US2993556A - Simulated stereophonic loud-speaker - Google Patents

Description

I July 25, 1961 E. c. WENTE 2,993,556

SIMULATED STEREOPHONIC LOUD-SPEAKER Filed Aug. 26, 1957 2 Sheets-Sheet 1 T 1 1 INVENTOR ATTORNEYS United States Patent ce SIMULATED STEREOPHONIC LOUD-SPEAKER Edward C. Wente, 42 Colt Road, Summit, NJ. Filed Aug. 26, 1957, Ser. No. 680,163 3 Claims. (Cl. 181-31) The present invention relates to a loud;speaker system that is particularly serviceable as an instrument for the faithful reproduction of music in a living-room or a small music chamber. Such an instrument should not only have a uniform response and be free from non linear distortion over a wide power level and audiofrequency range, but any part of the equipment exposed inthe living-room should be small, unobstrusive and adaptable to the general decor of living-room furnishings. Another requirement is that the reproduced sound should be appropriately diffused within the listening room. The character of this diffusion should ideally be such that a listener will experience the aural illusion of having been transported into the pick-up room where the' sound originates. The degree to which this objective can be achieved depends, of course, also on the type of pick-up microphone that is used and its placement, but with that problem we are here not concerned.

A general purpose of the invention is to satisfy the above requirements. Another object is to provide a compact high-fidelity loud-speaker system which does not require large baflies or cabinets or a large number and variety of loud-speaker units.

Other objects and advantages will become apparent and the invention will be fully understood from the following description and the drawings in which:

FIG. 1 shows a loud-speaker arrangement according to the invention;

FIG. 2 shows one of the panels of FIG. 1;

FIG. 3 is a graph of resistance and reactance characteristics;

FIG. 4 is a schematic connection diagram of 3 loudspeakers;

FIG. 5 is a graph of power output versus frequency; and

FIGS. 6 and 7 are circuit diagrams of equalizing networks.

-A pulsating sphere in free space with the same radial motion over its entire surface would generate true spherical waves whose power could be readily calculated in terms of the frequency amplitude of motion and the radius of the sphere. The wave pattern would be changed in no way if the whole space outside of this sphere were divided into eight equal sections by three mutually perpendicular rigid planes with their point of intersection at the centre of the sphere. The situation in one of these sectors would then be exactly the same as that which would obtain in a trihedral corner of the room if it were cut-off by a spherical shell having the same radius of curvature and radial motion as the above sphere and having its centre of curvature at the vertex of the corner, except for the reflections introduced by the oppositely located enclosing walls of the room. The smallest separation of one of these reflecting walls from the source in the living room would usually by the distance from floor to ceiling or about 9 feet. We should not expect reflection from a wall at this distance to have much effect on the radiation impedance of the source for wave lengths less than twice this ds-tance, i.e., for frequencies greater than 1-l00+18=60 c.p.s., at which frequency a rather strong resonance might assert itself. The magnitude of this'eifect would depend upon the other dimensions and the furnishings of the room. As it would thus be pe-. culiar to each room, we shall as a first approximation neglect it in computing the sound output.

2,993,556 Patented July 25, 1961 The radiation impedance per unit area of a pulsating sphere in free space is equal to C waml 0 'i'j ol.

(see Theory of Vibrating Systems and Sound, I. B. Crandall, p. 12.1), where R is the radius of curvature of the sphere, k is equal to and C is the velocity of sound. The area of the pulsating spherical shell in the trihedral corner of the room is equal to one eighth of that of a complete sphere of the same radius, or 41rR +8 so the total radiation impedance of this shell is 2 1 @wanam While the radiation impedance of a spherical diaphragm in the room corner as here postulated can be readily computed, the construction of a spherical shell vibrating radially at a large and uniform amplitude is impracticable. But a structure that is substantially equivalent in operation is one wherein the pulsating spherical diaphragm has been replaced by a rigid spherical shell of the same dimensions in which closely and evenly spaced holes have been cut and then closed with flush mounted diaphragms having rigid central and flexible rim portions, each of the diaphragms being provided with a separate driving unit, preferably of the moving coil type. Functionally this structure would differ from the other one in two respects. The radiation pattern throughout the trihedral projection angle would not be so uniform and the radiation impedance would be lower.

Each diaphragm with its rigid central and flexing rim portions acts like a piston from which the radiated sound becomes progressively more columnar with increasing frequency. The effect of this behavior on the uniformity of the sound field would be reduced to a minimum by an increase in the number and a corresponding decrease in the size of the diaphragms. But, as we shall see, the nonuniformity in the sound field resulting from the use of relatively large diaphragms need not impair the quality of the reproduced sound an appreciable amount.

A more serious disadvantage of the multi-diaphragm structure is its lower radiation impedance. This impedance is equal to that of the vibrating shell as given by the Expression 1, above, multiplied by the square of the ratio of the live, or effective, area to the total area of the shell. The effective area of an acoustic diaphragm is defined as the ratio of its volume displacement to its amplitude of motion. In the diaphragms here considered the effective area is less than the superficial area because the flexing annular portion does not take a full part in the motion of the rigid central portion. If the maximum linear amplitude of motion is specified then the required radial width of the flexing annulus is practically independent of the size of the diaphragm. The flexing area, therefore, varies linearly with the diameter of the diaphragm whereas the central area varies as-the square of its diameter. Hence the ratio of the effective area to the superficial area of each diaphragm increaseswith the size of the diaphragm. Then in order to keep this ratio as near to unity as possible it is of advantage to use a few large diaphragms rather than a multiplicity'of small ones.

The effective area of the entire shell is equal to the sum of the effective areas of all the diaphragms. The indicated inherent advantage in the use of a few relatively large diaphragms suggests a structure in which a single diaphragm is placed symmetrically in the corner with its axis passing through the vertex and as far back into the corner as the walls will permit. This arrangement could be efficient but it fails badly in respect to the generation of a diffuse sound field in the room.

Two diaphragms could not be so mounted in the spherical shell that they would generatea progressive wave that would be symmetrical with respect to the axis of the corner. A further disadvantage of this arrangement would be that the total effective area of the two diaphragms would be a relatively small fraction of the area of the shell because two equal circles cannot be drawn without overlap on a rectangular octant of a spherical surface so as to cover as much as /8 of its surface.

Three circles of equal size can, however, be drawn without overlap on such a surface so as to cover about 90% of the area. This amount of symmetrical coverage would be attained if one circle were placed in each of the three corners of the right spherical triangle that defines the boundary of the spherical ootant and were made as large as possible without any over-lapping. No greater fraction of the surface could be covered symmetrically by the use of a larger number of equal circles.

A loud-speaker system with the diaphragms of three cone-type loud-speakersmounted ina corresponding manner in the corner of a room thus has unique advantages.

FIG. 1 shows the installation of three loud-speaker diaphragms in the trihedral, cornerof the room in accordance with the above principles. They are not shown mounted in a spherical shell, but each one is flush mounted in a quadralateral, plate of the dimensions given in FIG. 2. When these plates are fitted into the corner in the manner indicated, the diaphragms will have the same positions relative to the walls of the room. as they would have if mounted in a spherical shell as previously described.

The distance, R from the vertex of the corner to each diaphragm is equal to 1.305 D where D is the rim diameter of the diaphragms clamping rings. The solidlined circles 2426 in FIGS. 1 and 2 represent openings in the bafflles 18-20 opposite the live portions of. the diaphragms -17 through which the sound emerges into the room. The dotted lined circles show the positions of the rims ofthe diaphragm clamping rings 21, 22, 23. With the mounting shown in FIGS. 1 and 2 the axes of the diaphragms extend to a point close to the vertex' of the corner and make equal angles. of about degrees with the axis of the corner.

Referring to FIG. 1,. in the arrangement of the three speakers there are three planes of symmetry defined by the axis of the corner and the points a, b, and 0 respectively. Across these planes there is no air flow or pressure gradient. They effectively divide thev solid angle of the corner into three parts. These three divisional solid angles have a common vertex, are congruent and are oriented symmetrically with respect to the three dihedral angles forming the room corner. Together with its respective loud-speaker unit each part forms a horn type of loud-speaker. The cross-sectional area of the horn varies as the square of the distance from the vertex. Acoustically it is therefore equivalent to a conical horn. If R is the distance from the vertex to the throat of, the horn, which is defined by the position of the diaphragm, then the area of the throat is equal to The impedance per unit area: at the throat of av conical horn is equalvto Q Q e RHjkRu so that the radiation impedance of the throat is equal to FR pc The radiation impedance of the diaphragm is equal to this impedance multiplied by the squareof; the ratio of the etfectivearea,

of the diaphragm to that of the throat area. We thus finally get for the impedance of the three diaphragms combined A particular loud-speaker which may be used is one that is manufactured by the Phillips Co. of Holland under the code. number 9710M. Its use in a high fidelity system is: described in the Phillips Technical Review of Marchv 23, 1957, p. 285. This unit has thefollowing principal properties:

one abampere of current):5.8 l0 dynes/abampere.

Substituting, the above numerical values in Equation la, we find that the radiation resistance,

R 28.2 cm.

obtained by these formulae are-plotted as a function of frequency in curves. 30 and 31 respectively, in FIG. 3. Curves 32 and 33 in this figure show the corresponding; values of and for a circular diaphragm in an. infinite baflle havingthe same effective area as the combined areas of the three diaphragms just considered. All values refer to the impedance on only one side of the diaphragm. These curves;

show not' only that in the 3 speaker arrangements the.v

radiation resistance at the lower frequencies, is about four times as high as that of a diaphragm of the; same total area in an infinite bafiie but also that at frequencies:

of several hundred c.p.s. where in general the diaphragm motion is' mass controlled the mass reactance isrelatively low. The data have not been extended above a thousand c.p.s. for it is doubtful whether even at this frequency the assumption that the diaphragms move as pistons is valid.

The driving coils of the three loud-speakers may be connected either in series or in parallel and coupled to the output circuit of an amplifier. We shall here assume that they are connected in series as indicated in FIG. 4. The output resistance of the amplifier or voltage source and the resistance of each of the loud-speaker coils are designated 3R and R respectively. It is assumed that over the frequency range of interest the amplifier develops an open-circuit voltage of a constant value, E, when an of fixed potential is applied to its input.

According to Thevenins theorem as applied to mechanical vibrating systems the velocity is equal to the driving force that would act on the system, if its motion were completely suppressed, divided by the total mechanical impedance, i.e., the blocked plus the motional impedance. In the case where the driving force is derived from an electrical current flowing through driving coils, as it is here, the blocked impedance is the mechanical impedance of the system when the coil circuit is opened. The motional impedance is equal to the force per unit velocity that would obtain if the impedance of the mechanical parts and the driving voltage, E, where both equal to zero but the driving circuit were closed in the normal way. It has been shown to be equal to the square of the force factor divided by the electrical impedance of the driving circuit, by R. L. Wegel, J. Am. Inst. Elec. Engrs. 40,791 (1921). This impedance with the loud-speakers and the amplifier connected serially as shown in FIG. 4 is equal to 3R +3R The force factor for the three speakers is three times that of a single speaker. The motional mechanical resistance of the three speakers in series is therefore equal to and the total mechanical impedance is T+37 +RT E)+j($+3mwin which r is the resistance due to frictional losses in each diaphragm. For the loud-speaker units here considered it is small enough to be neglected. The acoustical power delivered by the system when in operation is equal to the radiation resistance of the three diaphragms multiplied by the square of their velocity, or

Substituting the numeral constants that obtain for these speakers and the values of r and x as given in FIG. 3 we get the values of power as a function of frequency that are plotted on a decibel scale in FIG. 5. From 30 to 700 c.p.s., i.e., over a range of 4 /2 octaves the response does not vary more than 6 db as shown in curve A. This variation is of a magnitude and form that can be compensated by the insertion into the amplifier of a very simple network.

We have already noted the difficulty of generating low frequency sound of the desired level in a large living room with a cone loudspeaker. From available data it was estimated that the power output capacity at 50 c.p.s. should be about 0.15 watt. The three unit speaker assembly as described has a radiation resistance of 1170 c.g.s. units at this frequency. The peak velocity, aw, of

6 the diaphragms when delivering 0.15 watt would be 36 cm. per sec. which is 0.1% of the speed of sound. The frequency modulation that a high frequency tone would suffer through the Doppler effect by this amount of motion at 50 c.p.s. would be practically unobservable.

If we write, Eq. 4 in the form The first factor gives the power that the amplifier would deliver if the vibrating system were blocked. It is the maximum power that the amplifier can deliver to the loud-speakers for a given value of E. The second factor gives the fraction of this power that is projected as sound. It may thus be taken as the acoustic efficiency of the system. For the particular system disclosed here it has a maximum value at about c.p.s. Substituting numerical values appropriate to this frequency we obtain a value of 10% for the efiiciency, a respectably high value for a loud-speaker operating without a horn.

In the preceding discussion we have been assuming that the air in the rear of the diaphragms did not contribute significantly to the impedance of the moving system, in other words, that this air is not restricted to the space bounded by the diaphragms, their respective bafiles and the room corner but is freely coupled to a much larger air space as by the opening 27 in FIG. 1. Such coupling can be effected in most houses without serious difficulties, particularly in those of modern design where an attic space is usually found above the ceiling of the living room. When this cannot be done the confined air-space will give additional stiffness to the vibrating system, which in the particular case here considered is about twenty times as large as that contributed by the diaphragm supporting structure. Under these conditions the response vs, frequency characteristic of the loudspeaking system as computed by Eq. 4 is given by curve B of FIG. 5. Obviously a more complicated network is required for equalizing this response than for that shown by curve A of FIG. 5. The use of such a network effective to quite low frequencies is not impracticable but because of the steepness of the response characteristic below 200 c.p.s., the component elements would have to be held to close tolerances and because of the relatively poor efficiency of the system at low frequencies the associated amplifier would have to be capable of delivering a relatively large amount of power.

The design and construction requirements of the network and the demands on the power amplifier would be eased in this arrangement if the ratio 1 avie as it appears in Eq. 4, were increased. If for example it were increased by a factor of four, Eq. 4 would yield the response curve, C, in FIG. 7. This curve can be equalized from 35 to 1000 c.p.s. to within less than one db by an active electrical network consisting of three stages such as shown in FIG. 6 and two stages of the circuit shown in FIG. 7, when connected in tandem and the circuit elements are defined as follows. In FIGS. 6 and 7 R is the plate resistance of the amplifiers 35, 36, E is the input voltage, and V is the output voltage of each stage. Resistors R provide negative feedback.

Ca C

If these networks are used for equalization purposes only, each stage would ordinarily be adjusted so that at its maximum gain the output voltage, V, would be equal to the input voltage, E. Such adjustment would be made by control of the feed-back through the cathode resistors, R The large amount of feed-back required for this setting will reduce distortion in the network and increase its stability. Although the networks include several stages, the circuit elements are of the inexpensive sort; Because of the multiplicity of stages they need not individually beheld very exactly to specified values.

The question arises whether increasingthe ratio by a factor of four is practicable in the type of units assumed in our discussion. If theoutput circuit of the power amplifier is designed so that R is small in comparison with R then the above ratio is' quadrupled when the flux density is incerased' from 8000' to 11,500gausses, which is still a reasonable value, and the radial thickness of the coil is increased from 15 mils to 30 mils. latter change would require an increase in the air-gapof the magnetic circuit from 40 mils to 55 mils if the same clearances are retained. Both changes would require an increase in the permanent magnet from 1% lbs. to something less than 2 /2 lbs., if the same types of materials where used in the magnetic circuit.

Earlier in the specification it was stated that with only three loud-speakers the sound radiated into-the room would be less diffuse at the higher frequencies than that which would be developed by a radially pulsating; spherical diaphragm. We are now in a position to examine a little more quantitatively this loss in diffusivity for the particular loud-speaker units here postulated.

Each loud-speaker diaphragm in efiect operates in the throat of a conical horn having a solid angle equal. to

radians. The sound generated. by a diaphragm when moving as a piston will fill this angle up to a frequency defined by the following relationship the. diaphragm. moves as a. unit R. is equal to 8.9 cm; Substitution of thisv value into the above formula gives afrequency f. equal to 5500 c.p.s. The diaphragm does, however, not operate as a unit at this frequency. We know from other considerations that its effective radius hereismore nearly equal to 4 cm. In this case: the horn will be filled for frequencies: up to 12,500 c.p-.s. The sound generated by' the three speaker system, therefore, has-aclose approximation over the whole audio-frequency range. a spherical wave front with'the centre of curvature at the vertex of: the room corner.

The above discussion proceeded for the most part as if. the-speakers were mounted in. a corner of the ceiling. The conclusions would, however, be equally validv if they were installed in a corner of the floor.

I have described what I believe to be the best embodiments of my invention. I do not wish, however, to be confined to. the embodiments shown, but what I desire to cover by Letters Patent is set forth in the appended claims.

I claim:

1. A loud-speaker system comprising a unitary baflle comprising three equal planar parts eachhaving the form of a. face of a 24 equal-faced convex polyhedron, the three parts being contiguous in just thesame way that three corresponding faces are. contiguous:- in said polyhedron, each of the three parts of the battle-having a centrally located opening for the reception of a directradiating loud-speaker, the whole. baffle being mountable in a trihedral corner of a room and adapted to contact the walls thereof.

2. A system according to claim 1, comprising a plurality of loud-speaker diaphragms each attached to one of said parts of the bafile containing one of'said openings.

3. A loud-speaker system comprising a unitary baflle having three openings each being in and occupying a major portion of each of three contiguous faces of a 24 equal-faced convex polyhedron, each of said openings being centrally located with respect to one of said faces for the reception of a direct radiating loud-speaker, the whole bafile being mountable in a trihedral corner of a room and adapted to contact the walls thereof.

References Cited in the file of this patent UNITED STATES PATENTS 1,984,550 Sandeman Dec. 18, 1934 2,602,860 Doubt July 8, 1952 2,824,617 Roulet Feb. 25, 1958 2 ,915,588 Bose Dec. 1, 1959- FOREIGN PATENTS 447,749 Great Britain May 18, 1936 842,376 France Mar. 6, 1939 915,460 Germany July 22, 1954 OTHER REFERENCES Germany, K 284, June 7, 1956.

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