Dear Audio Enthusiast,
The field of crossover implementation is probably the most controversial area of loudspeaker design above all other factors. A seemingly endless number of research papers have been published on the subject and designers are usually well entrenched in their pet topology. In one regard, this is fine as it offers the end consumer an almost unlimited number of designs to choose from. On the other hand, depending on the popularity of a designer or just his or her market visibility, many consumers are mislead into the belief that a certain topology is inherently superior to all others. If a company’s products are well received by the marketplace and the designer is strongly and outspokenly committed to a certain topology, you can rest assured that many with a limited level of understanding and/or experience will elevate the designer’s opinion to the level of gospel.
Our purpose here is not to advocate one topology over another but rather, to help educate the consumer as to the choices and compromises which every designer faces. If we are able to convey this efficiently, the consumer will be better equipped to make a decision without falling prey to the opinions of designers that promote their views as the final word.
Crossover design is a subset of Filter Theory which is a fundamental mathematical discipline that applies to every field of physics. Crossover Topology is most commonly defined by the resulting “Order” or “Slope” of the network. “Order” refers to the largest exponent comprising the Laplace Transform equation that mathematically describes the transfer function of the network. “Slope” is defined as the rate at which the frequency response decreases in magnitude with respect to frequency at those frequencies beyond the selected corner or “crossover” frequency. Mathematically, it is the rate of change or “first derivative” of magnitude vs. frequency. In an idealized design, the slope is of a fixed and constant rate and is usually referred to as some value in decibels per octave (dB/Oct.)or per decade (dB/Dec).
A “First Order” network exhibits a reduction of signal magnitude that decreases by 6dB per octave. A “Second Order” network exhibits a similar reduction that decreases by 12 dB per octave. Successive orders decrease the signal magnitude or conversely, increase the “slope” by 6db for each increase of network order.
Complicating the matter is the response at the corner frequency where the filtering action becomes evident from a magnitude standpoint. The network can cause the signal magnitude to increase above the nominal level or begin to drop off further from the corner frequency. This property is referred to as the “Q” of the network and is characterized by the names of the researchers that first identified and popularized their attributes and advantages for various applications. Butterworth, Bessel, and Linkwitz-Riley (or cascaded Butterworth) are several of the types most commonly encountered in crossover design.
Do to the vast array of different qualities each type manifests, we will not list them for each order and type at this time. What we will attempt to do is outline the major differences between the most debated types. In general, there appears to be two major camps or points of view regarding crossover topology, and each camp has its ardent advocates. These two groups can be defined as either those: (a) to whom the inter- or intra-driver signal delay characteristics of the system are of paramount importance, or those (b) to whom they are not, or are so, but to a lesser degree than other parameters.
We at SP Technology, if forced to choose, must categorize ourselves as belonging to group (b). It should be noted that such a classification is rather “loose” at best. We understand and agree, to a point, with those of group (a). Then again, there is a limit to this agreement. What we advocate is a balanced approach that suggests the use of a certain topology where its use is appropriate. One must consider a multitude of variables and prioritize each performance criteria to its level of audibility in order to come to the best set of compromises. Every crossover topology has its advantages and disadvantages, each must be weighed according to a given application and design objective. At times, one may find the “First Order” network, with its superior signal delay characteristics, is a proper choice. At others, a higher order slope is called for. What we will not do is fall into the trap of philosophical adherence to one approach above all others.
At the heart of the debate between the two camps lies the question of signal delay audibility. Research has shown that under certain test conditions and applying certain test signals, some individuals report a definite ability to hear rather small variations in signal delay. This we do not question. What becomes obvious to us though is that if elaborate testing methods must be employed to discern the audibility of small signal delays, they clearly do not carry the same weight with regard to system fidelity as other, more clearly audible factors. Loudspeaker performance parameters that are clearly audible and repeatable under controlled test conditions rank at the top of the list with regard to priority, as far as we are concerned. This short list (somewhat by priority) would include: static distortion (THD & IM), dynamic linearity, frequency linearity, frequency extension, diffraction effects and dispersion, efficiency and signal delay performance.
The previous statement could easily be interpreted as suggesting that signal delay behavior is of no consequence. This could not be further from the truth. The fact is that the higher priority parameters must be optimized before delay characteristics can be effectively dealt with. Also, there is little point in attempting to do so when relatively far greater response errors exist. The sad truth is that most loudspeakers suffer greatly from shortcomings in those areas so attempting to correct for delay issues when they are being masked by gross distortions and other non-linearities becomes an exercise in futility. On the other hand, ultimate dynamic performance cannot be optimized if excessive signal delays exist in the system.
As has been stated countless times by others, music is not the same as test signals. This is true at least for the more commonly encountered test signals anyway. One can construct “packets” of complex signals with multiple overlaid harmonics to mimic those encountered in music though. If we think of percussive sounds produced by certain instruments with certain fixed note durations as test signals, then we can use them to test the system in question. What we find when we examine these percussive signals is that they have a beginning with a fast rising edge, a middle part with some dominant fundamental tone overlaid with various harmonics and a trailing edge that decays in amplitude over time. All of this may be on the order of a few, to many milliseconds. These packets manifest what we in engineering refer to as an “envelope.” This envelope should retain its original form from beginning to end of the record/playback signal chain if it is to be perceived as being a direct reflection of the original. The degree to which this envelope changes shape will determine the fidelity of the system under test.
One can easily envision the envelope being “stretched out” in time such that the note duration becomes effectively longer. This is what happens when a complex musical “packet” is passed through a circuit or network (crossover) and has certain components delayed in time with respect to others. This characteristic delay of the system is what is referred to as “Group Delay.” Usually such networks delay the higher frequency components less than the lower ones. As we can see from this illustration, it would tend to degrade the dynamic response or perceived “speed” of a system if the leading edge of a percussive envelope (which is composed of the higher frequency components) were to arrive at the listeners ears significantly ahead of the middle or trailing edge of the envelope. Such signal delay distortion would change the fundamental shape of the envelope and “soften” the percussive impact. It could also change the way the different harmonics that comprise the original waveform add and subtract from one another, potentially changing the perceived timbre of the reproduced instrument.
“Ah Ha!!!” - you may say, we have just supported camp (a)’s position. Well, yes… and no. Many other forms of distortion can alter the shape of that envelope, none the least of which are THD & I.M. that are introduced by driver cone break-up modes as well as driver motor and suspension non-linearities. In fact, these forms of distortion are far more prevalent, greater by orders of magnitude and easier to correct - to a certain degree. As we have said, without correcting these far more dominant forms of distortion, there is little point in addressing signal delay induced distortion.
Also, with regards to the issue of timbre, there is one caveat to the above statement that tends to support the argument of group (b). Recent research into human hearing seems to suggest the ear/brain system behaves as though it were a form of Fast Fourier Transformer (FFT). FFT’s are often used in engineering to analyze the spectral make-up of various complex signals. Although they can reveal with great precision the frequency content of a signal, over the specified sample period they are “time blind.” This blindness means that any time relevant information within the selected “time widow” cannot be discretely discerned. If it is true that human hearing does in fact work this way, then the upshot is that we are limited in our ability to hear small time/signal variations. It means that the spectral content of a signal is of significantly greater importance than when the information arrives in time.
In our opinion, the truth of the matter is likely to fall between the extremes. Time information is undoubtedly important with regard to the perception of dynamic realism, but is limited to within a time window of greater than a few hundred microseconds and less than 1 millisecond. Obviously, this has yet to be proven but the available research tends to support this view. In addition, a preponderance of anecdotal evidence suggesting this is true exists in the form of products that have received wide acceptance in the marketplace. A great many highly acclaimed loudspeakers do not offer linear phase and/or zero group delay performance. In fact, this author is aware of several highly praised models that exhibit rather poor response in this area.
So it is… that the problems the designer encounters are manifold. In his attempt to minimize the more dominant forms of distortion, he may actually introduce more delay into the system. This is most often the consequence of using “higher order” slope crossovers in combination with multiple drivers. The combination of higher order slopes and multiple crossover frequencies tends to represent the “worst case scenario” with regards to excessive signal delay. Conversely, the combination of “first order” slopes and fewer crossover frequencies/drivers tends to aggravate the more traditional and dominant forms of distortion.
Camp (a) is now saying, “Well… use better drivers and more of them and you won’t have that problem.” Upon first analysis, this would seem an obvious solution. Easier said than done. If one chooses to use more drivers to increase dynamic response when using first order slopes, the already existing problem of poor vertical dispersion is multiplied by each additional driver/crossover. On the other hand, due to these same dispersion issues, the most optimal application would be to employ a 2-way design. This is the designer's paradox.
One noted designer that has recently posted on AC has even suggested that the way to overcome the dynamic limitations of first order networks is “to use better drivers.” If this were truly the answer then there would be no other type of loudspeaker on the market, as every high-end manufacturer would just “use better drivers” with “first order” slope crossovers and be done with it. Yes, a true first order network can be difficult to achieve in practice, but competition would force the manufacturers hand.
The fact is, even so called “better drivers” have their limitations and driver design is limited to the materials available. No manufacturer has a monopoly on these constituent materials either, so the problem must lie within the limitations of the sub-components. As long as drivers are made with wire that does not exhibit room temperature super-conductance, their magnets have flux limitations and their cone materials lack the rigidity of diamonds in sizes large enough to produce bass frequencies, they will forever be limited in their ability to transform electrical current into a distortionless acoustic waveform.
To be sure, better drivers will always help and are called for universally to reduce every form of non-linearity. But to the degree of performance that is being asked of them, we have yet to develop ones that will overcome the demands that “first order” slope crossovers place on them, especially when used in 2-way designs. Of course, the above statement is based on the assumption that traditional forms of distortion are not to be tolerated. If you are willing to sacrifice this and accept higher conventional distortion to reduce a less offensive type, then of course there are products out there that offer this. We have not even discussed in any length the real world disadvantages that the poor vertical dispersion produced by first order networks cause. Even if one is willing to accept the seating limitations that result from their use, the erratic room reverberation that is another consequence degrades from the one advantage they do offer. If you do not listen to wide dynamic recordings at anything other than moderate levels, you only listen in the “sweet-spot” and you already have a very dead room, then the simple 2 or 3-way “first order” network design may be for you.
Just to throw one more monkey wrench into the whole first order issue, we have also read recently where a designer devoted to first order designs suggested that the difference in signal delay of 1 microsecond was clearly audible. We will not take issue with this as the research into human hearing is still ongoing and anything is possible. But if this is true, then such diehard advocates of the “first order” topology are in as much trouble as the rest of us. While we cannot disprove this statement, it can be easily proven that the drivers these designers are forced to use are a very source of signal delay distortion that no simple “first order” network can correct.
You see, many that have come before us have shown in various published papers that the acoustic center of a driver “wanders” throughout the operational range that it is used in. This effect occurs without any crossover network whatsoever connected to it. Such delay shifting is the source of the common question among designers, “where is the acoustic center of the driver?” The answer is somewhat ambiguous and most designers “tweak” the crossover in the lab to minimize this effect the best they can. Let’s just put it this way, the effect is not easily modeled by the various design software we all use.
To be specific, the types of drivers that manifest such behavior worst/most frequently are those bass/midrange units that are operated up to around 3KHz. If they are to be used in a “first order” design and with any form of “conventional” tweeter, then they must have a flat response out to at least 5 or 6 kHz. This is because most tweeters, even very good ones, cannot be operated much below 3 KHz due to power handling limitations. Even in designs that crossover a little lower, the woofer must have a flat response out to at least one octave beyond the crossover frequency. That requires the woofer in a 1.5 KHz design to extend out to at least 3KHZ.
In any such case, by default the woofer/ midrange driver will exhibit a form of designed-in “mechanical crossover” that permits the center of the cone to operate somewhat independently from the rest. Due to this “controlled break-up,” as frequency increases the acoustic center moves toward the center/rear of the driver. The amount of signal delay then changes correspondingly. This delay will be on the order of maybe less than ten (smaller midrange driver) and possibly up to 100 (larger woofer) microseconds, depending on frequency extension and other variables. This is well beyond and in excess of the 1 microsecond delay that is claimed to be audible. It is also uncorrectable without deviating from the minimum phase crossover topology.
If phase/group delay variations of such small magnitudes do indeed represent a significant source of error, we are all going to suffer from a considerable lack of sonic fidelity for some time to come. Also, if the designer making this 1 microsecond audibility claim chooses to tackle that problem, it would appear that he has his work cut out for him. May the Force be with him!
As a side note, designers of these type drivers know full well that at any time one chooses to develop such devices, they are automatically “building-in” a significant source of distortion. The controlled break-up of the cone that permits the driver to operate beyond its “mass cut-off frequency” will also open the door to undesirable break-up modes that generate all sorts of odd-ordered harmonic and intermodulation products.
What few companies will tell you is that this source of distortion is a far greater detriment to fidelity than even the worst cases of excessive phase shift/group delay due to crossover design. If you think about it, this fact becomes obvious to even the most unfamiliar individual. All you have to do is imagine the sound of a drum being struck. Drums are very discordant, so much so that it is difficult to mentally associate a particular drum sound with that of a specific note in the musical scale. The cones (or membranes of any driver for that matter) have more in common with the head of a drum than not.
To be sure, driver design is far more complicated than merely developing a crossover network for a loudspeaker system. If you doubt this, then answer this question. Why do you see many amateur speaker builders assembling their own “home brew” designs but very few attempt to build their own drivers? Very few speaker companies even attempt to build their own drivers for that matter. Why? – Because it’s hard to do!!! Virtually anybody can slap a couple of off-the-shelf drivers in a box, add a few crossover parts based on some formula and get decent results. It simply doesn’t work that way with designing drivers.
Due to the fact that designers generally have had little recourse, decades of research have gone into trying to tame these “cone generated” side effects. That is why many different cone shapes and formulations exist in the first place. Everything from “mineral loaded” polypropylenes -- to carbon graphites -- to various composite materials... all have been tried. A very large amount of money and time has been invested in order to extend driver bandwidth while reducing the inevitable distortion by-products. All of this could have been avoided if the decision to deviate from true “piston behavior” was never made in the first place.
On the other hand, drivers that do behave as true pistons do not suffer nearly as much from these cone-based distortions or from the “acoustic center shifting” effect - to any significant degree. They would be ideal candidates for first order designs except that they do not have the frequency extension needed. It would seem there must be an acceptable compromise.
One solution would be to use such a woofer/mid up to the highest frequency possible and cross over to a tweeter that has its low frequency response extended in some manner. Such a limited upper frequency response of the woofer along with the lowering of the tweeter’s response would undoubtedly require using a higher order crossover slope. What one would do is include the woofer’s natural roll-off above its mass cut-off frequency in the final crossover transfer function. If this woofer were of exceptional design, its lower frequency extension/excursion could be optimized as well. Such low frequency optimization would have little effect on its higher frequency performance other than reducing its efficiency/sensitivity. This would permit one to design a simple 2-way system, thus avoiding the pitfalls of multi-way design.
Although such a design would not offer true linear phase performance, its total group delay would still be quite low. This would be due to the fact that only one crossover is used to begin with and acoustic center variations are non-existent as well. One could also employ a method of recessing the tweeter from the front baffle of the woofer to help reduce the group delay error. From a time response standpoint, signal envelope distortion would still exist, but it would be greatly minimized compared to most other designs. The possibility of modifying this design at some future point to incorporate a simple delay line that would completely correct for the remaining error exists as well. Alteration of the crossover would be required but the physical assembly would not need to be altered.
Even though such a design would not be technically “perfect” from a phase response standpoint, it could still, never the less, become a world-class reference system. Especially if such a combination could provide the dynamic headroom needed to achieve the full 120dB dynamic range of human hearing AND significantly lower all other forms of distortion. In the end, the system’s group delay would still be minimal while providing the best possible set of compromises. If this “hypothetical” system also offered significant improvements in other performance areas such as dispersion, diffraction, and frequency linearity, that would be one serious improvement over the present state-of-the-art!
If the above essay seems to make reasonable sense to you, then we believe you are better equipped to make an informed decision when purchasing your next loudspeaker. We also believe you will be better equipped to judge the value of our products. Remember: When the debate remains unresolved and you're tempted to accept status quo, a paradigm shift is in order. Never accept status quo.
We at SP Technology do not accept the status quo of the industry’s imposed constraints on performance. We do not accept the here-to-fore paradox of choosing between every other significant factor and excellent time domain performance in our designs. We will not be constrained by ideology. What we will do is use the “first order” or any other crossover topology as well as any other method when the guidelines of NATURAL LAW dictate their need. By so doing, we will ultimately change the course of recorded music.
Bob Smith – president
SP Technology Loudspeakers
04-27-04
