As has been seen, radiating sound at low frequencies requires a large diaphragm, whereas radiation of high frequencies requires a small diaphragm. One solution to this is to use two or more drive units, each operating over a particular range of frequencies. As the use of two or more drive units is purely an engineering solution, the listener should not be aware that it has been done. In other words the two drive units must be combined in such a way that the listener hears something indistinguishable from the sound of a single ideal driver. This requirement is possible, but is seldom met in practice.

At some point prior to the drive units, a frequency-selective filtering device known as a crossover network, or just a crossover, will separate the input spectrum according to the frequencies needed by the drive units. Figure 1 shows that in addition to the crossover filter prior to the drive units, which acts in the electrical domain, there is a summing process located after the drivers, that works in the acoustic domain. If the electrical crossover fails to complement the acoustic summation, quality will be lost. This is an area that is traditionally neglected in legacy loudspeakers. Typically drive units are placed almost at random on the front of a wooden box and the sound has to make the best of it.

At the crossover frequency itself, half of the sound power is radiated by each driver, so the apparent size of the source is affected by the spacing between the drive units. Figure 2 shows what can happen. Directly ahead of the two drive units, sound has travelled an equal distance from both and so will add coherently. On the other hand at points above or below that the sound will have travelled different distances and at some frequencies the difference might be half a wavelength. In that case instead of addition, there will be cancellation. This is one of the reasons why legacy loudspeakers have sweet spots. Real sound sources, of course, do not have sweet spots.

There are some solutions to that problem. One solution is to use a low crossover frequency such that the wavelength is long enough that the path length differences of Figure 2 do not cause serious phase shifts. This will be assisted by placing the two drive units as close together as possible. Another solution is to employ a coaxial drive unit in which the high frequency sound is radiated from the center of an annular low frequency diaphragm. This solution was adopted in the coaxial speakers designed by Tannoy, over 50 years ago, in which the woofer diaphragm formed the mouth of the tweeter horn which ran up the center of the woofer magnet. The directivity characteristics of these speakers were well ahead of their time.

Returning to the radiation at the crossover frequency, it is clear that there should be no change in output power as the crossover is traversed. This leads to the oft-heard misconception that the signal supplied to each drive unit should be 3dB down at the crossover frequency, since -3dB is the half power level. In fact this is not the case, because of the way acoustics works between a pair of close-spaced drive units. What happens when two adjacent drive units radiate the same signal is that each one affects the acoustic impedance seen by the other and they make each other twice as efficient.

In order to see why that is, imagine building a wall between the drive units, so they could not affect each other. The presence of the wall means that each drive unit is now radiating into half the previous solid angle, so a given displacement produces twice the level. But if the drivers are radiating identically, conditions on both sides of the wall are equal and opposite, so it may as well not be there. It follows that the correct level to supply to a drive unit at the crossover is 6dB down. Coherent sound in the vicinity of multiple drive units adds linearly in just the same way as do voltages in an analog mixer or numbers in a digital mixer. That gives us some clues about what a crossover network should do.

The slope of the crossover has been the subject of much debate and in many cases the result is a compromise. Where the relative positions and characteristics of the two drivers are optimal, a very shallow crossover will work. However, when the rest of the speaker is sub-optimal, such that obtaining coherent acoustic addition of the sounds from the drivers is a challenge, a steep crossover may reduce the width of the frequency band where the problems can be heard. This does not mean that high-order crossovers are better; it means they are capable of palliating or concealing other problems. In passive speakers, high-order crossovers generally destroy the time domain information because their phase characteristics are less than ideal. When you see the tweeter connected in reverse polarity to make the crossover work in the frequency domain without a suck-out, be very suspicious indeed about what is happening to the phase. Expect a square wave to be unrecognizable, along with any percussive sound.

As sounds add linearly in the air in front of the drive units, it follows and indeed it is obvious, that one of the fundamental requirements of a crossover is that it should produce a pair of electrical signals that, if added, would reproduce the original audio waveform. A crossover that can do that is called a constant-voltage crossover.

It came as a surprise to me when I discovered, some time ago, that it is fundamentally impossible to obtain such a pair of signals from any passive crossover. In other words, passive crossovers cannot and do not work because they fail to provide the signals necessary for the drive units to linearly add together again. Passive crossovers will always be audible because in the vicinity of the crossover frequency the input waveform cannot be reproduced correctly. Passive crossovers have various other drawbacks including unwanted DC resistance that reduces the damping factor of the woofer and common impedances that reflect woofer distortion currents into the tweeter.

Although transducers do not adhere to Moore’s Law, electronic devices such as crossovers and amplifiers do, and the cost of the electronic parts of an active speaker falls every year. When it is considered that only an active crossover, implemented in digital or analog circuitry, can provide the required constant-voltage performance, the direction to take is obvious.

The reason passive crossovers cannot work is that subtraction in passive circuitry at power level is impossible, whereas in the digital domain or using operational amplifiers, subtraction is trivially easy. Nevertheless it is necessary to take some care, even with active crossovers. In the digital domain it is possible to make linear-phase filters easily. If, for example the woofer signal is derived from a linear phase low-pass filter, then subtracting that signal from the input will yield the tweeter signal. However, linear phase filters always cause delay. Although a loudspeaker that delays the input would not be a problem for listening to pre-recorded sound, it would certainly be a problem for PA or for amplifying a musical instrument.

Filters that cause no delay, on the other hand, are not phase linear. These include analog filters and Infinite-Impulse-Response (IIR) digital filters. If the output of such a filter is subtracted from the input, the result will still be a pair of signals that add to the original, but the crossover will not have symmetrical slopes. One frequency band may have a slope of 12dB/octave whereas the other might only be 6dB/octave, and that might cause difficulty.

If a symmetrical crossover is required, one solution is to use a state variable filter, a class of filter having more than one output which uses internal subtraction and can therefore provide constant voltage operation. State variable filters also set traps for the unwary. With inputs and outputs well inside the limits, internal signals can overload and it is necessary to take great care scaling the levels throughout the device.

A further advantage of active speakers is that following the crossover, each drive unit has its own directly connected power amplifier with no unwanted impedances in between and no possibility of intermodulation between the drivers. A serious drawback of active speakers is that the amplifiers are inside and the owner cannot be sold hopelessly over-specified and over-priced speaker cables.

Typically in passive speakers the drive units have to have similar sensitivities in order to match their sound outputs and this can result in quality compromises. In active speakers this is no longer a requirement and each driver can be optimized for the task and fed with whatever electrical level is needed to match sound levels. Level matching in a linear phase loudspeaker with a constant voltage crossover is simple. The levels are simply adjusted to get the best square wave.     

Editor note: John Watkinson is writing a tutorial series on loudspeaker design. Earlier articles can be found in the linked titles below: