JBL Technical Note - Vol.1, No.35 电路原理图.pdf

1 Technical Notes Volume 1, Number 35 CBT Constant Beamwidth TechnologyTM Introduction Column loudspeakers have become an important form factor for loudspeakers throughout the years. The tall and slender package fits nicely into a wide variety of architectural styles, and the columns provided performance characteristics that work nicely for certain application and room types. Recently, column speakers have become more popular than ever, and an even more important element in the sound designers toolbox for aesthetic reasons and the natural narrow vertical coverage. Large format line arrays have become increasingly common for large- scale sound reinforcement, and columns are a logical step-down in size from such line arrays. DSP technology and control interfaces have advanced to the point where powered column speakers having individual DSP processing for each driver and real-time remote control over the entire system is becoming economically feasible but still expensive. In addition, an appreciation of the importance of pattern control is expanding in the audio design community. This paper explains JBLs Constant Beamwidth TechnologyTM, which has been implemented in the CBT Series of non-powered line array column loudspeakers. These speakers solve many of the problems associated with traditional passive column speakers, as well as some issues present in powered columns, and in point-and-shoot loudspeakers. The end result is a line of affordable passive column speakers that provides constant directivity within narrow vertical coverage angles. They provide consistent frequency response regardless of distance or off-axis location within the listening zone, suppression of side lobes, switchable vertical coverage, asymmetrical vertical coverage for more uniform sound levels with in the room from front-to-back, and are practical for a wide variety of sound reinforcement projects. 2 History The use of an array of loudspeakers to increase directivity can be dated back to the early era of public address systems in the 1930s. Increased directivity has long been known to improve intelligibility of sound systems. In the late 1950s and early 1960s there was an explosion in the use of column line arrays1,2,3. Designers sought to control the directivity with configuration and filtering techniques on line arrays of multiple transducers. The traditional thinking was that the directivity is directly related to the size of the array. Therefore to keep the directivity constant the effective size of the array would need to change with frequency. In the early 1970s the first true constant directivity devices in the form of horns were introduced. While a great leap forward for point and shoot systems they yielded less than ideal coverage when used as components in large arrays and were limited in bandwidth. Early examples from Klepper and Steele1 and Novak2 show novel approaches for the time that include frequency tapering of the line and amplitude shading. The frequency shading attempts to use the outermost drivers to control directivity at the lowest frequencies and then moves the sound sources toward the center of the array as the response rises by low pass filtering the outer elements. This makes the apparent aperture or source size decrease with frequency which keeps the beam relatively constant in width with frequency. The authors of the early works acknowledged that the concept is challenged by the phase response of the filters which results in the sources not operating in phase at all frequencies, as would be desired, limiting the performance of the method. The idea is to make the effective size of the array a fixed ratio of the wavelength that it is producing. Figure 1. From Klepper and Steele1 shows a simple network for improving directivity control and Novak2 (on the right) shows more complex filtering 3 Klepper and Steele1 also show the value of amplitude shading (reducing the output at the ends of the array) in improving dispersion and reducing side lobes. Figure 2. From Klepper and Steele1, a novel passive approach to amplitude shading a line array with an absorbing medium. In the 1980s, as designers began to use computers and imagine the use of digital delay for beamforming, further refinement of line array beamwidth control was demonstrated. Augspurger and Brawley4 showed the computer modeling of a line array with delay and the use of a Bessel function for the amplitude shading. Figure 3. From Augspurger and Brawley4 showing that relatively even coverage off axis can be obtained with delay and that with the addition of Bessel shading very smooth off axis behavior can be obtained. 4 While the simulation does not show constant directivity (which would yield flat parallel off axis curves) the paper shows that delay arcing of the speakers and Bessel amplitude shading provides a very useful solution. This approach would pave the way for the CBT concept. Many analog approaches have been implemented over the years with limitations in performance. In recent years the method was improved upon by using zero phase shift digital FIR filters by Horbach and Keele5. They outline the expected performance of a log (driver spaced) array with new DSP filtering techniques. The system is very effective in controlling beamwidth. However this approach, like the earlier system, suffers from limited maximum high frequency output because the last octave is only being covered with two small drivers. Figure 4. Figures (15, 16, 17) from Horbach and Keele5, log array with zero phase shift Finite Impulse Response filters to achieve constant directivity. Straight line arrays without any frequency shading or amplitude shading have found favor in the marketplace for some time. The property that is most often claimed is that they create cylindrical waves. While a line source of infinite length will create cylindrical waves, finite size arrays only create wave fronts resembling cylindrical waves over a narrow region in space and frequency. The region is defined by the height of the array. Simple superposition models of straight line arrays with discrete radiation elements work quite well to show the actual behavior of real finite line arrays. While purporting to create a wedge of sound the array has a pattern than narrows constantly with frequency and is uneven. Additionally, the response changes with distance 5 Normalized off axis frequency Response of 16 driver 1m array flat at 25 feet on axis -30 -20 -10 0 10 10010000 Freq dB 2 4 6 Off axis response at 25 ft 2, 4 and 6 degrees off axis. Response changes radically within a very small forward beam. Normalized on axis frequency Response of 16 driver 1m array flat at 25 feet, versus distance -30 -20 -10 0 10 10010000 Freq dB 6 12 50 Figure 5. The simulated on and off axis behavior of a finite straight line array of 16 elements 1m tall and the response at 6, 12 and 50 feet normalized to flat at 25 feet. The one axis response changes with distance. The off axis response is very different even within a very narrow range (+/- 6 deg) and the primary forward beam gets extremely narrow at high frequencies. It is this narrowing that gives the array the sense that it is a laser beam of sound but in reality the beam is not constant in width or truly cylindrical. By examining the response and pattern at different points in space it can be seen that the array is different everywhere and in no way can purport to provide consistent sound within a defined wedge. The increasing high frequency output with distance (as the array becomes more coherent) is what gives the array the sense that it is projecting further and has a decrease with distance that is less than 6dB per doubling of distance. This is true at 6 higher frequencies but is different at every frequency. At lower frequencies (where the wavelength is large compared to the size of the array) the level drops at 6dB per doubling of distance. The speaker simply gets brighter with distance. At some point the response will no longer change (when the far field is reached) and then all frequencies will drop off at 6 db per doubling of distance. Additionally the wavefront will then become spherical, not cylindrical, independent of frequency. Straight line arrays of discrete sources will have severe side lobes. Figure 6. The measured vertical polar patterns from a popular straight line array of 1m in height with 12 discrete drivers. Side lobes can be seen as low as 800 Hz. The pattern continuously narrows with frequency and has clear lobes outside the main lobe. 7 Newer approaches, The CBT principle In 2000 Don Keele6 (the creator of JBLs BiRadial constant directivity horns) started writing about the concept of a constant beamwidth device made up of discreet transducers that were all spaced equally and driven with full bandwidth. The concept was nicknamed CBT for “constant beamwidth transducer”, but has taken on a broader meaning that JBL now refers to as Constant Beamwidth TechnologyTM. The idea is that a constant beamwidth array can be created by bending the array to a fixed arc and amplitude shading the drivers from inside to outside with a very specific mathematical expression (a Legendre function) that eliminates side lobes and creates a perfectly constant beamwidth that is 66% of the arc. In later publications Keele and Button7 showed that time delay could be used instead of physical arcing to create the effective curvature. The concept can be applied to very wide bandwidth and is only limited by the size of the array and the spacing of the drivers. Figure 7. Figures (80, 57) from Keele and Button7 showing that a constant beam width array can be achieved by delay curving (80) or physical arcing (57) and Legendre shading. The concepts, while simple, were a departure from the traditional approach of creating constant beamwidth by changing the apparent size of the sound source with frequency. 8 Figure 8. A virtual curved array can be achieved by bending it with time delay. The apparent point source is behind the array. Implementing similar concepts has been done by many engineers using discrete amplifier channels and DSP to create the time delay. This method, while effective, is expensive and complex. JBL has developed a Patent Pending method to mimic the performance of the digitally time delayed column array in a passive loudspeaker. The principal of operation starts with the premise that group delay that is flat with frequency is no different that digitally derived time delay. All passive reactive components have phase shift in degrees which can be expressed as group delay in time. The group delay of single passive components is not flat with frequency. However, networks of inductors and capacitors can be configured to have flat group delay over wide bandwidth. The drawback in many cases is that the group delay is very small. This turns out to be advantageous when developing the required delay to curve a straight line array. The amount of delay required between each successive driver is small especially if the drivers are small. In practice, digital-delay-derived CBTs require each delay line to be independently sent to each driver and the amount of delay must be quantized based on the sampling frequency. In a typical 48Khz system this is 20us in time or about 6mm distance. This limits the smoothness of the virtual curving of the array. In a passive CBT system the group delay can be tapped off at points along a ladder network. Each small amount of group delay between segments accumulates down the ladder. Because the amount of derived group delay is based on analog synthesis, and therefore continuously variable, the time quantization error is non existent. The CBT can also be thought of as a transmission line with delay and attenuation accumulating down the line. By appropriate design of the components in the group delay ladder network the right amount of delay to provide a smooth arc in time can be achieved. To complete the CBT principle the outward drivers must be amplitude shaded (attenuated) which is also realized through the network. Small amounts of delay and attenuation are accumulated down the network. 9 For the JBL CBTs a computer optimization was created to calculate the best component values for the network to achieve constant beamwidth. Figure 9. The passive CBT principle utilizing a ladder of passive components to create a delay line with increments of group delay to mimic the performance of a digital delay derived CBT array. The components chosen for a given arc can be changed to provide new arc if the pattern were required to change. 10 JBL introduces CBT passive line arrays CBT 50LA, CBT 100LA and CBT 70J. The new JBL CBT systems incorporate a Patent Pending passive group delay network that provides time arcing along with amplitude shading that provides performance rivaling the digitally derived solution. The CBTs act much like a large constant directivity horn in the vertical direction with similar pattern control. This results in very consistent coverage when used in the broad setting and resembles the control of a large point and shoot system. CBT 100LA Vertical beamwidth 10 100 1000 10010000 Frequency, Hz B eam w id th , d eg rees JBL 2360A BiRadial Vertical beamwidth 10 100 1000 10010000 Frequency, Hz B eam w id th , d eg rees Figure 10. The constant directivity capability of the CBT 100LA can be seen as compared to a large JBL BiRadial horn with even smoother and more consistent pattern control. The vertical pattern control of the CBT 100LA is nearly identical to the large cinema horn from the cinema industry standard JBL 4675. 11 Because the CBTs act more likes a constant directivity horn they have very consistent coverage off axis and with distance. Normalized off axis frequency response of CBT 100LA flat at 25 feet on axis -30 -20 -10 0 10 10010000 Freq dB 2 4 6 Off axis response at 25 ft 2, 4 and 6 degrees off axis. Unlike the straight