CA1221312A - Multidriver loudspeaker system with crossover filters having transfer functions with brick-wall amplitude vs. frequency response characteristics - Google Patents

Abstract

ABSTRACT OF DISCLOSURE

A loudspeaker system includes at least two loudspeaker drivers, together with an electrical crossover network having filter circuits with at least two separate mutually exclusive frequency passbands. The filter circuits comprising the crossover network each possess brick-wall ampliltude responses, i.e., passbands with very high band-edge amplitude vs. frequency response slopes, on the order of 100 dB/octave in the better embodiments. The high passband band-edge slopes, which are realized by the inclusion of transmission zeros in the seprate crossover filter transfer functions, taken together with further appropriate crossover filter transfer function synthesis causes the separate loudspeaker drivers comprising the loudspeaker system to function independently of one another in their contribution to total system acoustic output. It is shown that the loudspeaker system permits an accurate approximation to the ideal delay function in acoustic space, while minimizing acoustic wave interference among drivers operating in adjacent frequency bands, and also reducing overall system nonlinear distortion.

Description

background ox the Invention _ . . .
Field of the Invention The present invention relates to an improvement in means for converting electrical signals into sound as to control with high fidelity the acoustic response of a loudspeaker system. More specifically, the invention relates to a loudspeaker system cross over using passive or active circuit topology.
The background of the invention and the invention it-self will be described with reference to the accompanying drawings, in which:
Figure 1 illustrates a typical prior art loudspeaker system;
Figure 2 illustrates plots of the complementary low-pass and high-pass amplitude responses of the loudspeaker system of Figure l;
Figure 3 is a circuit diagram illustrating a passive embodiment of the invention;
Figure pa is a high-pass network illustrating the tweeter topology employed in the circuit of Figure 3;
Figure 4b is a network of Figure pa with a zero of transmission added;
Figure 4c is a pole-zero pattern or plot showing the pi yielded by the network of Figure 4b;
Figure pa is a half-section band-pass network employed in the mid-range topology of the circuit of Figure 3;

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Figure 5b is the half-section network of Figure pa with a first zero of transmission placed below the low frequency crossover point and a second zero of transmission placed above the high-frequency point;
Figure 5c is a pole-zero pattern showing the p-z yielded by the network of Figure 5b;
Figure pa is a basic T-section network illustrating the woofer or low-pass topology employed in the circuit of Figure 3;
Figure 6b is the network of Figure pa with a zero of transmission added;
Figure 6c is a pole-zero pattern showing the p-z yielded by the network of Figure by Figure 7 illustrates the frequency response of the in-dividual drivers of the circuit of Figure 3;
Figure 3 illustrates the composite frequency response of the whole system of Figure 3, that is, the total acoustic sum of all drivers on axis;
Figure 9 is a plot of the phase response of the system of Figure 3;
Figure 10 is a circuit diagram illustrating a passive embodiment of the invention with improved performance over that of Figure 3;
Figure 11 is a pole-zero pattern illustrating the p-z required for a perfect realization of the invention;
Figures aye, 12b and ].2c are pole-zero patterns thus-treating the dominant p-z for the low-pass, band-pass, and high I

pass filter circuits, respectively, of a general embodiment of the invention;
Figure 12d is a pole-zero pattern showing a summation of the dominant p-z of the pulsar plots of Figures aye, 12b and 12c;
Figures aye and 13c are circuit diagrams and Figures 13b and 13d are pole-zero plots used in a mathematical derivation of the p-z of tweeter and midrange networks similar to the embody mint of Figure 3;
Figures lea, 14b and 14c are pole-zero patterns justify-in the network topologies according to the invention;
Figure aye is a circuit diagram illustrating an active circuit embodiment of the invention;
Figure 15b is a circuit diagram illustrating an active circuit embodiment of the invention in detail;
Figure aye illustrates the amplitude response of the individual drivers of the embodiment shown schematically in Figure 10;
Figure 16~b) illustrates the overall on-axis frequency response of the entire system of Figure 10;
Figure 16(c) illustrates the delay response of Figure 10;
Figure aye illustrates the amplitude response of the individual drivers of the active embodiment shown schematically in Figure lob;
Figure 17(b) illustrates the overall on-axis response of the entire system of Figure 15b;

-pa-Figure 18 illustrates a means whereby the acoustic wave interference between drivers operating on adjacent frequency bands may be quantized;
Figure lo illustrates the amplitude vs. frequency response for the Figure 10 embodiment of the invention for response Do . or So measurements taken using different positions the microphone;
Figure lo illustrates the amplitude vs. frequency response for a prior art loudspeaker system for response measure-mints taken using different positions of the test microphone; and Figures aye 20(b~ and 20(c) illustrate, respectively, the amplitude vs. frequency response for (a) a loudspeaker driver that is not connected to a crossover filter network, (b) the same loudspeaker connected to a prior art crossover filter network and (c) the same loudspeaker connected to a crossover filter net-work of the present invention.
Description of the Prior Art and Definition of Terms In the present state of the art individual loudspeakers or drivers are not capable of accurately reproducing all audio frequencies that are detectable by the human ear. Flight fidelity loudspeaker systems have been realized in the prior art, however, by dividing the audio frequency spectrum into two or more frequency bands, and applying each of these portions of the audio spectrum to a separate driver or group of drivers.

I 3L3~
For this purpose special electrical jilters, called crossover networks, have been provided that allow the different arrivers or groups of drives, each adapted for best response to a particular range or band of frequencies, to be 5 combined in a single system capably of wide frequency coverage.
The crossover circuit directs the electrical signals of widely varying frequency to the appropriate driver or group of drivers in a multi driver loudspeaker system.
Crossover network topologies in general, belong to three classifications according to the frequencies passed and rejected, as follows:
(1) Low-pass for woofers/
I Band-pass for midranges, and I ~igb-pass for tweeters, where woofers are low frequency drivers and respond to the low frequencies, midrange drivers respond to the midrange frequencies, and tweeters are high frequency drivers and respond to the high frequencies. Where more than one filter is used, the frequency common to adjacent ranges or pass bands is called the crossover frequency.
For "perfect fidelity it can be demonstrated mathematically that a loudspeaker system crossover using passive or active circuit topology must realize perfectly the ideal all pass transfer function of Equation (1):
(1) f(s) - Cousteau Where s is the complex frequency variable s - + jaw K and T are real f positive constants; and e = 20718 s' 3L~2 or lo G(s) = Rest with s, R, T, and e defined as above, 5 where whichever form the transfer function implied by Equation (l) is relevant to a particular case will become clear when the separate meanings of fuss) and Go are defined hereinafter It is not possible, however, using current technology, to perfectly realize the ideal all pass transfer function in lo three-dimensional acoustic space with any known loudspeaker system Accordingly, all real loudspeaker system configurations or designs are based upon an approximation to one or both forms of the ideal transfer function of Equation (l) in three-dimensional space.
The simplest and commonest prior art approximation to the ideal loudspeaker system is based upon a "two-way" design using an assumed ideal woofer an tweeter combined with a simple SdB/octave minimu~-pha~e r low-pass-I ego high-pass, cross-over network, as ill~tcr~ in Fig. l.
Mathematically, this approach takes the ideal transfer function of Equation if) and attempts to reduce it to a function that is independent of frequency, ideally a constant.
This is accomplished by expanding the ideal transfer function of Equation (l) in a power series, as follows: when R = l, then to) fops) = east =
IT l+sT+(sT)~/21+(sT)~/31~...
Taking only the first term of this series of Equation I gives:

I Al =
lust Those skilled in the art will recognize Equation (3j as the simple one-pole low-pass transfer function G 122~31~

f the term s in Equation S 3) is replace by So the complementary high-pass transfer function with cross-over frequency 1 is obtainer:
I- 5 T I rlJ
(4) f2(s~ - 1 1 1 _ sty lust s I l+ 1 lust sty Plots of the complementary amplitude response flus and us of Equations (3) and (4) are given in Fig. 2.
. Equation I below shows that the sum of the simple low pass function of Equation (3) and its complementary high-pass function of Equation I is unity, that is, a lo constant that is independent of frequency:

(5) f3(s3 = flus) = 1 sty = lust = 1 lust lust lust If an ideal woofer were connected to a cross-over network having the transfer response of Equation I and an ideal tweeter were connected to a crossover network having the transfer response of Equation (4), and the woofer and tweeter were combined in a single system, the result would be a "perfect loudspeaker system. Its amplitude response would be perfectly flat for all frequencies and there would be no phase shift at any frequency.
Serious problems arise, however when it is attempted to construct a practical loudspeaker system following the foregoing design procedure These problems arise from three distinct causes:
flywheel) The woofer and tweeter do not have ideal amplitude and/or phase characteristics.
~1.2) The loudspeaker drivers function in three-dimensional acoustic space in which the simple energy zillion of Equation to is not valid at all points (1.3) The gradual crossover slope ~6dB/octave) allows too much bass energy to enter the tweeter, and too much treble energy to enter the woofer causing distortion.
Even with the reservations just mentioned the simple two-way loudspeaker system of Figure 2 approaches the ideal to a degree sufficient to achieve moderately satisfactory performance It should be noted that the transfer function us as discussed here so far is that of the electrical cross-over circuits alone, i.e., f(sj is defined as:
lay us = eon = Pus e Us wish in words, represents the ratio of electrical energy at the output of a general crossover band pass filter circuit, or combination of filter circuits including a complete crossover system, to the electrical energy at the input, expressed as a function of complex frequency.
The assumption has been implicitly made so far in this discussion that the transfer function of the loudspeaker drivers defined immediately hereinafter) is either unity, or an "ideal delay and thus may be ignored. This is, at best, only approximately true. The transfer function of a loudspeaker driver is an electroacoustical quantity and may be defined as the ratio of the sound pressure at a point in the listening environment to the electrical energy input to the driver terminals; this expression being a ratio of terms in complex frequency:
lo I = P - clue Thus one can consider the overall transfer function -, AL
,~_ of a complete speaker system taken as a whole - crossover plus loudspeaker drivers - which would be the product of the two above mentioned transfer functions and would be defined as:
(to) Gas) = oh Pi = Pi eye Q2(s~
The transfer function G(s) represents the ratio of acoustic sound pressure at a particular point in the listening environment to the electrical energy applied to the input terminals of the speaker system, both as a function of complex frequency. The terms Pus and Q2(s~ will contain the poles and zeros pi of the loudspeaker drivers as well as the p-of the crossover elements.
Well-designed loudspeaker drivers possess a band of frequencies in which the amplitude response is flat to desired accuracy, and phase response is linear to desired accuracy -such loudspeaker drivers may be referred to as n ideal" and will possess an ~lectroacoustical transfer function so which can be considered to be unity or a constant. Loudspeaker drivers will be considered to possess ideal delay - i.e., to approximate Equation I to a high degree of accuracy within their respective frequency bands of best performance - unless specifically stated otherwise. Hereinafter transfer functions designated as us will always relate to the crossover only, while transfer functions designated G(s) will always relate to the crossover filter circuits plus the loudspeaker drivers, with definitions as set forth hereinbefoxe.
Those skilled in the art will understand that the units of the right-hand terms contained in Equation (lo) are voltages and currents which relate to the electrical circuit ox the crossover network under consideration. The units of the right-hand terms of Equations lo and (to) are voltages, currents, forces, velocities, pressures, and volume Go ~22~312 -or-velocities, which relate to the electrical circuit crossover), the mechanical circuit (the loudspeaker driver, and the acoustical circuit (the air surrounding the loudspeaker driver). For a numerical solution to specific forms of Equations (lb) and Sly), or any other equation contained herein with mixed electrical, mechanical, and/or acoustical circuits t such as Equation to) expressed hereinafter, the method of dynamic analogies" must be employed. This method is amply treated in the text "Acoustics", Chapters 3 and 5, by Leo Beranek, McGraw ill - 1947. hereinafter, this method of dynamic analogies will be implicitly assumed to have been applied whenever an nacousticR
sum is discussed with respect to an equation containing "mixed, i.e. electroacoustical units.
Returning to the earlier discussion, it is observed that closer approximations to the ideal transfer function of Equation (1) have traditionally been realized by taking more terms of the infinite series of Equation (2), again attempting to reduce the-result to a function independent of frequency, and then using such function as a basis for design considerations. Some of these methods have been treated in the prior art an in particular, in several issues of the Audio Engineering Society Journal, specifically in the following articles: "Constant Voltage Crossover Network Design, Richard Small, January, 1971; "Active and Passive Filters in Loudspeaker Crossover Networks", Ashley and Kaminsky, June 1971; and PA Novel Approach to Linear Phase Loudspeakers Using Passive Crossover Networks," I. Backgaard, May 1977.
When such prior art loudspeaker topologies are considered with reference to the poles and zeros of the resultant system input-output transfer function, it is found that all poles and zeros that is all p-z, tend to disappear I
In genera] most prior art loudspeaker designs or configurations have utilized acoustic summations which caused the disappearance of as many p-z as possible in the summation while tending toward some good approximation of the transfer function of Equation (1). The present invention takes an opposite approach, that is, retaining all, or as many as possible, of the p z of the individual elements in the final summation. also crucial to the method of this invention is the inclusion of transmission Eros in the design of the crossover filter circuits These transmission zeros, taken together with retention in the total loudspeaker system of the dominant poles inherent in the separate crossover filter circuits allows the approximation of the transfer function of Equation I to a high degree of accuracy, while also overcoming the problems, mentioned above (I 1.2 and 1.3), of the prior art loudspeaker designs.
Summary of the Invention A descriptive name will be given to the present invention; operative embodiments of the same will sometimes be referred to hereinafter as "infinite-slope" speaker systems.
A general object of the invention is to provide an improvement in a loudspeaker system crossover using passive or active circuit topology which accurately approximates the ideal transfer function of Equation (1).
Another object of the invention is to provide an improved method for converting varying electrical signals into sound involving the utilization of crossover circuits that maintain all or as many as possible of the dominant poles of the individual crossover filter circuit transfer functions defined by equation (lo) herein before.
A further object of the invention is to provide an improved method of converting varying electrical signals into sound in which the poles of the transfer function of any filter circuit of the loudspeaker system may not be repeated in the transfer function of any other filter circuit of the loudspeaker system, thereby satisfying a necessary criterion assuring that the individual crossover filter circuits will possess mutually exclusive frequency passbandsO

I
A further object of the invention is to provide such an improved method for converting varying electrical signals into sound wherein the individual crossover filter-loudspeaker driver combinations comprising the invention are caused to function independently of each other in forming the total acoustic sum, or total acoustic output, by the use of two or more distinct "brick-wall" amplitude functions having separate mutually exclusive frequency pass bands which pass bands in addition possess very high band-edge amplitude vs. frequency to response slopes. Brick-wall amplitude functions are defined in the text "Circuit Theory and Design" Chapter 5, by John L.
Stewart, John Wiley and Sons, Inc., New York, 1956.
A more specific object of the invention is to provide an improved crossover network for a loudspeaker system wherein mutually-coupled coils are used in order to enhance the steepness of the pass band band-edge amplitude vs.
frequency response slopes.
Still another object of the invention is to provide an improved loudspeaker crossover network embodying all-pass delay equalization ox one or more filter circuits in order to achieve a more accurate approximation to the ideal transfer function of Equation ~13.
further object of the invention is to provide an improved loudspeaker system in which the crossover circuit parameters an driver placement are so adjusted that the band-width of audible frequency bands of mutual acoustic interference are reduced to less than 1/3 octave Another object of the invention is to provide an improved loudspeaker system in which the electrical parameters 30 of the crossover network include transmission zeros placed at frequencies just outside the pass bands of the individual crossover filter circuits Lopez, band-pass, and whops in order to achieve very high pass band band-edge amplitude V5.
frequency response slopes.

I

In accomplishing the foregoing and other objectives of the present invention active-or passive topologies may be employed. Since passive topologies are most commonly used in loudspeaker system crossovers, the discussion that follows is concerned mostly with passive circuitry Active circuit embodiments of the invention however, will also be discussed.
The present invention achieves a new approximation to the ideal transfer function in a novel manner. Particular attention is paid to the problems mentioned above (1~1, 1.2, an 1.3~. The invention will be shown to:
tl.4) Greatly minimize the undesirable effects of non-ideal driver amplitude and phase response on total system performance.
(1.5) Minimize the acoustic wave interference between arrivers at the crossover frequencies.
(1.6) Reduce total system harmonic and inter modulation distortion.
The method of the invention takes into consideration 20 two ideas:
(1.7) The total system performance must relate to an "acoustic sum of arriver energies in three-dimensional space.
~1.8) The ideal transfer function of Equation (1) is approached using embodiments of the present invention which operate by acoustically summing two or more approximations to ideal brick wall amplitude functions, all having separate mutually-exclusive frequency pass bands. If these amplitude functions are carefully chosen, the acoufitic sum will not only approach flat amplitude V5. frequency I

characteristic but will also approach a linear-phase us frequency characteristic Jo with, at most an ambiguity of phase of + on Jo where n = 0, 1, 2, 3, ...) at the Rhodes crossover frequencies. Observe that if no the drivers are absolutely as well as relatively in phase, and no phase ambiguity exists.
In accordance with the invention, a ~uasi-infinite crossover bondage pow is achieved my employing crossover circuit topologies which have zeros of transmission placed at frequencies outside their respective band edges.
Mutually-coupled coils may be used in order to improve out-of-band attenuation, in passive embodiments. Both minimum phase and non-m;nimum-phase topologies are Lydia In-band amplitude and phase characteristics of the loudspeaker drivers may be considered as part of the overall system transfer function. Crossover filter pass band band-edge amplitude vs. frequency response slopes in embodiments of the present invention approach 100 dB/octave with minimum out-of~band attenuation being greater than 40 dub. This is in sharp contrast to the monotonic 6, 12, or 18 dB/octave crossover slopes commonly used in the prior art loudspeaker systems I There is no fixed way to embody the invention. Any combination of active or passive crossover topologies satisfying the requirements of the idea statement of 1~8 above and fitting into the described three classifications of general crossover circuit topologies, while approximating the transfer function of Equation I will work. Crossover topologies in an operative invention embodiment will possess filter circuits having I separate and mutually exclusive frequency pass bands and (2) at least one transmission zero in AL

each filter circuit. Those skilled in the art will recognize -the aforementioned to be characteristic to one class of brick-wall amplitude functions.
Thus, in accordance with a broad aspect of -the invention, there is provided a multi driver loudspeaker apparatus comprising at least two loudspeaker drivers, a crossover filter network having at least two crossover filter circuit means, said loudspeaker drivers being each connected to a respective crossover filter circuit means of the crossover filter network, at least I one of the crossover filter circuit means of the crossover filter network including an additional circuit structure means for generating at least one zero or near zero transmission of response in the transfer function of said crossover filter circuit means for frequencies just outside the pass band of said crossover filter circuit means.
Description of the Preferred Embodiments For a better understanding of the preferred embodiments of the invention, reference is first made to the loudspeaker circuit diagram of Figure 3. In Figure 3 electrical signals representing sound to be reproduced appear at the output terminals of an exterior component (not shown) such as a suitable amplifier.
One output terminal, Al, of -the amplifier is connected to ground potential and the other output terminal, A, is connected to a conductor 12 of a - I -loudspeaker crossover circuit 10. Conductor 12 is common to the high-pass, band-pass, arid low-pass crossover filter or networks 14, 16, and 18 of circuit 10.
As shown in Fig. 3, a tweeter 20 is connected to the output of the high pass filter circuit 14 and responds to electrical signals in the range of 7 K~z to 20 KHz. The filter circuit I and tweeter 20 form a first crossover filter-loudspeaker driver combination. A delay network 22 is provided between the tweeter 20 and the output of the high-pass filter circuit 14. The purpose of the delay network 22 is explained hereinafter.
The band-pass filter circuit 16 includes a lower midrange section aye and an upper midrange section 16b. An upper midrange driver 24 is connected to the output of top upper midrange section 16b~ forming therewith a second crossover filter-loudspeaker driver combination Similarly, a lower midrange driver 26 is connected to the output of the lower midrange section aye, forming therewith a third filter loudspeaker combination. Lower midrange driver 26 responds to electrical signals in the range of 175 Ho to 800 Ho. Upper midrange driver 24 responds to signals in the range of 800 I
to 7 KHz.
A woofer 28 is connected to the output of the low-pass filter circuit 18 and responds to electrical signals in the range of frequencies from 20 to 175 Ho. The filter circuit 18 and woofer 28 form a fourth crossover filter-loudspeaker driver combination.
In accordance with the invention, the four separate filter circuit-loudpseaker driver combinations operate independently of each other in forming the total acoustic output of the system.
The tweeter topology selected for the Fig. 3 embodiment is based upon the high-pass network illustrated in ~2~3~
-16- .
Fig. pa and, as shown, includes a series connection from a first input terminal, indicated as conductor 12, of capacitor Of and C2 and a terminating resistor R to a conductor 32 that leads to a second input terminal G with an inductor Lo connected between the junction of capacitors Of and C2 and the conductor 32~ It is noted that most passive crossover networks are synthesized on the assumption that the network is terminated by a pure and constant resistance A zero of transmission is added to the high-pass network of Fig. aye as is illustrated in Fig. 4b, by connecting an inductor Lo and a capacitor C3 in series between the junction of capacitor C2 and resistor R to the conductor 32. Mutual coupling between the inductors Lo and Lo is not used here as it would cause the out-of-band input impedance to become excessively low. The network of Fig 4b yields the poles and zeros, that is, pi shown in the pole-zero pattern of Fig. 4c~ .
Midrange topology selected for the midrange drivers 24 and I is based upon the simple half-section band-pass network illustrated in Fig. pa. As shown, Fig. Spa includes an inductor Lo and a capacitor C4 connected in series with a resistor Al between a first input terminal 12 and a conductor 34 leading to a second input terminal G. There is also provided a parallel connection of an inductor Lo and capacitor Us between the junction of capacitor C4 and resistor Al and the conductor 34.
Zeros of transmission are added to the network of Fig. pa as is shown in Fig 5b. A single zero of transmission is provided for the lower midrange circuit aye by the addition in parallel to the inductor Lo and capacitor as of an inductor Lo and a capacitor C6 which are connected in series. Mutual inductance is provided, as shown in Fig. 3, between inductor Lo and I This zero of transmission is placed above the lower midrange crossover frequency.

~2~3~

For the upper midrange circuit 16b, there is further provided in parallel to the inductor Lo and capacitor Us an inductor Lo and a capacitor C7 which are connected in series.
Mutual coupling is provided between inductors Lo and Lo, as shown in Fig r 3 7 in order to improve the attenuation of the higher frequencies above the upper midrange.
More than one zero of transmission may be used for the midrange or band-pass frequencies. In the Fig. 3 upper midrange crossover, one is placed below the low frequency point point and the other above the high frequency point.
These zeros of transmission are generally placed one octave below the lower midrange crossover frequency, and one-half octave above the higher midrange crossover frequency. General p-z for the network of Fig. 5b are given in the pole-zero pattern of Fig. So.
Tune low-pass topology selected for the Fig. 3 embodiment is the basic T-section network as shown in Fig. pa and includes series-connected inductors Lo and Lo and a terminating resistor R2 between first input terminal 12 and a conductor 36 leading to a second input terminal G. The network also includes a capacitor Cog, one terminal of which is connected to the junction of inductors Lo and Lo an the other terminal to the conductor 36.
A zero of transmission is added to the network of I jig. pa as is illustrated in Fig. 6b by the connection of an inductor Lug and a capacitor Cog in series between the junction -of inductor Lo and resistor R2 and the conductor 36. The zero ox transmission thus added to the network as shown in Fig. 6b yields the p-z shown in the pole-zero pattern of Fig. 6c. The zero of transmission will usually use mutual coupling of inductances Lo and Lug, as is illustrated in Fig. 3, at 18.
This zero of transmission is placed one to two octaves above the woofer crossover frequency.

~;~2~L2 By way of illustration and not limitation it is noted that in the embodiment of the invention of Fig 3 the electrical parameters of the individual components of the high pass, upper midrange, lower midrange and low pass sections 14, 16b, aye, and 18, respectively, are as follows:
High pass section 14 Low ass section 18 P
Lo - 125 micro henries Lo - 6 millionaires Lo 320 micro henries Lo - 5.1 millionaires C1 - 2 micro farads Lug - 3.3 millionaires - 10 C2 - 2 micro farads C8 - 220 micro farads .
R - 27 ohms Cog - 47 micro farads Upper midrange section 16b Lower midrange section 16 Lo - 275 micro henries Lo - 1~75 millionaires Lo - 1.07 millionaires . Lo - 3~82 millionaires Lo - 1~92 millionaires Lo - 1.07 millionaires Lo - 190 micro henries C4 - 100 micro farads C4 - 12 micro farads Us - 22 micro farads c5 - 6.8 micro farads C6 - 22 micro farads C6 - 56 micro farads Al - 15 ohms 20 C7 - 2 micro farads Al - 15 ohms R2 - 3 ohms The frequency response of the individual drivers of the Fig. 3 system is illustrated in the chart of Fig. JO This chart represents close microphone tests on individual drivers, with all other drivers open or shorted. As those skilled in the art understand the term "close microphone refers to a technique for measuring the sound output of a loudspeaker diaphragm by placing the microphone very close to the diaphragm, typically 1/4" to 1/2~.
It is noted that the small loop under the tweeter response curve in Fig. 7 is a spurious response from the upper midrange arriver 24. This spurious response is a fault of the driver 24 and can be eliminated by placing a I Jo inductor in series with capacitor Us of Fog 3. The spurious response, however is of little or no consequence, being about 15 dub down and inaudible.
The chart of Fig 7 and that Allah of Fig. 8, now to be describer were run 4 inches per minute.
The composite frequency response of the whole system, that is, including the total acoustic sum of all drivers on axis, is illustrated in Fig. 8. It is evident that the amplitude response given in Fig 8 is a good approximation to the amplitude criterion of the transfer function of Equation I Consideration must still be given, however as to how well the embodiment of Fig. 3 approaches the ideal phase characteristic implies in Equation (1).
Fig. 9 is a plot of the phase response of the embodiment of Fig. 3. Ideally in order to satisfy the ideal phase requirements implicit in Equation (1), the phase response shall be a straight line throughout the entire frequency range. A compromise may be made however, by allowing the phase response to exhibit changes in slope and/or discontinuities at the crossover frequencies. In Fig. 9, the phase response exhibits a constant slope above 1000 Ho while breaking into a steeper slope below 1000 Ho and then becoming I irregular at low bass frequencies.
The phase curve of Fig 9 implies the existence of a relative time difference of about 800 microseconds between modern frequencies (175-1000 Ho and high frequencies Lowe - on zoo I ) . Acoustical researchers are in general disagreement as to whether small acoustical time delay errors of the order of 1 my.) are audible Whether such errors are audible or not is moot, as the present invention permits such errors to be essentially eliminated.
.

-20~
The invention embodiment of Fig 3 uses an all pass ; delay network for correction ox phase response. Thus, the all pass delay network 22 in series with the tweeter matches the delay of the tweeter 20 to what of the upper midrange 24.
A detailed discussion of the theory and design of delay networks will not be undertaken hero For those skillet in the art, the relevant theory is disclosed in the text "Network Analysis and Synthesis," by OF Duo, John Wiley, 1962, pages 315 to 321~ -It is noted that at low frequencies (175 I and lower) the ear becomes less sensitive to phase and directionality Thus irregularities in phase inherent in low bass loudspeaker response are relatively insignificant The present invention finds particular application above the low bass frequency region that is, frequencies above 175 Ho.
An embodiment of the invention with improved performance over that of Fig 3 is shown schematically in Fig.
10. Amplitude response of individual arrivers within the system is shown in Fig. aye Overall amplitude response of the entire system is shown in Fig. 16(b). It is clear that the crossover pass band slopes are steeper than whose of Fig. 7 while the frequency overlap between adjacent pass bands is reduced in Fig aye over that of Fig. 7. The embodiment shown schematically in Fig. 10 functions better than that of Fig. 3 in fulfilling the intent of this invention according to statements 1~4 through 1.6 inclusive as set forth hereinbefoxe.
An active embodiment of the invention with performance superior to that of the passive embodiment of Fig.
30 10 is shown schematically id Figs. aye and lob. Amplitude response of individual drivers within the system is shown in Fig. aye Overall amplitude response of the entire system is shown in Fig 17(b~ It is clear thaw the crossover pass band slopes are steeper than those of Fig. 10, while the frequency overlap between adjacent pass bands is reduced in Fig.
aye over that of Fig. 10, Although the active embodiment of Figs. aye and 15b of the invention do outperform the two above-mentioned passive embodiments of Figs. 3 and 10, it should be noted that the active embodiment is one of greater complexity. The circuitry used in active embodiments of the invention will be briefly described.
In the circuit diagram on Fig. aye there is illustrated an active circuit embodiment 35 of the present invention including a tweeter 37, a midrange driver 38, and a woofer 40. Electrical signals representing sound to be reproduced appear at the output terminals A and A ox a component (not shown) such as an amplifier.
The terminal A is connected to the conductor 42 of a loudspeaker crossover circuit 44. Conductor 42 is common to the active high-pass, band-pass and low-pass crossover filters indicated at 50, 48 and 46. Filters 50, 48 and 46 may comprise suitable electronic devices such as operational amplifiers incorporating the crossover p-z, as described herein before, of the present invention for the tweeter 37, midrange driver 38, and woofer 40. As shown a separate power amplifier 52, 54 and 56 is provided for amplifying the output of a respectively associated filter 46, 48 and 50. The outputs of amplifiers 52, 54 and 56 are applied, respectively, to the tweeter 37, midrange driver 38 and woofer 40.
Figure 15b illustrates the circuitry of Fig aye in detail. The design and method of operation of active filter air-cults to realize any p-z are sufficiently well explained, for those -aye-skilled in the art, in the reference "Handbook ox Operational Ampler Circuit Design," by David F. Stout and edited by Milton Kaufman, McGraw-Hill, 1976.

The phase response of the invention embodiments of Figs. 10 and aye and 15b can be shown by phase and time measurements familiar to those skilled in the art to fulfill the intent of the invention as contained in the idea statement 1.8. Acoustical measurements taken on the aforementioned embodiments show all drivers operating in the same relative phase at the crossover frequencies with, at most phase rotations of on radians. Translated to delay error, this phase shift never exceeds a maximum delay error of one millisecond, for frequencies above 175 I Delay response for one preferred invention embodiment, that shown in Fig. 10, is given in Fig. 16(c3~
It should also be noted that as a result of steeper crossover filter pass band band-edge slopes, the improved invention embodiments, especially those of Figs. 10, lea, and 15b will possess small wave interference between arrivers operating on adjacent frequency bands. Acoustical researchers have not determined a precise value of such aforementioned wave interference at which its audible effects become 2Q objectionable. however, it will be evident to twos swilled in the art that the present invention allows the level of wave interference to be reduced arbitrarily to a level such that drivers on adjacent frequency bands can be considered to radiate sound energy independently of each other, that is, the wave interference is rendered to be, at most, just barely audible.
Acoustical researchers are not in agreement as to the definition of audibly objectionable wave interference with respect to the sound radiated from a multi-driver loudspeaker system. This inventor has experimentally determine that if the overlap", defined immediately hereinafter, in amplitude responses at the -lode points of loudspeaker drivers sharing a common crossover frequency is greater than 1/3 octave, the interference becomes audible, and thus, objectionable.

Fig. 18 illustrates the definition of acoustic wave interference. The amplitude responses 60 and 62 of two drivers sharing a common crossover frequency We are shown The overlap region shown at 64 becomes just barely audible at a point 10 decibels below the flat portions of the amplitude responses shown at 10 and 20~ If this width of the same overlap region shown at 64 in Fig 18 is greater than lJ3 octave, centered on the crossover frequency We, the acoustic wave interference is arbitrarily, but necessarily, considered by the inventor to become objectionable.
Acoustic wave interference effects in multi driver loudspeaker systems are related to the steepness of the crossover filter pass band band-edge amplitude vs. frequency response slopes If the aforementioned slopes, shown at 65 and I in Fig. 18, become steeper, the width ox the overlap shown at 64, which is a measure of the energy causing acoustic wave interference, will decrease. Slopes in excess of 40 - dB/octave will result in an overlap shown at 64, of less than 1/3 octave in typical operative invention embodiments, with acoustic wave interference being just barely audible. This would yield acceptable porphyrins for an operative invention embodiment. Slopes greater 70 dB/octave, and approaching 100 dB/octave as in the better embodiments result in inaudible acoustic wave interference, with superior performance, as the width of the overlap region, shown at 64 in Fig 18, becomes much less than 1/3 octave, too narrow for the human ear to perceive.
The separate crossover filter-loudspeaker driver combinations comprising an invention embodiment which share a common crossover frequency, for which typical amplitude vs.
frequency responses in the crossover region are illustrated in Fig. 18, will be defined as functioning "effectively"
independently of each other if the acoustic wave interference becomes just barely audible. This will correspond to crossover filter pass band band-edge amplitude us frequency response slopes of about 40 dB/octave, and up to about 70 dB/octave.
The aforementioned crossover filter-loudspeaker driver combinations will be defined as functioning absolutely" independently of each other, if the acoustic wavy interference becomes inaudible. This will correspond to crossover filter pass band band-edge amplitude vs. frequency 0 response slopes equal to or greater than about 70 ds/~ctave~
In either of the aforementioned situations for "effective or "absolute" independence, the separate crossover filter-loudspeaker driver combinations will comprise an operative invention embodiment and will be considered to function independently of each other, without qualification since the lesser condition of effective independence, defined herein before, describes an acceptable or useful invention embodiment. The aforementioned distinction between effective and absolute independence is made merely in order to distinguish between "acceptable and "superior" invention embodiments, respectively. In summary, an operative or useful embodiment of the present invention wit exist, if at least at one system crossover frequency, and preferably at all system crossover frequencies it more than one such crossover frequency exists, the width of the overlap region shown at 64 in Fig. 18 is, at most, 1/3 octave, which will correspond generally to a crossover filter pass band band-edge amplitude vs. frequency response slope of about 40 dB/oct~ve.
Acoustic wave interference effects in multi driver loudspeaker systems cause the tumbrel balance, or Sweeney quality" of a single, or monophonic speaker system to vary as the listener moves about in the room in which the speaker system is sounding There will exist a different amplitude vs. frequency response for each and every listening position in the room. For a stereo pair of speakers, the aforementioned effect of acoustic wave interference still exists. In addition, acoustic wave interference within the individual speaker systems comprising a stereo pair will cause a blurring or "lack of focus" to the stereo image, because the accurate amplitude and phase information necessary to psycho acoustically reconstruct the stereo image becomes distorted by the same acoustic wave interference Sonic problems in loudspeaker systems caused by acoustic wave interference are common knowledge to those familiar with the art Designers of prior art loudspeakers have attempted to minimize the effects of acoustic wave interference in one of two ways:
(1) Elimination of the crossover network entirely, and devising loudspeaker systems which function by operating a single large loudspeaker driver or plurality of small loudspeaker drivers over the entire audio frequency range;
for example, in a speaker system presently marketed as the "901~ by the Bose Corporation of Framing ham, Massachusetts, VISA or

(2) Use of a conventional crossover system in the prior art as described herein before taken together with physical location of the .
loudspeaker drivers comprising the total loudspeaker system having their acoustic centers as close together as practicable;
for example as in a speaker system presently marketed as the "AURELIUS by the Acoustic Research Corporation of oared, Massachusetts, U.S.A.

I

The present invention presents a novel and superior crossover method which rectifies the aforementioned sonic difficulties caused by acoustic wave interference, specifically those problems relating to tumbrel balance and stereo image. Loudspeaker systems embodying the present invention possess separate crossover filter-loudspeaker driver combinations which function independently of each other in their contribution to the total system acoustic output, thereby exhibiting negligible acoustic wave interference among the same crossover filter-loudspeaker driver combinations comprising the total loudspeaker system, thereby producing within the entire listening environment a very uniform amplitude us. frequency sonic energy response yielding both an accurate tumbrel balance and a clear and well-focused stereo image anywhere within the aforementioned listening environment. Also, as an added benefit from the present invention, mentioned herein before in idea statements (1.4) and (1.6~ and repeated here, sonic difficulties resulting from the transmittal of energy to loudspeaker drivers outside their respective frequency bands of best performance are eliminated.
Figs. lo and lo illustrate the superior performance of the present invention over prior art, with regard to the projection of a uniform amplitude vs. frequency sonic energy into the space in front of the loudspeaker system box, shown at 68. Due to the elimination of acoustic wave interference effects among the separate crossover filter-loudspeaker driver combinations comprising loudspeaker systems embodying the present invention, more specifically the invention embodiment schematically depicted in Fig 10, this same invention embodiment exhibits nearly identical 1/3 octave pink noise amplitude vs. frequency responses, shown at 67 it Fig lea, for three different positions of the test microphone, said positions being shown at 69/ 70 and 71, for a box to microphone position of one meter. The same test results for a prior art loudspeaker system, of about the same size, shaper and cost of the aforementioned invention embodîmentJ namely the model "50" made by the Speakérlab Company of Seattle, Washington, USE is shown at Fig. lob.
Variations in amplitude vs. frequency response of this same prior art system, shown at 72, for the aforementioned same three microphone positions are clearly apparent.
Figs. aye 20(b~ and 20~c3 illustrate the superior performance of the present invention over prior art, with regard to the reduction of loudspeaker driver performance deficiencies stated in idea statements (1.4) and (1.6~. Fig.
aye shows the amplitude vs. frequency response for a high-quality 6 1/2" bass-midxange river when the same is operated over the entire audible frequency range without the use of a crossover filter. The frequency region of best, or ideal" driver performance is shown at 73. Above the frequency shown as lo cone breakup occurs, which is the main cause of the irregular frequency response shown at 74.
Audibly unpleasant "sonic colorations and high distortion occur in the same frequency region shown at yo-yo phenomena well known to those skilled in the art. Figure 20b shows the amplitude vs. frequency response of this same 6 1/2" driver when operated over the entire audible frequency range using a common prior art crossover filter topology, specifically a low-pass filter having a 6 dB/octave pass band band-edge slope.
The frequency region of best driver performance, shown at 73, is unaffected. The frequency region of poor driver performance, shown at 75, is clearly evident, and will be 30 audible as sonic coloration and distortion. Figure 20c shows the amplitude vs. frequency response of the some 6 1/2R driver when operated over the entire audible frequency range but using n infinite slope low-pass filter topology of the present I

invention. The frequency region of best driver performance, shown at 73, is unaffected but response in the frequency region of poor driver performance, shown at 76~ is eliminated and rendered inaudible.
For those skilled in the art, it should become evident upon study of the amplitude responses of invention embodiments riven here in Figs. 7, 16 and 17 that the amplitude us frequency response shapes characteristic to the separate crossover filter-loudspeaker driver combinations of the present invention are much closer to the ideal brick-wall response shape, than exists in prior art. Thus the present invention will, by virtue of its unique "infinite-slope"
crossover filter topology, improve over prior art, by permitting the mitigation of certain performance deficiencies in loudspeaker systems, namely the deficiencies caused by acoustic w Ye interference, and also deficiencies caused by operation of loudspeaker drivers at frequencies outside the same driver's respective frequency bands of best performance.
The reader is especially referred to the prior art designs given in this disclosure in order to make the comparisons just implied.
By way of illustration and not limitation it is noted that the electrical parameters of the individual components of the invention embodiments depicted in Figs. 10 and 15b are as follows:

1. Embodiment of Fig 10:
Lit - 5~1 my Coo - 470 micro farads L12 - 5.1 my Oil - 220 micro farads L13 - 3.2 my clue - 100 micro farad L14 - 8.4 my C13 - lo micro farads ~15 - 1.55 my C14 16 micro farads I
I
L16 1.7 my C15 36 m;crofara~s L17 - 757 micro henries C16 16 mlcrofarads Lo - 757 micro henries C17 - 14 micro farads ~19 - 2.1 my C18 10 micro farad L20 320 micro henries Cog - 3.3 microEaraas L21 540 micro henries C20 - 3.0 micro farads L22 215 micro henries C21 - 1.0 microfaraas L23 170 micron C22 1.68 micro farads L24 - 540 micro henries C23 - 24 micro farads Roll 30 ohms Al - 30 ohms R13 15 ohms 2. Embodiment of Fig. 15b:
R21 - lo ohms C31 0.13 micro farads R22 - lo ohms C32 0.033 micro farads R23 lo ohms C33 0.16 microfaraa~
R24 - 22k ohms C34 0.0016 micro farads R25 - ok ohms C35 1027 micro farads R26 - 22k ohms C36 0.127 micro farads R27 lo ohms C37 0.127 micro farads R28 - lo ohms C38 0.127 micro farads Rug 7.2k ohms C3~ - OKAY micro farads R30 ~50k ohms C40 0.0013 microfaradq R31 -2.8k ohms C41 0.~2 micro farads R32 lo ohms C~2 - 437 picofarads ~33 -lo ohms C43 0.343 micro farads R3~ k ohms C44 - 0.02 micro farads R35 -22k ohms C45 0.02 m;crofarads R36 ~22k ohms C46 0~02 microfarad8 R37 - 22k ohms ~47 1137 picofarads -30~

R3 10K ohms C48 - 0.89 micro farads R - 10K ohms R40 3.9K ohms All operational amplifiers R41 - 155K ohms Signetics NOAH or equiva-R42 620 ohms lent.
R43 - 22K ohms R44 - 22K ohms ~45 22K ohms R46 10K ohms R4 10K ohms Theoretical Basis for the Invention It is believed that a better understanding of the function of the crossover circuits of Figs. 3 and 10 (or other topologies based upon the concepts of the present invention) will be had upon an examination of the development of the character-fistic p-z of the invention. A general reference that describes the p-z concepts utilized according to the present invention is circuit Theory and Design", (pp. 168-173) John L. Stewart, John Wiley & Sons, Inc., New York, 1956. Other references that are pertinent with respect to the network analysis are "Network Analysis and Synthesis", First Edition, (pp. 320 and 321) Franklin F. Queue John Wiley & Sons, Inc., New York, 1962; and "Linear Network Analysis", (pp. 284 and 285) S. Swish and N. Balabanian, John Wiley & Sons, New York, 1963.
A pole-zero pattern or p-z as is illustrated in Fig. 11 would be those for a perfect realization of the invention.

-aye-These are the p-z of Equation (6) below;
(See the above mentioned reference by Stewart, pages 96-97 and pages 168-172; see also Swish and Balabanian, page 284 Fig. 27).

it. -`

-31- ~%~
I f4(s) = essay = l-sU+~sU)2~2l - (Sue!+...
east l+sT~sT~2/2l + (sty.

Taken to infinity in both U and T, real positive constants, the above function will yield an infinite vertical row of poles in the left hand s-plane and an infinite vertical row of zeros in the right-half s-plane, as illustrated in Fig. 11.
If the series in Equation (6) is terminated in a finite number of terms, with U = T, the following Equation 57) is obtained:
' -(7) f5(s~ = east = east = l-$t~(sT~2/2! - (sty!
east STY ( sty 2 Jo + ( sty which is a standard approximation to the Alps transfer function with the series of Equation I terminated after three terms. If the zeros in Equations I and (7) are omitted the function remains all-pass for an infinite expansion - Equation (63 becoming Equation (2) - and becomes low-pass for a finite truncation equation I without its Eros], both merely having half the delay at any frequency (see page 285 of the reference "Linear Network Analysis"
referred to above). When the zeros of Equation lo or I art removed, the earlier approximation based on Equation (2) is obtained:
(2) fops) = east =
1 eat l~sT~tsT~/2l Steele+...

It is noted that Equations I and I) are identical if U = T
in Equation (~) except for the content multiplier in the exponential Both represent an all-pass transfer function, the addition of the retooled plane zeros in Equation (6) merely doubles the delay. Since Equations (2) and I above %

each represent an approximation to the ideal all-pass transfer function, then any linear combination of them could also approximate an Alps transfer function. If a loudspeaker system is constructed such that its acoustical output may be represented mathematically by multiplying the electrical input by some linear combination of Equations (63 and I there will be obtained a good approximation to the ideal loudspeaker - system. It is noted that Equation (5) represents the simplest possible such approximation. This invention considers a novel and more accurate approximation.
By means of the present invention, a system input-output transfer function is generated such that it may be broken apart, using a method analogous to a partial-fraction expansion, into separate low-pass, band-pass, and high-pass representations, said representations each being brick wall amplitude functions, the individual dominant p-z of which can be represented as a linear combination of finite forms of Equations (2) and (6). Stated in another manner, there is developed by means of the present invention an acoustic sum whose mathematical representation as a system function has the form:

(8) Acoustic output = electrical input x P(s) = Go Q(s) where the loudspeaker drivers are assumed ideal and which is equivalent to an approximation to an all-pass transfer function in linear combinations of truncations of Equations (2) and (6) whose quotient Squeeze can be broken apart, similar to partial fractions, into two or more separate quotients of polynomials in s, each of which will take the form of the dominant p-z of brick wall filter transfer function. These fractional expansions will take the following forms:

(9) 2-way system Pluckily + P2(s)/Q2( (10) 3-way system Pluckily P2(s)/Q2( ) 3 3 where extensions to 4-way, 5-way, etc. systems may also be effected. In Equation (9) the terms Pluckily and P2(s)/Q2(s) are arranged in such a manner that they represent the dominant p-z of a low-pass and high-pass filter, respectively. Similarly in Equation (lO),Pl(s)/Ql(s~ represents the dominant p-z of a low pass filter; P2(s)/Q2(s) represents the dominant p-z of a band-pass filter; and P3(s)/Q3(s) represents the dominant p-z of a high-pass filter.
It has already been shown by Equation (5) that a very simple loudspeaker system can be realized which satisfies Equation (9). It is noted also that extensions ox this simple idea will satisfy Equation (1) and higher-order systems. All of the prior art designs, however, depend upon filter topologies that have gradual crossover slopes (6, 12, or 18 dB/octave in various combinations) which suffer from deficiencies (1.1, 1.2, 1.3) mentioned herein before. Novel means are provided according to the present invention to mitigate these aforementioned deficiencies.
In accordance with the invention, a loudspeaker system is constructed with crossover filter circuits having very high pass band band edge amplitude vs. frequency response slopes while generating an overall system transfer function having p-z in the forms implied by truncations of Equations (2) and (6). This is effectively done by the embodiments of the invention illustrated in Figs. 3, 10 and 15. Basic characteristics of any embodiment of the invention, including those of Figs. 3, 10 and 15, are as -aye hollows:
(1.9) The crossover filter pass band band-edge slope is large; it may be as high as 100 dB/octave, or even higher.

I

I
(2.0) At least two loudspeaker drivers are used, and at least two separate mutually exclusive frequency bands are covered ire., one woofer and one tweeter comprise the simplest possible embodiment.
(2.1) The crossover filter pass band slope and arriver placement are adjusted so that wave interference between adjacent frequency bands is minimized by keeping the audibly effective band-width of any such interference to less than 1/3 octave.
(202~ The electrical parameters of the crossover are adjusted such that a fractional expansion of the system transfer function will appear as in Equation (9) or (10) or any higher-order extension of these. The denominator polynomials QSs) will, in the best embodiments, have different poles, with no repeated common) poles, which it characteristic to a class of separate an distinct brick-wall amplitude functions employing both mutually exclusive frequency pass bands and transmission zeros.
(2.3) The electrical parameters of the crossover network, in the best embodiments, are so adjusted that all drivers in the loudspeaker system operate in the same relative phase, which allows phase cola no rotations of 2nll~at the crossover frequencies, in accordance with statement (1.8~ herein before.
When conditions (1~9) to (2.3) are met, an embodiment according to the invention is realized. Stated ~213~2 differently, when a loudspeaker system is constructed that satisfies condition (1.9) through (2.3), the p-z of its overall system transfer function will satisfy Equation (2) or Equation I or some linear combination of these.
A pictorial illustration of the p-z peculiar to a general embodiment of the invention will clarify how the concepts of conditions (2.1~ to (2.3) are realized Figs.
aye, 12b and 12c show the dominant p-z for the low-pass, band-pass, and high-pass filter circuits of an embodiment.
The p-z at the origin and those having large negative real parts (depicted herein before in Figs. pa, 6b and 6c; pa, 5b and 5c; pa, 4b and 4CJ respectively) are ignored as they contribute little to the system response inside the pass band.
When the p-z in Figs. lea, 12b and 12c are summed, the result will have dominant p-z as shown in Fig 12d~ Since the poles of Figs. aye, 12b and 12c are simple and distinct, all of those poles appear in Fig. 12d. all dominant let hand plane zeros inside the system total pass band response, in any embodiment of the invention, will disappear in this summation.
Dominant right half plane zeros, if and as they occur in any embodiment, will not disappear and instead will always be accompanied by corresponding mirror image left hand plane poles The simpler case, in which there are no dominant right half plane zeros, is treated in this discussion.
This concept may be depicted mathematically, as explained further hereinafter, but involves the use of certain expressions which will first be derived with reference to Figs. aye and 13c which respectively illustrate, in general, a tweeter network and a midrange-n~twork embodying the invention.
The following is a mathematical derivation for the p-z of the tweeter and midrange networks. The tweeter network is given as shown in Fig aye and has one zero of transmission -36~ I
placed about one octave below its pass band. Solving for the transfer function (output voltage vs. input voltage) of the network of Fig aye, yields t assuming no loss in the ICKY
series circuit:

eon = LlClC?Rs3(L2C~s2+1) AS5+BS4+Cs3+Ds2~Es~F

where the denominator coefficients do not appear explicitly as functions of the circuit elements; which has p-z as shown in Fig. 13b. It is noted-by reference Jo Fog. 13b that with no resistance in the L2-C3 branch the zeros are positioned on the jaw axis. On the other hand, with series resistance in the L2-C3 branch, the zeros are displaced to the left hand plane.
The midrange crossover network is given as shown in Fig. 13c and has one zero placed about 1/2 octave above its upper cutoff frequency. Solving for its transfer function as above yields:
.
eon = Cls21As2+B) e so s5~s3~ so us which has p-z as is illustrated in Fig. 13d. It is noted that zeros appear in Fig 13d on the jaw axis with no series resistance in the L-C branch, corresponding to infinite band-edge slope The zeros move to the left for real circuit elements having resistance, corresponding to finite band-edge slopes.
The concept that all dominant left hand plane zeros inside the system total pass band response will disappear in the summation, as noted above, is depicted mathematically a follows, where the following expressions are those obtained it the foregoing derivation.

~22~3 Let eel = Cls2~As2+B) represent the p-z of a e (six poles) band-pass midrange filter circuit of an embodiment of the invention.
Let e 2 = LlClC~Rs3(L?C~s~2~1) represent the p-z of (five poles of eon) a high-pass tweeter) filter circuit of an embodiment of the invention. The poles of eon and eon will be assumed to be mutually exclusive, i.e7, no common factors.
It is desired to sum these transfer functions in such a manner as to realize the invention. The sum is formed as in Equation I below:

(11) eo--eol~eo2 =
e e e Cls2~As2~B~Poles of eo2)+L~ClC?Rs3~L~C~s2+1)SPoles of cot) Eleven poles of cot and eon where choice of the plus or minus sign depends on the relative phase characteristics of the drivers.
A straightforward solution for the locations of the p-2 in Equation ~11), or in any other summation of the form of Equation lend peculiar to embodiments of this invention, is very difficult. Fortunately such a direct solution is not necessary. The essential disappearance of all dominant lightened plane zero in a summation of the form of Equation (11) r and the consequent realization of the invention, is easily shown heuristically from simple energy considerations.
Refer to Figs. Audi and consider statement (2.4) below:
(2.4) Since each filter circuit of any embodiment of the invention has very steep pass band amplitude vs. fxequenc~ response bounded slopes, combined with mutually exclusive ~l22~L?3 1~2 I
ranges or bands of frequency coverage, the energy at any given frequency in the total system transfer function can be considered -to be sensibly contributed by one, and only one portion, it crossover filter-loudspeaker driver combination (low-pass, ban pass or high-pass) of the total system.
The only frequencies on the jaw axis where the aforementinea statement becomes an approximation is in the small regions of frequency overlap at the crossover frequencies, Observe that it the invention were perfect having infinite bondage slopes - there would be no energy overlap at the crossovers and statement (2.4) would be absolutely true at all frequencies It can be shown that if statement t2.43 is true, and the total system frequency response is sensibly flat, as is the case in Fig. 8, there can be no dominant transmission zeros within the total system band pass. The heuristic proof that summations of the form of Equation (113 imply dominant p-z as in Figs. aye is as follows- Consider the summation of Equation ~11) and all the p-z involved in this summation (Figs. aye, 14b and 14c). Here all the p-z shown not just the dominant ones. Fig. 14c contains all the poles of Figs.
aye and 14b, which is fairly straightforward/ as all these poles appear in the denominator of Equation (11). These poles must appear since each of them is a non-common factor of the least common denominator formed in the summation.
Proof of the existence of all of the zeros is a little less obvious. We proceed using an argument based on the aforementioned energy consideration (2.4) and an examination ox the total system amplitude and phase response Consider Fig. aye in which we seek to evaluate the -39~
System amplitude and phase response at a point on the jaw axis within the midrange pass band, say at wow The p-z at Fig. aye imply that only the midrange driver is functioning in the total loudspeaker system, i.e., the woofers and tweeters are disconnected.
Now consider Fig. 14c~ Here, the tweeter has been connected. There are now five more poles in the total system response. Two of these are a dominant complex-coniugate pair, which extends the system response into the high-frequency (tweeter) region. The remaining three poles are real and exist on the far left real axis, contributing almost nothing to the total system amplitude response. They must also not change the phase response, since we know from (2.4) that connecting the tweeter has no effect on the system midrange amplitude or phase response. Thus the total system zeros of our example Equation (11~ must fall into positions which will guarantee that the midrange phase response, as well as the amplitude response is the same with the tweeter in the system or out.
Examination of the numerator in Equation (11~ shows that an so is common throughout, implying two zeros at the origin. The highest order of s in the numerator is eleven, so there are nine more zeros to account for. The positions of these remaining nine zeros cannot be explicitly found without 25 expanding and factoring the numerator of (11). But we do know enough to determine their approximate locations by induction.
What we do know about the zeros can be summarized as hollows:
(2.5) None of the zeros are dominant, it they cannot exist near the jaw axis within the total system pass band.
(2.6~ The zeros exit in positions such that the phase response defined within the _40~ I
individual pass bands of Figs. aye and 14b remain unchanged idyll in Fig. 14c.
A plausible set of locations for the remaining nine zeros is shown in Fig. 14c. The four transmission zeros which are dominant in Figs. aye and 14b move approximately horizontally to the left as in Fig. 14c, becoming no longer dominant. This supposed position of these zeros is supported by observation; for example, when one carefully measures the frequency response of an embodiment of the invention, very slight irregularities in amplitude of a fraction of a dub can be detected on the frequency response near the frequencies of the zeros.
The remaining five zeros are acerbated near or on the negative real axis. They must occupy positions such that lo the phase response within the pass band of Fig 14c is the same as that within the individual pass bands of Figs. aye and 14b. This may be confirmed by observation; in any embodiment of the invention total system phase shift is unchanged within any pass band when drivers associated with other pass bands are connected or disconnected. The aforementioned statement is exact it the crossover network frequency response band-edge slopes are infinite, and becomes approximate in the frequency band overlap of actual embodiments having non-infinite slopes.
Thus, there has been established, by intuitive arguments supported by observation the crucial concepts which underlie the operation of operative embodiments of the invention. These concepts may be presented as corollary of statement I
t2~7~ Jo The separate portions, or crossover filter-loudspeaker driver combinations of the invention (low-pass, band-passr Of whops, function independently of each other in their separate contributions to ~22~

the total system acoustic output, whereby the degrees of "effective" or "absolute"
independence are define, as in Fig. 18 end the textual explanation of this figure given hereinbeEore.
(2.8) The approximation to absolute independence among the same portions in (2~7) becomes more accurate as the crossover jilter pass band binge amplitude us frequency response slopes approach infinity. If the same band-edge slope becomes greater than about 70 dB/octave, acoustic wave interference becomes inaudible, and the acoustic outputs ox the portions, so crossover filter-loudspe~ker driver combinations in 2~7 are considered to be absolutely independent, as defined in Fig.
18 and the textual explanation of this same figure given herein before Statements I and (2.8), taken together with statements (1.7) and (2.4), inclusive, mentioned herein before, are characteristic to any embodiment of the invention, and serve to define its intent and operation Summarizing the foregoing and showing how the invention improves upon the prior art systems, and specifically, how the present invention solves the difficulties mentioned herein before, the following is noted with respect to statements (1.4~ through (1.6), inclusive:
Statement tl.4): Well-designed loudspeaker drivers generally exhibit a band of freguen-ales in which the amplitude response is very flit, and in which the phase response Jo is relatively linear. According to the invention, a driver is connected to a crossover filter circuit (1.8) having a "brick wall" passbana characteristic corresponding to its frequency region of best performance. Energy is transmitted negligibly -to the arriver outside its frequency band of best performance, so that problems of irregular frequency an phase response - i.e., non-ideal behavior -originating from an individual driver are minimized-Statement (1.5): Acoustic wave interference between drivers is caused by simultaneous radiation at the same frequency from two or more drivers, combined with spacing between the acoustical centers of the arrivers of about one-half wave length or more If the width of these frequency bands of simultaneous reedition, the overlap region shown at 64 in Fig. I is minimized, or reduced to zero r the same wave interference is correspondingly minimized or eliminated. The steep I crossover filter pass band slopes characteristic to this invention will minimize the width of these frequency bands of mutual interference to 1~3 octave or less, with the width of these bands of mutual interference tending towards zero as the crossover slopes approach infinity.
statement (1.6) Loudspeaker drivers tend to have low amplitude distortion only within their frequency bands of flat amplitude and linear phase response Outside these bands, the distortion generally rises rapidly. Since top invention minimizes the energy transmitted to the drivers outside their frequency bands of best response, nonlinear distortion in the total system will be reduced Finally, mention is made of two crucial discoveries which clarify the nature of the invention. First, and most important, is the discovery that a good approximation to the ideal transfer response (1) can be realized by properly summing two or more "brick wall" amplitude functions having mutually exclusive frequency pass bands lying adjacent to one another. By proper choice of system parameters such as driver placement, type, the size also crossover topologies, pass bands and slowest it is possible, by the methods of the invention, to achieve the aforementioned good approximation to the ideal system transfer function.
Also, observe that in forming the acoustic sum of the sound outputs of the individual drivers comprising the stymie as for example a sum in the mathematical form of Equation to) or ~10), in general, no poles or zeros disappear in the summation as was shown explicitly in the single case described by Equation (11). This follows logically from Statement I Contrast this aforementioned situation with a speaker system based on concepts of which Equation (5) is the simplest example. Here, all p-z disappear In general, prior art speaker designs have utilized acoustic summations which caused the disappearance of as many pi as possible in the summation while tending towards some good approximation of Gaussian (1). According to the prevent invention, the ~22~ Lo -44~
opposite approach is taken; i.e., retaining all, or as many as possible, of the p-z of the individual elements in the final summation This latter approach also approximates Equation I to a high degree of accuracy, while overcoming shortcomings of the prior art.
There are two possible (but not necessarily all inclusive) design approaches one may take in the realization of loudspeaker systems using methods of the invention.
I Exact approach: The designer chooses the dominant poles of a system transfer function which approximates Equation (1) to the desired degree of accuracy. This involves picking as many terms in the infinite series of Equation I as desire, and is generally best realized as the p-z peculiar to Bessel filter (Duo, "Network Analysis and Synthesis", p. 343-348). Then a loudspeaker crossover network with an acoustic summation implicit as the right-hand side of Equation (8) is designed to have dominant poles as near as possible to the aforementioned Bessel approximation.
The arithmetic will be cumbersome and will require a computer program for an accurate solution. The p z peculiar to the loudspeaker arrivers themselves should by considered as part of the analysis, these p-z being either approximated for the drivers assumed as ideal, or either calculated or measured for thy driver considered as non-ideal.
(2) Empirical approach: The designer chooses p-z of "brick-wall" amplitude functions which based ox previous experience, will yield a good (although not necessarily optimum) approximation to Equation (1) when an acoustic summation is performed as in Equation to). Driver p-z may or may not be considered curing the initial steps in the d~slgn. A prototype is then built and tested, and adjustments made to the crossover circuit components until the performance of the speaker system - in regard to the accuracy of its approximation to Equation I - is satisfactory The inventor used this empirical approach in realizing the embodiments of the invention discussed herein.
Empirical methods were used for design of the invention embodiments schematically depicted in Figs 3, 10 and 15. Passive crossover filter circuits, i.e., as shown in Figs. 3 and 10, were realized by utilizing an empirical extension of the well-known "image-parameter n method, described hereinafter. The active crossover filter circuit of the embodiment shown in Fig. 15 was realized by first determining the circuit element values using methods of the text "Handbook of Operational Amplifier Circuits" mentioned herein~efore, and then empirically adjusting said circuit element values for optimum performance. To illustrate the procedure for making an operative embodiment of the invention more clearly, it will be treated in some detail in the following An empirical method was used to realize a preferred embodiment of the invention schematically depicted in Fig. OWE
Numerical values for inductive and capacitative circuit elements comprising the crossover filter circuits of the aforementioned invention embodiment are calculated by use of the well-known "image parameter" method, which is described fully in the text "Electrical Engineering Circuits", by Ho Swilling, John Wiley & Sons ~1957), Chapters 18 and 19.
Tables of equations, amplitude and phase response graphs, schematic diagrams for filter circuit portions, and design aids for the image-parameter method are given in many reference books, one of which is reference Data for Radio Engineers" r Fourth Edition, Stratford Press (1963), Chapter 6 As mentioned herein before, the present invention is based upon the discovery by the inventor that a good and useful approximation to the ideal transfer function I can ye realized by properly summing two or more brick-wall amplitude junctions having separate and mutually exclusive frequency pass bands which pass bands when taken together encompass the entire audible frequency range. Furthermore, the inventor has discovered that ordinary image-parameter theory, augmented by empirical methods may be used to realize suitable brick-wall amplitude functions for crossover network filters used in operative invention embodiments Design of an infinite slope loudspeaker system begins with the selection of proposed loudspeaker drivers. Two or more of the same are needed in order to cover the audible range of frequencies, i.e., I I to 20 kHz. Selection of the I number of drivers required is based upon considerations of the cost and size of the prospective loudspeaker system. For the invention embodiment of Fig. 10, four loudspeaker drivers are chosen, one woofer, two midranges and one tweeter. Amplitude and phase measurements are made on all available and known drivers; from these, drivers are chosen which have performance, with respect to their amplitude and phase response, which can be considered to be ideal over separate frequency ranges which when taken together will encompass the entire audible frequency range. These frequency ranges for the four drivers chosen appear in Fig. 10 and also hereinafter.
Crossover network filters having brick-wall amplitude response characteristics are synthesized to possess pass bands matching the frequency ranges of best performance of the aforementioned drivers. This is accomplished using enhanced image-parameter theory. If transmission zero frequencies, mutual coupling of coils, and filter pass bands are chosen and adjusted properly, the acoustic sum, i.e., the total acoustic amplitude and phase response of the invention embodiment will become an accurate approximation to the ideal transfer function of equation I
The empirical design procedure begins with computation, using image-parameter methods of initial crossover network circuit element values. Calculations for four separate pass bands are required, i.e., the crossover network will have four separate filter circuits. Each filter circuit will need at least one transmission zero, in this case, six transmission zeros are incorporated into the crossover network filter topology, one zero each for the woofer low-pass filter and tweeter high-pass filter, and two zeros each for the two separate midrange band-pass filters Frequencies for filter pass bands and transmission zeros are tabulated us:
DRIVER PASS BAND TRANSMISSION ZERO(S) woofer low - pass 280 Ho I ~2~3~2 lower band - pass 80 Ho midrange 150 - 800 Hz1450 Ho .

upper band - pass 550 Ho midrange 800 Ho - 5 kHz 6000 I

tweeter High - pass 300U Ho 5 kHz - 20 kHz In the above table frequency ranges for the crossover filter pass bands correspond to the respective driver frequency ranges of best performance. Frequencies for the transmission zeros are determined by intuition based upon past experience in working with the invention Using the data tabulated herein before image-parameter methods are used to calculate initial circuit element values. Two sets of illustrative calculations are shown:

1. low-pass response for lower midrange driver:
lo = 150 Ho impedance = 8 ohms Of= 1 = 1 = 132~f war (2 ~)(150)18~

Lo = R = 8 = 8~48 my wow Sly) 2. lower transmission zero for upper midrange driver:

lo = 800 Ho f = 550 Ho Impedance - 8 ohms m = I - f 2/C2 _ Al _ ~550)2/~800)2 = 0,726 ~49-Lug = Lo = R = 8 = 2.19 my m wcm (2~)(800)(.726) C = m Ok m . ]. = _ .726 23 1_m2 l_m2 war (1 - .726 ) (2~)~800)(g) = 38.1 of It should be noted that some initial circuit element values as just calculated will change later after empirical adjustments. For example, C13 became 100 of, and L14 became 8.4 my in the final circuit (Fig. 10), representing a slight change after empirical adjustments. One component in the design required a large change, C23 calculated above as 38.1 of became I of in the final circuit (Fig. 10). All circuit element values given in the table herein before for Fig. 10 represent the final empiric gaily adjusted circuit element values for the same invention embodiment.
Calculations for the remaining circuit element values will not be shown here, but proceed in a manner similar to that just illustrated, except for resistive elements Roll, R12, and R13, which were determined purely empirically. These resistors serve to damp the efficiency of the three higher frequency drivers, matching the efficiency of the same to that of the woofer, such that all four drives will sound with equal loudness, thereby producing a flat total system amplitude response.
After computation of all reactive circuit element values and selection of the damping resistors for the hither frequency drivers, the crossover circuit is constructed, using components and techniques common to the art. Mutual coupling of some coil pairs is used where it has been empirically found to enhance the , . Jo I
-aye-steepness of the pass band band-edge response. This same mutual coupling of coil pairs is achieved by methods common to the art;
including winding the two coils on a common 'I

-50~ 73~
iron core or winding the two coils on separate cores and then mounting them physically close together so their magnetic fields interact to provide mutual coupling.
The completed crossover network along with the loudspeaker arrivers is assembled in a cabinet or box, in a manner common to the art, i.e., with the crossover network mounted inside the box, the drivers arranged physically close together in a vertical array on the front face of the box, and suitable electrical connections being made between the crossover network filter circuits and the respective loudspeaker drivers, and a pair of input terminals provided for connection of the loudspeaker system to a driving signal.
Amplitude, phase and delay measurements are made on the completed speaker system, and the crossover circuit reactive and resistive element values together with the mutual coupling of coil pairs are empirically adjusted until the system performance with respect to amplitude, phase, and delay response is, as recognized by those skilled in the art, an accurate and superior approximation to either form of the ideal delay function of Equation (1).
More specifically, part of the acoustical test procedure during empirical optimization and final evaluation of an invention embodiment makes use of the Wilkinson n fast Fourier transform" method. This same method employs a digital computer to analyze the time domain impulse response of a loudspeaker system. Software is used by this same method to produce thy usual frequency domain amplitude,phaser and delay spectra from the time domain impulse signal response of the loudspeaker system under test. The aforementioned computer-produced spectra of amplitude, phase, an delay rosins are then confirmed by further measurements made directly in the frequency domain, using sine-wave and "pink-noise" test signals, together with wave analyzers, AC

-51~ I
voltmeters, oscilloscopes, and chart recorders, in a manner common to the art.
Thus, there has been provided, according to the invention a method of and a means for reproducing by a loudspeaker system sounds from electrical signals representing sounds to be reproduced. A plurality of crossover filter circuits are provided to separate such signals into bands of different frequencies there being established for each of the crossover filter circuits very high pass band band-edge frequency response slopes by means of transmission Eros appropriately placed at frequencies just outside the pass bands of the individual filter circuits while simultaneously insuring that all or as many as possible of the dominant poles of the individual crossover filter circuits remain in the lo acoustic summation. this insures that each of the individual crossover filter circuits will posses a brick-wall amplitude vs. frequency characteristic so that as the same filter circuits direct electrical energy to their respective loudspeaker drivers over the frequency ranges of best performance of the same loudspeaker drivers, each of the individual crossover filter - loudspeaker driver combinations so formed will function independently of each other in their separate contributions to the total loudspeaker system acoustic output. This same independence is characteristic to operative embodiments of the present invention, in which embodiments by virtue of this same aforementioned independence the acoustic output of any one crossover filter - loudspeaker driver combination will not audibly impinge upon the acoustic output of any one another crossover filter-loudspeaker driver combination, as implied in idea statements (2.4) t I and I given herein before, thereby enhancing, by means of the present invention, the fidelity ox response in the reproduction of sounds encompassing the audible frequency range from electrical signals representing said sounds.

~2~3~

Of particular significance in connection with top transfer function employed according to the present invention is the use of different poles in the best embodiments for the low-pass, band-pass and high pass functions. For example, in the empirical method based on image-parameter theory just described, the individual low-pass) band-pass, and high-pass functions will not in general share any common poles, because each of the aforementioned functions are calculated, and later empirically adjusted, independently of the others. It is characteristic to independently chosen brick-wall amplitude functions having mutual exclusive frequency pass bands, that the denominator poles of their respective transfer functions he generally different, as illustrated earlier in Fig. 14 and the textual explanation of this same figure given hereinhefore.
The functions that have been used according to the proposals of the prior art have mainly had the same poles in the denominator parts or low-pass, band-pass and high-pass functions. The prior art workers, in attempting to achieve a closer approximation to the ideal transfer function, have concentrated on the numerator parts of the functions, as is evident from the three papers of the Journal of the Audio Engineering Society mentioned hereinbe~orev An example of a prior art crossover system having crossover jilter transfer functions not possessing brick-wall amplitude vs. frequency characteristics but in which different poles appear in the denominator parts for low-pass and high-pass functions is contained in U.S. Patent 2,612,558 issued to POW. Klipsch on August 13, 1946. However, crossover designs in which different poles appear in the denominator parts of the transfer functions of individual elements have fallen into disfavor in recent times.

Claims (24)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. A multidriver loudspeaker apparatus comprising at least two loudspeaker drivers, a crossover filter network having at least two crossover filter circuit means, said loudspeaker drivers being each connected to a respective crossover filter circuit means of the crossover filter network, at least one of the crossover filter circuit means of the crossover filter network including an additional circuit structure means for generating at least one zero or near zero transmission of response in the transfer function of said crossover filter circuit means for frequencies just outside the pass band of said crossover filter circuit means.

2. The loudspeaker apparatus as specified in claim 1 wherein the crossover filter circuit means comprise passive circuit elements.

3. The loudspeaker apparatus as specified in claim 1 wherein said additional circuit structure means include one inductor connected in series with one capacitor.

4. The loudspeaker apparatus as specified in claim 1 wherein said additional circuit structure means include at least one additional inductor, said additional inductor mutually coupled to an existing inductor of the crossover filter circuit.

5. The loudspeaker apparatus as specified in claim 4 wherein the mutually coupled coils are adjusted so that the currents are in phase, i.e., balanced, in the filter pass band and out of phase in the filter stop band.

6. The loudspeaker apparatus as specified in claim 1 wherein the crossover filter circuit means which include the additional circuit structure means achieve very high pass band band-edge amplitude vs. frequency response slopes.

7. The loudspeaker apparatus as specified in claim 1 wherein the crossover filter circuit pass band band-edge amplitude vs. frequency response curve for the crossover filter circuit means which include the additional circuit structure means in 40 dB per octave.

8. The loudspeaker apparatus as specified in claim 1 wherein the crossover filter circuit pass band band-edge amplitude vs. frequency response curve for the crossover filter circuit means which include the additional circuit structure means is over 40 dB per octave.

9. The loudspeaker apparatus as specified in claim 1 wherein the crossover filter circuit pass band band-edge amplitude vs. frequency response curve for the crossover filter circuit means which include the additional circuit structure means is about 100 dB per octave.

10. The loudspeaker apparatus as specified in claim 1 wherein said separate crossover filter - loudspeaker driver combinations all operate in the same relative phase.

11. The loudspeaker of claim 1 wherein the crossover filter circuit means employs at least one all pass delay equalization network.

12. The loudspeaker apparatus as specified in claim 1 wherein each crossover filter circuit means of the crossover filter network includes additional circuit structure means for generating at least one zero or near zero transmission of response in the transfer function of each crossover filter circuit means for frequencies just outside the pass band of the respective crossover filter circuit.

13. The loudspeaker apparatus as specified in claim 1 wherein the element values comprising the crossover filter circuit means are determined such that the crossover filter circuit means possess distinct and approximately mutually exclusive frequency pass bands together with at least one zero or near zero trans-mission of response in the transfer function of said crossover filter circuit means for frequencies just outside the pass band of said crossover filter circuit means.

14. The loudspeaker apparatus as specified in claim 1 wherein the element values comprising the crossover filter circuit means are initially determined using image-parameter methods followed by emperical adjustment of said same element values, such that the crossover filter circuit means possess distinct and approximately mutually exclusive frequency pass bands together with at least one zero or near zero transmission of response in the transfer function of said crossover filter circuit means for frequencies just outside the pass band of said crossover filter circuit means.

15. A loudspeaker apparatus as specified in claim 1 wherein the frequency range of audible overlap, said overlap being between the pass band responses of any two separate cross-over filter-loudspeaker driver combinations in the loudspeaker system sharing a common crossover frequency, is less than l/3 octave.

16. A loudspeaker apparatus as specified in claim 1 wherein the crossover filter circuit means used in said crossover filter network comprise two separate filter circuit means each having approximately mutually exclusive frequency pass bands, said separate crossover filter circuit means being each electrically connected to a respective loudspeaker driver.

17. A loudspeaker apparatus as specified in claim 1 wherein the crossover filter circuit means used in said crossover filter network comprise more than two separate crossover filter circuit means each having approximately mutually exclusive frequency pass bands, said separate crossover filter circuit means being each electrically connected to a respective loudspeaker driver.

18. A loudspeaker apparatus as specified in claim 1 wherein each of said loudspeaker drivers has a particular band of frequencies of best response that is different for each of said loudspeaker drivers, and the individual crossover filter circuit means used in said crossover filter network each have a pass band corresponding to the frequency band of best response of the associated drivers, whereby said crossover filter network is operative to direct electrical signals of widely varying frequency to the appropriate loudspeaker drivers comprising said loud-speaker system.

19. A loudspeaker apparatus as specified in claim 1 wherein said loudspeaker system has an error of delay response for frequencies above 175 Hz of less than one millisecond.

20. A loudspeaker apparatus as specified in claim 1 wherein said loudspeaker system has an ambiguity of phase response of + 2n.pi. radians (where n = 0, 1, 2,...) at said crossover fre-quencies.

21. A multidriver loudspeaker apparatus comprising two loudspeaker drivers, said drivers being a woofer and a tweeter, a crossover filter network having two crossover filter circuit means, said crossover filter circuit means including a low pass and a high pass filter, said loudspeaker drivers being each connected to its respective crossover filter circuit means of the crossover filter network, the high pass crossover filter circuit means of crossover filter network including additional circuit structure means for generating at least one zero or near zero transmission of response in the transfer function of said high pass crossover filter circuit means for frequencies just outside the pass band of said high pass crossover filter circuit means, said additional circuit structure means of the high pass crossover filter circuit means including an inductor connected in series with a capacitor, the low pass crossover filter circuit means of the crossover filter network including additional circuit structure means for generating at least one zero or near zero transmission of response in the transfer function of said low pass crossover filter circuit means for frequencies just outside the pass bands of said cross-over filter circuit means, the additional circuit structure means of the low pass crossover filter circuit means including one additional inductor, said additional inductor mutually coupled to an existing inductor in the low pass crossover filter circuit means.

22. The loudspeaker apparatus as specified in claim 21, wherein said mutually coupled inductors are adjusted so that the currents are in phase, i.e. balanced, in the filter pass bands and out of phase in the filter stop bands of the low pass cross-over filter circuit means.

23. A multidriver loudspeaker apparatus comprising four loudspeaker drivers, said drivers including a woofer, a lower midrange driver, an upper midrange driver, and a tweeter, a crossover filter network including a low pass crossover filter circuit means, a band pass crossover filter circuit means, and a high pass crossover filter circuit means, said band pass crossover filter circuit means including a lower midrange section and an upper midrange section, said loudspeaker drivers being each connected to its respective crossover filter circuit means of the crossover filter network, each of the four crossover filter circuit loudspeaker driver combinations operating independently of each other in forming the total acoustic output of the loudspeaker apparatus, the low pass crossover filter circuit means, the lower midrange section of the band pass crossover filter circuit means, and the upper midrange section of the band pass crossover filter circuit means of the crossover filter network each including an additional circuit structure means for generating at least one zero or near zero transmission of response in the transfer function of each of the respective crossover filter circuit means for frequencies just outside the pass band of the respective crossover filter circuit means, said additional circuit structure means for the low pass crossover filter circuit means, the lower midrange section of the band pass crossover filter circuit means, and the upper midrange section of the band pass crossover filter circuit means of the crossover filter network including one additional inductor, said additional inductor mutually coupled to an existing inductor in each respective crossover filter circuit means, the high pass crossover filter circuit means of the crossover filter network including an additional circuit structure means for generating at least one zero or near zero transmission of response in the transfer function of said high pass crossover filter circuit means for frequencies just outside the pass band of said high pass crossover filter circuit means, said additional circuit structure means for the high pass crossover filter circuit means including an inductor connected in series with a capacitor.

24. The loudspeaker apparatus as specified in claim 23, wherein the mutually coupled inductors are adjusted so that the currents are in phase, i.e. balanced, in the filter pass band and out of phase in the filter stop bands of the low pass and band pass crossover filter circuit means.