|Elliott Sound Products||Benefits of Bi-Amping (Not Quite Magic, But Close) - Part 2|
Rod Elliott - ESP
Last Updated 18 August 2012
It would be remiss of me to not mention a few salient points about the choice of crossover frequencies. This applies to all system types where fidelity is expected (or demanded) - high power music, sound reinforcement, or hi-fi.
It is not at all uncommon to see systems where the crossover frequency is set right in the middle of what I call the 'intelligence band'. This is the range of frequencies from 300Hz to 3600Hz, and is extremely important from a psycho-acoustic point of view.
It is no accident that this is the range of the telephone system, and has been for many years - ever since electronics became involved in telephony. If we are only to hear a limited range, then this band of frequencies is by far the most important. Just from this we can recognise a person's voice, which musical instrument is being played (even bass instruments!), and - more importantly - what is being said. It contains nearly all the 'intelligence' of the sound, which is to say that if this band is corrupted, intelligibility is greatly reduced.
So why do speaker manufacturers insist on placing their crossover frequencies within this band of frequencies? The public address (PA) systems used by many rock bands are a case in point - how often does one find that the vocals are completely unintelligible? Mind you, it may also be the case that the band's lyrics just don't make sense, but that's another story altogether.
Often this occurs because the system is so loud that the amplifiers are clipping badly, but even at lower levels it is quite common. Place a common-or-garden crossover filter right in the middle of the intelligence band and this is exactly what will (and does) happen. With phase aberrations and cancellations, this most important frequency range becomes muddied and indistinct causing loss of intelligibility - not only on voice, but instruments as well.
The effect is also noticeable with some hi-fi speaker systems, except that it usually less pronounced, and it is far less likely that the amplifier will be driven to clipping. Reviewers will often say of a speaker that the vocals seem veiled, or that there is noticeable colouration of either male or female vocals. These effects are often caused by the effects of phase shift around the crossover frequency, coupled with the fact that the crossover frequency falls right in the middle of the intelligence band.
Should a crossover be unavoidable in this region - due (for example) to available loudspeaker drivers - then the manufacturer must go to great lengths to ensure that artefacts created by the crossover are not audible. This often causes greater problems with amplifier loading at the crossover frequency, since impedance dips seem to be a common problem with many speakers. It will be found that these almost invariably occur at the crossover frequency.
By using an active crossover network, it should be possible to get excellent performance almost regardless of what the crossover frequency may be. The final setup will still have to be carefully aligned to make sure that there are no major issues with either driver at the selected frequency. In the course of many experiments and tests, it is safe to say that a properly set up active crossover gives one far more flexibility than almost any passive version, with the great advantage that no loudspeaker impedance correction is needed.
Since we have already discussed the 'equal power' crossover frequency between low and mid+high frequencies, it should come as no surprise that the author prefers between 275Hz and 300Hz as the ideal frequency. This is outside the intelligence band (albeit only just), but as discussed, a phase-coherent crossover network and a bi-amped system will tend to be far more tolerant than conventional (passive) crossover networks.
One problem this technique does cause, is that the demands placed on the midrange driver are greater than will normally be the case. This is because the low frequency end of the midrange is now extended to around 300Hz rather than the more 'conventional' frequency of 500 or 600Hz. Few (none that I know of) so-called 'enclosed' (i.e. those with their own integral enclosure) midrange drivers are capable of reproducing 300Hz accurately - indeed, many are quite inadequate even at 600Hz!
Even ruling out this style of driver altogether still leaves relatively few speakers which are small enough to be considered a point source at 3kHz (one wavelength at this frequency is only 115mm - assuming 'British Standard' air temperature, etc.), yet is capable of reproducing signals down to 300Hz accurately. Ideally one would want a driver whose radiating surface is no greater than 100mm diameter (this is already a significant compromise), having high compliance for low frequency reproduction, and a stiff cone structure to prevent cone break-up at the upper limits.
Bear in mind that a loudspeaker which is going to be used to reproduce frequencies down to 300Hz should ideally be capable of uncoloured reproduction for at least one octave (and preferably two octaves) above and below the crossover frequencies. This means that a suitable midrange driver must be capable of reproducing from 150Hz to 6kHz with good efficiency and without significant colouration. This is not an easy task for any loudspeaker.
Many otherwise fine midrange drivers do not provide a wide enough safety margin below their recommended minimum crossover frequency, which causes resonances and other effects to colour the sound. Also affected will be phase response, which will start to suffer badly as the driver approaches resonance - this rather negates the advantages of using a phase-coherent crossover network!
Yes, I know the heading is an oxymoron, but that is what we really have to find. We cannot go further into discussion at this point (at least not without naming names, and deciding on some suitable loudspeaker drivers), since the 'ideal compromise' will be different for every loudspeaker combination available, with added problems incurred by the selected cabinet design and the maker's design goals (price - as always - being a major player in all these calculations).
Having examined some of the factors which affect the performance of a speaker system, it is apparent that there are few hard and fast rules which can be applied, since there are so many variables. What has been presented here is a guideline which - assuming that suitable drivers can be obtained - will have a standard of performance well above average. This web site has now been updated many times, as more information comes to hand, and as I get responses from readers who have similar (or wildly different - rare!) views from my own.
It is to be hoped that this information will at least provide some further discussion and feedback from readers who share my interest in "the ultimate loudspeaker" - however it is configured (even with passive crossovers, perhaps).
Not everyone wants to use a 3-way or 4-way system, and just want to use a mid-bass driver with a tweeter. Although it's often difficult to keep intermodulation distortion down to respectable limits with such systems, at moderate listening volume they are often all that's needed for smaller rooms. They are a popular choice, and there are many very good kit designs on the Net and in magazines. Indeed, I have a pair of 2-way boxes in a back room of my house, and that's all that is needed for casual listening to music or while watching TV. Mine are still passive, but active 2-way systems are much better in almost all respects.
When you go to 2-way active, don't expect to get a useful increase in SPL or effective amplifier power - when you cross over at around 3kHz there is almost nothing to be gained there. What you do get is a crossover that behaves itself properly, and you no longer need to add Zobel networks or other impedance correction techniques. You also get the ability to play with different amplifiers for the two sections. Although most of the differences you are likely to hear are likely due to the 'experimenter expectancy effect', if you do happen on a combination that you find especially pleasing, then you still win.
In general, the mid-bass driver for any 2-way system will need to be in a vented enclosure to minimise cone excursion at low frequencies. A sealed box demands far too much voicecoil travel, and few drivers will remain linear if pushed anywhere near their claimed maximum excursion. As with all loudspeaker designs, this is yet another example of the compromises that must be made to achieve a result that you'll be happy with.
For most systems of this type, there is a major compromise between mid-bass diameter and crossover frequency. Because few tweeters will tolerate frequencies much below 3kHz, the upper frequency of the mid-bass is pushed to its limits. Off-axis response is usually very poor, because the driver diameter is commonly greater than the wavelength at 3kHz (for example). When piston diameter approaches the wavelength of frequencies to be reproduced, the speaker starts to 'beam' - there is a major lobe directly in front of the driver, and lesser lobes (which change with frequency) as you move off-axis. Some driver datasheets include a polar plot showing the off-axis response lobes and nulls, while others just show the frequency response on and off-axis (typically 45°).
The mid-bass driver's upper limit and the tweeter's lower limit determine the crossover frequency that you have to use. You can use a waveguide to allow the tweeter to operate down to a lower than normal frequency - see Practical DIY Waveguides for more information on this technique. Using a 24dB/octave electronic crossover (such as ESP's Project 09), you can sometimes run the tweeter to a lower frequency than that recommended, because the default crossover network is nearly always a 12dB/octave passive design.
By using an electronic crossover with sharp cutoff, there can be less stress on the tweeter than normal, even if the frequency is reduced below that recommended by the manufacturer. You need to be very careful though, because tweeters are easy to damage with lower than normal/ recommended xover frequencies. Making changes needs a good understanding of the possible ramifications, which include but are not limited to tweeter failure. In particular, make sure that the available power that can reach the tweeter is limited - use of a 100W amp (for example) is a very bad idea indeed.
The following section discusses the other issues that you need to address. From the tweeter's perspective, it doesn't matter if the midrange driver is dedicated to midrange, or handles everything from the tweeter crossover frequency down to perhaps 40Hz or so.
I have had many enquiries about extending the bi-amp principle to tri-amping, and offer a few thoughts here. There are some points which must be made, largely to protect the tweeters in such a system, but also to ensure that the system as a whole is coherent, with no one component of the music receiving more or less attention than the others.
Three-Way speaker systems offer many advantages, and the extra cost of making the whole system active is comparatively small. The increase in performance will depend on how good (or not) the passive crossover section might be. 'Good' means that the system uses a high quality passive section between the midrange and tweeter, and includes impedance correction, and has no bad habits from the amplifier's perspective. Bad habits include impedance dips - some speakers may have the impedance falling to less than 2 ohms at the crossover frequency for example.
Even if the passive crossover is really well designed, it is unlikely that it will beat the performance of an active system. The reasons are quite simple - with an active system, each loudspeaker driver has its own amplifier (operating over a limited frequency range), and there is zero mutual electrical interference between the drivers. No passive crossover can achieve this, because even a small impedance variation from one driver affects the performance of the other. Inductors are imperfect (to put it mildly), and it is economically unrealistic to attempt to get any passive crossover to be the equal of its active counterpart.
However, there are still things that one must be aware of, as discussed below ...
With a bi-amped 3-way system, the tweeters are protected by the mid-high passive crossover. Once the loudspeaker is tri-amped, this protection is lost, since the capacitor which is used to determine the crossover frequency is no longer present.
With most 'solid-state' amps, this places the tweeter at great risk during the (generally short) switch-on and switch-off periods. As the supply voltage is applied (or removed), some amplifiers will create a DC transient (if such a thing is possible) as the circuitry starts to operate. This causes the all-too-common speaker thump.
This is mildly annoying when applied to the low frequency drivers, but is capable of destroying a tweeter if allowed to persist for more than a few milliseconds.
In the case of amplifier failure, the tweeter is almost certain to protect any speaker fuse by blowing first - not exactly the desired effect! The 'Poly-Switches' now available might help, but I don't like the idea of a non-linear resistor in series with my speakers. Having said that, Poly-Switches are certainly a viable way to protect a tweeter, but not from short-term DC. They are fairly slow-acting, and are more useful for providing protection from long term overpowering ... such as an amplifier driven to clipping for example.
If the direct coupled approach is contemplated, I would suggest the following:
A suitable circuit is available - see Project 33 in my Project Pages, which can be easily be modified to protect tweeters, where its DC detection circuit can be made very fast indeed.
A humble capacitor will prevent DC from reaching the tweeter voice coil, but the selection is critical to ensure that the sound is not degraded.
Value - The capacitor will almost always have to be at least 20µF, which for an 8 Ohm tweeter, will create a 3dB high pass crossover at about 995Hz. Given that this additional crossover should be ideally 1.5 to 2 octaves from the 'real' crossover frequency (even more if possible), the values likely to be needed in real life will tend to get quite large. The reason that the protection cap needs to be so large is that smaller values introduce phase shift, which is significant for all frequencies within 2 octaves of the crossover point.
An alternative (I hope your maths are good) is to use a modified high pass section in the electronic crossover, and then use the protection cap to provide the last pole of the filter. This will work (it will work very well), but the mathematical complexities will be such that I expect few constructors to go this way. If you decide to do this, impedance compensation is essential to prevent the variable speaker impedance from affecting the crossover frequency.
A further disadvantage is that the electronic crossover cannot simply be swapped for a different type to allow comparisons, and with some filter types the approach will not work at all.
Type - When we contemplate high value caps (greater than 20µF) there is an immediate tendency to think about using a bipolar electrolytic. For this application, I do not recommend them, but sometimes you may have little choice. According to some, they are not recommend for any application, since they are (supposedly) sonically disgusting. I have not been able to measure distortion in a bipolar electro used sensibly, but there are many who claim that they destroy the sound. I shall not continue this debate.
The ideal is to use polyester or polypropylene caps, since their stability is so vastly superior to bipolar electrolytics that there is no comparison. They also have a comparatively unlimited life, but bipolar electrolytics gradually lose capacitance (and sometimes not so gradually), thus changing the crossover frequency (or disabling the tweeters completely when they eventually fail.
Good caps can cause some degree of financial hardship, but be assured, that is as nothing compared to the utter despair when smoke is seen escaping from your precious tweets.
If you are on a budget (decent caps at these values are expensive), one possibility is to use power-factor correction or induction motor start capacitors. These used to be oil-filled paper (some still are), and are much cheaper than 'electronics shop' devices. I can vouch for the sound quality, as I use these to protect my tweeters - most are polypropylene and of film and foil construction, although metallised film is used as well. The stability and power handling will certainly be superior to that of bipolar electrolytics.
These caps should normally be available from electrical supply outlets, since they are commonly used in electrical (i.e. mains house/ factory/ office) installations.
The amplifiers for a triamped system may have an effect on the final sound quality. This is especially true of the tweeter amp, which will generally not require a lot of power (depending on crossover frequency). If we assume that the power drops off at 3dB/octave above 1kHz for 'typical' music signals, we can do a quick calculation - this is not difficult (nor is it terribly accurate), but will give an idea of how much power will be needed for the tweeters. Note that this formula errs on the side of safety (i.e. the tweeter amp will have more power than is really needed), and this provides a good margin - a tweeter driver amplifier which is clipping is not likely to enhance the sound quality!
We might quickly re-examine the power of the low and mid amps first, assuming that we have selected the 'equal power' low/mid frequency of about 300Hz. For a typical system for home use, 50 Watts for each will generally be enough - especially when you remember that biamping can give up to the approximate equivalent of double the actual power of the amps - i.e. 200 Watts.
So, for this example, given that we have arrived at using a 50 Watt amp for mid+high, we are now going to triamp, with a crossover frequency of (say) 3kHz. This is approximately 1.7 octaves above 1kHz (it's a little more, but it is not worth worrying about).
At 3dB/octave, and 1.7 octaves, this results in a power requirement for the tweeters of -3 x 1.7 = -5.1dB relative to the midrange amplifier. Reversing the dB (power) formula, it can be seen that the high frequency amp will need 0.31 of the midrange amp's power.
0.31 x 50 Watts = 15.5 Watts. I suggest that a 20-25 Watt amp will be appropriate, and will have more than enough headroom. This hypothesis has been proven in practice - my own system uses 70W midrange amps and a 20W tweeter amp. I doubt that it has ever clipped since the system was first set up.
For 20 Watts, we can look seriously at using a Class-A amplifier, something that many people would die for, but is unrealistic for higher powers.
High power Class-A amps are seriously expensive to build or buy, and create a lot of heat. At the small power of 20 Watts however, they start to become much more attractive. They still create a lot of heat, but since this is proportional to their output power it becomes manageable at low powers.
A typical 20 Watt Class-A amp will dissipate about 100 Watts worst case, and although this is not insignificant, it can still be dealt with by conventional heatsinks and no fan cooling. This is not to say that the heatsinks will be small - they most certainly will not - but 50W per device (assuming transistors) is not too hard to get rid of.
At these powers, one might even consider a valve (vacuum tube) Class-A design, but I would not be inclined to this approach (personal opinion), however it may be that this could make musical magic. It you try it and love it, then you have a winning combination. Bear in mind that some tweeters do not like being driven with any appreciable impedance - the response may become uneven, with lots of small deviations from the ideal. In such cases, you need to use a transistor amp - the output impedance of most valve amps is at least a couple of Ohms.
Refer to the Project Pages for a design of a couple of transistor 15 to 20 Watt Class-A amplifiers designed for general use, but are ideal for driving tweeters. Includes the design and basic/generic construction details. As yet, I have not had time to test one of these circuits, so final specifications are not complete, but the DoZ is a fairly nice little amp.
Also, have a look at the (now old but still useful) design - 10 Watt Class-A Amplifier (By John Linsley Hood). You can also have a look at Project 72. While the LM1875 or TDA2050 is not normally suggested for true hi-fi, this is by omission rather than due to any major deficiency (although the TDA3050 is a better choice). However, a TDA7293 or LM3886 based amp is probably seen as more appropriate, and it's hard to argue against this.
When an electronic crossover is used together with the respective amplifiers for each channel, there is always going to be a temptation to experiment with the levels of the filters or amplifiers to act as a sort of tone control. To extract the maximum benefit from bi- or tri-amping, this should not be done, since it will effectively do a few things (all undesirable)
The optimum settings for the relative gains are dependent on only one thing - speaker sensitivity.
In order for this to make some degree of sense, we must return to our previous examples, and look at a few more diagrams. First, let's look at the ideal, where both speakers have a sensitivity of 90dB/m/W. In this case, the gains of the crossover sections (if gain controls are provided) should be exactly equal. Likewise, the sensitivity of the power amplifiers must also be equal.
In many cases, different amplifiers will be used, often with differing power ratings as well. This is where some measurements are needed, since both amps must have the same gain.
This is quite easy to do, but you do need a single frequency stable tone source - music is of no use, because it is too dynamic so levels are constantly changing. However you might consider the use of a test CD, which will have various frequencies at predictable levels. In many respects, this will be easier to use than any other method, since it requires only that the CD is inserted, rather than dragging oscillators or other signal sources about.
Unless the amplifier is a valve unit, it is not necessary to have a speaker load connected for these tests, or a suitably high-powered resistor can be used as a load if you want.
If a known level (say 100mV) is injected into the input of the amp you are going to use for bass (for example), you will measure an output voltage of about 2.5V at the amplifier output (this represents a fairly typical gain of 28dB). This must be identical for the amp being used for mid+high - assuming that the speakers have the same sensitivity. If the gains are not the same, you must install a volume control on the amplifier whose gain is the higher, and adjust until both amps produce exactly the same voltage at their outputs for 100mV input. The ESP Project 09 crossover has trimpots to allow the levels to be set.
For the test frequency, use an oscillator at about 400Hz, or if you don't have an oscillator at all, you can use the attenuated output from a small power transformer. This will not be as good, but it will work. The frequency will be either 50Hz or 60Hz, depending on your local supply. (If you don't know how to use a transformer to do this, ask someone to help - you can easily damage the input stage of the amp (and the rest of it !) if the level is too high). Alternately, use a test CD as mentioned above.
Figure 6 - Test Setup For Gain Measurement
The dummy load resistor should be equal to the speaker nominal impedance, and be rated at 5 to 10 Watts. Do not attempt to operate the amp at full power (especially if rated at more than 20W) into the load, or it will get very hot indeed. If you want to do this, then the resistor power rating should be at least double the expected amplifier output power. (Either that, or use lower power resistors and suspend them in a bucket of water - it will not cause a short circuit, fear not).
The voltmeter used may be digital or analogue - as long as it can read the voltage at the test frequency accurately - note that not all can do so!
This is where things start to get a bit tricky. You will need to be able to calculate the required gain to suit the speaker sensitivities - not hard, but you might find that the scientific mode on the Windows calculator is useful (unless you already have a full scientific calc, of course).
Depending upon the crossover frequency, you might need to use a higher powered amp for the bass end, if its speaker has a lower sensitivity. For the purposes of the exercise, we will assume that the midrange (plus high frequency) speakers have a sensitivity of 90dB / W @1m as before. But the woofers have a sensitivity of 88dB / W @1m so we need to calculate the power and gain differences (assuming that the 'equal power distribution' frequency of about 300Hz is being used - you want to use a different frequency? If you follow these procedures, you will become an expert at this stuff - guaranteed - because you will have to determine the relative power levels for the crossover frequency you are using - and I'm not going to help !
First, we will calculate the gain difference. Assume that the mid+high amp has a gain of 28dB, so the bass amp needs a gain of 30dB (the speaker is 2dB less efficient, so we just add the 2dB to the 28dB of the mid+high amp).
We will use the same 100mV input signal, so:
Gain = antilog (dB / 20) = antilog (30 / 20) = antilog (1.5) = 31.623
Since we started with 100mV (0.1V), the output voltage must be 3.16V from the output of the amp. That wasn't so hard. Now we need to determine the power output of the bass amp, if it is to exactly match the mid+high amp. Let's assume that we will use a 50W amplifier for the mid+high (with 28dB of gain).
P2 = antilog (dB / 10) * P1 (where P1 is the known power, and P2 is the unknown (higher) power)
P2 = antilog (2 / 10) * 50 = antilog (0.2) * 50 = 1.585 * 50 = 79.25W
Note that with the power calculation, the value of 10 is used, rather than 20 for voltage or current calculations.
We have now discovered that an 80W amplifier is needed with a gain of 31.6 (30dB), to exactly match the amp power and speaker efficiency of the mid+high combination.
Ah. So you have measured the amps, and have an output voltage, but cannot relate him to decibels. Fear not, another formula is at your disposal:
dB = 20 * log (V1 / V2) (where V1 is the higher (i.e. output) voltage and V2 is the smaller)
So if you measure an output of 2.32V at the output of the amp with an input of 100mV, its gain is ...
dB = 20 * log (2.32 / 0.1) = 20 * log (23.2) = 20 * 1.365 = 27.3dB
Note that in all calculations I have rounded the values to 3 decimal places, but when you do the calculations, retain all decimal places available for best accuracy. The difference is not great, but there is no need to introduce inaccuracies for no good reason.
To see what happens when the gain is not correct, we need to look at the crossover curves again. Refer to Figure 7 - the red and green traces. This is the optimal frequency response of the crossover/amplifier/speaker combination, with the resulting output being virtually flat (there is a slight rise at the crossover frequency which can be corrected using Linkwitz Riley alignment, where the crossover point is 6dB down - see Project 09)
Have a look at what happens when the amplitude of one filter is different from what it should be. This is also shown in Figure 7, and it is clear that the effective crossover frequency is shifted. What is not so clear is the final frequency response, and in the case of any crossover filter that is not phase-coherent, the adverse effects of the relative phase relationships. These are extremely difficult to quantify, but may be apparent in listening tests. The problem is that if you are unaware of the problems that can be created by modifying gain indiscriminately, it will be very hard indeed to determine why the system just doesn't sound right.
Figure 7 - The Effect of Changing Gain on Crossover Frequency
It is very obvious that the effective crossover frequency has changed. At normal gain, the crossover is 295Hz, but if the gain is increased as shown, the crossover frequency shifts up to 500Hz. If the gain is reduced, the effective crossover frequency is now about 150Hz. Naturally, the same thing happens if we change the mid+high gain. Note that the filter cutoff frequencies are not changed, only the level with respect to the adjacent filter.
This is not just the output of the filter we are looking at, but rather the final output from the speakers - as shown above, it will often be necessary to change the gain of amplifiers to match the efficiency of the loudspeaker drivers used. This does not alter the crossover frequency as you might expect, but brings it back into proper alignment. In fact, if the gain is not changed, then you will get a result similar to that shown, by effectively amplifying one frequency band more than it should be for the correct tonal balance.
Somewhat remarkably, it is actually fairly easy to get the balance very close to optimum purely by ear. If you have a pair of good headphones, this provides an excellent reference, and any appreciable response deviation in the loudspeaker system can be corrected quite accurately. It is even possible (although not recommended) to use the crossover level controls as a 'tone control' - this can even help make some recordings acceptable to listen to. Some speakers using passive crossovers provide level controls for mid and high frequencies, and the same can be done with an active system (but with no power loss).
With any electronic crossover, it's possible to use pots at the output of each filter. This allows you to adjust the levels to get an overall flat response, but it also lets you use the crossover as a tone control of sorts. In the DJ world, this is known as a 'frequency isolator', but with a fully active system it comes (almost) free. The cost is only a few pots and knobs, and you can use trimpots to preset the optimum flat response. All this is provided on the Project 125 PCB, so you can play with the system to your heart's content. It goes without saying that doing the same thing with passive crossovers is well-nigh impossible.
The crossover / amp / speaker combination has to have the correct gain structure if a flat response is desired, and any variations can be quite audible. The audibility varies with the type of music, and depends a lot on your hearing. In some cases, a slight unbalance can sound better than a perfectly flat system, and can be used to compensate for some room influences, minor driver anomalies or personal preference. Some passively crossed loudspeakers have a L-Pad level control for the tweeter, although these are a lot less common that they once were. If available, this does the same thing as changing the amp gain in an active system.
With a phase-coherent crossover, I have found that the ability to use the crossover gain controls as a 'tone control' seems to work fine, and there are no real anomalies that I have heard (apart from the obvious prominence of the louder frequency band). This is something I often do with my workshop system. This unit runs from my tri-amped, phase-coherent 3-way variable impedance test amplifier (that's a mouthful). I am forever fiddling with the gain structure, amp output impedance and crossover frequencies, and although not ideal (although it has come close with some of the loudspeaker drivers I have there), it nearly always manages to sound much better than it has any right to.
With a conventional passive crossover network, the correct amplitude matching of the loudspeaker drivers is very important, but is usually fixed and cannot be altered. Even with an active system, correct level matching is not just to ensure a flat response, but to ensure that there are no additional phase problems created by the variations. There will nearly always be phase problems with passive crossovers even where the design is very complex, and these errors must create problems in either frequency response or overall accuracy (these don't necessarily coincide, although in an ideal situation they would).
Amplifier loading is another issue that cannot be ignored. The load presented should be essentially resistive (again in this mythical ideal situation), but in reality this is rare. Using electronic crossovers and separate power amplifiers alleviates the issue somewhat, especially for the mid+high section, but the variable reactive load posed by a typical bass reflex type enclosure is always going to cause amplifiers to get a little hotter than expected. Reducing some of the problems by eliminating a passive crossover network (or part thereof) can go a long way towards improving the load seen by the amp, and potentially reducing amplifier intermodulation distortion (in particular). The reduction is largely brought about by making the amp work over a more limited frequency range than normal.
In short, there is no reason for a DIY enthusiast to avoid biamping, since the costs involved are very much lower if you make the crossover and power amplifiers. In addition, it is possible to obtain results that are startlingly good, without the considerable difficulty and expense of tweaking a passive crossover network. The latter can easily cost a hundred dollars or more, and if it's not quite right one can easily spend another hundred dollars trying to get it to sound like it should. By comparison, an active crossover costs between nothing and a few cents to change. Need I say any more?
Although this is a topic I've mentioned briefly, it needs to be discussed properly. Using two amplifiers and two sets of speaker cables to drive the existing passive crossover is something I call 'passive biamping' or 'active biwiring'. Various websites may claim that it's true biamping, but it's not, never was and never will be.
In some cases users may hear an improvement, but make sure that it really is an improvement and not just a difference. Because you have separate amps driving the two sections of the crossover, you can easily have a level mismatch that leads you to think that the sound is 'better'. The gains of the two amps used must be identical, or the original balance between mid and high will be changed. Naturally the specific frequency depends on where the passive crossover splits the signal. Apart from (usually) a slightly easier load on the amps, both amplifiers still reproduce the full audio bandwidth, so there is no effective power gain.
In general, it is likely that the improvement - assuming there is an actual improvement of course - will be small. It will commonly be so small that the additional cost cannot be justified, but this is cold comfort if you've already bought the amplifiers and speaker cables. Speaking of which, make sure that you read the articles on this site about 'high end' (rip-off IMO) speaker cables before parting with large sums of money.
For some additional details on the real differences between active an passive systems, see Active Vs. Passive Crossovers. In particular, loudspeaker damping is always affected (sometimes seriously) by any passive filter, and commonly right at those frequencies where good damping may help control cone breakup and other unwanted effects.
This really isn't a topic that can be concluded, because there are so many possibilities and variations that there is enough to fill a complete book. Books have already been written about a great deal less, however this is not going to happen and this article (and the others referred to herein) will have to suffice. However, it would be remiss of me - and has been up until now - not to include a very important diagram.
The diagram below was originally produced by Altec, and shows the musical scale, our range of hearing, and various instruments and their most prominent harmonics. I added guitar to the diagram - when it was originally produced the guitar was never taken seriously. I don't have the original publication date, but I recall having seen the diagram a great many years ago. My guess is that the first publication dates from some time in the 1940s. Concert pitch (A440) is shown highlighted in yellow, Middle C is C4 (261Hz) and a grand piano (88 keys) covers the range from A0 to C8.
Figure 8 - Comparative Ranges Of Human Voice And Musical Instrument Frequencies
The above is based on a scan sent to me from the book "Stereo High Fidelity Speaker Systems", by Art Zuckerman 1978. It has been completely re-drawn and this version is copyright © 2010 Rod Elliott. The original is credited to Altec Sound Products.
It is notable that no harmonics are shown for voice - not because they don't exist, but because voice contains other noises (plosives, sibilance and other non-harmonically related sounds). The sound of a "p" right next to a microphone can generate frequencies below 20Hz, and sibilance can create sound above 20kHz. Many of the other harmonic limits shown are considered to be well shy of reality - cymbals can generate frequencies up to around 100kHz for example, but virtually no-one records them and they are considered redundant by most people. I have not attempted to amend the original in this respect, but preferred to leave it as originally created. Interestingly, it seems that no-one is interested enough to re-create this diagram using modern measurement techniques (pity).
The diagram is interesting and included here because it shows the general balance of musical instruments very well. The 'intelligence band' I referred to in several places on this site covers from roughly 300Hz to 3kHz (D4 to F7) and is indicated at the bottom of the drawing. Somewhat surprisingly, with only this frequency band, we can discern who is speaking and what is being said, or which instrument is playing - we can even hear the bass! This is as heard through telephones ... fixed line, not mobile (the latter are often digital effects units more than telephones) or small portable AM/FM radios through their little speakers. That our ear-brain combination can gather so much from so little is nothing short of astonishing, so this is an area I like to cover with a single driver if at all possible.
Of course, it is not only an important frequency band, but a difficult one to reproduce accurately. This is the true mid-range band. Mess this up, and your best efforts at speaker building will never sound right.
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