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| Elliott Sound Products | Project 254 |
P09 PCBs (revision C) are available that can be used for this project. Click the image for details. (some components are omitted or bridged).
"Oh no! Not another bloody crossover circuit." I can almost hear the cries of anguish as people read this, especially since the last project was a crossover as well. Indeed, it was Project 253 that got me started on this version, especially after I found the offset in acoustic centres of the drivers in (yet another) test enclosure that I have. This cause some thinking on the issue, and also prompted the article Finding the Acoustic Centre of Loudspeakers, which was published a couple of days before this.
This is not a complete project, but rather a starting-point for people who are willing to experiment and are able to take measurements. A digital oscilloscope is essential (in single-sweep mode to catch transients), and you need to read the article linked above. The crossover can be constructed using the P09 board (Stereo 2-Way Linkwitz-Riley Crossover) with a few minor changes. For testing, you'll need a simple electret mic setup, shown later in this article.
The asymmetrical crossover filter featured here has a deliberate offset, intended to provide around 35-70μs delay (12-25mm acoustic centre offset) between the tweeter and midrange outputs for time alignment. While there will be a small ripple across the xover frequency when the outputs are summed electrically, once the mid-bass driver's acoustic centre is accounted for the acoustic output will be pretty flat without the need for all-pass filter phase delays or a stepped baffle. The aim is to keep any ripple below ±1dB.
The design is optimised for 2-way operation for the high crossover. A conventional P09 Linkwitz-Riley crossover would typically be used for the low frequency section. This will typically be between 200Hz and 300Hz, although that depends on the drivers you intend to use. With good opamps, it's performance will generally be better than (supposedly) equivalent DSP (digital signal processor) implementations, because there's no requirement to convert the signal from analogue to digital and back again.
The photo shows the finished board, using the circuit shown in Fig. 2. I wired it so it can be either 2-way or 3-way, so the PCB is fully populated. If you only need a 2-way version, both channels will be on a single board. Each will be made using links to bypass unused resistor positions. These links can be see in the upper half of the PCB, which create the circuit shown in Fig. 1. Full details for assembly will be provided in the construction guide, concentrating on the stereo 2-way configuration. The input is wired as unbalanced, and one half of U1 is unused. Note that the level pots should have their adjustment screws at the bottom so clockwise rotation increases the level (I failed to verify that before I installed mine, but it works just as well.)
Please note that the PCB for the P09 crossover is a stereo 2-way design, and has balanced input buffers (which can be connected as unbalanced if preferred), high and low pass filters, level controls and output buffers for each channel. Each output buffer is configured for variable gain to allow your system to be set up correctly. The suggested power supply is the P05, which also has an auxiliary output suitable for operating muting relays (see below for reasons you may want to include muting).
An asymmetrical crossover is not just 'any old crossover' that you can use in any application. It's specifically intended where you are prepared to experiment to get the best results when the tweeter and midrange (or mid-bass) have a known acoustic centre offset.
You might think that a 'subtractive' (aka 'derived') asymmetrical crossover would produce the same result, but it probably won't have enough difference in the group delay to make it worthwhile. These are covered in the article Derived/ Subtractive Crossovers, and they are rarely as useful as their protagonists proclaim. These are not discussed further here.
Figure 1 shows the circuit for one channel, with two filter sections. The high-pass filter is a slightly modified Linkwitz-Riley alignment. With the component values shown, this has a nominal frequency of 2kHz. This can be varied by changing the resistor or capacitor values. A formula doesn't work well for this because the filters are non-standard, but if you use the ESP L-R crossover calculator you can get the base values. Some experimentation will be required to get the minimum ripple over the crossover region.
This unit does not provide a completely flat frequency response across the crossover frequency when summed electrically. However, with a more-or-less 'typical' acoustic centre offset of 75μs (25mm) the acoustic signal from both drivers maintains a reasonably stable 22° phase shift across the xover frequency, with a group delay offset to compensate for the offset acoustic centres. Note that the frequency shown here is simply an example - it can be anything you like within the audio range.
You can see that the 18dB/ octave filter is set for a slightly lower frequency than the 24dB/ octave section. This was done to increase the effective group delay (and therefore tweeter offset distance) to get the offset distance to be at least 25mm. As shown, the low-frequency group delay difference is 40μs, and if you use 3.9k instead of 4.3k, that's increased to 58μs. Using 3.3k increase it further to 85μs. Beware though - the nominal LF group delay is not the same as the relative acoustic offset. With an offset of 12mm to 25mm (35μs to 73μs) the 4.3k resistors give the best overall response (less than ±0.5dB deviation (summed electrically) over the crossover region.
The 2-Way unit is separated into 3 sections per channel ...
It is important with both versions that the filters are properly matched, both within the individual filters, and between channels. While small variations between channels will not be audible, if the high and low pass sections are not accurately matched, then phase and amplitude errors will result. In practice, normal component tolerances cause surprisingly small errors, but matching the capacitors is recommended.
There's only so much info that I can provide here, because of the differences between various drive units. Tweeters are probably fairly consistent, but midrange/ mid-bass drivers vary widely. If you can, select one with a relatively shallow cone, as that will have less AC offset than one with a deep cone. However, this alone isn't the final answer, because there are so many interdependencies. You need to be able to carry out tests to locate the acoustic centre reasonably accurately. The following will help to reconcile timing in microseconds vs distance in millimetres. You can convert the distance to inches if you like (I will not provide this), but millimetres are far more sensible.
d = t × 0.343
t = d / 0.343 So (for example) ...
d = 20 × 0.343 = 6.86mm
t = 6.86 / 0.343 = 20μs
Sound travels at roughly 0.343mm/ μs, so a 34.3mm AC offset introduces an effective delay of 100μs. This is far easier than working with metres/second, or (even worse) feet/second. When you use the formulae, you simply use the distance as (for example) '25' for 25mm, or '75' for 75μs. You don't use the suffixes because the formulae already make the conversions. This minimises errors caused by multiple zeros or using powers of 10.
Figure 2 shows the way to connect a 3-Way crossover. The use of asymmetry is only used for the mid-tweeter crossover, with the 18dB filter as the midrange high-pass. This unit should produce excellent results, with good phase coherency and a fairly flat response across the entire frequency band. The tweeter to midrange low-pass is suited for an acoustical offset of up to 100μs (roughly 34mm). Better performance is obtained if the offset is less (around 70μs or 24mm).
Figure 2 - 3-Way Mono Asymmetrical Crossover (2 Needed for Stereo)
I know the circuits look complicated, but each is basically repetition of a common circuit block - the filter section. Since the opamps are all used as unity gain buffers, the use of premium devices is not really essential, so the TL072 type would be quite serviceable in this role (however I do recommend that you use something 'better'). Needless to say, if you want to use better devices (even discrete opamps) you can easily do so. Make sure that any device used is stable for unity gain - this is not always the case with some devices, especially when external compensation is used. In this case, use the manufacturer's recommended value of stability cap for unity gain operation.
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Power supply connections (and bypass capacitors) have not been shown, but the diagram shows the standard connections for a dual opamp. The IC is viewed from the top. The ±15V power supply described (see Project 05 - Power Supply For Preamps) is suitable for this crossover as well, and will easily power your preamp and a 3-way version of the crossover. For dual opamps, power is connected to Pin 4 (-ve) and Pin 8 (+ve). Most opamps will function just fine with supplies between ±5V and ±15V |
NOTE: Only one channel is shown for the 3-Way - for a stereo setup, two identical filter circuits are required.
As can be seen, the 3-Way unit is separated into 4 sections, and with the values shown in Fig. 2, the outputs are as follows ...
In 3-Way mode, the bandpass filter has a high pass section whose frequency is equal to that of the main low pass (bass) filter, but the frequencies for the tweeter to midrange are asymmetrical (the tweeter uses a 24dB/octave filter and the midrange/ mid-bass uses an 18dB/octave filter. You would expect this to have a terrible summed response, but it's better than you'd expect. Once the acoustic centre offset of the midrange is accounted for, you should expect summing to be within ±0.5dB. This may appear confusing, but it all makes sense in the final design.
If it helps, I have included a block diagram (one channel) that may make things clearer. This is shown below, and has all the sections for a 3-way crossover network. Again, this is mono, so two complete blocks are used for a stereo system. I've shown the connections I used, including the optional 2-way output. If you don't need the 2-way connection you can omit this.
Frequencies shown are for reference only, and are the same as described above. Naturally, these will need to be changed to suit your application. Note the dotted connection between the input buffer's output and the input to the low-pass filter. If you were to connect the filters like that (rather than as shown), phase shifts through the system will cause the summed output to be different from what you expect. The sections are connected together to give the best outcome - changes will cause unexpected variations, none of which is likely to be good. Opamps always add some phase shift (albeit small), which can make matters worse.
The frequency responses of each section are shown below, note that the crossover frequency is at the -6dB point, and not at the traditional -3dB frequency. This is an important difference between a Butterworth and Linkwitz-Riley filter, and allows the signals to be in phase across the audio band, regardless of which filter section they are being passed by. The electrically (and acoustically) summed output of this filter is flat, there are no peaks or dips (unless you count 0.11dB as a 'dip'), and no phase reversals are produced (unlike 12dB/octave filters).
A simple test with any electronic crossover is to connect a 10k resistor to each output, and join the other ends together. Run a frequency sweep from an audio oscillator into the input, and observe the output level at the output of the resistor summing network. Most traditional (typically Butterworth) crossover networks exhibit a 3dB increase at the xover frequency, and drop back to the reference level about an octave or so each side. This is a less than ideal situation, since in most cases a similar effect will occur from the speaker's summed acoustical output - assuming that the drivers are 'time aligned' so the output of each is in phase (acoustically speaking) at the crossover frequency. If time alignment is not done, and the physical distance difference between speaker voice coils is large (more than 0.1 wavelength of the frequency concerned), then other acoustical differences caused by phase will tend to overshadow any anomaly in the crossover network.
Frequency response is shown from 20Hz to 20kHz, although the bandwidth is much wider (less than 1Hz is easy, and 100kHz or more can be expected with fast opamps). Insertion loss is 0dB, since there is no gain or loss introduced by the filters in their pass-band. The crossover points are defined by the -6dB points for the mid-low filter, but are different for the mid-high section. With the demonstration values I used, there will be a dip of ~1.3dB if the tweeter and midrange outputs are summed electrically. When the midrange driver's delay is included (35μs or 12mm), this is reduced to less than ±0.5dB ripple. This remains the case for up to a 70μs delay (24mm).
The connections shown should be as indicated. Phase anomalies will cause usually minor (but easily measured) response variations if the filters are not cascaded. If you use the ESP boards, the correct wiring is shown in the construction article. There are other connection possibilities, but the one shown has been used by hundreds of constructors and is known to work well. One of the goals was to ensure that the treble passes through the minimum number of opamps, because there is less feedback at high frequencies, and distortion may be a little bit higher as more opamps are included in the signal path. This is rarely an issue in practice, but it seems to be a worthy goal 
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When you use an electronic crossover, you need some way of equalising the levels from each output to match the power amp sensitivity and speaker efficiency. The circuit for a suitable buffer is shown in Figure 5. There is nothing special about it, but it is designed to give a gain of 2 to allow maximum flexibility, and ensures that the impedance of the pots does not cause any high frequency loss with long interconnects. The gain can be changed by varying the resistor values (Rf1 and Rf2). For unity gain, omit Rf2 and use a link for Rf1.
These buffers should use high quality opamps, and provision for them is included on the PCB, including the trimpot (see the photo at the beginning of this article). If you fine that more gain is required (most likely for the low-pass outputs), simply reduce the value of Rf2. If you need around 6dB more gain, use 3.9k resistors (a gain of 4 or 12dB). You're unlikely to need more as this is twice the gain with 10k resistors.
Several people (including me) have found that the crossover unit has a short 'chirp' or 'snap' (depending on the opamp characteristics) as power is removed, and this may be accompanied by some DC swing. If you use the new version of the P05B preamp power supply, the auxiliary output can be used to activate a 6-pole relay (or as many smaller relays as needed) to short all outputs to earth when there is no power. The normally closed contacts simply short the outputs to ground, and when power is applied the short is removed. P05 (Rev-B and above) boards have a power-on delay and a loss of AC detector that will mute the crossover for a few seconds at power-on, and almost immediately when power is turned off.
Because all common opamps have short circuit protection, this will not cause any damage, and current is limited further by the 100 ohm output resistors.
If you need to perform the calculations for a different frequency, the Linkwitz-Riley part is easy, and the formulae are shown below. It's quite easy to set this up using a spreadsheet (OpenOffice, LibreOffice, Excel, etc.) or you can use the calculator program I wrote (see below for details).
R = 1 / (2π × 1.414 × f × C)Where R = resistance in Ohms, π = 3.14159, 1.414 is √2, f = frequency in Hertz and C = capacitance in Farads
C = 1 / (2π × 1.414 × f × R)
f = 1 / (2π × 1.414 × R × C)
This assumes that you have selected the capacitance first, which is the most sensible. Caps are available in fewer different values in each decade than resistors. Capacitors generally follow the 'E12' series, which has 12 values per decade, so:
1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2, 10
These are multiplied by 10, 100 (etc), to obtain all the values from 1nF - 10nF, 10nF - 100nF, and 100nF - 1µF. Values above 1µF and below 1nF are generally not as readily available in all values, and should be avoided for this design, since very large or very small values will create impedances which are too difficult to handle. Very low capacitor values mean high resistor values (noisy), and even small amounts of stray capacitance on PCB tracks or wiring will create errors. Large values of capacitance mean low impedances, which many opamps may not be able to drive without excessive distortion or clipping.
Starting with the resistor value is the least useful, since the range of capacitor values is less than half that of 1% resistors (especially if you have access to the 'E24' series resistors - 24 values per decade). Really strange values can be assured, which will require parallel combinations of smaller caps - messy and not necessary.
It's useful to check that the components selected will give you the frequency that you first thought of, or something reasonably close after standard component values have been substituted for the theoretical values you will get with the calculation. In general, a variation of less than 1/3 octave will not cause any problems.
The calculator program is far easier and more fun, too. (Of course I like it - I wrote it 
!)
The formula for the 3rd order section is far harder, and the frequency is not the same as for the L-R section(s). Because the filter is optimised for providing significant group delay, there is no simple way to determine the frequency. One method that is 'close enough' is as follows ...
f1 = 1 / ( 2π × R × C )
f2 = 1 / ( 2π × R × C × 2 )
f = ( f1 + f2 ) / 2
When this is applied to the default values I used in the schematics, this gives a frequency of 1.44kHz (vs. the measured -3dB frequency of 1.45kHz). It's not especially critical though, because the filter is designed to be asymmetrical. If you were to use the next highest resistor value (4.7k), then the 4.3k resistors should be increased to 5.1k. This maintains the ratio between them, and therefore the effective offset cancellation.
Capacitor values need to be accurate - the standard offering is ±10% (sometimes ±5%), which is not good enough. If you have (or can get access to) a capacitance meter, simply buy more than you need (they are inexpensive), and select the values to be within 2% or better if possible. My experience is that the tolerance of most MKT and MKP caps is actually better than that quoted, but you do need to check! The absolute value is not particularly important, but fairly close matching is needed to ensure flat response across the crossover frequency, and to preserve the stereo image.
The easiest way to get the '2C' value is to use two capacitors in parallel, each of value 'C'. The PCB is designed for this. In addition, the PCB also provides two places for each '2R' value, and they are in series. This means that you can always get the exact '2R' value, without having to resort to E48 or E96 values which still may not provide the exact value needed.
Resistor values also need to be accurate, and 1% metal film resistors are perfectly acceptable. These are generally available in the E24 series (24 values per decade), allowing a much wider choice of values. Both the E12 and E24 series values are available in the Component Calculator (Help-Preferred Values) for reference. In some shops (oh, really?) you might even be able to get resistors in the E48 or E96 range - these offer an almost limitless range of possibilities (48 or 96 values per decade - awesome!), just don't count on it. There's also the E192 series, but these are likely to be harder to find.
Some opamps create a transient signal upon application or removal of power. Because of this they will create a loud sound, and many builders may want to incorporate a delayed action switch, to ensure that the outputs of the circuit are not connected to the load until the operating conditions have stabilised. The P05 Rev-B power supply has an auxiliary output that is designed to be used for muting. The TL072 is one of the worst for this problem, and it is usually not a problem with NE5532, LM4562 or OPA2134 opamps.
Although the transients are unlikely to cause damage to any amplifier or loudspeaker, they do not sound very nice. For a system that you build yourself, there is a great satisfaction in having it perform flawlessly, so it is probably worth the small effort to use the P05-C supply's aux. output to drive muting relays.
If you examine the output waveform, be aware that if your audio generator has more than 0.1% distortion, the high pass output will appear very distorted when you select a frequency more than one octave below the crossover frequency. This is not a fault of the crossover. Because the fundamental is attenuated the most, the harmonics are effectively increased by 24dB (for the second harmonic) and about 36dB for the third. This makes the output waveform look very distorted, yet your input signal will appear to be clean on an oscilloscope. It is difficult to see any distortion below 1% on an oscilloscope, but this amount of distortion will make the output look very nasty indeed. Do not despair - all is well.
In general, avoid capacitors less than 2.2nF or greater than 470nF. As noted above, low values become susceptible to stray capacitance and high values may cause excessive opamp loading. Likewise, resistors values should be between 2.2k and 22k. Lower values can be used if the opamps can drive low impedances with minimal distortion (e.g. NE5532, OPA2134, LM4562, etc.). If you use TL072 opamps, keep resistor values above 2.2k, and remember that you'll probably need to include a muting circuit to prevent 'thumps' and 'chirps' when power is applied or removed.
The tweeter output is the blue trace, and the midrange is the yellow trace. Normally (with an L-R xover for instance) the two would be simultaneous, but the peak of the tweeter output is delayed by 70.7μs, arriving after the midrange signal. The mid-bass driver will add (for this example) 70μs because its AC is 24mm further from the listener than the tweeter. This puts the two signals back in phase, in exactly the same way as a 24mm stepped baffle would do. However, it's been done electronically rather than with carpentry, and is a great deal easier to modify if you need to.
The two methods could be combined, with a modest step in the baffle for 'aesthetic effect', and the rest of the delay done electronically. I verified that the delay doesn't change significantly at 1kHz and 3kHz (roughly 1kHz above and below the design frequency). There is a change, but it's not significant In real life these measurements are not easy to get with high accuracy, but if you're within ±5μs for a 70μs delay you're probably doing pretty well.
As pointed out in several places, this is not a 'complete' project unto itself. The constructor is expected to take measurements to find the acoustic centres, then experiment with component values (either with a simulator or on the test bench) to verify that the delay is within acceptable limits. You may decide that the AC of your drivers is pretty close to those I determined, in which case you only need to determine the crossover frequency (or frequencies) you need for your drivers. These are also fairly reasonable, so in that respect it might be a complete project for some constructors.
Remember that if your crossover is within ±0.5dB, that's far better than probably 99.5% of drivers (including expensive ones). This is simply another tool that can be used to improve overall performance, but it's definitely not going to be for everyone. One thing that this project has done it to highlight the flexibility of the P09 PCB. The board has been available for many years, and there are several thousand happy constructors who've used it (along with countless people who've made their own PCBs).
This 'new' adaptation is very different from those that came before, but it is almost trivial to make the required changes to the component values. Even the long link seen in the photo above is catered for on the board, along with the cut track to make the PCB mono 3-way (all will be covered in the build instructions).
There is no requirement for time alignment of the midrange to woofer section because the wavelength is around 1.8 metres, and even a rather huge 150mm offset (almost 440μs) causes less than 30° phase shift at 200Hz. This will create a 'disturbance' below 0.5dB from 100Hz to 400Hz, which will not be audible with any moderately sensible design. At this frequency, room effects are completely dominant and will create far more havoc than any reasonable AC offset.
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