Crossover Theory
3 octaves or 3.2 octaves (1 decade) is the optimum bandwidth for a speaker as previously described. The crossover decreases power at a given rate from either or both sides of a given bandwidth. The slopes rotate phase in opposite directions. In some passive crossovers this is adjusted for by reversing the polarity of adjacent speakers. Electronic active crossovers can have extra compensating circuitry.
Crossover points and Order
At the crossover point, power to each speaker is reduced -3dB (1/2) so total sound energy is 1. At the crossover point sound comes from 2 sources and on-axis directivity is increased. Recent design trends are for power to be decreased to -6dB (1/4) to each speaker, at the crossover point. The slope rate can be selected.
1. First order (-6dB /octave) reduces power to 1/4 per octave, adequate for cheap low power systems.
2. Second order (-12dB /octave) reduces power to 1/16 per octave. Provides the best technical accuracy, with the least complications and harmonic distortion. For mid and high speakers the cone or driver diaphragm movement is kept constant as the frequency decreases (constant excursion).
3. Third order (-18dB /octave) reduces power to 1/64 per octave. Is good for protecting speakers at higher power. Also helps reducing bass energy from harming compression drivers with truncated horns.
4. Fourth order (-24dB / octave) reduces power to 1/256 per octave. Is best for maximum control of speakers, but requires critical alignment which is rarely achieved.
Fourth order has become the standard crossover for professional systems.
3 laws of Crossovers
1. It is not possible to stitch 2 different speakers together, perfectly.
2. A crossover should have the minimalist complexity to achieve the desired outcome.
3. The more complex a crossover, the more difficult the system is to control.
Selecting crossover points
Our ears are most sensitive to detail between 300Hz to 3kHz. The telephone system operates between these 2 points. Sound system distortion between these points can easily be heard and therefore the worst position to cross speakers over, but we have no choice. The best crossover points for our ears do not line up with the physics of speakers. There has been many attempts to force speakers to be crossed over at 300Hz and 3kHz but without success.
The sound spectrum is large 20Hz to 20kHz (3 Decades or 9 octaves). For home use a passive full range 3-way speaker system is cost effective and adequate for most people. The best way to understand a 4-way speaker system is to approach it a 3-way, with an added active bass (sub-bass). Hopfully the explanations below will make this understandable.
Why 4 - Way?
(1) Harmonics. For high frequency, most tweeters can be crossed over at 3kHz but can easily be destroyed at high power. The lower a tweeter is crossed over the less power they can handle. Below 6kHz the power rating of most dome, ribbon, and bullet tweeters, reduces at -6dB/octave (1/4 power for each octave decrease). Eg. A tweeter rated at 40 Watts will only be capable of 10 Watts at 3kHz. Tweeters should be crossed over at approx 4kHz - 6kHz for maximum dynamic power response. A compression bullet tweeter is approx 12dB - 20dB more efficient than a dome tweeter.
(2) Upper voice. A 4in - 5in speaker may just reach 6kHz linearly, but below 400Hz, efficiency reduces at approx -6dB/octave. Compression drivers for professional sound systems are capable of reaching 6kHz but rarely capable of going below 800Hz. A compression driver may be capable of 50 Watts - 100 Watts above 1kHz, but below 800Hz a few Watts can easily destroy them. A compression driver and horn is approx 12dB - 24dB more efficient than a cone speaker.
(3) Lower voice. approx 100Hz - 400/800Hz is in-between the bass and upper voice. A heavy cone speaker designed for bass may be able to cover this frequency range but it will not have the efficiency to match the upper voice speaker. An 8in - 12in MB (mid-bass) is similar to a bass speaker but will have a low weight cone with a short voice coil. The MB speaker will be approx 3dB more efficient than a bass speaker but it will still be less efficient than the upper voice speaker (-3dB approx). For professional application, MB lower voice speaker should be at least x 2 power rating of the upper voice speaker, to maintain equal spectral balance.
(4) Bass. At high power, the large physical movement (excursion) of the speaker cone will inter-modulate and distort the lower voice. A separate bass (sub-bass) should be added, to cover the bass notes, and be crossed at the lower end of the voice range approx 100Hz. Making the system into a 4 way. Because the bass (sub-bass) speaker is less efficient, 2 bass speakers are required for correct spectral power balance to equal the MB lower voice speaker. For professional sound systems, 2 bass (sub-bass) speakers for 1 lower voice speaker is essential. For home, 1 bass (sub-bass) speaker will be adequate but x 2 power will be required, for it to reach the same level as the lower voice speaker.
The best way to understand a 4-way speaker system is to approach it a 3-way with an added active bass (sub-bass). The words bass and sub-bass are ambiguous and often include each other. The lowest bass note on a bass guitar and double bass is open E 42Hz. The musical bass register refers to the lowest 1.5 octaves on the bass instrument 42Hz - 120Hz.
Note Below open E 42Hz (lowest bass note on a double-bass) the efficiency of most bass speakers, decreases at -12dB/octave. At 20Hz, a bass speaker may require x 16 power to bring it to the same level at 40Hz. Our ears are -20dB (1/100) less sensitive to hearing sound at 20Hz compared to 42Hz. Almost no music CDs or vinyl records have music information below 42Hz. Against popular belief, very few action movies have sound effects below 42Hz. There are a few audiophile sub-bass speaker systems that go down to 20Hz and are crossed over at approx 60Hz. Professional bass musicians find these audiophile sub-bass systems unusable (un-musical) as a bass speaker system in a band or orchestra.
Efficiency
Efficiency is measured on axis, 1 Watt at 1 meter.
Cone speakers vary between 86 - 96 dB/mW.
Compression drivers and horns, and bullet tweeters, approx 110 dB/mW.
A general rule. An 8in - 12in lower voice speaker is approx 3dB - 6dB more efficient than the bass speaker. A 4in - 5in upper voice speaker is approx 3dB more efficient than the 8in - 12in lower voice speaker. A dome tweeter, is approx 3dB more efficient than the 4in - 5in upper voice speaker. For professional sound systems a compression driver horn and bullet tweeter are approx 12dB - 20dB more efficient than cone speakers.
The efficiency difference between speakers, using passive crossovers, is managed by attenuators called L-pads (similar to a large volume control at the speaker). For active speaker systems the efficiency difference between speakers is managed by adjusting the level controls of the amplifiers.
What is a L-pad?
L-Pad is a level control used in passive speaker systems to attenuate (reduce) power to the mid speaker and tweeter. Most mid range speakers and tweeters are approx +6dB more efficient than woofers.
Inside the L-Pad is 2 wire wound elements, which are arranged to maintain a constant impedance of 8R to the crossover.
An L-pad can be purchased as a variable control (single or dual) as in above pic.
But variable L-pads are for 8R speakers only. For 4R speakers, use a dual 8R variable L-pad, with both sections in parallel. L-pads can also be made with fixed values of large wire wound resistors. For 4R speakers, the value of the resistors is 1/2.
L-pad fire warning. An L-pad adjusted to attenuate power by -3dB, will allow 1/2 power to the speaker and the other 1/2 power as heat in the L-pad resistors. The resistors should be as higher power rating as possible. Not less than 20 Watts.
Passive Crossover
For home use, a full range, 3-way passive speaker system is cost effective and adequate for most people. It is possible, but not practical, to make a 4-way passive crossover system. To make a 3-way passive system into a 4-way, the bass (sub-bass) should be active (driven by a separate amplifier).
Speaker systems of woofer, mid and tweeter, driven by one amplifier are called passive. Passive refers to the components (inductor and capacitor) between the amplifier and speakers. These components separate the frequencies, so bass goes to the woofer and high frequencies to the tweeter.
The capacitor and inductor can be in simple or complex arrangements. Passive crossovers are effective but not accurate, requiring energy from the amplifier to function (insertion loss), they reduce efficiency of the speaker system and contribute distortion, especially at high power.
L Inductor mH (a coil of wire) limits high frequencies going to the woofer.
C Capacitor μF (like a small instant re-chargeable battery) limits low frequencies going to the tweeter.
A single Capacitor and Inductor (6dB/octave) are used for cheap 2-way speaker systems, but does not give sufficient control to accurately manage quality speakers.
How does a 3 - way passive crossover work?
L Inductor (mH milli-Henry) approaches being a short circuit at low frequencies, and an open circuit at high frequencies. C Capacitor (μF micro-Farad) approaches being an open circuit, at low frequencies, and a short circuit at high frequencies. The Impedance of L and C (expressed as resistance they represent), at any one frequency, is called Reactance, symbolised by the letter X. This Reactance changes x 2 or 1/2 for each double of half the frequency (6dB/octave).
The Reactance XL and XC, reduces power, by shifting the phase, between Volts and Amperes (of the signal) in opposite directions. The phase shifting of the signal, at the crossover point, has to be compensated, by reversing connections to one of the speakers, or by other means. A physical experience of phase shift, is being in a motor vehicle, that is accelerating or breaking, being thrust forward or backward.
12dB/octave 3-way passive crossover, provides effective management of speakers. To extend a 3-way passive system to 4-way, the bass (sub-bass) should be active, because sub-bass speakers are inefficient, and require extra amplified power.
Bass (low pass). The Inductor L1 in series with the bass speaker, approaches being an open circuit at high frequencies (6dB/octave). The Capacitor C1 across the bass speaker approaches being a short circuit at high frequencies (6dB/octave). The Inductor and Capacitor combined, limit high frequencies getting to the woofer at -12dB/octave.
Bass to Mid range (band pass). The second Capacitor C1 in series with the mid range, approaches being an open circuit at low frequencies (6dB/octave). The Inductor L1 across the mid range approaches being a short circuit at low frequencies (6dB/octave). The Inductor and Capacitor combined, limit low frequencies getting to the mid range at -12dB/octave.
Mid range (band pass).The Inductor L2 in series with the mid range speaker, approaches being an open circuit at high frequencies (6dB/octave). The Capacitor C2 across the mid range speaker approaches being a short circuit at high frequencies (6dB/octave). The Inductor and Capacitor combined, limit high frequencies getting to the mid range speaker at -12dB/octave.
Tweeter (high pass). The Capacitor C2 in series with the tweeter, approaches being an open circuit at low frequencies (6dB/octave). The Inductor L2 across the tweeter, approaches being a short circuit at low frequencies (6dB/octave). The Inductor and Capacitor combined, limit low frequencies getting to the tweeter at -12dB/octave.
Danger. The reactance (X) of L and C, shift phase between Volts and Amperes, therefore reducing power (Watts). L and C are in series, and phase is shifted in opposite directions between them. This is called a 'series resonant' circuit. If the speaker is not connected to the crossover, or the speaker has blown up, the LC 'series resonance' becomes a short circuit, at the crossover point.
The amplifier can easily be destroyed.
12dB/octave passive crossover design
At the crossover frequency, XL and XC, must = root 2 (1.414) of the speaker Impedance.
L Inductors may have approx 150 - 300 turns of 1mm wire.
The resistance of the wire can be between 0.5R - 1R. This can be included in the calculations.
Capacitors may be between 4.7μF - 47μF
Capacitors should be non-polarized and ≥ 100 Volt rating.
Speaker Impedance should be measured at the cross over frequency. The specified Impedance will be accurate, for the majority of dome tweeters, bullet tweeters and compression drivers. Most cone speakers will be accurate between 200Hz - 600Hz. An 8R speaker will be 8R, a 4R speaker will be 4R. But from 600Hz and above (upper voice), most cone speakers will have a higher Impedance than specified.
- R or Ω measured in Ohms
is constant Resistance over frequency. - XC Capacitive Reactance measured in micro-Farads (μF)
is variable Impedance over frequency. (Amperes leads Volts 90deg) - XL Inductive Reactance measured in milli-Henry (mH)
is variable Impedance over frequency. (Volts leads Amperes 90deg) - Z Impedance measured in Ohms
is variable Resistance over frequency, with any combinations of (R - XL - XC)
Some designers, go into extraordinary detail to adjust for the rising Impedance of the mid speaker. Adjustment for this rising impedance does make the crossover technically accurate. This correction has little effect on musical performance and no effect on reliability of speaker or amplifier. Often, only the designer can hear the difference, and if you are the designer you can choose to do it.
The exceptions. 18dB/octave passive crossovers, are essential in professional systems, for stopping low frequencies getting onto compression drivers. These drivers are expensive and can easily be destroyed with a few Watts of power at low frequency. Many of these systems are small, portable 2-way passive speaker boxes, 12in - 15in and horn.
Passive Crossover Danger The reactance (X) of L and C, shift phase between Volts and Amperes, therefore reducing power (Watts). L and C are in series, and phase is shifted in opposite directions between them. This is called a 'series resonant' circuit. If the speaker is not connected to the crossover, or the speaker has blown up, the LC 'series resonance' becomes a short circuit, at the crossover point.
The amplifier can easily be destroyed.
There are many excellent books, web sites and software programs that give precise construction detail and formulas for passive crossover design. But require good math and basic electronic knowledge.
Magical Passive Crossovers
Passive crossovers of higher order than 12dB/octave can be made, but are difficult to construct. Most are inefficient and inaccurate, regardless of the academic theory that describes them as being superior. The more complex a passive crossover, the more energy is required from the amplifier, for it to function. This increases insertion loss, which generates distortion that often outweighs the benefits.
Early research, referred to 'transient distortion' as the major problem of passive crossovers, greater than 12dB/octave. Early Audiophiles only accepted first order crossovers, claiming this has least effect on colouring the music. Their descriptions were, '1st and 2nd order crossovers allow the sound to be open, whereas higher order crossovers cause the sound to be closed'.
Recent audiophile trends are, for very complex passive crossovers, greater than 12dB/octave that use magical Capacitors. The larger the number of magical Capacitors the more magical the sound becomes. These passive crossovers attempt to adjust for time alignment and Impedance variations, within each speaker. Often, only the designer can hear the difference, which becomes self perpetuating to justify the design time spent and the cost of magical components. In almost every case (there are exceptions) where these magical crossovers are replaced, with a straight forward 12dB/octave crossover, the system springs to life.
However, active crossovers cannot be generalised in this way.
Active Crossover
Traditionally, the market had been opposed to active systems, but this is changing. An incorrectly set up active system will sound worse than a passive system. People who make speakers systems rarely have electronic knowledge. Most electronic people have limited electro-acoustic knowledge. Most applications are 2-way. A separate amplifier and speaker for extra sub-bass power. Active Crossovers are often used for high-powered professional systems. Active is rarely taken to its fullest extent as a 4-way across the frequency spectrum, because of limited technical understanding and cost.
Active systems require technical skill to set up correctly. Audiophiles believe in magic, not technology. Magical speakers, connected to magical amplifiers, with magical cable. This may sound, funny etc, but these beliefs are real. Merchandisers make money by selling speakers, cable and amplifiers separately. The problem has been lack of education. Most sound engineering courses are superficial, with little or no meaningful electro-acoustic content.
An electronic circuit, separates the frequencies before the amplifiers. The auditory difference between an active and passive speaker system, is noticed by everyone. A correctly set up active sound system has greater clarity and realism and free from inter-modulation distortion. For an active system to be compact and affordable, the amplifiers can be included within the speaker cabinets.
Electronic crossovers can be purchased as a rack mount unit, 2-way, 3-way, 4-way, mono or stereo. Crossover points can easily be changed. Slope 12dB/octave (Q 0.707) -3dB at crossover point (Butterworth) will give the best performance, with least complications.
The compression driver and bullet tweeter, must have a Capacitor in series with the amplifier. 47μF for the compression driver, and 4.7μF for the bullet tweeter. The turn on/off pulses and DC offset, from amplifiers, could easily destroy driver and tweeter. The capacitors also provide an extra -6dB/octave roll off (total 18dB/octave). This will insure no bass energy will get to the drivers.
Professional Benchmark
Linkwitz-Riley. Professional electronic crossovers, referred to as Linkwitz-Riley, have fixed slopes, fourth order, 24dB/octave (Q 0.5) and -6dB at crossover point (Bessel). The crossover points can be changed. This has been adopted as the standard for professional systems. The steep 24dB/octave slopes give maximum protection, control and power capability for the drivers. This Linkwitz-Riley bench mark is a mathematical calibration, that is dependant on the listener being unable to make changes, once the system is calibrated. www.linkwitzlab.com
Theory behind this method is comprehensive and can be questioned, not as being right or wrong but suited to the outcome. One part of the theory states that, at the crossover point, sound comes from 2 sources, acoustic directivity is increased, therefore power to each speaker should be reduced -6dB (1/4). This increased directivity is on-axis only, off-axis energy decreases. The total sound energy remains the same. For near-field monitor listening, -6dB at the crossover point can be argued as correct, but for far-field -3dB can be argued as correct.
This Linkwitz-Riley bench mark is dependant on the listener being unable to make changes after the system is calibrated. But with active systems, level to each speaker can simply be changed to whatever balance the listener wishes to enjoy. Choice to change levels between speakers, for personal musical enjoyment, makes bench marking technically meaningless. The decision between right and wrong, now becoms one of choosing or not choosing, the right to choose.
Listen to a mid speaker crossed over in isolation. 2nd order 12dB/octave crossovers, attenuate the music without hearing a tone or colour change. Higher order crossovers, attenuate the music, causing a subtle but noticeable tone or colour change (hardening) in the music. When recombined with the other speakers this tonal change is not directly noticeable.
Active Crossover are created by electronic L. C. resonant circuits, or software digital assimilations of them. The slopes of crossovers, represent a part (one side) of a resonant note. This note is not heard directly, but the steep slopes of third and fourth order crossovers, can reflect harmonic interference (sideband distortion) within the music. Early research referred to this ghost resonance as transient distortion. Conclusive research in this area has not been completed.
Filter Shapes
Chebychev, Butterworth, Bessel, are names honouring early physicists, and represent the math behind filter shapes, used by electronic design engineers. The Q of the slope (Quality of resonance), refers to the circuit, and its D (Damping), including the geometry, of shifting phase, in the slope. These names are mostly used by people who wish to impress, but do not know what they mean.
Some electronic crossovers are designed for research, and use computing power, to change filter shapes, slopes, crossover points, and time alignment, These crossovers are complex to set up. Stoned, roadie sound engineers, love to randomly twiddle with these functions, during live performances. This behaviour, guarantees distorted colouration in the music, and destruction of compression drivers.
Time Alignment
Many years ago the term 'time alignment' referred to speaker placement in large auditoriums, churches, stadiums, race courses, etc. Sound travels at approx 344 meters / sec. The large distance between speakers could cause excessive echoes. Signal to distant speakers is electronicly delayed, at the equivalent of 344 meters / sec. In recent years modern marketing trends have made 'time alignment' also refer to the very small distances, between voice coil alignments, of woofer and tweeter.
At the point where the woofer crosses over to the tweeter, both cones should be moving in phase. When mounted in a box, the woofer and tweeter voice coils are slightly out of vertical alignment. Technical management of time alignment has always been known. Recent marketing trends have made 'time-alignment' into an obsession. Time alignment can also be looked at when listening to a musical group or an orchestra. The musicians being in different places, left, right, forward or back.
In the examples given, sound from the woofer arrives late by less than half a milli-second (1/2 a thousandth of a second) relative to the tweeter. This causes a lobe or small shift in polar response, on axis, at the crossover point only. Time alignment shifts effect detail points in the frequency and polar response but do not effect overall sound energy and enjoyment of music. Some audiophile systems have speakers at the sides, rear or facing upward, spreading sound around the room. Facing speakers in different directions increases time-alignment shifts, lobeing, and comb filter distortion, decreasing intelligibility, while making contradictory marketing statements about 'time-alignment' correction.
Small shifts caused by vertical crossover alignments are difficult to hear and measure. A trained ear can hear subtle differences of alignment shifts, during real time switching comparison only but not when stationary. That is, the ear is unable to pick which speaker is in alignment, forward or back, in a double blind test. Correction for time alignment is purely academic and it can be done. There are those who can not sleep unless this correction is implemented.
One solution is to simply move the speakers so the voice coils are physically aligned. The other, is to use complex high order passive crossovers designed with time alignment correction. This introduces other losses which are often more detrimental. Most domestic and professional passive speaker systems rarely use this correction. Active crossovers can have time alignment correction that does not contribute losses in other areas.
Exaggerated Time Alignment Experiments
Time Alignment experiments can be exaggerated with 2 microphones at full range, one physically forward of the other. With exaggerated continual large movement of one mic (3ft/1m) a choral flanging effect is heard but not when stationary. The experiment repeated with the 2 mics crossed over, high pass and low pass, (similar to a speaker crossover). With small static movements similar to the distances of woofer and tweeter alignments the ear cannot pick which mic is in alignment, forward or back. Meaning, the ear cannot hear small static shifts in phase.
The experiments can be repeated with 2 speakers at full range, one physically forward of the other. With exaggerated continual large movement of one speaker (3ft/1m) a choral flanging effect is heard but not when stationary. Again, time alignment can also be questioned when listening to a musical group, or an orchestra. The instruments are in different places, left and right, forward and back.
Marketing Fads
There are fads in marketing inferring that the words 'time-aligned' alone, magically transform the whole sound quality, believing this is more important than using quality speakers. The term 'time-aligned' can be used at random, stamped on products similar to washing machines stamped with 'heavy duty'. There are audiophiles who have obsessions with 'time alignment' that go beyond having a sense of perspective. These obsessions are equivalent to painting a single grain of sand a different colour, throwing it back in the beach and expecting to find it when one is allready unable to find ones keys.
Harmonic Sidebands
In the visual world we can photograph (freeze) an image and it remains intact. If we freeze music it appears as filtered noise. The unfolding of this is extensive. This is a simple explanation
Music is a multitude of notes shifting in frequency, amplitude and phase. These notes create interference patterns with each other (auditory equivalent of a rainbow). In nature these patterns are of infinite complexity and form moving mirrored structures on both sides of the musical notes that created them (upper and lower harmonic side-bands). Music is the richness, detail and beauty of these side-bands. If we freeze music at any one note the harmonic side-bands disappear.
Music through a speaker system deviates from the original by the harmonic side-bands becoming shifted and unbalanced. Accumulation of all limitations in system design (previously mentioned throughout this text) results in the unbalancing of harmonic side-bands.
Listen to music while switching between different speaker systems (all having a flat response) and notice how different they sound, particularly in tonal colour. Frequency response measurement alone, is of insufficient complexity to reveal a speaker systems capacity to accurately reproduce the harmonic side-bands and sound natural. Realism can only be achieved through 4-way active technology.