Why horns?

What are the reasons for using these large speakers today, when amplifier power is cheap and plentiful, and everything is getting smaller, better and cheaper? Or is it really getting better?

And do horns sound good? Aren't horns full of resonances and colour the sound? What about horn distortion? We have all heard bad PA systems and megaphones, which both use horns. Is this how horns sound?

Historical background

From the earliest times of sound reproduction, the horn has been looked upon as a necessary evil that is too big and clumsy for home use. Its size could be tolerated in theatre and public address sound systems, but for home use, even in phonographs, its size has for the most time been reduced as much as possible, even to the extent of introducing severe resonances. Only a very few enthusiasts could tolerate the large cabinet gramophones or loudspeaker horns.

In the good ol' days, horns were necessary. In phonographs it was the only way to get any usable SPL from the records, and when it came to electric loudspeakers, efficiency was important since amplifier power was very expensive.

Today, horns are used mainly in public address and sound reinforcement systems, because of their high efficiency (even though amplifier power is cheap, high efficiency is needed to get the required SPL without too many speakers, and without frying the voice coils), and because of their ability to control directivity.

So the use of horns in PA and SR is quite obvious. What then about home use? The need for two speakers for stereo removed many of the large home speakers used for mono reproduction, and since amplifier power became cheap (the introduction of the 6L6 helped a lot), smaller speakers and more powerful amplifiers became the trend. But then came the single ended triode amp revival. With output powers in the 2-10W range, the usual 80-90dB/1W/1m speakers made the amp reach their clipping point at low SPLs, with the result that this combination worked best for music like simple jazz. The intermodulation gets too obvious on more complex sounds. A solution was needed, and old horn designs like Altec Voice of the Theatre, Klipschorns and Lowther/Voigt designs became popular. With efficiencies in the 100-110dB/1W/1m range realistic SPLs can be had with a single triode watt or two.

To show the difference, let's assume we have two speakers, a) one direct radiator (DR) with 88dB/1W/1m efficiency, and b) a horn speaker with 110dB/1W/1m efficiency. What amplifier power will we need to reproduce 105dB SPL and 120dB SPL at 1m distance? (One might say that no one plays music at 120dB SPL, but consider this as peak SPL, and that the average level will be quite a bit lower, depending on the crest factor of the music. In any case, the peaks should not be clipped).

This means that we can get realistic levels with a single-ended 300B triode amp, and that even a 2A3 amp isn't too far off. And we still have heaps of power to spare at more sane levels!

But there is more to horns than high efficiency, although many of the other advantages come from this property.

Power compression

For a low-efficiency speaker, most of the supplied power (95-99.9% of it, actually) is used for heating the voice coil, and only 0.1-5% used for producing sound. This temperature rise causes the resistance of the voice coil to rise, with the result that less power is drawn from the amplifier. To maintain the same SPL, one has to turn up the amps, heating the voice coils even more, and so on. In the example above, assuming speaker a) could handle 1590W, it is doubtful that the SPL would be 120dB, as efficiency falls dramatically when the voice coil resistance rises.

Distortion

No loudspeaker is completely linear. For a loudspeaker driver, distortion is more or less proportional to diaphragm displacement. At large diaphragm amplitudes there is variation in the force factor (BL), the suspension is no longer linear and the diaphragm breaks up. The smaller the amplitudes, the less the distortion. Most people don't know the distortion figures of loudspeakers. The manufacturers almost never quote them, as they can often be as high as 10% at maximum excursion. (One can ask if it makes any difference if the amp driving such a speaker has 0.1% THD or 0.0001% THD...) As we'll see, horn loading of a driver reduces the diaphragm amplitude, so that instead of quadrupling the excursion for every octave lower frequency, there is only a doubling for every octave. Why? The secret is to give the driver a resistive instead of a reactive load. Let's have a look at this.

Here is a simplified equivalent diagram of an electrodynamic driver:

Mat is the total moving mass.

Rat is the total loss in the driver, including voice coil resistance and friction losses.

Cat is suspension and box compliance.

Ral is the acoustic load, where the diaphragm movement is converted into acoustic power. P = v²Ral, i.e. power is cone velocity squared times load resistance.

Let's now take a look at how Ral varies with frequency for a 10 in woofer.

The black line is the resistive part of the radiation impedance, where the acoustic power is dissipated. This is Ral. For low frequencies, this is very low, but it rises 6dB/oct up to the frequency where the wavelength is equal to the driver circumference (kr = 1). This means that the response of the driver is largely controlled by the reactances in the system below this. For low frequencies, below resonance, Cat controls the response, and since it is a 1. order filter, it rises 6dB/oct. Since Rat also rises 6dB/oct, we have a 12dB/oct roll-off below resonance. At resonance efficiency is at its highest. Above resonance, because of Mat, the response rolls off at 6dB/oct. But since Ral rises at 6dB/oct, this compensates for the drop due to the mass, and response is flat up to kr = 1, where Ral flattens out, and the response drops off again due to the mass (this is called the mass roll-off frequency). Usually, the response extends several octaves beyond this, because the cone breaks up and the effective mass is less.

If cone velocity was constant, the power output would rise 6dB/oct. But as we have seen, because of the mass, the output is flat in the so-called mass-controlled region (between resonance and kr=1), which means that cone velocity will double as frequency is halved, which again means that diaphragm displacement increases four-fold.

Then enter the horn:

This is the radiation resistance seen at the throat of an infinite 40Hz exponential horn. As we can see, Ral rises quite rapidly to its final value. This means that Ral will dominate the response down to quite low frequencies. Starting again at low frequencies, Cat dominates, but it quickly reaches the value of Ral, and the response is then flat. As frequency increases, we reach a point where Mat starts to take over and roll off the response. Between these two frequencies Ral is the dominating factor, and the horn does not exhibit any resonance.

When working into a constant resistance, the cone velocity must be constant for a constant power output with frequency, which means that as frequency is halved, diaphragm displacement only doubles. If we look at this over several octaves, we see a distinct advantage over DR's. Assuming 0.1mm displacement at 800Hz, a mass-controlled DR would have 25.6mm displacement at 50Hz, while a horn-loaded driver would only have a 1.6mm displacement. That is quite a difference!

Then comes the distortion in the horn itself. This is a quite important issue in PA and SR systems, where sound pressure is very high. It has often been an argument against horns, that they have high distortion in the throat because of the non-linearity of air. In their investigation on what contributes to "horn sound", Keith Holland and his colleagues at Institute of Sound and Vibration Research investigated this, both through simulations and measurements.

The following chart shows the levels of the different harmonics at the throat for a distortionless sine wave of 150dB SPL at the mouth of the horn. Cut-off is just above 300Hz.

At this level, at 1kHz say, 2^nd harmonic distortion is about 30dB below the fundamental, or about 3% distortion. Also note that distortion increases for frequencies far above the fundamental.

What about lower levels? Here are curves for the level of the harmonics at 1kHz vs SPL out:

So at 110dB SPL at the mouth, 2^ndharmonic is about 65dB below the fundamental. On the basis of this, we can conclude that horn distortion due to the non-linearity of air is very small for SPLs encountered in home listening, and will most likely be swamped by driver distortion.

Let us compare this to a direct radiator. Here are measurements done by Klipsch on a midrange horn and an 8in driver. F1 is 540Hz @ 100dB SPL @ 2ft, F2 is 4400Hz @ 92dB SPL @ 2ft. 10DB/div.

The upper spectrogram is the horn. IMD is about 1% (includes driver distortion). The lower shows the spectrum of the DR, with about 10% IMD.

Damping and dynamics

It is well known that horns have a dynamic and "forward" sound. Transients often sound more like transients, so percussion sounds more real. Why? Let us first compare some aspects of direct radiators and horns:

The combination of well damped resonances and a small moving mass moving a short distance driven by a coil immersed in a powerful magnetic field results in a fast response. Here is the impulse response of an Altec 288B on a plane-wave tube:

The result of this is a fast, dynamic presentation of transients. Some may argue that as long as the frequency response is flat, the reproduction of transients will be perfect. But that only applies to a minimum-phase system. A loudspeaker is not a minimum-phase system. There are frequency dependent time delays, resonances, diaphragm breakup, mass has to be accelerated and decelerated, and the effective mass of the diaphragm changes with frequency. Getting the frequency response flat will not fix everything. But if we get the impulse response right in the first place, the other things will fall in place too.

Progress?

Who wouldn't have an impulse response like the one shown above? This is a compression driver from 1956, optimally loaded. It makes you ask, has there really been progress in the art of sound reproduction since then? Well, of course there has. But at the same time there have been great side steps and steps backwards. We have made progress in certain areas, but gone backwards in others. The mass controlled upper frequency of compression is nearly unchanged since the 1920's. But we have increased high frequency output drivers by using diaphragm breakup and stiff suspension. This has the consequence that the lower limit of the range has been raised, so that the resistance controlled region has become smaller. Western Electric 555W was resistance controlled from about 50Hz to 3kHz, and Altec 288B is in the same league. JBL 2470 (phenolic diaphragm) rolls off at about 500Hz, see measurements below. Red line is Altec, black line is JBL.

Why has this happened? Since the mid-1930's, horns and drivers have been developed by the PA industry, where the main objectives have been high power, high efficiency and directivity control. Using horns is the only way to obtain this. But other important factors, that have become more and more important, are size and cost. Bass horns are large, heavy and expensive. So the industry has changed to cone drivers and bass reflex enclosures in the low range, and pushed the range of horn loading further and further up. Horn loading below 2-3kHz is not very common in newer systems, and this is in fact the upper limit of the resistance controlled region of most drivers! So why do PA systems often sound screaming and nasty? They use their horn drivers in a range they can't cover without diaphragm breakup, which in itself is non-linear and uncontrolled. In addition, they often use conical horns for directivity control, and conical horns do not have much loading to offer the driver in the important range. Modern drivers on modern horns do in fact not operate in the resistance controlled range at all...

Then, Why Horns?

From the above discussion, it should be quite clear. Horn loading gives huge gains in dynamics and distortion reduction, if it is done right. And this means, simply, that a horn driver has to be operated in its resistance controlled region, connected to a horn that offers the driver a constant high load resistance. By just adopting current sound reinforcement practice we can't expect to experience what horn loading really has to offer. But by exploring the old horn art, we can get tight bass, dynamic midrange and clean highs, all presented with a purity and detail unmatched by other speakers.