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.W:60 .L:60 .J:8 .H: ...Page $$$ .H: Loudspeaker Crossovers What They Should Do and How to Get Them To Do It 0. Abstract. Crossover network technology has undergone considerable change in the last 10 years. Since there are still a lot of loudspeaker systems built with what amount to be old fashioned crossovers, discussion of the "new" technology is seems to be in order. I. Tasks for the crossover network. Crossover networks must do at least three things to be at all effective. They are: route signals in different frequency ranges to different drivers, maintain desirable phase relationships between acoustical outputs of individual drivers, and compensate for differing driver efficiencies. If any of these requirements are not met, the over-all sound quality of the resulting loudspeaker system is likely to be severely compromised. Let's look at the requirements individually: Requirement 1. Route signals at in different frequency ranges to different loudspeaker drivers. Loudspeaker system quality is based on wide frequency response range, smooth response, small size, low distortion, good dynamic range, and low cost. To date, no single driver system has been developed that has all these characteristics. Systems composed of multiple drivers seem to come closer to the ideal, but they introduce the need for crossover networks to divide the input signal between drivers operating in two or more frequency ranges. The signal is divided between drivers operating in different frequency ranges, to avoid wasting amplifier power and to avoid feeding signals to drivers that may disrupt their operation. If significant power in a range of frequencies is absorbed by a driver that is not an efficient transducer in that frequency range, then the power is wasted. If a driver receives significant amounts of power in ranges where it has poor power handling capacity, then the driver's operation will be disrupted. Requirement 2. Maintain desired phase relationships between acoustical outputs of individual drivers. There are two reasons to try to maintain desired phase relationships between the acoustical output of the drivers: one that is obvious, but sonically irrelevant; and one that is not so obvious, and is important to sound quality. An obvious reason for maintaining desired phase relationships between the acoustic output of individual drivers is to control the over-all phase response of the loudspeaker system. Controlled listening tests have failed to show any reason to be interested in system phase response above 1 kHz. In addition, controlled tests that are presented as being positive for the audibility of phase response below 1 kHz relied on esoteric, non-musical signals, and still did not develop results with 99 percent confidence that they were not due to random guessing. Therefore, over-all system phase response is at best marginally related to listening quality. A less-obvious reason for maintaining desired phase response is to control system directivity through frequency ranges where two or more drivers have significant acoustic output. When there are two acoustical signals radiated from drivers into a common space, but one acoustical signal has lagging phase with respect to the other, the joint coverage pattern will be tilted toward the lagging driver. This situation causes dips in the on-axis frequency response vis-a-vis power response. It is therefore highly desirable to control the phase of the acoustic output of the various drivers to be in phase through the crossover regions. If two or more drivers have significant acoustical output at some frequency, the acoustic outputs should be, ideally, in phase. There are three sources of phase differences between drivers, which are the phase response of the drivers themselves, phase differences due to the relative positioning of the drivers, and phase differences due to the crossovers. Requirement 3. Compensate for differing driver efficiencies. It is not likely that drivers will have the same efficiency unless they are designed for use with each other. Woofers tend to be inefficient, while tweeters are relatively easy to make efficient. Most systems include some prevision, fixed, variable, or trimmable; for matching driver efficiencies. Because woofers usually demand a low source impedance, padding down the woofer to match the tweeter is almost never done. The converse is common. In addition, drivers tend to be a little non-uniform, and system performance may be optimized by adjustment of the completed system in the acoustical environment in which primary use takes place. B. Things that are nice to have done: When building complex systems, it is very helpful if one or more components in the system are able to accommodate the peculiarities of other components. Crossovers may have the potential to compensate for driver and/or enclosure deficiencies, facilitate use of cost-effective amplifiers, reduce "Up-front" design work, and reduce "Cut-and-try" elsewhere in the system. Accommodation 1: Compensate for driver and/or enclosure deficiencies. Many drivers have desirable characteristics such as good power handling capacity and smooth response, but lack other desirable characteristics such as flat frequency response. Crossover designs usually assume ideal driver response. However, it is often convenient to include equalization for driver characteristics "In the same box" as the crossover. A most common, but highly intractable enclosure fault is positioning of of drivers in ways that create significant phase shift. This situation is often described as: "mounting drivers with non-coincident acoustic centers". Often, it is difficult to position drivers ideally because doing so may create obstructions in the radiation pattern of other drivers in the system. Crossover designs usually assume ideal positioning of the drivers, but it is often convenient to include equalization for enclosure characteristics "In the same box" as the crossover. Accommodation 2: Facilitate use of cost-effective amplifiers. Power amplifier costs are often a non-linear function of their power output. In addition, there is a "Barrier" of sorts that makes amplifiers with power output much in excess of 400 watts per channel into 8 ohms much less common. Integrated circuits that would make power amplifiers more economical are currently limited in power to the 20-30 watt per channel range. Therefore, a crossover that permits use of amplifiers whose power rating allows them to be more cost effective can provide benefits that offset some of the crossover's cost. Individual loudspeaker drivers are not the easiest load for amplifiers to drive. Unfortunately, some crossover designs make the situation worse. In contrast, other designs help minimize amplifier quality requirements. Therefore, reducing power amplifier size and quality is a desirable, and possible accommodation of the crossover network. Accommodation 3: Reduce "Up-front" design work. Loudspeaker system design requires knowledge of a wide range of technologies, from the disciplines of both mechanical and electrical engineering, including both static and dynamic system analysis. Crossovers, as components, can reduce the span of technology required of the system designer, when they are pre-packaged solutions. However, poorly designed components can create more problems than they solve. Accommodation 4: Reduce "Cut-and-try" elsewhere in the system. If a crossover design makes over-all system performance less sensitive to parameters that are hard to control, then it reduces the need for final "tweeking". In addition, the crossover can include electrical adjustment capabilities that provide the same function as mechanical adjustments. For example, it is possible to electrically adjust the location of acoustic centers, by providing small amounts of time delay via all-pass filters. II. Alternative crossover designs. Historically there have been many alternative designs for crossovers that have been selected from. In some cases, it has been only recently that the full implications of certain choices has been understood. Alternative A: 6 dB/octave filters. The most common, and simplest possible crossovers are the 6 dB/octave filters. In the case of a woofer with carefully chosen voice coil inductance, and a piezoelectric tweeter, this type of crossover may be achieved with no additional electrical components. Filters of this variety spread the range of simultaneous operation of adjacent drivers over a wide range. In addition, there is a 90 degree phase shift between the electrical signal applied to the drivers at all frequencies. When combined with an additional 90 degree or more phase shift in the crossover region due to driver phase shift, a situation is created where best performance is often obtained when the drivers are wired out of phase. When it is desired to obtain a 6 dB/octave filter using passive crossover designs, care must be taken to ensure that variations in driver voice coil impedance do not significantly modify or totally wipe out the effect of the electrical components in the crossover. Alternative B: 12 dB/octave Butterworth filters. 12 dB Butterworth, or maximally-flat filters are the usual next step up in sophistication. Sometimes 12 dB octave low-end roll-offs can be obtained as inherent properties of the drivers. Some horn-loaded, or sealed box designs with their resonant frequency at the crossover frequency, and a Q near 1.414, result in an upper driver crossover with this characteristic. Similarly, by allowing the woofer voice coil to decouple from the diaphragm with appropriate mechanical Q, this characteristic is obtained in the low frequency side of the system without additional electrical components. Passive 12 dB octave designs will have twice as many components as 6 dB crossovers, and are also significantly affected by driver impedance characteristics. This is a nice way of saying that some passive "12 dB" designs are effectively "6dB" designs because they do not correct for driver impedance characteristics. The electrical outputs of the usual "Butterworth" 12 dB/octave crossovers are usually 180 degrees out-of phase. There is often an additional 90 or more degrees of phase shift due to the drivers. Thus there is a total of 270 to 360 degrees of phase shift between the acoustical outputs of the drivers. The flattest frequency response is usually obtained with the drivers wired in phase. 12 dB octave crossovers have reasonably narrow areas of overlap of adjacent drivers. They are used with horn-loaded tweeters to minimize distortion due to operation below the flare cut-off frequency. Alternative C. 18 dB/octave Butterworth filters. Crossovers with higher slopes than 12 dB/octave are almost always implemented actively. High slopes obtained with these crossovers do a good job of minimizing both the region of driver overlap and out-of band electrical input to the drivers. The electrical inputs to the drivers are approximately 270 degrees out-of phase. This is essentially a throw-back to the 6 dB/octave case, in terms of phase. When the drivers are connected out-of-phase, a degree of phase linearity is obtained in the summed response, were it not for the additional phase shift of the drivers. Alternative D. All-pass designs: All of the crossover designs described so far are minimum phase. This means that the phase characteristics of the summed response of high and low pass sections has a phase response that is related to amplitude response by the Hilbert transform. For those who are not totally conversant with calculus this year, minimum phase means that the if you equalize the frequency response to be perfectly flat at all frequencies, the phase response will also be perfectly equalized. Furthermore, the equalizer will be itself, minimum phase. Two points about minimum phase are important. First, drivers that do not operate in diaphragm break-up mode are often minimum phase, as are some drivers that do operate in break-up modes. Loudspeakers with whizzer cones are almost never minimum phase. Secondly, while common loudspeakers can be thought of being minimum phase, systems of two or more minimum phase loudspeakers are not often minimum phase because it is difficult for two loudspeaker drivers to perform as if they occupied the same space. Since the drivers are displaced from each other, there are time delay differences off-axis. Time delay is not a minimum phase effect. All-pass crossovers cannot be equalized to have both ideal frequency and phase response in the summed response with common minimum phase equalizers. This begs the question: "Does anybody hear the difference." The answer is: "Probably not." The most significant benefit of all-pass crossovers is that in many cases. it is possible to get the acoustical outputs of the lower and upper drivers to be in phase. All-pass crossovers are readily constructed by cascading two Butterworth filters. 1. 12 dB/Octave all pass crossovers are created by cascading two 6 dB/octave filters in such a way that they are electrically buffered from each other, and do not affect each others response through loading. The electrical outputs of the crossover are 180 degrees apart at all frequencies. If the drivers are wired out of phase, they will be in phase. As usual, driver phase response will affect the phase of the acoustical outputs. 2. 24 dB/Octave all pass crossovers are created by cascading two 12 dB octave filters in such a way that they do not affect each other's response. The electrical outputs of the crossover are 360 degrees at all frequencies, which is very similar to being in-phase. In addition, the sharp slopes minimize driver overlap, and avoid providing significant out-of band inputs to the drivers. The cascade of two 12 dB/octave filters can often be obtained using a combination of driver roll-off characteristics, which often have 12 dB/octave slopes, and a single 12 dB/octave electrical filter. Linkwitz of Hewlett-Packard described the desirable mathematical properties of 24 dB/Octave crossovers in 1976. His associate, Riley described their implementation in common Sallen and Key type op-amp filters at the same time. 3. Phase compensation of 3-way and up all-pass crossovers. Because of the residual phase shift of one crossover point, phase compensation is required to preserve desirable over-all phase characteristics of all-pass crossovers operating with more than two bands. As a practical matter, 3-way designs have marginal need for compensation, but frequency response variations of from 1 to 10 dB, or more will be caused by leaving phase compensation out of crossovers with from 4 or more bands. Phase compensation also depends on how the crossover is laid out. With three way crossovers the system can be built as three filters: a high pass filter, a low pass filter, and a band pass filter; or it can be composed of a low pass-high-pass filter pair, which has one output further divided by another filter pair. The latter is a "Tree" configuration, and is preferable to minimize the need for additional phase compensation. With more bands, several different lay outs are possible. D'Appolito pointed out that the ones that are shaped like trees have fewer parts and are easier to phase compensate than the ones that are laid out as a series of parallel band pass filters. As previously noted, some loudspeaker drivers have the same response as 12 dB octave electrical filters. Therefore, with some sacrifice in power-handling capacity, an acoustical 24 dB octave all-pass crossover can be obtained using a combination of electrical and mechanical 12 dB/octave filters From the standpoint of on-axis and off-axis frequency response, this is ideal, and reduces the cost of the crossover itself. E. Delay-derived filters. One way to minimize the parts in a crossover is to develop one filter characteristic by subtracting the output of one filter from its input. The elegance of this technique is upset by the fact that the output of the crossover that is derived by subtraction has a very gentle slope, often as gentle as 3 dB per octave. This situation has been mathematically analyzed by Lipshitz and Vanderkooy, who found that the gentle slope is due to a time delay inherent in a minimum phase filter. For example, a low pass filter with a corner frequency of 1 kHz has an approximate time delay of approximately 1 millisecond at all frequencies below 2 kHz. This makes it difficult to get total cancellation at the output of the subtraction circuit. One solution, totally obvious in retrospect, but requiring a lot of thought moving forward in time, is to delay the unfiltered path. Unfortunately, pure time delay is hard to achieve at this time. An unexpected result is that some forms of this filter have a linear phase characteristic in their summed response. For example, a filter utilizing a fifth-order Bessel filter, and appropriate time delay has almost as good off-axis response as a 24 dB octave all-pass design. The advantage is that the over-all summed electrical response is linear phase. There is some question whether this ideal mathematical characteristic has audible significance. Of course, implementing such a filter with good distortion characteristics will cost hundreds instead of tens of dollars per crossover point. F. Driver Frequency response correction. It is unlikely that anybody who does not actually manufacture drivers would be able to develop a collection of drivers with complementary response. Furthermore, doing so might involve considerable sacrifice of power handling capacity. In general, there are two approaches to this problem. One is to select drivers that are flat about an octave past the crossover point, and accept the resultant minimal phase shift. The other is to provide a minimum phase equalizer that provides the desired response. Zaustinsky suggests the use of selectively combined outputs of an state-variable filter to transform the acoustic response of many drivers to be one of the two required 12 dB/octave filters in a 24 dB octave all pass (Linkwitz-Riley) design. One advantage of this form of equalization is that it yields near-ideal inter-driver phase response. In some cases, bandpass filters with appropriately chosen center frequency and Q can give useful results. The designer need to be sensitive to the possibility that equalizing the response to be flat over a limited range does not cause excessive phase shift. Recall that equalizing drivers only yields flat phase response when amplitude response is flat at all frequencies. In practice, this means controlling amplitude response for several octaves outside the bandpass. III. Performance of alternatives: Now that the choices are laid out, what are the trade offs? The areas being considered here are frequency response on and off axis, ease of design, power handling capacity, and expense of implementation. A. Passive versus Active crossovers. Active filters are always the choice when price is no object. They allow the designer to largely ignore driver impedance characteristics. Active crossovers can be cost-effective in two cases. The price performance of power amplifiers is non-linear. Two or more small amplifiers that can be implemented by an inexpensive integrated circuit are more cost-effective than one amplifier built from discrete parts. The power ceiling for inexpensive integrated circuits is around 30 watts per channel at this time. At the opposite end of the spectrum, amplifiers that exceed the capacity of readily available discrete semiconductors are very expensive. At this time, the technology of high-power transistors is largely dictated by the most common applications: high frequency power supplies for computers and voice-coil drivers for high performance computer disk drives. This puts an effective ceiling in the range of 200 to 400 watts per channel. Higher powered amplifiers exist, but they tend to be less cost effective. Systems with power requirements outside this range are often more cost effective when implemented using active crossovers and multiple power amplifiers. In addition, active crossovers minimize amplifier quality requirements by reducing intermodulation distortion, and decreasing the possibility of excessive reactive loading. Finally, amplifier clipping in one frequency band can be partially masked by clean output in another band. B. Butterworth versus All-Pass crossovers. Whenever flat response on and off axis is desired, All-pass crossovers are the most desirable. Cost of crossover networks is more a function of ultimate slope than tuning. C. Delay-derived versus All-Pass. As the cost of high quality time delay decreases, delay-derived crossovers will be more practical for the mathematically inclined perfectionist. For all intents and purposes, time delay implies active crossover networks. There may be no reliably detectable subjective advantage to delay-derived crossovers when listening in most rooms using most commercially recorded program material. Even if there were a reliably detectable difference, preference may be hard to establish. D. Constant voltage versus Constant Power E. Time delay alternatives: Besides delay-derived crossovers, time delay is also useful for repositioning the acoustic location of a loudspeaker driver. Direct radiator tweeters tend to have the effective source of their acoustical output ("Acoustic Center") close to the mounting board. Cone woofers tend to have their acoustic centers some distance back from the mounting board. Stepping the tweeter back causes the woofer to block part of the radiation of the tweeter, which can be minimized, but is undesirable. An alternative, first suggested by Linkwitz, is to use time delay to position the acoustic centers of the woofer and tweeter in a plane parallel to the baffle board. Significant amounts of time delay dictate the use of active crossovers. 1. Digital Delay. The quality of digital delay can be raised to almost any desired level by simply spending more money. The majority of the cost lies in digitization of the analog signal. This cost can be avoided by using digital program material sources in digital form. Major problems remaining are the high cost of multiple digital to analog conversions and the need for a rather large number of ganged level controls (1 for each loudspeaker). 2. CCD delay. The quality of CCD delay is slowly improving, and may be almost good enough for top quality applications, providing the delay is shorter than 20 or 30 milliseconds. Loudspeaker applications are usually for less than 5 milliseconds. Cost is around $100 per frequency band. 3. Delay via all-pass filters. Bessel tuned all-pass filters provide inexpensive high quality delay when the product of highest frequency delayed accurately and time delay is small. A single op-amp can provide a highly accurate 10 microseconds of delay over the entire audio range, or 1 millisecond of delay good to 500 Hz. IV. Loudspeaker system construction. Crossover networks by themselves are not very exciting to listen to. It is only when they are used in conjunction with loudspeaker drivers that they become interesting. While the purpose of this paper is not to provide a complete guide to loudspeaker design, a few comments on loudspeaker design will be made. Loudspeaker systems are composed of crossovers, transducers or loudspeaker drivers, and enclosures. Evaluation techniques will also be touched on. A. Driver selection. While crossovers can help a good driver sound better, or at least allow it to develop its potential, they cannot create quality where there is none. 1. Direct radiators commonly having cone-shaped diaphragms in units designed for use at the lower frequencies, and dome shaped diaphragms for the high frequencies, can have good performance and relatively low cost. Specifications or low frequency drivers that are presented in terms of the well-known Thiel parameters are about the specifications for direct radiators that can be relied on because they are so easy to verify. Of the Thiel parameters, Qt, or total system Q is perhaps the most easily evaluated. Poor quality drivers usually have high Qt's, on the order of 0.5 or above. Good quality drivers usually have lower Qt's, on the order of 0.25 to 0.35. It is a good idea to use a computer program to design some trial enclosures, and verify the suitability of the driver for the application. Thiel parameters for low frequency drivers tend to be subject to sample-to-sample variations, and ideally are measured individually, as a guide to tuning. In general, specifications for mid and high frequency direct radiator drivers are not overly reliable. Measurements of driver response should be made with the driver mounted as it will be in the final application, particularly for midrange drivers. 2. Horn loaded drivers have been shunned by many picky listeners for some time, but have never been out of style in high quality public address systems and are regaining favor for all applications. At this time it is pretty well understood that the so-called "horn resonance" and poor quality sound was the result of using horns that were not designed for good power response. Constant directivity horns require equalization for flat response, and can be quite large, but afford unequalled control over the radiation pattern, and can be cost effective when total system cost, including power amplifiers, is considered. B. Enclosure Designs. Enclosures can subtly affect sound quality of loudspeaker systems. Obviously, the enclosure should be of an appropriate geometry to ensure adequate volume for the low frequency driver, and facilitate orientation of the radiation patterns of the upper drivers towards the listeners. Enclosures can subtly effect the sound when they affect the directivity of the drivers or have undesirable undamped resonances at spurious frequencies. 1. Conventional free-standing enclosures are usually built with a pressed wood core veneered with hardwood or thermoplastic laminate. Wave guides may be incorporated into the design of the front of the enclosure to control directivity. The edges of the enclosure are usually rounded to reduce diffraction, though pleasing sound is sometimes obtained by encouraging diffraction by placing the edges of the drivers near the edges of the enclosure. Since the drivers have decreasing dimensions, a "pyramid" shape results. 2. Built-in loudspeakers allow avoiding disruption of the listening room decor with large boxes. Some subwoofers can be placed in the floor, ceiling, or wall to utilize the structure of the building as their enclosure. Higher range drivers are not often installed this way because they are more critical of placement. 3. Esoteric enclosure designs include those made of concrete, sand between concentric cardboard tubes, etc. Good suppression of enclosure wall resonance can be obtained in this way. C. Evaluation techniques are important to any design effort, especially those involving loudspeakers. Obviously, the goal is subjectively perceived "Good sound", but subjective perceptions have limited reliability unless good experimental controls are used, in which case they are also very time consuming. A rule of thumb in carpentry is if you cut two boards to have equal length by eye, you can always see the errors by eye, while good quality measurements speed the process, often yielding results that are perceived as being essentially perfect. This is also true with loudspeaker construction. 1. Microphones have always been a stumbling block to loudspeaker construction, but recently miniature electret capsules with outstanding response over the entire range have come on the market for very low prices, often on the order of a few dollars. There is now no excuse for any loudspeaker constructor to not have one or more good measurement microphone(s) in his possession. The reliability of acoustic measurements is enhanced by using multiple microphones with separate rectification for each microphone prior to summation into a single measurement. 2. Ordinary audio oscillators are very inexpensive, and can give remarkably good results as long as measurements are not affected by standing waves in the room. This is usually true above 500 Hz. Results may be manually plotted when cost is an object, and time is available. 3. Swept oscillators and chart recorders can give good repeatable results at a much higher system cost than using normal audio oscillators, but the results are plotted automatically, and a wide range of tests can be performed in a brief period of time. 4. Pink noise sources include relatively inexpensive test sets, or even more inexpensive digital compact disks, such as marketed by Denon. Standing waves are less of a problem than when using audio oscillators, but integrating results over a period of several seconds is required to get reliable results below 200 Hz. 5. Coherent fractional octave sources have been described by Linkwitz and others. Their major advantages are: reduction in the amount of integration time required for reliable results, and a relatively pleasing sound. 6. Spectrum analyzers such as the ever-popular and highly effective one third octave real time analyzer are very effective, at a price. They often lack fractional dB resolution on their LED displays, but can be used with external CRT displays for greater accuracy. 6. Computerized techniques include the highly effective and expensive Time Energy Frequency (TEF) test set, at one extreme, combinations of third octave filter banks and personal computers in the other. A broad middle ground is filled by dedicated and personal computer FFT analyzers, where the trade off is low price versus fast response and good resolution. As the cost of computation and digital-to-analog conversion decreases, all known and future audio test instruments will be implemented using general purpose hardware and sophisticated software. V. Conclusions. A. Electronic crossovers are desirable for many reasons. These include: easy design, use of more cost-effective amplifiers, greater flexibility in possibilities for compensating for driver and enclosure characteristics, and ease of final set-up. B. Best price-performance in crossovers is obtained with 24 dB/octave acoustical all-pass. There is only one alternative that has the possibility of "Better" performance, the delay-derived design, and it is prohibitively expensive and has benefits of marginal audible significance at this time. There is a possiblity that program material, driver, and listening room characteristics along with implementation cost cuts will change this situation within a decade. C. It is important to know actual driver characteristics. Optimizing the performance of the combination of the crossover and the drivers is the goal, and this goal cannot be achieved by knowing only the characteristic of the crossover. While useful woofer characteristics can be determined from specification sheets, this is not the general situation for midrange and tweeters. D. Relatively sophisticated acoustic measurements are possible at a reasonable cost. The major stumblig block has been obtaining sophisticated, reliable signal sources and microphones. Compact discs with sophisticated test signals recorded on them are becoming availible, and are quite reliable. Small, inexpensive, electret microphones costing a few dollars provide omnidrectional response that is flat with one or two dB's from 20 Hz to 20 kHz. Small general-purpose computers are capable of inexpensive analysis of electrical signals. Their cost, and the cost of analog-to-digital conversion will continue to fall.