Constant Directivity Horn Equalisation

A very curious thing was discovered when I did a search.  There are very few CD horn equalisation circuits published on the Web.  Anywhere.  There are a few passive circuits, but almost nothing that is actually useful for the budding PA system builder.  I have no doubt that they exist, and there are plenty of graphs showing the response after EQ has been applied.  The missing link is the actual circuit.  Somewhat predictably, that was the impetus I needed for this project.

Constant directivity (CD) horns are rather unique amongst high frequency reproducers.  Conventional (exponential or tractrix) horns have a flat on-axis response, but generally provide reduced high frequency energy off axis.  The CD horn was developed to ensure a reasonably constant response both on and off axis, and they mostly use a diffraction technique to obtain the best possible off axis frequency response.  Horns are coupled to compression drivers, which exhibit very high acoustical efficiency, with a typical output being around 110dB/ 1W/ 1 metre.  While there are also waveguides that can provide a similar effect, these are typically used with conventional tweeters, which don't even come close to the efficiency of a compression driver.

The line array speakers that now make up the majority of sound reinforcement systems use a diffraction horn, with the 'line' supposedly providing constant directivity at all frequencies.  However, this only really works at mid to high frequencies, where the line is large compared to wavelength.  The equalisation needed for these is usually customised to the length of the array and how it's set up.  The equaliser described here is unlikely to have the range to compensate for the response anomalies that are inevitable with these systems.

Because a CD horn has (at least in theory) constant directivity regardless of frequency, the higher frequencies no longer 'beam', and thus produce constant sensitivity on and off axis.  However, the total HF energy rolls off at 6dB/ octave above a frequency where the horn driver starts to roll off naturally.  The diffraction frequency varies between horns, and the frequency above which boost is required depends on the size of the diffraction aperture (aka 'slot') and the driver response.  It is essential that you have all the information provided for the compression driver and CD horn before you start to work out the electronics.

There are many claims both for and against CD horns, and there are a few people who either don't like them, or hate them with a passion.  This is not an argument I'm about to enter, and the project is simply an equaliser that is designed to provide the required 6dB/ octave boost, but is more flexible than any alternative (other than a carefully adjusted parametric equaliser perhaps).  You need to decide on the frequency where boost starts, and for this you need the data for the horn and compression driver.

High-frequency compression drivers have an output roll-off above a frequency determined by the mass of the diaphragm assembly (the 'mass break-point').  The mass of a larger diaphragm is greater than that of smaller units, as is the voice coil.  A larger magnet and an increase in the length of wire in the magnetic gap provide more driving force, allowing a larger driver to maintain its mass break-point close to the same frequency range as some smaller drivers.  This is not readily apparent with 'conventional' horns, because they restrict the coverage angle at high frequencies, and this (at least in part) compensates for the driver's inherent roll-off.

For most drivers intended for high quality sound reinforcement, the mass break-point is typically between 2.5kHz and 3.5kHz.  Above that frequency, the response falls off at 6dB/ octave.  In some installations, the roll-off can be ignored, since it may be within accepted system equalisation practice, or is not apparent because conventional horns are used and listening tests may only be performed on-axis (or at limited off-axis positions).  In the cases of studio monitoring and music reinforcement, the inherent roll-off of the driver usually has to be compensated.  In some cases, this might only be via existing equalisers in the playback system.

Because of the high efficiency of a horn loaded compression driver, the high frequency components of a system are always operated at reduced power level relative to the low-frequency section.  That means there is usually power to spare, allowing the frequency compensation to be added without the need for higher amplifier power.  This is helped greatly by the nature of music itself, where the power requirements above ~2kHz also fall at around 6dB/ octave (20dB/ decade).

CD horns require equalisation (EQ), with a response that rises at 6dB/ octave.  The frequency where the output starts to roll off depends on both the compression driver and the horn, and it's essential to get the data from the manufacturer, or run your own frequency response tests and work from there.  The latter approach is essential if the horn and compression drivers are not from the same maker, a common situation in PA systems in particular.

The frequency where high frequency boost is needed is variable, but it is usually in the range between 2.5kHz and 4kHz (for smaller drivers), and sometimes higher with some of the more advanced offerings.  While the theoretical slope is 6dB/ octave, there may be situations where this makes the HF too prominent, and a lower slope may be preferable.  In fact, a lower slope will almost always be the case, because a perfect 6db/ octave slope is actually much harder than it sounds.  We tend to think of simple RC networks providing a true 6dB/ octave rolloff, but that really only happens at a frequency well removed from the nominal ±3dB frequency.  It's also necessary to ensure that boost does not continue above audio frequencies, and a low pass filter is absolutely essential.  This should be set no higher than around 22kHz, but is always a compromise.

The combined response of a low pass filter and HF boost circuit may have a theoretical boost of 6dB/ octave, but in reality it will rarely be much better than around 4.7dB/ octave.  For most applications, this will be all that's needed.  The horn's roll-off is subject to the same laws of physics as the compensation circuit, but acoustic influences can easily mean that less boost is needed.  If applied in full at all times, the acoustics of many rooms will make the resulting sound overly 'bright', with excessive HF energy.

In all things audio, it's up to the individual and/or sound engineer to ensure a good, natural balance.  Frequency response measurements can help, but microphones are dumb - they never 'hear' things the way we do.  Ultimately, the room has a far greater influence on the final sound than anything else, but (contrary to popular belief) the room cannot be 'equalised'.  Response deviations are due to reflections and time delays, and you cannot correct time with amplitude. However, you should have the tools needed to make the system sound 'decent' (excellence takes a bit more effort).

Despite the statement above, reducing the HF level can make the overall sound more balanced in an excessively 'bright' room.  You absolutely cannot correct for response anomalies caused by time delay, but you can still adjust the system so it sounds more acceptable (or perhaps less unacceptable).  In a venue that has failed to provide adequate room treatment you can only do what you can do.  Live sound 'miracles' are rare in my experience. 

The ideal equaliser will be adjustable.  This allows the user to adjust the amount of boost to account for whatever happens in the venue, or even to suit personal taste.  A good sound engineer ensures that the sound not only suits his/her tastes, but (and more importantly) suits expectations of the band and the audience.  This applies to the mix, the overall level and the venue, so at the end of the gig everyone is as happy as they can be.  This is rarely easy.

Figure 1 - Constant Directivity Horn Details

A CD horn ^{[ 1 ]} is shown above.  The diffraction aperture is the vertical parallel-sided section near the throat.  The wavefront gets its constant directivity characteristics from the aperture, but impedance matching (from the high pressure at the compression driver to the low pressure of the air at the mouth) is provided by the horn (or waveguide) profile.  Not everyone in audio is convinced that the use of diffraction in this way is optimal, but it does solve an otherwise difficult problem relatively cheaply.

The horn shown is just one example - there are a great many different arrangements used by various manufacturers, and it's not possible to cover them all.  However, the general principles don't change, even if the horn looks radically different.  One of the earliest CD horns was the JBL 'bum' horn, nicknamed as such because of its uncanny resemblance to a pair of buttocks, replete with central orifice.   An image search for "jbl bum horn" will show you plenty of photos if you haven't seen one.  The 'official' name for these horns was 'Bi-Radial ^®', and they were the forerunners of the design shown above.

Over the years there have been many attempts to obtain better directional control from horns, with one of the favourites of many (including me) being the now ancient Altec multi-cellular horn.  Multi-cells were very expensive to build, but provided many benefits over simpler designs.  Another attempt was the Altec 'sectoral' horn, which used baffles inside the horn itself to improve coverage.  JBL used acoustic lenses - a series of sloped (and sometimes folded) parallel shaped plates in front of the horn mouth that were 'sculpted' to improve dispersion.  Most of these are now considered obsolete, as are many of the earlier CD horn designs (such as the 'bum horn' mentioned above).  Another notable early version was the Altec 'Mantaray' horn ^{[ 3 ]}, which used a standard flare from the throat to the diffraction aperture, and a waveguide to the mouth.  Opinions vary widely on most CD horns, both old and new.

Diffraction horns such as the JBL 2397 were also once fairly common.  The horn flare was used to define the horizontal dispersion, with a narrow parallel-sided horn profile.  The diffraction at the curved mouth (usually an arc of around 90-110°) was then able to produce the vertical dispersion pattern.  At least that was the theory, but the frequency range where diffraction works is determined by the size of the diffraction aperture, and with most commercial and DIY versions performance was usually sub-optimal.

I expect that the arrangement shown below is unique, and is probably a fairly radical departure from the traditional equalisers (if you can even find a schematic for one).  Naturally, it is a requirement that the input is fed from the output of an electronic crossover (such as Project 09 or similar).  The turnover frequency is set by VR1, and the EQ slope is adjusted by VR2.  With VR2 set to 0% rotation (fully anticlockwise), there is only a small amount of residual boost, which is due to the low pass filters.

Figure 2 - Equaliser And Low-Pass Filters

U1A is a balanced input and buffer (U1B would be used for the second channel), needed to provide the balanced connection, and due to the low input impedance of the filter.  The first filter stage is based around U2A, and it's set for a -3dB frequency of 27kHz (relative to 1kHz output).  The filter Q is higher than normal, so there's a small boost (0.75dB) at 15kHz.  The second low pass filter has the same Q, but is set for a higher frequency (39kHz).  This is done to ensure minimal rolloff at 20kHz, but to roll off supersonic frequencies as quickly as possible.  Ultimate HF rolloff is 24dB/ octave above around 35kHz.  When there's no boost applied (VR2 at minimum) the filters don't do much, but at maximum boost they are essential to prevent high gain at supersonic frequencies.  The two filters do create a small boost (about 2dB) at 15kHz, but with most systems this will be an advantage.

No opamp types are given above, but the use of dual types is implied (single opamps can be used, but the pin numbers are different).  The second half of each opamp would be used for the second channel - assuming a stereo setup.  Which opamps you use depends on your budget and what you think is 'the best' in your application.  I would use NE5532 opamps because they have excellent performance, are quiet, and are very cost-effective, but you may prefer TL072 (cheap and cheerful) or LM4562 for lowest possible noise and distortion.  Impedances are deliberately kept fairly low to minimise noise, but not so low that opamp outputs will be stressed.  Remember that the opamps must have supply bypass caps to prevent parasitic oscillation.  The expected supply voltage is ±15V.

The boost circuit itself is an asymmetrical Baxandall feedback tone control.  I've not seen this arrangement used, but it is ideal for this application.  The frequency response at five different settings (VR2 at 0, 25, 50, 75 and 100%) is shown below.  The effect of VR1 is also shown below, and it is used to set the frequency where boost starts (defined by the +3dB point).  The minimum is 2.6kHz and the maximum is 5.5kHz.  This lets you change the frequency to compensate for different horn and compression driver combinations.

While a 'normal' Baxandall tone control can be used (but without the bass section), it's rather pointless, because you'll never normally need to cut the treble going to the horn.  Tone controls also have a frequency turnover frequency that's fixed, and the typical circuits you'll find have ±3dB frequencies that are far too low to be useful.  By making the control asymmetrical, you can provide what you need, and leave out facilities that aren't required.

If you would like to provide a small amount of cut (because your horn/ driver combination is too 'bright' perhaps), then reduce the value of R11.  If it's changed from 12k as shown to 6.8k, that allows a 2dB cut at 8-10k when VR2 is at minimum (depending on the setting of VR1).  The intermediate settings of VR2 are also affected, but the maximum remains (close to) unchanged.  There is about 0.24dB reduction in the maximum as shown in the graph below.

The maximum boost (VR1 at minimum, VR2 at maximum) is 18dB, which seems fairly radical.  However, if you look at the response of most compression driver and CD horn combinations, it's obvious that you really do need that much boost to flatten the response.  A typical (if there is such a thing) compression driver on a CD horn will be around 20dB down at 20kHz, referred to the 2-3kHz reference level.

It's essential that you understand that some of the latest compression drivers are coaxial, typically having two drivers in the one housing.  Many of these require little or no equalisation, but most do need a crossover to separate the mid and high frequencies.  There are also some drivers that do not roll off at 6dB/ octave, and need a shallower boost slope than traditional fixed CD horn EQ systems, which will provide way too much boost.  By making the slope variable, this unit will suit far more drivers than 'lesser' equalisers that have no options available.

The frequency response curves are shown below.  All the traces shown in the boost control graph are with adjustments to the boost control (VR2), while VR1 (turnover frequency) is set to the minimum frequency of 2.64kHz (maximum resistance).  The responses shown let you tailor the response.  The full 6dB/ octave slope is with VR2 at maximum, with intermediate slopes at lower settings.  The low frequency rolloff cause by the crossover is not shown, as it's not part of this circuit.  The horn will usually be crossed over at somewhere between 500Hz and 2kHz, depending on the size of the horn and the ratings for the compression driver.

Figure 3 - VR2 Boost Settings (VR1 At Minimum Frequency)

The boost slopes are tabulated below, measured at five settings (0, 25, 50, 75 and 100% rotation).  The slope is measured between 6kHz and 12kHz.

This allows the user set the system for exactly the slope needed for the horn and driver being used, and also lets you reduce the slope if the system sounds harsh or is otherwise producing too much treble.  In some cases, it will be found that one setting is fine for general use, so VR2 can either be a preset or replaced with appropriate value fixed resistors.

As VR1 is adjusted, the turnover frequency is changed.  This is provided so that the frequency can be set to suit the compression driver (and to a lesser extent, the horn).  As shown, all traces are with VR2 at maximum (6dB/ octave boost), and VR1 is at 0, 25, 50, 75 and 100%.  Most of the time, you'll only need somewhere between 2.6kHz and perhaps 4.5kHz with typical horns and drivers, but the higher frequencies may be useful for horns specifically designed for the top octaves (5k to 20kHz).  A higher frequency range can be obtained by reducing the value of C3 (shown as 2.2nF) and the range can be lowered by increasing its value.  I wouldn't expect that anything greater than 3.3nF would be needed, and it's doubtful that you'd ever need less than 1.5nF.

Figure 4 - VR1 Turnover Frequency Settings (VR2 At Maximum Boost)

The +3dB frequencies for various settings of VR1 (100, 75, 50, 25 and 0%) are shown above.  The +3dB point has been provided with its own graph grid line, and each frequency point has been shown.  The frequency is at maximum when VR1 is minimum resistance.  Because of the way the asymmetrical 'tone control' works, the standard formulae can't be used to calculate the frequencies.  There are also interactions from the low-pass filters, so the only easy way to determine the frequencies is by measurement.

It's also apparent that as the frequency is changed, the boost slope changes as well.  This is unavoidable, and is simply the result of physics getting in the way of what we want.  The boost slope is not reduced substantially until the maximum frequency is used, and is due to the limited frequency range left to work with when the +3dB point is at over 8kHz.  At most settings that will be used in practice, the 6dB/ octave slope is maintained as closely as with any other equaliser.

One thing that this circuit cannot do is correct for uneven response across the passband.  Horns and drivers often have anomalies in their response, and these can be almost impossible to correct.  Small deviations (±3dB) are quite normal, but if you have a sharp audible peak or notch in the response you'll need to change either the compression driver, the horn, or perhaps both.  Even if gross anomalies are corrected (with parametric EQ or DSP), the end result is often still unsatisfactory for critical listening.

Overall, this circuit gives you many options so the EQ can be adjusted until it's just right.  In theory, maximum boost is required, but you may or may not need it in your system.  As noted above, there are too many different requirements to simply make a fixed equaliser and tell users that it's all they need.  In outdoor environments the full boost almost certainly will be necessary, but indoors you have the choice.

Running the system with less than 'optimum' boost will never hurt anything in the system, but amplifiers and level pads (however that's done in your system) must be arranged to ensure that the horn driver is working well within its ratings at all times.  Despite the sometimes silly power claims made for some compression drivers, ultimately the limiting factor is the air itself.  At the high pressures encountered in the horn throat, air becomes non-linear and adding more power only increases distortion.  The apparent level may seem to increase, but that's often just your ear-brain combination reacting to high distortion.

There is currently no PCB planned for this equaliser, but that may change if there's sufficient interest.  It's not overly complex, and should go together quite easily on Veroboard or similar.  The parts aren't critical, and you should use the opamps you prefer.  Supplies should be ±15V, but ±12V can also be used.  All opamps should be provided with 100nF ceramic power supply bypass caps, mounted close to the ICs themselves.  As shown, the input and output are balanced, but unbalanced operation is also available.  Simply connect your input to 'Input+' and earth/ ground 'Input-'.  For the output, use the 'Output+' connection (do not earth 'Output-').

If you have measurement facilities, you should ideally run on and off axis frequency response tests for the driver and horn, so you can verify that the end result is reasonably flat response.  You can then experiment with the amount of boost, so you know what to expect with different settings.  It's possible that you may prefer not to use the full boost, especially if it makes the horn sound harsh at the top end, but you can adjust everything you need with this design, so nothing is fixed.  The horn level is controlled either from the crossover or at the power amplifier.  There is no point adding yet another level control, because it's just one more thing that needs to be set up and checked each time the system is operated.

Both input and output are balanced, using U5A to provide the non-inverted signal (the frequency slope control is inverting).  The 100 ohm output resistors are essential to prevent the opamps from oscillating when a coaxial cable is connected.  If you don't need balanced outputs, omit R17.  The numbers next to each set of input and output ports are those used for standard XLR connectors (female input, male output).  Input and output capacitors are not shown, but must be included if there is any likelihood of DC offset from the crossover.  The power amp input will also normally be capacitor coupled, so adding extra caps should not be necessary.

Once the system parameters have been set up (whether using variable or fixed EQ and turnover frequency), the equaliser is generally 'set and forget'.  Unless you find that the top end is too bright (or too dull) and it can't be corrected using normal system EQ (if available), you don't need to change anything.

References are few, because there is (strangely) so little useful information on the Net.

1. Mid-Format Optimized Aperture Bi-Radial ^® Horn Family - JBL
2. How to Equalise CD Horns - BSS Audio FDS 310 User Manual, p20
3. Altec Lansing Mantaray ^® Constant Directivity Horn
4. Electro-Voice PA Bible 6: Constant Directivity White Horn Paper (sic) - use web search to find a copy

Main Index

Projects Index