Constant Beamwidth Transducers (CBTs)

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D.B. Keele, Jr.  -- The Official Website

A member and fellow ("for contributions to the design and testing of low-frequency loudspeakers") of the Audio Engineering Society, Mr. Keele has presented and published over thirty-five technical papers on loudspeaker design and measurement methods and other related topics, among them the paper for which he won the AES Publication Award, "Low-Frequency Loudspeaker Assessment by Nearfield Sound-Pressure Measurement" (J. Audio Eng. Soc., vol. 22, p. 154 (1974 Apr.). He is a frequent speaker at AES section meetings and workshops, has chaired several AES technical paper sessions, and has been a member of several AES committees including being on the AES review board. Mr. Keele is a past member of the AES Board of Governors and is past Vice President, Central Region USA/Canada of the AES.

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1. "The Vented Loudspeaker: A Restatement," Presented at the 42nd Convention of the Audio Engineering Society, Preprint No. 842 (L-10), (May 1972).

Additional information on the use and application of Thiele's alignments for the vented loudspeaker cabinet is presented. A rewritten alignment table which has all the frequency terms normalized to the speaker resonance frequency is included. Computer-run frequency responses for all the alignments are displayed along with a new fourth-order Chebyshev alignment beyond no. 9. Variations and sensitivity functions for the vented cabinet output with respect to various system parameters (both Thiele system parameters and driver physical parameters) are derived and plotted.

2. "The Design and Use of a Simple Pseudo Random Pink-Noise Generator," J. Audio Eng. Soc., (Jan./Feb. 1973).

The current high usage of frequency-equalized sound systems in the commercial sound and recording fields places increasing demands on the user-operator of the system to ensure that the overall system holds its designed value of spectral flatness during normal day-to-day operation. An inexpensive generator of pseudo random pink noise with adequate spectral purity is described which can be used as a stable known test source for quick on-site sound-system tests. The generated pink noise is accurate enough for use with an elaborate real-time spectrum analyzer (if available) for quantitative measurements or can be used for qualitative operator subjective measurements in the absence of other test equipment.


3. "Sensitivity of Thiele's Vented Loudspeaker Enclosure Alignments to Parameter Variations," J. Audio Eng. Soc., (May 1973)

Additional information on the use and application of Thiele's alignments for the vented loudspeaker cabinet is presented. A rewritten alignment table which has all the frequency terms normalized to the speaker resonance frequency is included. Computer-run frequency responses for all the alignments are displayed along with a new fourth-order Chebyshev alignment beyond no. 9. Variations and sensitivity functions for the vented cabinet output with respect to various system parameters (both Thiele system parameters and driver physical parameters) are derived and plotted.

4. "Optimum Horn Mouth Size," Presented at the 46th Convention of the Audio Engineering Society, Preprint No. 933 (B-7), (Sept. 1973).

Loudspeaker exponential horn computer model studies indicate that there is an optimum mouth size for a horn of specific cutoff to minimize mouth reflections. Evaluation of the reflection coefficient at the horn's mouth reveals how large the mouth must be to optimally radiate into different size solid angles.

5. "A Tabular Tuning Method for Vented Enclosures," J. Audio Eng. Soc., (March 1974).

Computer-generated tables greatly simplify the selection of vent dimensions for a vented loudspeaker enclosure. Fine adjustment of vent length may be guided by a simple partial derivative expression relating resonance frequency to vent length.

6. "Low-Frequency Loudspeaker Assessment by Nearfield Sound-Pressure Measurement," J. Audio Eng. Soc., (April 1974).

A loudspeaker test technique is described which depends on nearfield pressure measurements
made in a nonanechoic environment. The technique allows extremely simple
measurements to be made of frequency response, power response, distortion, and
electroacoustical efficiency.

7. "What's So Sacred About Exponential Horns?," Presented at the 51st Convention of the Audio Engineering Society, Preprint No. 1038 (F-3), (May 1975).

The maintenance of constant directivity with frequency in high-frequency exponential horns is quite difficult. Two main sound industry solutions are the multicell and radial/sectoral horns. While the multicell exhibits fairly constant directivity, both designs suffer from mid/high-frequency polar lobing and midrange narrowing, and the radial shows continually decreasing vertical beamwidth as frequency increases. A new series of horns which optimally joins a modified conical horn with an exponential throat section corrects these problems, while offering very well behaved polar patterns and constant directivity up to 16 kHz.

8. "A New Set of Sixth-Order Vented-Box Loudspeaker System Alignments," J. Audio Eng. Soc., (June 1975).

A new and useful set of low-frequency assisted alignments contain Thiele's sixth-order Butterworth (B/6) alignment as a central member. The new alignments provide the same low cutoff with moderate amplifier boost (+6 dB) and low out-of-band driver excursion as the assisted B/6 alignment 15 of Thiele. The method of alignment generation is based on shifts of driver suspension compliance.

9. "Application of Recent Australian Loudspeaker Research to Producible Loudspeaker Systems," Presented at the 1976 IEEE International Conference on Acoustics, Speech, and Signal Processing, (April 1976).

The old cut and try methods of direct radiator loudspeaker system development have been minimized by the recent work of Australians Thiele, Small, and Benson. The operation of systems in the so-called low-frequency piston range where the wavelength is larger than the radiator is now quite predictable and predetermined. The Australians have contributed substantially to the storehouse of information that can aid and direct a systems designer. Well developed theory has been made available, permitting a designer to proceed from the specification of important end goals (such as efficiency, system size, low frequency limit, and power output) to a usable system with a minimum of empirical investigation. Applications of this theory to the design of several loudspeaker systems will be discussed.

10. "An Efficiency Constant Comparison Between Low-Frequency Horns and Direct-Radiators," Presented at the 54th Convention of the Audio Engineering Society, Preprint No. 1127 (M-1), (May 1976).

Evaluation of the efficiency constant for exponential horns reveals that the horn is quite wasteful in its use of enclosed volume when compared to direct-radiator systems. The main advantage of horns lies in the realizability of rather high efficiencies in the 10% to 40% range which is beyond the capabilities of most direct radiators. Use of direct radiators in arrays increases the low frequency efficiency but not without a decrease of high frequency bandwidth. The areas discussed in this paper are illustrated by comparative experimental measurements on three low frequency systems: 1) A dual driver front loaded folded horn, 2) a single driver direct radiator vented-box system, and 3) a four-driver vented-box system consisting of a 2x2 array of a single driver system of item #2.

11. "Low-Frequency Horn Design Using Thiele/Small Driver Parameters," Presented at the 57th Convention of the Audio Engineering Society, Preprint No. 1250 (K-7), (May 1977).

The design formulas for low-frequency horns which yield various physical and performance related horn data can be recast in a form which utilizes the Thiele/Small direct-radiator driver parameters. This conversion simplifies computations of items such as required back cavity volume and throat area for desired performance. Performance data such as operating bandwidth, upper rolloff frequencies and low-frequency maximum acoustic output power are easily calculated.

12. "AWASP: An Acoustic Wave Analysis and Simulation Program," Presented at the 60th Convention of the Audio Engineering Society, Preprint No. 1365 (D-8), (May 1978).

A report on the preliminary version of a general purpose computer program for the analysis and simulation of two-dimensional acoustic spaces under steady-state sinusoidal conditions. The program employs finite element methods to predict the sound pressure magnitude and phase in an arbitrary region at any desired frequency. AWASP is similar to concept and usage to well known electronic circuit analysis programs such as ECAP and SPICE. The program has wide application in the analysis and design of a large number of electro-acoustic situations including: sound in ducts, horn propagation, sound in enclosures, diffraction effects, etc. Appications analyzed include: sound in straight and bent pipes, sound in a live room, and simulation of a Helmholtz resonator.

13. "Automated Loudspeaker Polar Response Measurements Under Microcomputer Control," Presented at the 65th Convention of the Audio Engineering Society, Preprint No. 1586 (C7), (Feb. 1980).

An automatic polar response measurement and analysis system controlled by an industrial/small business grade microcomputer is described. A Z80 microprocessor based S100-buss computer (a Cromemco System 3) interfaced with a one-third octave realtime analyzer and remote controlled turntable is used to gather response spectra at different angles. The disk stored spectral data is subsequently analyzed to generate polar/frequency response curves and beamwidth/directivity data. This paper emphasizes the practical aspects and problems encountered in development of the system's hardware and software.

14. "Direct Low-Frequency Driver Synthesis from System Specifications," J. Audio Eng. Soc., (Nov. 1982).

The usual procedure for direct-radiator low-frequency loudspeaker system design leads to the calculation of the driver's fundamental electromechanical parameters by an intermediate specification of the Thiele-Small parameters. A reformulation of the synthesis procedure to eliminate the intermediate Thiele-Small calculation leads to a set of equations that yield the driver's electromechanical parameters directly from the system specifications. These equations reveal some moderately surprising relationships when the different system types (closed box, fourth-order vented box, and sixth-order vented box) are compared. For example, for a specified low-frequency cutoff f(3), midband efficiency, and driver size the fourth-order vented-box driver is found to be roughly three times more expensive (judged on the amount of magnet energy required) than the closed-box driver. Conversely for a given f(3), enclosure volume V(B), maximum diaphragm excursion X(max), and acoustic power output P(AR) the fourth-order vented-box driver is some five times cheaper than the closed-box driver. It is also found that for direct-radiator systems in general, specified f(3), V(B), X(max), and P(AR) lead to the total moving mass M(MS) depending inversely on the sixth power of the cutoff frequency, that is, a one-third-octave reduction in f(3) results in a fourfold increase in mass. Furthermore, the same conditions reveal that the sixth-order vented-box driver moving mass is some 42 times lighter than that of the closed-box driver, providing the same midband acoustic output and f(3). If cone area and efficiency are held constant, the direct-radiator system driver actually gets less expensive as the low-frequency limit is extended.

15. "Improvements in Monitor Loudspeaker Systems," J. Audio Eng. Soc., (June 1983).

As the recording industry enjoys the benefits of both digital and advanced analog recording technology, attention is appropriately focused on the use of compression driver and horn designs which are some 25-30 years old. Evolutionary improvements in woofers, compression drivers, and dividing networks combined with new constant-coverage horn designs have resulted in a frequency response more consistently uniform at all coverage angles (yielding flat power response) along with lowered distortion and increased acoustic power output at the frequency levels.

16. "A Microcomputer Program for Central Loudspeaker Array Design," Presented at the 74th Convention of the Audio Engineering Society, Preprint No. 2028, (Oct. 1983).

A microcomputer program is described which accurately calculates the direct-field SPL at points on a seating area generated by an arbitrary configuration of loudspeakers. The program solves inverse square losses as seen through the loudspeaker's directional pattern at up to 230 points on the searing plane. When multiple loudspeakers are used, their coverage patterns are merged by two strategies: phasor summation takes into account interference phenomena, while non-phasor combination provides the maximum envelope of response that can be expected of the combination of loudspeakers. When acoustical data is provided, direct-to-reverberant ratios can be calculated, and estimates of intelligibility, using the method of Peutz, can be made. A graphics portion of the program provides front, side, and top orthographic views of the loudspeaker array.

17. "A Loudspeaker Horn That Covers a Flat Rectangular Area from an Oblique Angle," Presented at the 74th Convention of the Audio Engineering Society, Preprint No. 2052 (D-7), (Oct. 1983).

A constant-directivity defined-coverage loudspeaker horn that approximately covers a flat rectangular area from an oblique angle is described. The horn compensates roughly for the inverse rolloff of sound pressure in the forward-backward direction by varying the horizontal coverage as a function of the elevation angle. The horizontal coverage angle of the horn at the 6-db-down points at each elevation angle is matched to the required horizontal angle of the rectangular area as seen by the horn. Measurements on a prototype horn which covers a two by three unit area from a point one unit above the center of the narrow end are shown. This horn roughly covers a 70-deg vertical angle with the horizontal coverage smoothly changing from 90 deg at 0-deg elevation (straight down) to 38 deg at 70-deg elevation.

18. "The Effects of Interaural Crosstalk on Stereo Reproduction and Minimizing Interaural Crosstalk in Nearfield Monitoring by the Use of a Physical Barrier," Presented at the 81st Convention of the Audio Engineering Society, (Nov. 1986).

A study of the effects of interaural crosstalk on normal spaced-speaker stereo listening environments is presented. Interaural crosstalk detrimentally affects both imaging and frequency response. Imaging is affected by restriction of the sound stage to between the speakers and by the loss of realism and preciseness of the sonic images. Interaural crosstalk also creates very severe comb filtering in the frequency response of the direct sound field in which the listener's ears are placed. Furthermore, the amplitude and frequency characteristics of the response comb filtering are found to depend heavily on the positions of the panned images, and are at their worst for a centered image. The interaural crosstalk signal can be thought of as a high level early reflection coming from the direction of the opposite speaker, but whose timing and amplitude depend on the signal in the opposite channel. Current studio monitoring design techniques tend to accentuate the problems of interaural crosstalk. Preliminary psychoacoustic test results of a simple method to minimize the effects of interaural crosstalk in a nearfield stereo/binaural loudspeaker monitoring setup are described. The results show accurate horizontal imaging and localization over a 120° frontal angle for both intensity-difference and delay-difference stereo program material. The method depends on the use of a flat vertical boundary erected between two front-positioned, side-by-side nearfield monitor loudspeakers. The listener is situated facing the monitors with his/her ears on opposite sides of the boundary. Advantages include: independent control of amplitude, phase, and delay at each ear; solid frontal out-of-head imaging for side-to-side head shifts and head rotations; extremely good center image; creation of realistic lateral beyond-the-speaker acoustic images; minimization of crosstalk frequency-response comb-filtering effects; and excellent results with both stereo and binaural program material.

Part 1: Preprint No. 2420-A (B-10)
Part 2: Preprint No. 2420-B (B-10)

19. "Speech Intelligibility Measurements Using TEF Analysis," Presented at the 113th Meeting of the Acoustical Society of America, Paper T5, (May 1987).

Recent investigations into the measurement of speech intelligibility using large listener groups (three groups of 30 each) in a cathedral, a concert hall, and a classic motion picture theater of the early 1930s suggest that a listener's subjective intelligibility score will be best matched in objective testing by dividing the sound considered to be direct sound from sound considered to be reverberant sound at the highest level return within the first 50 ms. This, in a majority of cases, results in using only the first arrival and no integration of early sound. Evidence will be presented that indicates that the use of impulse squared measurements that fail to process the signal as a complex analytic signal often fail to properly record major reflective signals unless extensive spatial averaging is resorted to. The paper will be supported by actual postprocessing of data taken with a Techron TEF analyzer using the Heyser technique for energy time curve measurement. In such measurements, minor movements of the microphone dramatically affect the impulse and doublet responses while the same change barely affects the energy time curve measurement, thus demonstrating the need for the complex analytic signal in such analysis.

20. "Evaluation of Room Speech Transmission Index and Modulation Transfer Function by the Use of Time Delay Spectrometry," Presented at the Audio Engineering Society 6th International Conference, Preprint 2.E, (May 1988).

The literature shows that the modulation transfer function (MTF) and speech transmission index (STI) can be computed from the squared impulse response of a linear passive system. This paper describes an extension of this method to measurements of systems using time delay spectrometry (TDS). The new method makes use of both the real and imaginary parts of the complex analytic impulse response of the system (the energy-time response). This allows more accurate determination of STI and MTF because the calculations are based on measurements that more closely follow the true energy decay in the room.

21. "Effective Performance of Bessel Arrays," J. Audio Eng. Soc., (October 1990).

The Bessel array is a configuration of five, seven, or nine identical loudspeakers in an equal-spaced line array that provides the same overall polar pattern as a single loudspeaker of the array. The results of a computer simulation are described, which uses point sources to determine the effective operating frequency range, working distance, efficiency, power handling, maximum acoustic output, efficiency-bandwidth product, and power-bandwidth product of the array. The various Bessel configurations are compared to one-, two-, and five-source equal-spaced equal-level equal-polarity line arrays. As compared to a single source, a five source Bessel array is 14% (0.6dB) more efficient, can handle 3.5 (+5.4dB) more power, and has 4 times (+6dB) the maximum midband acoustic output power, and is usable for omnidirectional radiation up to the frequency where the overall length is 11 wavelengths long. As compared to a two-source equal-level in-phase array, a five-source Bessel array is 43% (2.4dB) less efficient, can handle 1.75 (+2.4dB) more power, has the same maximum midband acoustic output power, and is usable for omnidirectional radiation 10 times higher in frequency. A working distance of 20 times the length of the Bessel array was assumed, with the length of the Bessel array (center-to-center distance of outside sources) being four times that of the two-source array. Analysis reveals that the three Bessel arrays have equal maximum acoustic output, but that the five-element Bessel array has the highest efficiency and power-bandwidth product. The seven- and nine-source Bessel arrays are found to be effectively unusable, as compared to the five-source array, due to much lower efficiency, requirement for more sources, and poor high-frequency performance. Judging polar peak-to-peak ripple and high-frequency response, the performance of the Bessel array is found to improve in direct proportion to the working distance away from the array. Unfortunately the phase versus direction and phase versus frequency characteristics of the Bessel array are very nonlinear and make it difficult to use with other sources.

22. "Measurement of Polarity in Band-Limited Systems," Presented at the 91st Convention of the Audio Engineering Society, Preprint No. 3168 (K-2), (Oct. 1991).

Polarity is usually measured by energizing the system under test with a wide-band asymmetrical test stimulus, such as a raised cosine pulse, and then observing the system's output on an oscillioscope. For a well-behaved flat-response minimum-phase system, such as an electronic device, the polarity determination is straightforward. However, for a general band-limited non-minimum-phase system with non-flat frequency response, such as a loudspeaker, the policy assessment can be quite difficult due to waveform distortion. A measurement method is presented that uses a narrow-band asymmetrical Hann-windowed tone burst, along with synchronous detection, to evaluate polarity at many points across a desired bandwidth. For a general system evaluated with tone bursts over a narrow frequency range, polarity is not just a simple two-valued function, but a continuum of values over the range of +/- 180 degrees, that varies with frequency. A preliminary theory is presented that allows prediction of the tone-burst phase, and hence time-constrained narrow-band polarity (herein called polarity phase), from the systems's conventional steady-state sinusoidal phase and group-delay responses.

23. "Maximum Efficiency Of Direct-Radiator Loudspeakers," Presented at the 91st Convention of the Audio Engineering Society, Preprint No. 3193 (G-3), (Oct. 1991).

The Thiele/Small method of low frequency direct-radiator loudspeaker system analysis neglects the radiation impedance components in the equivalent electric network model. When these components are included some surprising results are evident. Due to the definition of efficiency widely used in direct-radiator loudspeaker analysis, the absolute maximum efficiency is limited to 25%. With voice-coil inductance neglected, inclusion of the radiation impedance components transform all responses from high-pass into band-pass functions. Fow low frequencies, the maximum achievable nominal power transfer efficiency is found to be proportional to cone diameter. For a specific diameter, the maximum efficiency depends only on the moving mass to air-load mass ratio. Relationships and graphs are presented which relate the true nominal power-transfer efficiency to the Thiele/Small derived efficiency.

24. "Loudspeaker Production Testing Using the Techron TEF System 20 TDS Analyzer and Host PC," Presented at the 11th International Conference of the Audio Engineering Society, Paper No. 11-032, (May 1992).

A comprehensive system for doing production testing of loudspeakers and systems is described. Multiple TEF analyzers can be controlled by a single host computer to create elaborate test environments. The software allows the test engineer to orchestrate very complex test sequences while simultaneously minimizing the perceived complexity of the system as viewed by the test operator. Tests that can be incorporated in the test sequence, with pass/fail window parameters, include any or all of the following (in any order): frequency response, phase response (polarity), harmonic tracking, harmonic distortion (of specific harmonics), THD, THD and noise, spectrum analysis (FFT), and impedance. Options include the capability to completely store all the raw data from a test run for after-the-fact review and analysis.

25. "The Analytic Impulse and the Energy-Time Curve: The Debate Continues," Presented at the 93rd Convention of the Audio Engineering Society, Preprint No. 3399 (I-5), (Oct. 1992).

The analytic impulse is used as a complex-excitation signal to produce the energy-time curve (ETC) of a system. The ETC, usually displayed on a wide-dynamic-range log scale, is the envelope of the system's impulse response and is loosely related to the energy decay in the system. Additional information is presented, using heuristic arguments and simulations, to show that: 1) The ETC is acausal in the same sense that the time response of a theoretical zero-phase filter is acausal; 2) a time-derivative-based complex-excitation signal (rather than Hilbert-transform-based signal) does not work to extract the envelope of a system's impulse response; and 3) even though the ETC is a good general approximation of the energy decay in a system, it does not predict details of the decay such as exact timing and roll-off behavior. The intent here is not to present any radical new information in this debate, but to explain and clarify some of the concepts.

26. "Anechoic Chamber Walls: Should They Be Resistive or Reactive at Low Frequencies?," Presented at the 94th Convention of the Audio Engineering Society, Preprint No. 3572 (G2-2), (Mar. 1992).

The theoretical design and the preliminary practical implementation issues of an anechoic chamber designed specifically for spherical-wave propagation are described. Conventional anechoic chamber design methods dictate that the acoustic impedance of the chamber's boundaries should be purely resistive (complete absorption) over the whole operational range of the chamber. For good loudspeaker measurements at low frequencies, this means large chambers and long absorptive wedges. Theory suggests that a relatively small spherically shaped chamber, with the source constrained to the center of the sphere, could be designed that operates down to any arbitrary frequency, if the chamber walls are mass reactive at lower frequencies where the wavelengths are much larger than the chamber dimensions, and absorptive at higher frequencies where the wavelengths are much shorter than the chamber dimensions. A first-order mechanical model of the wall impedance is a massless plate for the sound waves to impinge upon, connected to a free-standing mass through a damper. At low frequencies the whole assembly moves, thus presenting a mass reactance to the wave, while at high frequencies the mass would be essentially immobile, and thus energy would be absorbed by the damper. The crossover point between the two modes of operation occurs at the frequency where the wavelength is equal to the circumference of the sphere, or equivalently, the radius of the sphere is about one-sixth wavelength. Derivations show that the total movable mass of the chamber's walls should be exactly three times the mass of the air contained in the sphere. These ideas are explored.

27. "Log Sampling in Time and Frequency: Preliminary Theory and Application," Presented at the 97th Convention of the Audio Engineering Society, Preprint No. 3935 (K-1), (Nov. 1994).

The impulse response of real-world physical systems decays faster at high frequencies than low frequencies. This is due to the approximately constant Q behavior of the resonators that often make up these systems. Considerable efficiency can be obtained in digitizing, storing, and manipulating impulse-response data that has been sampled at a rate that starts high initially, and then falls inversely with time. This paper explores the concept, and develops an efficient log-log time-frequency transform that converts back and forth directly between log-spaced time samples and log-spaced frequency samples. A very efficient FIR convolver/equalizer configuration with logarithmically spaced time taps is described.

28. "Time-Frequency Display of Electro-Acoustic Data Using Cycle-Octave Wavelet Transforms," presented at the 99th Convention of the Audio Engineering Society, New York (Oct. 1995).

A cycle-octave time-frequency display is created by plotting the magnitude of the wavelet transform, using a Morlet complex Gaussian wavelet on a log-frequency scale versus time in number of cycles of the wavelet's center frequency. This type of display is quite well suited to plotting the decay response of wide-band systems, such as the impulse response of a loudspeaker, because the time scale is long at low frequencies and short at high frequencies. If the response of typical filters is plotted on this display, the resultant 3-D responses are independent of the filter's center frequency, i.e., the decay response shape of a particular filter remains the same as its center frequency is shifted up and down in log frequency.

29. "The Application of Broadband Constant Beamwidth Transducer (CBT) Theory to Loudspeaker Arrays," presented at the 109th Convention of the Audio Engineering Society, Los Angeles (Sept. 2000).

A brief tutorial review of Constant Beamwidth Theory (CBT), as first developed by the military for underwater transducers (JASA, 1978 July and 1983 June), is described. In this paper the transducer is a circular spherical cap of arbitrary half-angle with Legendre function shading. This provides a constant beam pattern and directivity with extremely low side lobes for all frequencies above a certain cutoff frequency. This paper extends the theory by simulation to discrete-source loudspeaker arrays, including: 1) circular wedge line arrays of arbitrary sector angle, which provide controlled coverage in one plane only; 2) circular spherical caps of arbitrary half-angle, which provide controlled axially symmetric coverage; and 3) elliptical toroidal caps, which provide controlled coverage for arbitrary and independent vertical and horizontal angles.

30. "Development of Test Signals for the EIA-426-B Loudspeaker Power Rating Compact Disk," presented at the 111th Convention of the Audio Engineering Society, New York (Sept. 2001).

The EIA-426-B standard: "Loudspeakers, Optimum Amplifier Power" (April 1998) specifies a test CD that contains the calibration and test signals for all the tests defined in the standard. This CD is intended to improve the consistency and convenience of the standard and will be made available through the EIA and other sources. This paper describes the development process of the signals placed on the CD with emphasis on the spectral-shaped random noise signal used for life testing and the variable-rate sine-wave sweep test signal used for power compression tests. All signals were generated analytically using a signal processing and data analysis program. In the process of creating the signals, a couple of errors were detected in the standard in its description of the method for generating the variable-rate sweep signal. The paper also develops the math for generating variable-rate sweeps whose spectrums roll-off at an arbitrary given rate. Complete statistics and measurements are described for the signals as placed on the CD and for the signals as played back on a typical CD player. Also described are a series of 6.5-cycle shaped tone bursts that are included on the CD. These are intended for use as a test stimulus for short-term power assessment of loudspeakers and electronics, and for testing the frequency response, energy decay and narrow-band phase/polarity of systems.

31. "Suspension Bounce as a Distortion Mechanism in Loudspeakers with a Progressive Stiffness," presented at the 112th Convention of the Audio Engineering Society, Munich (May 2002).

The stiffness of a progressive suspension is fairly constant for small excursions and then gets progressively stiffer for larger excursions. When the moving assembly enters the region of increasing stiffness, forces are generated that rapidly reverse its motion much the same as when a bouncing ball hits the ground. Contrary to the common wisdom that predicts a squared-off displacement waveform, the bouncing-ball analogy predicts that the displacement waveform will be turned into a triangle wave. Under some conditions, the moving assembly will repetitively bounce at a frequency tens of times higher than the excitation frequency with acoustic output that exhibits high-level harmonics several times higher in amplitude and frequency than the fundamental. Time-domain simulations and experiments are presented to illustrate the effects.

32. "Implementation of Straight-Line and Flat-Panel Constant Beamwidth Transducer (CBT) Loudspeaker Arrays Using Signal Delays," presented at the 113th Convention of the Audio Engineering Society, Los Angeles (Oct. 2002).

Conventional CBT arrays require a driver configuration that conforms to either a spherical-cap curved surface or a circular arc. CBT arrays can also be implemented in flat-panel or straight-line array configurations using signal delays and Legendre function shading of the driver amplitudes. Conventional CBT arrays do not require any signal processing except for simple frequency-independent shifts in loudspeaker level. However, the signal processing for the delay-derived CBT configurations, although more complex, is still frequency independent. This is in contrast with conventional constant-beamwidth flat-panel and straight-line designs which require strongly frequency-dependent signal processing. Additionally, the power response roll-off of the delay-derived CBT arrays is one half the roll-off rate of the conventional designs, i.e., 3- or 6-dB/octave (line or flat) for the CBT array versus 6- or 12-dB/octave for the conventional designs.

33. "The Full-Sphere Sound Field of Constant Beamwidth Transducer (CBT) Loudspeaker Line Arrays," J. Audio Eng. Soc., (July/August 2003).

The full-sphere sound radiation pattern of the CBT circular-wedge curved-line loudspeaker array exhibits a 3D petal-shaped sound radiation pattern that stays surprisingly uniform with frequency. Oriented vertically, it not only exhibits the expected uniform control of vertical coverage but also provides significant coverage control horizontally. The horizontal control is provided by a vertical coverage that smoothly decreases as a function of the horizontal off-axis angle and reaches a minimum at right angles to the primary listening axis. This is in contrast to a straight-line array that exhibits a 3D sound field that is axially symmetric about its vertical axis and exhibits only minimal directivity in the horizontal plane due to the inherent directional characteristics of each of the sources that make up the array.

34. "Practical Implementation of Constant Beamwidth Transducer (CBT) Loudspeaker Circular-Arc Line Arrays," presented at the 115th Convention of the Audio Engineering Society, New York (Oct. 2003).

To maintain constant beamwidth behavior, CBT circular-arc loudspeaker line arrays require that the individual transducer drive levels be set according to a continuous Legendre shading function. This shading gradually tapers the drive levels from maximum at the center of the array to zero at the outside edges of the array. This paper considers approximations to the Legendre shading that both discretize the levels and truncate the extent of the shading so that practical CBT arrays can be implemented. It was determined by simulation that a 3-dB stepped approximation to the shading maintained out to '12 dB did not significantly alter the excellent vertical pattern control of the CBT line array. Very encouraging experimental measurements were exhibited by a pair of passively-shaded prototype CBT arrays using miniature wide-band transducers.

35 "Comparison of Direct-Radiator Loudspeaker System Nominal Power Efficiency vs. True Efficiency with High-Bl Drivers," presented at the 115th Convention of the Audio Engineering Society, New York (Oct. 2003).

Recently Vanderkooy et al. [1, 2] considered the effect on amplifier loading of dramatically increasing the Bl force factor of a loudspeaker driver mounted in a sealed-box enclosure. They concluded that high Bl was a decided advantage in raising the overall efficiency of the amplifier-speaker combination particularly when a class-D switching-mode amplifier was used. When the Bl factor of a driver is raised dramatically, the input impedance magnitude also rises dramatically while the impedance phase essentially approaches a purely reactive condition of ±90° over a wide bandwidth centered at resonance. This is an optimum load for a class-D amplifier, they note, which not only can supply power, but can also efficiently absorb, store, and return power to the speaker. Unfortunately, the system designed with a high-Bl driver requires significant low-frequency equalization and increased voltage swing from the amplifier as compared to systems using typical much-lower values of Bl. This paper considers the effect on the driver's efficiency of raising the driver's Bl factor through a series of Spice simulations. The nominal power transfer efficiency defined in traditional loudspeaker design methods is contrasted with true efficiency, i.e. true acoustic power output divided by true electrical power input. Increasing Bl dramatically increases the driver's true efficiency at all frequencies but radically decreases nominal power efficiency in the bass range. Traditional design methods based on nominal power transfer efficiency disguise the very-beneficial effects of dramatically raising the driver's Bl product.

36. "Maximum Efficiency of Compression Drivers," presented at the 117th Convention of the Audio Engineering Society, San Francisco (Oct. 2004).

Small-signal calculations show that the maximum nominal efficiency of a horn loudspeaker compression driver is 50% and the maximum true efficiency is 100%. Maximum efficiency occurs at the driver's resonance frequency. In the absence of driver mechanical losses, the maximum nominal efficiency occurs when the reflected acoustic load resistance equals the driver 's voice-coil resistance and the maximum true efficiency occurs when the reflected acoustic load resistance is much higher that the driver’s voice-coil resistance. To maximize the driver 's broad-band true efficiency, the Bl force factor must be increased as much as possible, while jointly reducing moving mass, voice-coil inductance, mechanical losses, and front airchamber volume. Higher compression ratios will raise high-frequency efficiency but may decrease mid-band efficiency. This paper will explore in detail the efficiency and design implications of both the nominal and true efficiency relationships including gain-bandwidth tradeoffs.

37. "Interpolating Linear- and Log-Sampled FIR Filtering and Convolution," presented at the 117th Convention of the Audio Engineering Society, San Francisco (Oct. 2004).

his paper describes a class of FIR filter/convolvers based on interpolation that allow sparse specification of the filter’s impulse-response waveform or equivalently its frequency spectrum in both linear-and log-spaced domains. Interpolation allows the filter 's impulse response or frequency response to be specified in significantly fewer samples. This is turn means that farless filter taps are required. Linear-and log-sampled interpolating filter/convolvers can further be categorized into two types: Type 1, interpolation in time, and Type 2, interpolation in frequency. Type 1 provides direct specification of the filter’s impulse response in linear or log time, while Type 2 allows direct specification of the complex (real-imaginary) frequency response of the filter in linear or log frequency. Each form of filter vastly reduces the number of filter taps but greatly increases the processing complexity at each tap. Efficient implementations of the log-spaced filter-convolvers are presented which use multiple asynchronous sample-rate converters. This paper is a continuation of the author 's" Log Sampling "paper presented to the AES in Nov. 1994. This paper represents work in progress with a conceptual description of the convolution technique with minimal mathematical development.

38. "Ground-Plane Constant Beamwidth Transducer (CBT) Loudspeaker Circular-Arc Line Arrays," presented at the 119th Convention of the Audio Engineering Society, New York (Oct. 2005).

This paper describes a design variation of the CBT loudspeaker line array that is intended to operate very close to a planar reflecting surface. The original free-standing CBT array is halved lengthwise and then positioned close to a flat surface so that acoustic reflections essentially recreate the missing half of the array. This halved array can then be doubled in size which forms an array which is double the height of the original array. When compared to the original free-standing array, the ground-plane CBT array provides several advantages including: 1. elimination of detrimental floor reflections, 2. doubles array height, 3. doubles array sensitivity, 4. doubles array maximum SPL capability, 5. extends vertical beamwidth control down an octave, and 6. minimizes near-far variation of SPL. This paper explores these characteristics through sound-field simulations and over-the-ground-plane measurements of three systems: 1. a conventional two-way compact monitor, 2. an experimental un-shaded straight-line array, and 3. an experimental CBT Legendre-shaded circular-arc curved-line array.

39. “An Important Aspect of Underhung Voice-Coils: A Technical Tribute to Ray Newman.” presented at the 121th Convention of the Audio Engineering Society, San Francisco, (Oct. 2006).

In the 1970s, Ray Newman while at Electro-Voice, single handedly and very successfully promoted the use of the then new concept of the Thiele/Small parameters and related design techniques for categorizing loudspeakers and systems to the loudspeaker industry. This paper posthumously recounts the contents of three significant Electro-Voice memos written in 1992 by Ray Newman concerning a comparison of overhung versus underhung loudspeaker motor assemblies. The information in the memos is still very relevant today. He proposed a comparison between the two assembly types assuming motors that had the: 1. same Xmax, 2. same efficiency, 3. similar thermal behavior, and 4. same voice coil. He calculated the required magnetic gap energy and discovered to his surprise that the magnet requirements actually went down dramatically when switching from an overhung to an underhung structure and depended only on the ratio between Xmax and the voice-coil length. This is in contrast with “common sense” that dictates that longer gaps mean larger magnets. He showed that for high-excursion motors, a switch could be made from a ferrite overhung structure to an equivalent high-energy neodymium underhung structure with little cost penalty. This paper recounts this early work and then presents motor predictions using present-day magnetic FEM simulators illustrating his concepts. Ray’s original memos and notes will also be included as an appendix to the paper.

a. Preprint No. 6911.
b. Addendum: handed out at the presentation but not preprinted.

40. “High-Accuracy Full-Sphere Electro Acoustic Polar Measurements at High Frequencies using the HELS Method”, presented at the 121th Convention of the Audio Engineering Society, San Francisco, Preprint No. 6881, (Oct. 2006).

Traditionally, high-accuracy full-sphere polar measurements require dense sampling of the sound field at very-fine angular increments, particularly at high frequencies. The proposed HELS (Helmholtz Equation Least Squares) method allows this restriction to be relaxed significantly. Using this method, far fewer sampling points are needed for full and accurate reconstruction of the radiated sound field. Depending on the required accuracy, sound fields can be reconstructed using only 10 to 20% of the number of sampling points required by conventional techniques. The HELS method allows accurate reconstruction even for sample spacing that violates the Nyquist spatial sampling rate in certain directions. This paper examines the convergence of HELS solutions via theory and simulation for reconstruction of the acoustic radiation patterns generated by a rectangular plate mounted on an infinite rigid flat baffle. In particular, the impact of the numbers of expansion terms and measurement points as well as errors imbedded in the input data on the resultant accuracy of reconstruction is analyzed.

41. “Comments on Smart Digital Loudspeaker Arrays,” Letters to the Editor, J. Audio Eng. Soc., vol. 54, no. 12, pp. 1203-1214 (December 2006).

I read with much interest Malcolm Hawksford’s above
paper1 on the design and implementation of what he terms
“micro drive unit” loudspeaker arrays, which provide constant-
beamwidth sound radiation. The paper’s FIR-filterbased
design procedure for the driver transfer functions
was very useful and informative, particularly given that
the array can be designed to provide multiple beams of
arbitrary size and direction. However, he analyzed only
one type of array and did not provide any references to
past work concerning the design of line arrays that provide
broad-band constant-beamwidth radiation. No mention
was made of other design methods [1]–[3] or other array
types such as log arrays [4] or the so-called “constantbeamwidth
transducer” (CBT) arrays [5]–[11], both of
which provide wide-band constant-beamwidth acoustic

42. “Application of Linear-Phase Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers,” presented at the AES 32nd International Conference, Hillerød, Denmark (September 2007).

Various methods exist for crossing over multi-way loudspeaker systems. These methods include those loosely classified as Linkwitz-Riley filters, constant-voltage filters, and D’Appolito configurations. All these methods do not provide broad-band constant-beamwidth or constant-directivity operation because their vertical radiation patterns change shape as a function of frequency. This paper describes a simple, non-iterative linear-phase crossover filter design technique that provides uniform frequency responses vertically off-axis for a given multi-way loudspeaker. Distances between the individual drivers, and desired off-axis attenuation are prescribed as input parameters for the design process, the outcome of which is a set of crossover frequencies and unique filter frequency responses in each band. In order to obtain wide-band constant-beamwidth, a loudspeaker array configuration composed of a single central tweeter surrounded symmetrically by pairs of lower-operating-frequency transducers arranged in a vertical line is required. Practical implementation issues are outlined in the paper by means of various design examples. Two design methods are presented in two-parts: Part 1: a general method which emphasizes flatness of arbitrary off-axis frequency responses and Part 2: a simplified method that emphasizes frequency uniformity of beam shape and coverage angle (vertical beamwidth) of the polar patterns.

a. “Part 1: Control of Off-Axis Frequency Response”
b. “Part 2: Control of Beamwidth and Polar Shape”

43. “A Performance Ranking of Seven Different Types of Loudspeaker Line Arrays,” presented at the 129th Convention of the Audio Engineering Society, San Francisco, Paper Number 8155, (November 2010).

Seven types of loudspeaker line arrays were ranked considering eight performance parameters including 1) Beamwidth uniformity, 2) Directivity uniformity, 3) Sound field uniformity, 4) Side lobe suppression, 5) Uniformity of polar response, 6) Smoothness of off-axis frequency response, 7) Sound pressure rolloff versus distance, and 8) Near-far polar pattern uniformity. Line arrays analyzed include: 1. Un-shaded straight-line array, 2. Hann-shaded straight-line array, 3. “J”-line array, 4. Spiral- or progressive-line array, 5. Un-shaded circular-arc array, 6. CBT circular-arc array, and 7.CBT delay-curved straight-line array. All arrays were analyzed assuming no extra drive signal processing other than frequency-independent shading. A weighted performance analysis yielded the following ranking from best to worse 6, 7, 5, 4, 3, 2, 1, with the CBT Legendre-shaded circular-arc array on top and the un-shaded straight-line array on the bottom.


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