart is created.

The principle is usually applied in a push-pull arrangement, as illustrated in Fig. 6-6. A pair of plates is connected to a balanced audio-frequency output source as shown. Another plate, mounted between these two plates, is free to move and drive a diaphragm.

The movable plate is polarized with a positive charge, as shown in the diagram.

When the polarity of the audio-frequency signal is such as to make the top capacitor plate negative, the positive armature plate is attracted to it and is repelled by the positive capacitor plate. The use of a push-pull arrangement reduces harmonic distortion, which is inherent in most capacitor-type speakers.

As is the case for the crystal speaker, the input impedance to the capacitor speaker is almost a pure capacitance; accordingly, similar problems of coupling power into it are encountered. Although a few are in use, they are very much in the minority.

Fig. 6-6. Schematic representation of a capacitor-type speaker.


Of the functional blocks of the speaker system illustrated in Fig. 6-1, we have discussed the driver only. The next step is the diaphragm which converts energy of mechanical motion into energy of air motion, called acoustic energy. There are two commonly used forms of diaphragms: ( 1) the cone type and ( 2) the horn type. The cone type acts as both diaphragm and radiator because it not only converts the mechanical energy of the driver into acoustic energy but also at the same time couples this energy into the room or area where the listeners are located. On the other hand, the horn-type diaphragm provides only mechanical-to-acoustic conversion; its acoustic energy output must be fed to the throat of a horn which couples it to the listening area. First, we will consider the cone-type diaphragm and radiator, which is more common than the horn-type diaphragm.

It is the purpose of the cone or any diaphragm-radiator combination to convert mechanical energy from the driver into acoustic energy in the listening area. The conversion must be such as to provide the greatest amount of acoustic power output for a given electrical power input, with a minimum of distortion of the output sound waveform. Although the speaker cone is a power transducer, output quality is more important than output power. Although efficiency ( ratio of output acoustic power to mechanical power input) should be as high as possible, the modifications necessary to keep distortion to desirable low levels make the majority of speakers inherently low-efficiency devices. Most speakers have overall efficiencies ranging from 5 to 15 percent; some very elaborate systems approach 40 percent.

For higher efficiency in transfer of the mechanical energy to the air, it is desirable that the greatest possible area of contact be made between the radiator and the air. Since it is desired that the air mass be alternately moved forward and backward ( and not up and down or sideways), it is natural to envision a large flat sheet driven by the speaker driver, as shown in Fig. 6-7 A. The greater the area of con tact, the better the air mass loads the driver unit. Unfortunately, such a flat structure is not mechanically practical, because when it is constructed light enough for good high-frequency response it does not retain rigidity over its entire surface. To retain better overall mechanical rigidity with comparable large-area air contact, the cone type of radiator has been used; this type is shown in Fig. 6-7B. It has been found that, with such a shape, a relatively large area of air may be activated with a relatively high ratio of strength to weight.

Treated paper is universally used in cone construction. The more rigid the paper, the greater is the sound output obtained, but the poorer is the frequency response. Soft, blotter-like cone materials improve uniformity of response in the low- and medium-frequency ranges but give poor response at high frequencies. Soft cones are also better for transient-response rejection. High-fidelity speakers often use a two-piece cone of different materials, as will be explained later.

The size of the cone is important because it influences both the low-frequency response and the power-handling capacity. The larger the cone diameter is, the greater is the power capacity for all (A) Flat-sheet radiator. (B) Cone-type radiator.

Fig. 6-7. Representation of two types of radiators.

frequency components combined, and the better is the low-frequency response. However, such improvements are not necessarily derived from larger cones unless the voice coil is appropriate. The acoustic impedance offered to the cone rises as the cone is made larger; the voice-coil impedance must then also be made larger for proper energy transfer and efficiency. The larger the cone is, the lower is the lowest useful frequency of operation. But frequency range is not the only factor improved by increase of cone size. Because the major portion of the ordinary AF signal power is in the low-frequency components, the overall power-handling capacity is also improved, as mentioned previously. The increase in the frequency range at the low end of the spectrum by an increase of cone size is illustrated in Fig. 6-8. Note that these curves show a response peak just before the response falls off at the low-frequency end of the range. This peak occurs at the resonant frequency of the speaker, which will be explained later.

Fig. 6-8. Effect of cone size and resonance on low-frequency response.

Now Electronic Industries Association ( EIA).

The designation of the cone diameter is one of the most important speaker specifications. For this reason, the definition set up by the Radio-Electronics-Television Manufacturers Association ( RETMA) for designating the size of a speaker is of special interest. This definition is as follows: The designating size of a loudspeaker employing a circular radiator (cone) shall be twice the maximum radial dimension, measured to the nearest eighth inch, of the front of the speaker, except that the designating size shall not exceed the maximum diameter of the unsupported portion of the vibrating system by more than 25 percent.

The size of the cone is also important in the choice of an enclosure in which the speaker is to be mounted. Enclosures are designed to operate with speakers of specified characteristics which depend mostly on size; that is why a given enclosure is stated to be used only with a speaker ( or speakers) of a given size. Of course, it is assumed that the overall design of the speaker is consistent with high-fidelity performance with the nominal cone size. A large cone with a small voice coil is not considered adequate for high-fidelity output.

The shape of the cone also influences performance. It has been found that a circular cross section as illustrated in Fig. 6-9A gives the best performance. Elliptical cones ( Fig. 6-9B) tend to have a lower acoustic impedance than those of a circular cross section, and it is thus more difficult to couple power into them with good efficiency. For this reason, elliptical cones are not used in high-fidelity equipment. Also important is the shape of the flare of the cone.

Straight sides are most common, but they tend to concentrate high frequency sound components in the small area surrounding the axis of the cone. Better distribution of the high-frequency components is obtained by use of a curved flare ( illustrated in Fig. 6-9C) in the cone sides, and some speakers are manufactured with this shape.

However, this is a more difficult manufacturing process than that of the non-flared speakers, and these speakers are therefore more ex pensive than straight-sided versions. In dual-speaker arrangements in which a separate high-frequency driver unit is employed, the operation of the large cone at high frequencies is not so important, and the straight-sided cone may be as good as the Hared one. In speakers in which the response of a single cone is extended over the full desired range, the curved, Haring shape shown in Fig. 6-9C is often employed.

(A) Straight-sided circular. (B) Straight-sided elliptical. (C) Cross section of flared cone.

Fig. 6-9. Three variations in cone shape.

The higher the frequency is, the smaller is the portion of the cone around the center which is used for radiation. In fact, for many cones, the highest frequencies in the audible range are radiated only by the voice coil itself. The portion useful at a given frequency is approximately a fixed quantity independent of the overall size of the cone; therefore, the larger the cone, the smaller the percentage of area employed at high frequencies. This accounts for the general fact that the larger the speaker is, the poorer the relative high frequency response is and the better the relative low-frequency response is.

Fig. 6-10. Typical cone-radiator response curve.

A generalized speaker response curve is shown in Fig. 6-10. First, there is the resonant peak at about 100 Hz ( often at lower frequencies). Below resonance, response falls off rapidly. Above resonance and up to about 1000 Hz, the whole cone acts as a unit, all parts of it vibrating in phase. Response in this region is about constant.

Above 1000 Hz, breakup occurs; that is, parts of the cone vibrate independently of each other, as shown in Fig. 6-11. In this portion, the response increases gradually until losses and impedance in the system increase sufficiently to cause final drop-off at the high-frequency end of the range. In some speakers, efficiency at high frequencies is improved by incorporating into the cone a more flexible material in the form of circular rings or corrugations coaxial with the cone to allow greater Hexing ( see Fig. 6-12). This makes it easier for the small inner portion of the cone to operate independently at high frequencies, but the structure will also transmit low-frequency vibration so that the whole cone will act as a unit at the lower frequencies.

Fig. 6-11. Typical cone breakup at high frequencies.

(A) Multi-ring unit. (B) Hartley-Turner two-unit speaker.

Fig. 6-12. Use of corrugations in cone to improve efficiency at high frequencies.

The cone is mounted to the speaker frame in two places: ( 1) at the outer edge or rim and ( 2) at the center, near the voice coil.

These mounting agencies are called suspensions of the cone assembly. The stiffness of the suspension affects the frequency response and other performance features, as is explained later. The inner suspension near the voice coil is often referred to as the spider because of the physical resemblance of some versions to a spider.

Spiders may be divided into two main groups. One group employs a phenolic or plastic sheet cut out so that the voice coil will be suspended by relatively narrow cross members, as illustrated in Fig. 6-13A. The other type, now more common, is a piece of solid, flexible material with circular corrugations, as illustrated in Fig. 6-13B. The outer suspension is sometimes just an extension of the cone structure itself, where it fastens to the metal rim of the basket.

In other cases, the material at the outer edge of the cone is feathered ( made thinner) or corrugated to provide increased flexibility. Some ...

(A) Sheet type. (B) Corrugated type.

Fig. 6-13. Two types of spiders.

... speaker units have been manufactured with suspensions of leather or other damping materials. This soft, flexible material is excellent for minimizing transient distortion at low frequencies.


It has been pointed out previously that the impedance looking into the voice coil is not merely the self-impedance of the coil itself but a combination of the self-impedance and the more important reflected acoustic impedance. A parallel may be drawn with a trans former or electric motor. Each of these devices draws a small current when operating unloaded, indicating a relatively high input impedance. When the transformer secondary is loaded by an electrical resistance or the motor shaft is coupled to a mechanical load, the input current rises and the input impedance of each device is lowered in proportion. In other words, the load impedance has been reflected into the input circuit in each case, whether it is an electrical load in the transformer or a mechanical load in the motor.

The voice-coil winding is similar to any other coil in that it has resistance (of the wire used in the winding), inductance, and a small amount of capacitance (distributed, between turns). The resistance and reactance of the coil combine to form the self-impedance of the winding, without any impedances coupled into it from its association with the other parts of the speaker.

In a speaker, the principle of total impedance is the same as in our motor and transformer analogies. The self-impedance of the voice coil (in a vacuum) is modified by the reflected impedance of the load on the diaphragm. It may be difficult at first to think of a diaphragm as having an impedance; this will be made more clear if the following analogies between mechanical and electrical systems are considered.

Mechanical inductance is called inertance. When the diaphragm starts to move some air, that air resists the force tending to set it in motion, due to its inertia. After the air is in motion, it tends to stay in motion when the diaphragm stops or reverses its motion. The degree to which the air tends to stay at rest or in motion is a :mea sure of its inertance. In the electrical analogy, it is the inductance of a circuit which provides electrical inertia, and it is the current which tends to stay at rest or in motion in proportion to the amount of inductance present. Mechanical inductance, when applied to the air, is also referred to as acoustic inductance. The term "inertance" is more especially applied to the acoustic system and the air in contact with the diaphragm. The mechanical inductance of the cone and voice-coil structure and of its suspensions is also a factor in the input impedance to the voice coil, and is reflected back to it with the acoustic inertance.

Mechanical capacitance is called compliance. This is the "springiness" or "give" of the mechanical assembly or the air. The best example of a mechanical capacitance is a spring. Force applied to a spring stores work ( force times distance) in the spring. Then, when the spring is released, the stored energy is released. This is exactly what happens electrically in a capacitor in which energy is stored by the flow of current into the capacitor by application of a voltage.

The applied voltage is analogous to the applied mechanical force, and the resulting current is analogous to the motion or change of displacement of the spring. When speaking of mechanical systems, we call this effect mechanical compliance. Although the speaker does not contain a spring, the cone suspensions do act as springs and offer to cone motion resistance which increases as cone displacement increases. The suspension compliance is the main capacitive effect, although the "springiness" of the air load and the cone and voice-coil structures during flexing add other capacitive factors.

When applied to the air, the capacitive effect is known as acoustic compliance.

Mechanical resistance is friction. It is the resistance force developed between two surfaces, two layers, or two or more groups of particles within a material when they rub together. In a speaker of the dynamic type, there are no material surfaces which rub together ( under normal operating conditions). Purely mechanical resistance arises in the friction within the cone and suspension materials when they flex during operation. The useful resistance component is that of the acoustic load. The latter is developed by the friction of the particles and layers of the air surrounding the cone or diaphragm when they bear upon each other or along the mechanical surfaces of the speaker assembly when motion is imparted to the air in the form of acoustic vibrations.

Mechanical components of impedance ( explained in the fore going) have the same relationships among themselves as exist among their counterparts in the electrical circuit. Power is dissipated only by the resistance component. The inertance and compliance produce mechanical reactance which varies with frequency in the same way that electrical reactance varies.


Fig. 6-14. Equivalent circuit of a speaker.


The resistances and reactances of the system ( including acoustic, mechanical, and electrical effects) combine in the effective impedance looking back into the output transformer. This combination is best visualized by means of an equivalent circuit, illustrated in Fig. 6-14. The diagram of the corresponding portions of the system in the upper portion of the figure help symbolize the corresponding physical locations in which the impedance factors appear. The efficiency of power transfer can be seen to be dependent on the proportion of the impedance represented by RA, which represents actual acoustic power dissipated in overcoming air friction and in radiating the acoustic power.

We have observed that there are two types of mechanical and acoustic reactance in the speaker system. They are mass or inertance, corresponding to electrical inductance, and compliance, corresponding to electrical capacitance. As in a purely electrical system, the capacitive reactance which is the compliance Cc resonates with the combined inductive effects Lv, M0 , and MA at some frequency.

This frequency is known as the resonant frequency of the speaker.

At the resonant frequency, all reactance is cancelled out of the system, and output and efficiency increase greatly over what they are for other frequencies. Rather than being beneficial, such an increase in efficiency is actually detrimental because it occurs only in the vicinity of the resonant frequency. If the effect of speaker resonance is not reduced considerably or if the resonant frequency is not made lower than the lowest frequency to be employed, extremely annoying frequency, amplitude, and transient distortions result.

The system is then highly sensitive to signals at or near the resonant frequency. Every time changes in signal amplitude occur rather suddenly, the system tends to self-oscillate at the resonant frequency even though it is excited by sound-signal components of other frequencies. The reader has probably heard this effect in sound systems which, when listened to from a distance, give the impression of producing nothing but a "booming" noise. The "boom" is a result of the reaction of the speaker system at its resonant frequency.

The curves of Fig. 6-8 show the effect of speaker resonance on response. The response rises to a peak at the resonant frequency; then it falls rapidly at lower frequencies. The shape of the response curve shows how the resonant frequency can be used as an indication of the limit of low-frequency response. Undesired sharpness of the resonant peak can be lessened by electrical, mechanical, or acoustic damping. Damping is the addition of a resistive load.

One method of providing damping is through design of the output stage of the amplifier. The latter should have as low a source impedance ( R8 in Fig. 6-14) as possible. The amplifier impedance is reflected through the output transformer and is effectively connected across the voice coil. If this reflected impedance ( resistance) is low enough, it reduces the Q of the resonance of the speaker and thereby reduces the severity of the response peak at the resonant frequency and the sharpness of the drop-off below it. The reduced Q also minimizes transient distortion because the tuned circuit represented by the speaker has less "flywheel effect." The impedance of the output amplifier stage is lowered by use of low-impedance tubes and by the use of negative feedback. Triodes have a much lower plate impedance than tetrodes and beam tubes, and that is one important reason for the preference of some for triodes.

Another method of providing speaker damping is through design of the speaker enclosure, as will be explained in the Section on baffles and enclosures.


A horn is a tube so flared (tapered) that the diameter increases from a small value at one end called the throat to a larger value at the other end called the mouth. A basic horn-driver combination is illustrated in Fig. 6-4. Horns have been used for centuries for in creasing the radiation of the human voice and musical instruments.

The horn does acoustically what the cone does mechanically. It couples the small voice-coil area to a large area of air. In this way, the horn acts as an acoustic transformer and converts the relatively high impedance at the throat and driver. The horn is a fixed physical boundary for its enclosed column of air and does not vibrate itself.

Acoustic energy fed to its throat must therefore be obtained from a vibrating diaphragm which converts mechanical motion from the driver voice coil ( or other armature) to acoustic energy. Although the cone-type radiator acts as both diaphragm and radiator and transduces from mechanical to acoustical energy, the horn acts only as a radiator, with both input and output energy being acoustic.

We have seen that the high-frequency response drop-off of a cone type radiator is caused by the inertial effect of the mass of the cone.

Because the transformation in a horn is through an air column rather than through solid material, the high-frequency response of the horn is much better than that of the cone. The overall efficiency at all frequencies is better.

In spite of these advantages, straight (unfolded) horns are not commonly used for general-frequency coverage systems or low frequency units in homes because of their bulk and their relatively high cost of manufacture. They do find wide use, however, in two forms, as follows:

1. In straight form. In dual speaker systems ( to be discussed later) and in connection with the tweeter speakers, which re produce only the high-frequency portion of the audio-frequency range.

2. In modified folded form. In special speaker enclosures ( to be discussed later). The high-fidelity sound enthusiast should therefore be familiar with some of the fundamentals of horns. The following basic information about horn design is included to clarify these fundamentals rather than to act as constructional information, although a few audiophiles have constructed their own horns with good results.

The most common type of horn design is the exponential horn.

where, A.,,

-=emx Ar A.,, is the cross-sectional area at distance x from the throat, in square inches,

Ar is the cross-sectional area of the throat, in square inches,

e is the natural logarithm base, 2.7183,

m is the flare constant of the horn, in inverse inches,

x is the distance from the throat, in inches.

This equation is of importance primarily in defining the flare constant, m. The greater the flare constant is, the faster the diameter of the horn increases.

The flare constant determines how long a horn with a given mouth to-throat area ratio must be, but it is of much greater importance in another connection. Each horn has a cutoff frequency below which no sound energy can be coupled through it. Below the cutoff frequency, the throat area offers to the driver a pure acoustic reactance and no resistance; thus, no power can be transmitted. The cutoff frequency is dependent solely on the flare constant for a given horn in air of a given temperature and humidity. The relation between them is as follows: where,

V fc=m 47T fc is the cutoff frequency, in hertz, m is the flare constant, in inverse inches, V is 13,500 inches per second, the velocity of sound in air at 20°C. Linear measuring units must be consistent throughout and in this case are inches because they are the units most appropriate to horn structures of practical size.

We are primarily interested in the type of flare required for a given cutoff frequency. A convenient and commonly used method of specifying flares is that of stating the distance along the axis of the horn over which the cross-sectional area doubles. Doubling the area is the same as multiplying the diameter by 1.414 ( the square root of 2); consequently, the shape of the desired horn can be laid out if a series of diameters at the proper distances from the throat are plotted.

Fig. 6-15. Relation between cutoff frequency and distance in which cross-sectional area doubles for exponential horns.

The relation between the area-doubling distance ( xD) and the cutoff frequency for exponential horns is plotted in Fig. 6-15. Notice that a horn must have a doubling distance of 25 inches for a 30-Hz cutoff frequency. Another horn, which need only be used for frequencies above 3000 Hz, can double its area each quarter inch! This indicates why tweeter horns are relatively short and flare out very rapidly, especially if designed for a high-frequency crossover such as 3000 Hz.

If the cutoff frequency were the only consideration, the throat and mouth diameters could be made so nearly the same that even with a small flare ( large Xn) for low frequencies the horn could be made short. For the best frequency response, however, there are important reasons for keeping the throat small and the mouth large; they are as follows:

1. When the horn is to be used for full-frequency coverage, the throat must be small to couple properly to a small diaphragm. If the diaphragm is not kept relatively small, it suffers attenuation at the high frequencies because of its mass, just like the cone. If the throat diameter is not nearly the same as the diaphragm diameter, there is loss of energy in the acoustic transfer from the diaphragm to the horn. When the horn is to be used only at low frequencies, such as for a woofer in a dual system, then the throat can be very large.

2. If the mouth is not made large enough, the sound tends to be reflected back toward the throat, and serious attenuation of the low-frequency components takes place. For this reason, the diameter of the mouth should be kept to a minimum of a half-wavelength at the lowest frequency to be reproduced. A wavelength is equal to the distance the sound wave travels during the period of one cycle.

It is thus equal to 13,500 inches per second ( the velocity of sound) divided by the frequency. Since we are interested in a half-wave length and this is our suggested minimum size for the mouth, the following relation is pertinent: where, DM = 6750 ti Dx is the diameter of the mouth, in inches, ti is the lowest frequency to be reproduced, in hertz.

For example, to maintain good operation down to 67.5 Hz, the mouth diameter should be 100 inches. This gives an idea of just how bulky horns with good low-frequency response could become.

All of the foregoing discussion of horns has implied the use of a circular cross section, but a square cross section can be used also.

The same relation holds as far as cross-sectional area is concerned, except that the dimensions of the sides instead of the diameter are given.

When a low-frequency horn is designed, the cutoff frequency closely approximates the lowest frequency to be reproduced. However, a tweeter horn must have a cutoff frequency appreciably lower than the crossover frequency at which the tweeter stops operating.

This is because crossover should be gradual rather than sharp, as explained further in a later discussion of crossover systems.

A horn may be driven by any of the previously described driver types. Tweeter horns sometimes feature crystal or capacitor drivers, but in general the moving-coil dynamic driver is most common.

This arrangement is illustrated in Fig. 6-4, which shows the magnet, voice coil, and small diaphragm of a typical unit. As previously explained, the diaphragm is small enough to vibrate with efficiency at the highest frequencies in the reproduced range. If the diaphragm were open to the free air, it would have very poor efficiency at low frequencies because of the small area of contact; however, because of the transformer action of the horn, the large area of air at the mouth of the horn is effectively coupled to the small diaphragm area in the driver.

The diaphragm is closed in on all sides, except for the port which accommodates the throat of the horn. The space between the diaphragm and the throat of the horn is known as the sound (air) chamber. In air chambers of simple annular shape, attenuation at high frequencies is sometimes encountered. At high frequencies, the wavelength is small and the different portions of the diaphragm are at different distances from the mouth of the horn. This means that appreciable phase differences appear, and resultant cancellations occur between the high-frequency sound components coming from different parts of the diaphragm, as illustrated in Fig. 6-16A. To overcome this phase problem, special chamber designs like those of Fig. 6-16B are often used. These make it necessary for all the sound energy to flow through ports of roughly equal length to the horn mouth, thus minimizing high-frequency phase differences and cancellation. This path equalization is also aided by use of a curved diaphragm like that shown.

Up to this point, we have been discussing straight horns, that is, horns whose axis is a straight line. The advantages of horns can also be obtained by using the same flare and by curving or folding the length of the horn to have space. Folded horns in high-fidelity systems are most often employed as, or in conjunction with, speaker enclosures. They are discussed later in the Section on that subject.

(A) Cancellation of out-of-phase components. (B) Two types of construction to overcome cancellation.

Fig. 6-16. Methods for overcoming out-of-phase cancellation of high-frequency components in the air chamber of a horn driver.


It is desirable that listeners in any part of a listening area receive sound of the same quality. This ideal can be approached but never quite reached because speakers have a directivity characteristic.

As could be expected, greater volume of sound is obtainable from the front of a cone or the mouth of a horn than from other parts of the radiator. However, overall volume loss with direction is not so important as long as there is a reasonably low level of distortion and good balance of frequency components. It is the change of directivity of a speaker with respect to frequency which constitutes an important problem.

Radiators of both the cone and the horn types tend to concentrate radiation of the high-frequency components of sound in a narrow cone about the axis of the radiator. The degree of directivity of a speaker is indicated by a directivity pattern, the basic function of which is indicated in Fig. 6-17. The axis of the radiator is considered the reference line with an angle of zero degrees. Directivity patterns are normally shown as a top view in a horizontal plane through the radiator axis. A cone or a circular or square horn in free space should have the same pattern in a vertical plane; but, of course, room reflections and speaker mounting may cause it to be different.

The pattern line in Fig. 6-17 indicates the relative sound intensity radiated in any direction by its distance from reference point O in that direction. For example, line OA indicates by its length that the ...

Fig. 6-17. Radiation pattern of a typical cone at one frequency.

...sound radiated along it is a maximum compared with that in any other direction. At a 45-degree angle, line OB is a measure of the relative sound intensity in that direction. Since OB is only about half as long as OA, a listener along that line would hear only about half the volume that a person along OA at the same distance from 0 would hear. At angles near 90 degrees, the pattern indicates zero radiation; of course, in any practical setup, such a zero area would not exist because sound would reach there by reflection.

Because directivity normally varies considerably with frequency, a complete diagram must show separate patterns for each of at least several frequencies. Typical variation of directivity with frequency for a 12-inch cone is illustrated in Fig. 6-18. It is assumed that the speaker is mounted in an infinite baffle ( baffles are discussed later) . Notice how much narrower the radiation pattern is at highs than at lows.

Fig. 6-18. Variation of directivity with frequency for a typical cone radiator.

The directivity of horns is not much different from that of cones when the cone diameter is approximately the same as the horn mouth diameter. However, at low frequencies at which the wave length approaches the mouth diameter, the horn directivity becomes much broader. Contrary to what might be expected, directivity for these frequencies becomes broader as the mouth diameter decreases.

Then at higher frequencies at which the mouth diameter is several times the wavelength, the directivity narrows slightly as the mouth diameter becomes smaller. All in all, for cones and horns of practical sizes, it may be said that the directivity of the cone is little different from that of the horn, except at the highest frequencies, at which the horn gives wider distribution.

Fig. 6-19. A multicellular horn.

The limited directivity of speaker radiators at high frequencies is a factor given considerable attention in speaker system designs.

One approach is to use more than one speaker, pointing each of several units in a different direction. This is more frequently done with horns than with cones for the following two reasons:

1. Because of the small throats of the horns, they are much easier to mount at an angle and close together than the cones.

2. Homs suitable for high frequencies are more compact and give slightly better distribution.

A typical example of how a number of horns may be combined to give better high-frequency distribution than is possible with one horn is shown in Fig. 6-19. This type of structure is very popular for tweeters in dual systems and is frequently referred as to a multi cellular horn. With such an arrangement, distribution of high-frequency sound components can be made almost as broad as that of the low-frequency components. In most cases, the throats of all the horn units are fed by the same driver unit; in a few more elaborate installations, separate drivers are used.


It has previously been explained that a simple single-cone speaker has definite limitations as far as frequency range is concerned. For good low-frequency response, the cone should be relatively heavy, its suspension should be as soft as possible, and its area should be as great as possible. At the highest audio frequencies, these measures are all detrimental, and the cone should be as light and small as possible with a stiff suspension. Thus, we have the generally accepted conclusion that a cone of conventional design cannot pro duce acceptable high-fidelity response ( from 60 to at least 12,000 Hz). This conventional cone, if designed for reasonable low-frequency response, ordinarily becomes unacceptable at about 8000 Hz.

In some cases, the fall-off at the high end is such that it can be at least partially compensated for by treble boost in the amplifier, but, in many speakers, "hitting the highs harder" leads to annoying distortion.

All speaker designers agree about this limitation, but they do not agree about the best way to overcome it. There are three main approaches to the problem of extension of frequency response of the conventional speaker to satisfy high-fidelity requirements:

1. Special design of a single cone to extend its response.

2. Combination of two radiators, one for high frequencies and one for low frequencies, into one physical assembly, or closely attached to each other usually along a common axis ( exemplified by the coaxial type of construction). Sometimes three radiators are used in the same arrangement. In some units, the radiators are coupled through mechanical compliance between them; in others, separate voice coils are employed.

3. Use of two or more completely separate speakers, each de signed to reproduce only a specified portion of the frequency range.

No one of these approaches is universally recognized as best. The proponents of each approach present convincing arguments, but the subjective nature of any final test has prevented any obviously conclusive choice. It is this which helps lend fascination to the pursuit of high fidelity, and the reader can expect to enjoy many hours of speculation concerning his own choice of a speaker system. Rather than favor one method over another, we present the most common arguments for each system, and this should equip the reader to form his own opinions.

Single-Cone Radiators

This type is favored by its proponents not only because of its relative simplicity but also because it is claimed that separate tweeters (high-frequency radiators) have a tendency to become "fuzzy" be cause of a phenomenon called rim resonance. The contention is that the rim of the tweeter cone or horn resonates at some high frequency and oscillates at that frequency, causing interference when high frequencies are being reproduced. It is claimed that a single cone can be so designed that a high-frequency portion in the center will operate independently at high frequencies and that it will be loaded by the outer portion of the cone to prevent rim resonance.

It is also claimed that no dual arrangement can make the high- and low-frequency sounds appear to the listener to be coming from the same source, and that the difference in construction of the high and low-frequency portions causes detectable quality differences (coloration) to the trained ear. In the single-cone arrangement, both high- and low-frequency sounds emanate from the same cone; this is supposed to eliminate the problem of duality.

Coaxial Arrangement

Proponents of this type point to the limitations of response of a single-cone unit because of the conflicting requirements for size, mass, and suspension at the two ends of the audible frequency range. This means that some additional unit must be introduced to divide the frequency range into two or more parts; and with each part designed for optimum operation in its own range, the best response and minimum distortion are obtainable. The coaxial enthusiast, although favoring a dual arrangement, eliminates the completely separate systems because of the danger of phase differences and the tendency claimed that the high- and low-frequency sounds seem to come from different sources. ( This is a similar argument to that used by single-cone proponents.) To minimize such spatial distortion, this design has the tweeter radiator right inside the low frequency (woofer) cone and coaxial with it; therefore, the apparent source of both frequency-range components is the same.

Separate Woofer-Tweeter Arrangement

Those who favor the woofer-tweeter arrangement argue that interaction and loading resulting from the placement of the woofer and tweeter together in the coaxial arrangement cause distortion not present in separate arrangements. They state that there is also a rather narrow distribution of the high-frequency components of reproduced sound from the coaxial type, and this distribution is due at least partly to the action of the woofer cone as a wide-mouth horn at the high frequencies. This can be overcome by separating the tweeter so that its energy distribution will not be influenced by the woofer.

As can be concluded from the review of pros and cons, each approach has inherent potential advantages and weaknesses. How ever, the designers and manufacturers of the better speakers of each type have taken measures to minimize each weakness, and speakers of high quality can be obtained in any of the three categories. We reiterate that the choice is the buyer's and should be exercised only after careful consideration of all claims, plus his own application problem. Even better, listen to each type under as well-controlled conditions as possible; but unfortunately it is seldom practical to find these conditions.


To help in a study of the various models of speakers in all categories, let us now consider some of the constructional features which are used to ensure high-fidelity performance.

Extended-Range, Single-Cone Type

Some of the measures taken to extend the response of a single cone have already been mentioned. One of the most important is the division of the cone into two parts: ( 1) one part which resembles a small cone and which is the center portion of the main cone, and ( 2) the second part, which is coupled to the first ( the remainder of the main cone) by a compliance which extends this second part to its full dimension. This is illustrated in Fig. 6-20. The high frequency portion of the cone is connected to the remainder of the cone through a mechanical compliance which is a ring of softer material than the cone. This compliance material allows the center high-frequency portion to operate as a separate unit but transmits low frequencies to the remainder of the cone with a blending action in midrange. The whole cone assembly acts together as a low frequency radiator.

The cone, especially its center portion, of this type of unit is made with a curved flare. As previously explained, this helps high-frequency response. Frequently, the center portion of the cone is also made of harder material than the outer portion; this helps the center portion to operate independently at the high frequencies.

An example of another type of extended-range speaker is shown in Fig. 6-21.

Coaxial Type

The coaxial principle is probably exemplified in more different commercial models than any other. We cannot review all combinations and types, but a few representative ones will give the reader sufficient general information to recognize the others. First, consider the generalized diagrams of the two main types of dual coaxial units shown in Fig. 6-22. Fig. 6-22A shows the type employing a single…


Fig. 6-20. Construction of a typical single-cone, extended-range speaker. Courtesy Whitley Electric Co.

Fig. 6-21. Typical single-cone, extended range speaker.

…voice coil for both high and low frequencies. The voice-coil form is fastened rigidly to the tweeter radiator so that the high-frequency components will be efficiently transmitted to it. It is fastened to the woofer cone through a soft mechanical compliance which transmits low-frequency components but which tends to reject high-frequency components and keep them out of the low-frequency radiator. In this…

(A) Single-voice-coil type. (C) Tweeter horn with separate diaphragm and voice coil. (B) Separate-voice-coil type.

Fig. 6-22. Basic arrangements employed in coaxial speakers.

…way, the physical construction causes the unit to function as a mechanical divider network which automatically separates high and low-frequency components. It will be noted that actually the extended-range, single-cone speakers described previously are similar to the coaxial type because the tweeter section operates separately in its range, and because the total cone and the high-frequency portion are mounted coaxially with each other.

The other general type of coaxial unit is shown in Fig. 6-22B. In this type, each radiator has its own voice coil. Because the voice coils are separate, an electrical dividing network must be employed; therefore, only the high-frequency AF currents are fed to the tweeter voice coil, and only low-frequency currents are fed to the low-frequency voice coil. If appreciable signal power at frequencies outside its intended range is applied to either voice coil, distortion and overloading will result. Divider networks, also called crossover net works, are discussed later.

When a horn is used for the tweeter, a separate diaphragm and voice coil must be used to excite it, as illustrated in Fig. 6-22C. Some representative coaxial speakers as they appear in models commercially available are illustrated in Fig. 6-23. The speaker in Fig. 6-23A may be considered a transition between the extended range single-cone and the duo-cone ( single voice-coil) coaxial types.

Small conical domes are fastened to a special corrugated single-cone structure, and a small radiator is added in the center. The domes break up the surface of the cone for the high-frequency components, reducing losses and helping to distribute radiation better.

The type of coaxial unit in Fig. 6-23B employs a separate high frequency cone coupled to the common voice coil through a mechanical connection. Besides its function as a high-frequency radiator, the small cone is said to improve low-frequency response by addition of its mass to that of the large cone, and to act as a diffuser for the large cone in the middle range of frequencies.

A coaxial unit employing a separate cone-type tweeter is shown in Fig. 6-23C. The tweeter is mounted on brackets fastened to the metal rim-support frame of the woofer.

The problem of proper distribution of high-frequency sound components in coaxial speakers has led some manufacturers to the use of multicellular horns for the tweeter. An example of this type is shown in Fig. 6-23D. The tweeter has a completely separate driver of the type required for excitation of a horn. This driver fits inside the woofer, which has a voice coil 3 inches in diameter. The horn is a single unit divided into sections by baffles at the mouth. This division into sections directs the high-frequency components over a wider radiation angle than would be obtainable without such division. In the unit illustrated, the flare cut-off of the horn ( which is exponential) is 1800 Hz, which is far enough below the 3000-Hz crossover frequency to ensure smoothness in the transition between woofer and tweeter. Fig. 6-24 shows another method of achieving better high-frequency distribution with coaxial design and the use of an acoustical lens in the high-frequency horn.

Separate Woofer-Tweeter Systems employing physically separated woofers and tweeters are commonly custom-built or at least are composed of units by different manufacturers. A few systems are sold by one manufacturer as integrated units, but we shall concentrate on the separate woofer and tweeter units and how they are combined.

Courtesy RCA (A) RCA Duocone.

Courtesy Quam-Nichols Co.

(C) Quam coaxial speaker.

Courtesy North American Philips Corp.

(B) Philips Type 971 OM. Courtesy Altec Lansing (D) Altec Type 604C.

Fig. 6-23. Various types of coaxial speakers.

(A) General appearance. (B) Internal construction. (C) Distributions with and without acoustic lens.

Fig. 6-24. Coaxial speaker with horn-type tweeter and acoustic lens.

Because the tweeter takes over above the crossover frequency, the woofer does not have to have extended range in the high-frequency direction as is the case with full-coverage, single-cone speakers. Full coverage, single-cone speakers are frequently good woofers but are overly expensive for the purpose because the special design effort expended in improvement of their high-frequency response is wasted in this application. On the other hand, just any good-sized cone

speaker is not necessarily a good woofer because, in spite of their large size, single-cone speakers do not always have good low-frequency response. Low-frequency response is doubly important in a woofer: ( 1) because this is the primary function of the woofer, and ( 2) because reproduction does not seem balanced if high frequencies are well reproduced by the tweeter without the low frequencies, or vice versa. The woofer should therefore have a resonant frequency as low as possible, with 50 Hz or lower being a rough guide. As will presently be explained, the resonant frequency of the low-frequency system ( as opposed to the speaker unit itself) depends on the type of baffle or enclosure used. However, the speaker should be designed and constructed so as to have as low a self-resonance as possible in any event.

Although any good conventional speaker with the aforementioned features will do as a woofer, greatest economy can be effected in the purchase of a unit expressly designed as a woofer. The economy arises from the fact that most conventional speakers when designed for better-than-average low-frequency response are also designed with some improvement in high-frequency response in mind. The latter is, of course, not needed in the woofer application; however, the woofer must have good response well beyond the crossover frequency to ensure good transitional operation. This is no problem at all when low crossover frequencies of 300 to 1000 Hz are used, but some speakers may start to show some drop-off or other poor response characteristics when the crossover frequency is as high as 3500 Hz ( in which case the woofer should have good response to about 4500 Hz). As mentioned, speakers designed expressly and solely as woofers in dual or multiple systems are few and far between, so no representative types are illustrated here. What many audiophiles do is to build up their speaker systems gradually. For example, a first step could be a full-range, single-cone speaker with carefully checked low-frequency resonance. This unit can be used alone for very good high-fidelity reproduction until a tweeter and suitable divider net work can be purchased. With the addition of the latter, the speaker system is extended to the dual type.

When a speaker is to be used only for reproduction of low-frequency components, in other words as a woofer, it is sometimes mounted in back of a slot instead of a circular opening. The slot is usually rather narrow, and its length is less than the diameter of the speaker cone. (Such a slot is shown schematically in Fig. 7-2C in the next Section). Such a slot acts as an acoustic low-pass filter.

It attenuates all sound components above a certain frequency. It also improves the loading and impedance match to the speaker cone at low frequencies.

Unlike woofers, tweeters cannot normally be used alone. All types therefore have the same special purpose-to reproduce only the higher-frequency portion of the audio-frequency range. One of the most important characteristics of a tweeter is its low-frequency cutoff point. The minimum frequency of operation of the unit must be below the crossover frequency of the system so that it will overlap the range of the woofer. If a low cutoff frequency (300 to 1000 Hz) is employed, the range of the tweeter from the crossover frequency to the limit of audibility for full-range fidelity in the system makes it difficult to obtain a unit with uniform response, minimum distortion, and wide-angle distribution over that range. On the other hand, relatively economical and simple driver and radiator arrangements will handle the range necessary with a high crossover frequency such as 3000 or 3500 Hz.

The construction of separate tweeter units is much like that of the tweeter portions of the examples of coaxial units given in the previous section. Horns are more popular than cones because of their greater efficiency and greater potential frequency range. A typical tweeter assembly is shown in Fig. 6-25.

Fig. 6-25. Typical tweeter-unit construction. Courtesy Electro-Voice, Inc.

Standard stock models of cone-type speakers can sometimes be used as tweeters. However, it must be emphasized that just because a speaker is small it is not necessarily a good tweeter. In fact, most ordinary small speakers are not good tweeters and often have no better high-frequency response than an average woofer. Obviously, such a speaker would provide no improvement at all over just a woofer and would be likely to add considerable distortion resulting from application of high-frequency signal components ( from the divider network) to which it does not properly respond. If you are able to hear tones up to 15,000 Hz very well," it is advisable to test a prospective tweeter speaker by applying a signal from an audio signal generator or oscillator and by noting how well the output holds up to the limit of your own audibility. In making the test, it is important to remember that as frequency rises, directivity sharpens; so, be sure to stay directly in front of the cone when listening for the upper-limit signal.

Multiple Combinations

Some audio engineers believe that the audio-frequency spectrum should be divided into more than two parts with speakers for each part for proper full-range reproduction. For example, systems employing three or four speaker radiators are commercially available some in the coaxial form, others in the separate form. The use of three or more ranges will reduce the width of each range so that uniformity of coverage for each unit is much more easily obtained.

For example, the woofer need cover only from the low limit, say about 30 to 60 Hz, to about 500 or 1000 Hz. For this range, it is certain that the woofer cone will operate as a whole and that no attenuation due to breakup will occur. Another separate radiator is employed for the middle range of frequencies, from 500 to 1000 Hz to about 3000 to 8000 Hz, with the exact limits depending on individual design. This middle-range speaker unit is sometimes refer red to as the squawker, and the three-speaker system is known as a woofer-squawker-tweeter combination. Because of the extended range of the squawker over the normal top frequency of a woofer, the tweeter can start at a relatively high frequency, and its design requirements are not so rigid as for a tweeter in a two-way system.

An example of a three-way coaxial or triaxial speaker is shown in Fig. 6-26. The woofer and squawker cones are mechanically connected ( or divided) in a duocone arrangement. The tweeter, with its own separate driver, is mounted inside the squawker. An electrical crossover network is used to divide the amplifier output between the tweeter and the woofer-squawker unit.


Children and adolescents can often hear sounds of frequencies up to 18,000 Hz, but each person's limit of audibility decreases with age and often drops to 10,000 Hz or lower.


Commercial units are also available for systems employing four sections. Typical frequency ranges are: low-bass section, 35 Hz to 200 Hz; mid-bass section, 200 Hz to 600 Hz; treble section, 600 Hz to 3500 Hz; very-high-frequency range, 3500 Hz and above.

Multiple systems have the advantage of allowing relatively simple driver-radiator units to be used for each range. Since the unit for each range does not have to work as hard as in single-radiator systems, uniform frequency response should be and usually is easily obtained. However, in the rush to a dual or multiple system, the reader should not forget that there are other things of equal and sometimes even greater importance. The changes in directivity and in fine shadings of harmonic content between different components in a multiple system sometimes cause a consciousness in the listener of the takeover from one unit to the other. Some critics claim the apparent change of source location, particularly between the high and low notes of a single instrument, is evident in some systems.

Then, in addition, if there is even a slight slip-up in the design or fabrication of the crossover network or the assumed takeover frequencies, severe distortion may result. In multiple systems, there are more parts which can self-resonate and cause trouble. These things are brought up not as pure criticism but to give the reader as much perspective as possible. While the dual or multiple system may be the complete answer for some enthusiasts, it is by no means a panacea in general. It should be remembered that any system-single, dual, or multiple-can give excellent results only when carefully designed and installed.

Fig. 6-26. A three-way coaxial speaker.


In dual or multiple speaker systems, the audio-frequency energy from the amplifier must be divided so that only the appropriate frequency components are fed to each unit of the system. In most cases, the individual parts of the system, although designed for optimum operation in their specified respective portions of the frequency spectrum, are subject to distortion and sometimes even overheating if they are driven to full power rating at frequencies outside their normal range. This is an important factor adding to the more obvious one: overall efficiency is substantially reduced by feeding too much low-frequency energy to a high-frequency unit and high-frequency energy to a low-frequency unit.

In dual systems employing a common voice coil, the mechanical compliance between the high- and low-frequency radiator sections of the cone divides the energy after it has been converted to mechanical motion of the voice-coil form. The compliance acts as a low pass filter, eliminating most of the high-frequency components from the woofer, or larger section of the cone. Low-frequency energy is fed to the high-frequency portion of the radiator, but not to it alone, because at low frequencies it acts only as part of the total mass composed of both the low- and high-frequency portions.

When each of the units in a multiple system has it own voice coil or at least two have separate voice coils, the division of low and high-frequency energy must be done electrically by divider networks.

The simplest type of divider network consists merely of a single capacitor, as illustrated in Fig. 6-27. The fact that the reactance of a capacitor is inversely proportional to frequency is employed to distribute the audio signal. In the arrangement of Fig. 6-27 A, the tweeter and woofer voice coils are connected in series, and a capacitor is connected across the woofer. The value of capacitance is made such that at frequencies above the desired range of the woofer the reactance of C becomes so low that it shunts the woofer ( C acts as a bypass capacitor). Low-frequency components can be kept out of the tweeter if a parallel connection of the voice coils is used with a capacitor in series with the tweeter circuit, as illustrated in Fig. 6-27B.

(A) Series connected. (b) Parallel connected.

Fig. 6-27. Simple divider circuits employing single reactances.

Inductance can be used with capacitances to make the divider network more complete. For example, in Fig. 6-27B the inductance ( L) can be connected in series with the woofer as shown. The inductance, the reactance of which increases with frequency, chokes the high-frequency components out of the woofer, and the capacitor ( C) blocks low-frequency components out the tweeter. The values of C and L must be such that the reactance in each case is about equal to or a little lower than the voice-coil impedance in the frequency range to be attenuated.

[ An octave is a range in which the frequency doubles. ]

A capacitor or inductor provides gradual attenuation with frequency, as the range of undesired frequency components is approached. Although the crossover range should not be too narrow, simple reactance circuits as in Fig. 6-27 are ordinarily too broad in the changeover region. Instead, a combination low-pass ( for the woofer) and high-pass ( for the tweeter) filter circuit is usually employed. With this type of circuit, much more rapid attenuation can be made near the crossover frequency than is possible with simple capacitor and inductor arrangements as illustrated in Fig. 6-27. Attenuation of about 12 dB per octave0 is considered proper in most applications. Gradual crossover arrangements attenuate at about 6 dB per octave. Filters with sharper cutoff than this can be constructed by use of additional components, but power losses in the filter become excessive, and the additional sharpness is not necessary anyway. A typical divider-network response graph is shown in Fig. 6-28. The curve of woofer output crosses the curve of tweeter output response at the crossover frequency. This intersection is also at the -3-dB, or half-power, level; at the crossover frequency, half the output power is being fed to each unit. From this, it can be seen why the respective individual response characteristics of the woofer and tweeter units must overlap substantially. If the crossover level were lower, there would be a lessening of total output in the cross over region, and this would result in frequency distortion in the system. The dash-line curve of Fig. 6-28 represents a gradual cross over attenuation of 6 dB per octave, compared to the more commonly encountered solid-curve value of 12 dB per octave.

The construction of divider networks is not as simple as the schematic diagrams may indicate. Some of the reasons are:

1. The capacitors ordinarily require fairly accurate odd values that are hard to obtain without connecting several components together.

2. There is no polarizing voltage, applied voltages are purely ac voltages at audio frequency, and electrolytic capacitors cannot be used. At the values necessary, other types of capacitors are relatively bulky and expensive.

3. Current at low impedance is appreciable; therefore, fine wire cannot be used for the coils, which have hundreds of turns for the values required. Again, the values are odd, so standard units are not applicable.

To illustrate the problem, the schematic diagram of one of the more popular types of divider networks is shown in Fig. 6-29, with formulas for calculating the values required for any crossover frequency fc and speaker impedance Z and an example of its use in a practical application.

Fig. 6-28. Divider-network response curves.

[ For those familiar with filter theory, these are m-derived half sections with equations simplified for m = 0.6. ]

The values obtained in the solution of this example illustrate the previous statements about the odd values of the capacitances involved. The circuit shown in Fig. 6-29 can be expected to give an attenuation of about 12 dB per octave.

Although the difficulties mentioned must be taken into consideration, they are not insurmountable, and some audiophiles prefer to construct their own divider networks. If the reader wishes to do so, it is suggested that he consult some handbook for data as to diameter, number of turns, etc., for his calculated inductance value.

Although the number of turns and overall size of the coils can be reduced by the use of iron cores, this is not recommended, because the later introduce nonlinearity. The capacitors can be of the oil filled variety and can be made up from standard sizes connected in series or parallel.

Fig. 6-29. A filter-type divider circuit, formulas, and sample calculation.

Courtesy Klipsch & Associates, Inc.

(A) Construction. (B) Response. (C) Circuit.

Fig. 6-30. Design features of a commercial three-way divider network.

For those who prefer to buy their crossover networks ready made, the latter are available from a number of manufacturers of audio-frequency equipment. The physical construction, schematic diagram, and response curves of a commercial three-way network are shown in Fig. 6-30. Note from the response curves ( Fig. 6-30B) that the crossover between the woofer and squawker is 500 Hz and that the crossover between the squawker and the tweeter is 5000 Hz.

This model employs gradual attenuation of 6 dB per octave, except for the low end of the squawker response where it is 12 dB per octave. The input and speaker impedances are 16 ohms. The schematic diagram is analyzed in Fig. 6-30C. The tweeter portion includes simply the two series capacitors, C2 and C3, for a total capacitance of slightly less than 1 µF. The squawker circuit em ploys a series capacitor, a shunt inductor, and a series inductor to form a band-pass filter. The woofer portion of the circuit is simply a series inductor ( L1) which is small enough to pass the low frequencies but at the same time large enough to attenuate all but the lowest frequency components in the woofer circuit. The tweeter and woofer circuits are of the single-reactance type and cause the slow rate of attenuation ( 6 dB per octave). The squawker circuit has more rapid attenuation because it is of the composite filter type.

When a horn-type tweeter is used with a cone-type woofer, there is a tendency toward energy unbalance between the high and low frequencies because of the higher efficiency of the horn. Some divider networks are designed to provide adjustment of the output of either section, relative to the other, to compensate for the difference in reproduced efficiencies. A typical commercial crossover network of this type is illustrated in Fig. 6-31A. The response characteristic of the network is shown in Fig. 6-31B. The response shown applies for the 0-dB position. Note that the tweeter response can be reduced either 2 dB or 4 dB with respect to the woofer response by moving the tap.


(A) Circuit. (B) Response characteristics.

Fig. 6-31. A divider network that provides adjustment of tweeter output to compensate for tweeter-horn efficiency relative to woofer efficiency.


Courtesy Mcintosh Laboratory Inc. (A) Response ranges. (B) External appearance. Courtesy McIntosh Laboratory Inc . 4-10" RADIATORS (12" LOUDSPEAKERS) l-5" RADIATOR (8" LOUDSPEAKER) 4-1 1/2" DOME RADIATORS 2-COAXIAL SUPER RADIATORS (C) Speaker arrangement.

Fig. 6-32. Eleven-speaker system.


Fig. 6-32A shows response ranges for an eleven-speaker system arrangement developed by McIntosh ( shown in Figs. 6-32B and 6-32C). A twelve-inch bass speaker is limited to an upper frequency of 250 Hertz. A midrange eight-inch speaker radiates to 1500 hertz, and several dome midrange speakers radiate from 1500 to 7000 hertz. A compound coaxial speaker continues the radiation up to 14,000 hertz on one diaphragm, and the super-tweeter on the other diaphragm increases the range to over 20,000 hertz with almost flat response. This dispersion arrangement using a large number of speakers allows the listener to hear the complete audio range regardless of listener position.

When divider-network response is considered, it should be remembered that the actual acoustic attenuation at the crossover frequencies may be much greater than that indicated by the electrical circuit. This is because, even when separate voice coils are employed, there may be between units mechanical compliance which acts as an attenuator.

Fig. 6-33. Dual-speaker system in which frequency components are separated at low power level and fed through separate output stages to speakers.

The divider networks described thus far are connected between the output transformer and the speaker units. Because the power level is high and the impedance low, the inductors must be capable of handling fairly high current and are therefore bulky. Because of the low impedance, the capacitors must also be large, as has been explained. For these reasons, some systems provide frequency division in the amplifier ahead of the power-output stage. At that point, the power level is so low and the impedance so high that simple resistance-capacitance-type filters can separate the high-frequency components from the low-frequency components. From this dividing point to the speakers, two separate channels are provided. There are separate output amplifiers and separate output transformers, one for each channel, as illustrated in Fig. 6-33. This is not as expensive an arrangement as it might seem at first because, since each channel ...

Fig. 6-34. Altec Lansing 771B Electronic Crossover Bi-amplifier.

Fig. 6-35. Typical dual-voice-coil unit for use as middle speaker in stereo arrangement.

... need have only a limited frequency response, the output transformers can be relatively inexpensive.

Fig. 6-34 shows the Altec Lansing Electronic Crossover Bi-amplifier, which provides built-in crossover circuitry prior to the power amplification with separate low-frequency and high-frequency amplifiers in a single compact unit. The electronic crossover circuit divides the input signal into two signals, one feeding the low-frequency amplifier (bass) and the other feeding the high-frequency amplifier (treble). The low-frequency amplifier provides 60 watts to drive the bass speaker, and the high-frequency amplifier provides 30 watts to drive the treble speakers. In this way, more effective use of the full power output makes available more speaker drive where it is most needed (bass). In addition, extreme low-frequency power demands do not affect high-frequency reproduction because separate amplifiers drive separate bass and treble speakers. Separate external crossovers are not needed. The crossover frequency is switchable to 500 Hz, 800 Hz, or 1500 Hz with 12 dB/octave slope to adapt to several combinations of speakers. This unit may be mounted inside the speaker cabinet and driven directly from a tuner.


Individual speaker requirements for stereo reproduction are substantially the same as for monophonic reproduction. The same low-distortion and wide-frequency-range requirements must be met in each unit of the stereo system.

One special feature developed especially for stereo is the dual voice coil. A typical speaker of this type is illustrated in Fig. 6-35.

Two voice coils are wound on the same form on the cone structure of the speaker. This arrangement forms a convenient method for mixing the left and right stereo signals for the center speaker. Since the center speaker is usually required only to reproduce the lower frequencies, which are not as directional, the dual-voice-coil speaker is usually a woofer. It is normally used with additional left and right speakers, which must reproduce only the frequency components above approximately 200 Hz.

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Updated: Saturday, 2022-03-26 10:51 PST