The disappearance of the traditional amplifier

Kirkus, again I have to kindly disagree on some points. Also omnidirectional source directivity is constant, and in power response terms the driver type has no inherent effect. In most practical cases the limited radiation angle is achieved in a certain bandwidth, not from 20 to 20k. Horns and waveguides can both be mathematically modeled and optimized and there are several BEM packages doing this. They usually model also the diaphragm radiating into the waveguide, as without that the picture is incomplete. The modern directivity control appeared first in sound reinforcement field, where the coverage is important. Altec made their Mantaray horns, using basically two flares and an abrupt joint between them. First expansion created the vertical pattern, opening into a narrow arc-like slit - being in itself a (horizontally) wide radiator- and the second flare controlled the horizontal pattern. The JBL Bi-radial horns use the same principle. In very simple terms a waveguide could be interpreted as the outer flare of a constant directivity horn, if you so wish. The fact that the throat area is equal to diaphragm area, i.e. there is no compression, mainly affects efficiency, which is higher with horn drivers. However, also waveguide improves efficiency in two ways: the actual radiating impedance is better matched, and the same energy is radiated into smaller solid angle than without waveguide. These factors are connected and the net result can be seen in the raw responses of the link, the sensitivity at the low end of the tweeter passband is higher. This is very good result as the improved sensitivity is easy to equalize and it improves tweeter reliability.
I do not understand what you actually mean with saying, that "for true constant-directivity performance to be possible, the wave-front propegation has to be constant with frequency." For constant directivity the radiation angle has to be independent of frequency. In practice the radiation angle vs. frequency has some ripple, as can be seen also from the O500 graph. O500 has a 300 mm woofer and its radiation angle (-3 dB) can be seen changing from 180 degrees at around 140 Hz( there seems to be measurement errors due to room limitations) to about 80 degrees at 500 Hz, then there is small ripple at upper crossover around 3 kHz,because the soft dome midrange becomes a more directive ring radiator, then it is getting narrower to about 40 degrees and again widening to 80 degrees at 15 kHz and getting narrower above that. As a whole this is can be regarded a good practical approximation of constant directivity, just like the performance of its predecessors, Genelec 1037, having also a 300 mm woofer and a bit smaller MF/HF waveguide, and 1038, having 385 mm woofer and larger waveguide. Those came to market already in early 90's (about 10 years before K+H O500) while their first predecessor, Genelec 1022A came to market in 1985.

Two-way speakers can be designed to constant directivity as well, but due to smaller woofer, the bandwidth of this behavior is not as wide and starts at least one octave higher. Even then the practical improvements are clearly audible. To make the woofer more directive at lower frequencies you can naturally use cardioid designs and accept the consequences in available power.

I kindly disagree with some of the comments concerning Genelec waveguides. In non-anechoic conditions we always listen both direct and reverberant field, most often the reverberant field is dominating. The reverberant field balance depends on speaker system's power response, i.e. total radiated power in all directions, not only on axis. Systems without any directivity control exhibit uneven power response having dips around crossover frequency(-ies) due to the simple fact, that lower frequency driver is more directive at its high end cutoff, than next smaller driver at its low end. The waveguide limits the directivity of the higher frequency driver (MF or HF) to the same as that of the lower frequency driver, and makes the total directivity uniform. This happens with the Genelec waveguides and for example with the JBL Bi-radial horn used in 4430/35. The frequency range depends on the size of the waveguide. The other important consequence is reduction of diffraction from the cabinet edges, and this is obvious in stereo imaging. A trivial mono signal reveals the truth easily.
If the power response is not uniform, the perceived balance depends heavily on the room and listening distance, and these simple facts are source of endless discussions.

As for field coil drivers, they still suffer from the very basic source of nonlinearity, iron. Regardless of that, field coil drivers would be easiest to use with active speakers, as power supply is inherently available. The drawback is naturally heat dissipation.

IMO active speakers can definitely be better performers than passive - there are many inherent technical reasons for that - but in addition to skills in electroacoustic design it requires a second skill set for proper amplifier design.

Kirkuk,

Power response predicts the perceived balance for all types of systems, also for those with constant directivity. Another factor affecting that balance is room absorption vs. frequency.

" It's pretty much irrelevant for the issue of establishing the best directivity characteristics of the driver(s) themselves. Consider that (for a single driver) electronic equalisation is supremely effective in altering the summed power response, but completely ineffective at solving directivity issues."

First: The Directivity Factor (DF) is the ratio of the intensity of a source in some specified direction (usually along the acoustic axis of the source) to the intensity, at the same point in space, due to an omnidirectional point source with the same acoustic power. Directivity Index (DI) is logarithm of that factor. The whole issue is defined as intensity ratio, and in itself it does not matter what kind of source you have. For constant directivity it is sufficient to have DI which does not, within tolerances, depend on frequency. In practice this can be achieved in many ways, horns and waveguides being good examples of them.

For simple cone or dome radiators, electronic equalization can be used to equalize the pressure response at a certain axis (mostly the main axis) of the driver. However, equalizing response very flat on one axis often means the response is worse on some other axis. This is a common problem with powerful DSP and diffraction ripple. Electronic eq cannot change how the driver does its radiation job, it can affect only the signal you put into it. Equalizing power response without simultaneously affecting on-axis pressure response is not possible.

As said, power response depends on the radiation characteristics of the driver, i.e. how much its radiation is attenuated off axis compared to on-axis radiation. Most important factor affecting this is the radiator effective diameter in relation to wavelength. When the diameter is much smaller than wavelength, the source is omnidirectional. Hence a 1" dome at 3 kHz is practically omnidirectional but at 20 kHz it is not. However, a 1" throat of a compression driver has same diameter and its directivity characteristics then depend on the shape of the wavefront propagating in the throat and later in the horn. Often also CD horns are pretty directive at 20k as well, but I agree with you that with a good 2" compression driver and well designed horn you can get about 4 octave bandwidth with good directivity control, acceptable frequency response and distortion. With a larger diameter driver you can add an extra octave on the low end at the cost of HF performance. This is a nice system if size and price are not too important. Like all drivers, compression drivers have their own set of compromises and it depends on the desired performance what features are regarded valuable. For example: compression drivers suffer from air nonlinearity causing distortion at high levels, but on the other hand, there is no better way of generating high SPLs. Therefore there have been long standing efforts to eliminate the distortion, one possible way is to predistort the signal in a predictable way. This is basically similar to analog tape recording. DSP can do audible improvements in this respect.

You are right in referring to the aim to match directivity of drivers. However, I see no practical problem in rotating the waveguide in 3-way Genelecs as the MF/HF section still remains vertical. Because the LF/MF crossover is somewhere around 400 Hz (i.e. pretty low) there will be no practical difference whether vertical or horizontal, but of course the room reflection pattern will change due to different height of the woofer. The woofer directivity remains as it is and so does the MF, the only changing parameter is their relative position. You see the same off-axis performance between woofer and MF driver either in vertical or horizontal off-axis measurement, i.e. when going sufficiently off axis you start seeing the crossover. You can naturally calculate the first off-axis zero from the driver distance. If you take 400 Hz as crossover, wavelength is 0.85 m and half of that is 0.43 m. The first zero is at angle where the distance difference is half of wavelength.

I think all two-ways should be used vertical, because of the same off-axis dip appearing at crossover. Naturally the same dip exists also when a two-way speaker is vertical but its audibility is small. Naturally if you have brickwall filters there will be no interference, then you might only notice the changing source position.