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Topics Technical Discussions of Audio and Loudspeaker Issues |
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An Overview of Crossovers - Part Two By John Murphy and Jim Ford |
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| Our exploration of
loudspeaker crossovers continues this month as we reveal a fundamental design flaw of some
of the most widely used crossover types: summing error. Last month in this space we presented a discussion of crossover basics which covered the requirement for multiple loudspeaker drivers in full-range systems, the role of the crossover in these systems and the difference between systems employing passive crossovers and those employing active electronic crossovers. This led to a discussion of multiamplfication (biamplification, triamplification, etc.) and the advantages of a multiamped system over a loudspeaker system employing a passive crossover powered by a single power amplifier. We concluded the column last month with guidance for crossover frequency selection. This month we will cover the problems with current crossover designs and identify the crossover types that provide solutions to the crossover problem. We hope that this overview of crossovers (and the series of crossover product reviews to follow in upcoming months) will help our readers better understand their loudspeaker systems and make more informed decisions when purchasing crossovers. Problems with Current Crossover Designs As we discussed last month, the function of a crossover is to divide the audio signal frequency spectrum into two separate bands which can be individually reproduced by separate loudspeaker drivers. The drivers should be selected for their ability to cover the assigned frequency range and also for sufficient overlap in response over the crossover region.
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Although rarely discussed, it is obviously assumed
that these separate frequency bands will be recombined at some point in the listening
chain. Actually, the recombination occurs as the signals from the separate drivers are
radiated into the listening environment. The resulting frequency response of the system
depends not only on the response characteristics of the individual drivers, but also on
the way the outputs of the crossover combine. This brings us to the subject of the
crossover's summed response. In order for the individual signals from the separate drivers of a loudspeaker system to combine to produce a flat frequency response, it is first necessary that the signals applied to the drivers combine to provide a flat frequency response. This is, flat response requires that the output signals from the crossover sum correctly. At first this might seem like an obvious requirement, but the sad truth is that crossovers without summing error are rare. Most of the crossovers we have observed over the past year or so do not produce a flat summed response. The primary reason for this poor performance is the persistence of one particular crossover design: the 12-dB-per-octave Butterworth filter pair. As a member of that family of filters known as "even-order Butterworth" filters, the 12 dB/octave Butterworth filter is
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page 74
| incapable of delivering a flat
summed response.' The individual filter response curves of a typical 12 dB/octave
crossover are shown in Figure 3. This particular unit has a crossover frequency
of 500 Hz at which point the response of each filter is down 3 dB. When the high- and
low-frequency outputs of this crossover are electronically summed, the result is a flat
frequency response with a deep notch at the crossover point as shown in Figure 4;
note also the aberration in the phase response of the combined signals. A significant
improvement can be made by inverting the polarity of one of the outputs of the 12
dB/octave crossover. The summed response then exhibits a 3 dB peak at the crossover
frequency (Figure 5) which is a big improvement over the 30 dB notch of Figure
4. It might be argued that it is not valid to electronically sum the outputs of the crossover since, in use, the
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crossover output signals will
always be summed acoustically. However, even when the outputs are acoustically summed
(using high quality loudspeaker drivers with adequate overlap) the result is the same:
either a notch or a peak at the crossover point depending on the relative polarities of
the drivers. Others have reported, and our own listening tests have confirmed that this
notch at the crossover is readily audible. As a result, replacing a 12 dB/octave crossover
with a unit that has no summing error can eliminate a significant source of coloration in
a loudspeaker system and bring the listener a step closer to the original performance. Although the units designed with 12 dB/octave cutoff slopes consistently exhibit summing problems, they are not the only culprits. We've seen at least one 18 dB/octave crossover with gross summing error. In this particular case the manufacturer was claiming that the crossover employed " 18 dB per octave Butterworth filters." Inspection of the frequency response curves of the unit revealed that the filters did in fact have an ultimate cutoff slope of 18 dB/octave. However, the filter response curves displayed a broad, gentle cutoff indicative of an "overdamped" filter rather than the maximally flat response and quick cutoff characteristic of a true Butterworth filter. When the
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page 75
| high and low outputs of this
crossover were summed the resulting amplitude response had an unusually wide notch at the
crossover. Inverting the polarity of one output produced a wide 3 dB peak at the crossover
frequency. The point is this, there are many ways to make bad crossover filters even
though the 12 dB/octave Butterworth pair is the most infamous. Solutions to the Crossover Problem The solution to the problem of crossover summing error is to use as crossovers only those filter types which can sum to provide a flat frequency response. In our observations of products available over the last year or so we've seen only two types of crossovers that are capable of properly summing. The first is the 18 dB/octave Butterworth filter pair which is currently employed in several units on the market. The other type we've seen that will properly sum occurred in a product that is rather unique. This particular unit employed 12 dB/octave Butterworth filters with a front panel control for adjusting the attenuation of the filters at the crossover point. By setting this control for 6 dB of attenuation at crossover (rather than the -3 dB response of a "normal" filter pair) and inverting the polarity of one output, a flat summed response could be obtained. Unfortunately, using a straightforward polarity connection or any other setting of the "attenuation at crossover" control resulted in the typical summing errors of 12 dB/octave crossovers. The fact that a flat summed response could be obtained with this unit seemed as much an accident as good engineering. We should note here that these are by no means the only two types of filters that are capable of an accurate summed response; they are just the types that have found their way to market. Probably one of the best solutions to the crossover problem is the 18 dB/octave Butterworth filter pair. The individual response curves for a typical 18 dB/octave crossover are shown in Figure 6. When the high and low outputs of this filter pair are summed, the
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result is a flat amplitude response regardless of whether the relative polarity of the outputs is inverted or not. The summed response characteristics for both cases are shown in Figures 7 and 8. Comparing the two cases it can be seen that inverting the polarity of one output provides the best phase characteristic-that is, the least total phase shift across the spectrum. Whether or not such a phase shift is audible has, to the best of our knowledge, not been firmly established. One report that we are familiar with indicates that this phase shift is not audible; another researcher reports' that some change can be noticed on certain sounds (clicks) when a phase shift of this type is introduced into the listening chain. Our own listening tests to this point have indicated that this phase shift is not audible. However, we suspect that it may require a very high quality monitor with accurate phase response to reveal such a subtle effect. (Can you really expect to hear the introduction of a subtle phase distortion over a monitoring system which has severe phase distortion?) For the most critical monitoring systems where accurate phase response is desired (and the quality of the drivers warrants it) there is a class of accurate phase
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page 76
crossovers which can be employed. These filters constitute what are known as "constant-voltage" crossovers and their use was first described in detail' by Dick Small, one of the pioneers of scientific loudspeaker design. One example of this class of filters is the filter pair shown in Figure 9. The high-pass filter is an 18 dB/octave Butterworth type. The low-pass signal here is "derived" from the high-pass signal in such a way as to force the sum of the outputs to equal the input signal. This is done by subtracting the highpass signal from the input signal to obtain the low-pass signal. (IF: LOW = IN - HIGH, then: HIGH + LOW = IN.) The resulting low-pass response is a bit unusual in that it has a 4 dB peak at the crossover frequency and a cutoff slope of only 6 dB/octave, but as Figure 10 shows, the summed response has not only a flat amplitude response but a flat phase response as well. Because of this it will do something no other class of filters will do: it will pass a square wave without distorting the shape of the waveform. The filter pair shown in Figure 9 is only representative of the constant-voltage filters since many different filter shapes are possible. In fact, whenever one of the filter outputs is derived from the other as we've described, the constant-voltage characteristic results. Whenever a 12-dB/octave Butterworth crossover is used (and there are many of them out there!) there is a choice between the response shown in Figure 4 and that shown in Figure 5. The 3 dB peak is clearly preferred over the 30 dB notch. This response is obtained by reversing the polarity of one crossover output with respect to the other. In practice this is typically accomplished by reversing the leads to one loudspeaker driver or the other (but not both!). The situation is complicated by the fact that in some crossovers the manufacturer has already performed the phase inversion so that a second reversal by the user then results in the "in-phase" connection of the drivers and the corresponding notch in response. |
Our discussion has been concerned mainly with 12 and 18 dB/octave Butterworth crossovers because these are the types most frequently employed in electronic crossovers. However, it should be noted that a flat amplitude response can be obtained with 6 dB/octave crossovers and also 30 dB/octave crossovers (these are both so-called "odd order" filters like the 18 dB/octave type). Similarly, we should note that 24 dB/octave and 36 dB/octave filters will exhibit the same problems as 12 dB/octave types since these are all "even order" filters. In conclusion, we recommend 18 dB/octave Butterworth crossovers for general purpose use in high quality loudspeaker systems. These filters provide an accurate summed response whether the relative polarity of the outputs is inverted or not. However, the inverted polarity connection offers a better phase characteristic than the non-inverted connection. At this point in time the indications are that the phase shift resulting from these crossovers is not generally audible. For critical monitoring where it is felt that accurate phase response is required, constant-voltage crossovers should be employed. Because constant-voltage crossovers sum to provide both flat amplitude and flat phase response they have a unique capability to pass square waves intact. REFERENCES 1J. R. Ashley and A. L. Kaminsky, "Active and Passive Filters as Loudspeaker Crossover Networks," Journal of the Audio Engineering Society, XIX, (June 1971), 494-502. 2S. H. Linkwitz, "Active Crossovers for Noncoincident Drivers," Journal of the Audio Engineering Society, XXIV, No. 1. 3R. H. Small, "Constant-Voltage Crossover Network Design," Journal of the Audio Engineering Society, XIX, No. 1 (January 1971). |
Reproduced from Modern Recording & Music magazine, September 1980. |
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Comment: An Exciting Crossover Development |
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In previous reports we have discussed the relative advantages and disadvantages of the various types of filters used as loudspeaker crossovers. One of the most appealing filter types that we discussed was the "derived" crossover, where the low pass signal (in this example) was derived by electronically subtracting the high pass signal (18 dB/octave Butterworth) from the Input signal. The unique advantage of such derived crossovers Is the fact that the high and low output signals will recombine to reproduce the input signal with a very high degree of precision. There is no summing error with respect to either the amplitude or phase response of the audio signal. The net result is accurate reproduction of the input waveform; even square waves can be accurately reproduced. Conventional crossovers are incapable of accurately reproducing waveforms because of the phase response error they introduce. As attractive as derived type crossovers are, they have one serious drawback: steep cutoff slopes cannot be obtained in both filter bands so there is an excessive amount of overlap in the frequency response curves of the filter pair. This is undesirable since it implies that the loudspeaker drivers that the derived crossover is used with must have a correspondingly generous degree of overlap in their response range for optimum performance. This shortcoming of the derived type crossovers has led us to ultimately recommend 18 dB/octave Butterworth filter pairs with their steep slopes and minimal overlap as the preferred crossover filters for most applications. But there's a new development on the horizon. |
At the Audio Engineering Society's 69th convention held recently in Los Angeles we heard a technical paper given which holds the promise of a significant advance In loudspeaker crossover technology. In this report the authors describe a family of high-slope, phase accurate crossovers where the high-pass signal is derived from the input signal and the low-pass signal through the use of a short time delay. The high-pass filter which can be derived from an 18 d B/octave Butterworth low-pass filter, for example is actually an improvement over the standard 18 dB/octave Butterworth high-pass response since there is about one-half octave less overlap between the delay derived filters. This reduced overlap combined with the accurate amplitude and phase response of these time delay derived crossovers makes them very attractive prospects for future crossovers. Until the time that these delay derived crossovers come commercially available, however, the 18 dB/octave Butterworth filter pair will remain the crossover of choice for general purpose use. REFERENCES 1 John Murphy and Jim Ford, "An Overview of Crossovers, Parts I and II," Modern Recording & Music, V (August 1980), 68-72 and V (September 1980), 75-77. 2 Stanley P, Lipshitz and John Vanderkooy, "A Family of Linear-Phase Crossover Networks of High Slope Derived by Time Delay," paper presented at the 69th Convention of the Audio Engineering Society, Los Angeles, May 12-15, 1981. (Preprint No. 1801 (1-5).] |
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