The Human Ear

Posted By Andy Kos

Something often overlooked, but I believe to be an important part of designing, building and configuring loudspeakers systems is understanding some of the basics of the human ear, and the effects of sound on the human body. This article is intended as a brief introduction, and is by no means exhaustive.

The smiley face equaliser


I’m sure you’ve seen this used, and possibly even done it yourself at some point in time.

Some would argue this is wrong, others that it is right.

The ‘smiley’ face curve often seen on graphic equalisers is similar to the effect achieved by the ‘loudness’ button on many hi-fi systems. It boosts the bass and treble to make it sound ‘better’ – but why do we think it sounds better?

Is it the speakers arent working properly? Maybe… we’ll discuss this later

But is something else wrong?

You might assume your ear works like a high quality studio microphone, with a flat frequency response across the audio spectrum, research has shown this is not the case. The way the ear responds to different frequencies varies considerably.

human ear


The graph above shows lines of perceived equal volume. First thing you will notice is that the smiley face equaliser curve is remarkably similar to the frequency response of the ear, but offset a little with the centre point around 3kHz and more emphasis on low frequencies. To some extent the smiley face can be explained as just naturally compensating for the human ear, making lower volume program material sound like we would expect it to sound at high volume.

Key Points:

Essentially deaf to bass frequencies:  This goes some way to explaining the loudness functions on hi-fi systems, at low volume, we find bass very difficult to hear, and it needs boosting significantly. As the volume increases the curve flattens, requiring less bass boost. In effect the loudness function is giving our ears the same balance as ‘loud’ music, but at low volume. Many people are unable to hear detail in bass frequencies, and some actually prefer the sound of distortion in bass frequencies, as they feel the sound is ‘warmer’

Most sensitive to mid-range frequencies peaking at around 3-4 kHz: Approximately the same frequency as a human high pitched scream or yell, which is not dissimilar to a baby’s cry. This means our ears are most efficient at detecting important sounds, research suggests this is down to years of evolution. Many alarm designers utilise these frequencies to maximise effectiveness. With out ears being so sensitive in the mid frequencies, poor quality sound, particularly distortion will be extremely noticeable, perhaps this goes some way to explaining the smiley curve; a way of masking problems in the mid-band by overpowering with bass and treble? Many people find distortion in the upper-mid frequencies painful, and this is often linked with occurrences of tinnitus.

Response varies with volume: As the volume increases, our ears hear differently. This is one of the reason many high-end large scale PA Systems utilise Dynamic EQ, where the equalisers are programmed to change as the volume increases. If you do apply equalisation to your sound system, you may need to adjust it for low/high volume.

So is the smiley curve correct? In my opinion, most of the time it isnt, particularly if you are playing back pre-recorded music the original recording will have been tweaked by the engineer to sound ‘right’. What is definitely correct is to equalise your system to make it sound right at the volume it is being used, and the room it is being used in, and the type of program material being played through it. If this happens to be a smiley curve, so be it, but as a system operator you should resist the urge to just boost bass and treble in the hope it will sound better. If you find you are doing this a lot, you might want to consider upgrading your sound system.



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Totally Addicted to Bass?!?

Posted By Andy Kos

Its well known that a heavy bass line is in dance music is often very popular, and many people believe it is absolutely essential in order to create the best atmosphere for certain styles of music, but could we actually be addicted? Some people think it may be possible, and there is some research to suggest they are right.

To understand how this may be possible, we need to understand how sound affects our bodies. In modern life, one of our primary needs to hear is to communicate, often at moderate volume, but our ears can be much more useful than this, allowing us to be aware of things further away than we can see, and some of these things may help explain how our bodies react to sound.

Thousands of years before we had amplified music, bass frequencies, and how we reacted them, could have been critical to our survival. In nature, loud sounds, with an emphasis to low frequencies are often connected to danger. Just think of the sounds created by a stampeding herd of animals, an earthquake or a volcano erupting. Research suggests that years of evolution have developed the ‘fight or flight’ response in humans when presented with danger, this stimulates the production of adrenaline, enhancing the bodies ability to react to the danger.

You’ve heard of adrenaline junkies right? Well, it is possible that the brain associates high levels of bass with pleasure due to the mild adrenaline rush that bass frequencies may cause, and over time, coupled with other stimulants, could contribute to an addiction.

Another field of research suggests exposure to very high sound pressure levels (commonly found in bass frequencies) damages our ears and causes ‘pain’, however our bodies naturally react to this pain by creating numerous chemicals within the body, including adrenaline, endorphines and encephalons, collectively acting to blunt pain, but at the same time causing a pleasure enhancing morphine-like effect. This has yet to be proven, but the theories seem to hold true, and could also contribute to this concept.

One researcher has even gone as far as to suggest that extreme bass frequencies that penetrate the human body, causing you to literally ‘feel the bass’ may cause temporary damage to cellular structures within your body, cause the same pain blocking chemicals to be produced. These chemicals make you ‘feel good’ and may go some way to explaining the positive feeling experienced by high intensity bass frequencies.

So, is it possible to be totally addicted to bass?




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What’s up with the Watts?business path choice

Choosing the right driver for your speakers can be something of a minefield, particularly if its your first time. There are a number of things to be aware of, one of which is the power rating (specified in Watts)

Technological advances in materials are allowing Loudspeaker drivers to be developed with larger power handling, at the same time we have seen some loudspeakers drivers have their power ratings changed, with increases of 25% or more, but with apparently no change to the driver. Add to this the confusion of RMS Power, Continuous Power, Program Power, and Peak Power and it’s not suprising some of you are getting confused. This article aims to explain some of terms used, and dispel a few myths.

Q: My amp is rated at 400W per channel, will a 600W driver break my amp by drawing too much power?

A: NO. The power rating of your amplifier is a measure of how many watts it can deliver to the speakers before it reaches the limitations of its internal power supply and starts to clip/distort.  The power rating of your speakers is the maximum power they can accept from an amplifier before they are in danger of overheating and burning out. Providing you have the corrent impedance load, your speakers are unable to draw more power than the amplifier is willing to give.

Q: If I replace my 400W speakers with 450W speakers will they go louder?

A: Not necessarily, the limiting factor is generally your amplifier, if you amp is rated at 400 Watts, you wont get any more than 400W output without severely distorting the sound, and potentially damaging your amplifier. If your amp can output 450W, then an increase in power handling may make your speakers go a little louder, but its possible they may be no louder, or in some cases quieter. The key factor here is efficiency, some speakers are more efficient than others. If you have two speakers operating at the same power level, and one is more efficient at converting electricity into sound, it doesnt take a rocket scientist to figure out which of the two will be louder. Most manufacturers give an indication of efficiency using the sensitivity figure measured in db@1W/1M (link to sensitivity)

Q: Which power rating should I look at?

If you’re reading this, chances are you are a novice, so for simplicity we suggest you use the continuous RMS power rating. Luckily, this is the one most manufacturers specify. You may also see Music Program Power Ratings, typically these are double the  RMS power rating. If you see a peak power rating, its often meaningless, and serves little purpose. Peak power ratings are often four time the RMS rating, so if you see this anywhere, divide it by 4 to give you an idea of the real power rating.

Q: What do the power ratings mean?

RMS Power.

Sometimes referred to as Average Power, or Continuous Power. The term RMS here is incorrectly used, it is not RMS power in the true sense of the term, as Power does vary from positive to negative, it is the Voltage. The RMS Voltage is used in the power calculation, hence giving rise to the term ‘RMS Power’.

Over the years, various standards have been used in this ‘RMS Power’ calculation, including;

The IEC268-5 (1978) standard (IEC = International Electrotechnical Commission)

The EIA RS-426-A (1980) standard (EID = Electronic Industries Association)

The AES2-1984 standard (AES = Audio Engineering Society)

The AES2-2012 standard – which is becoming the most commonly adopted standard. Previously many manufacturers used the EIA standard, re-ratings some speakers using AES saw increases in power ratings of 25%, sometimes more. One example we are aware of was a high power 18″ driver, which was previously rated at 600W, and had the power rating changed to 800W overnight – with no changes whatsoever to the speaker design.

How is this possible? The AES power rating has a higher crest factor than the EIA rating, and is also for a shorter duration 2 hours for AES whereas the EIA rating was over an 8 hour test period. Some would argue this is not a totally realistic test. However for the layman, it is a useful benchmark for matching up driver power to speaker power. We’ll explain why:

Music Power:

Also know as Program Power, this is an indicator of the power rating of speaker use with ‘typical program materal’, which most of us call music. The RMS Power test is not done with music, it is generally done with bandwidth limited pink noise, which is a continuous signal. When was the last time you played music that sounded like static? Not often I bet. Music power takes into consideration that a bass beat is not continuous, it is a series of pulses. In between the pulses, there is no power being applied to the speaker, so when you average out the power over time, you can handle much more power.

What does this mean? Well you can exceed RMS Power for short periods of time, but not with a continuous signal. So if you play average music, you can usually run above RMS Power level quite happily in most instances, and with appropriate limiters in place, somewhere between RMS power and Music Power is generally a safe level. This is why I’m saying the Music Power is a useful benchmark – it helps determine amplifier power choice ‘roughly’ and is a good level to aim at to keep your drivers operating within safe parameters, if like most people, you try to push things just a little harder every now and then, you should still be fine, just as long as you don’t start treating music power as a long term continuous power rating, as you will almost certainly cause your speakers to fail if you do this.

Peak Power:

This is the maximum short term power that can be applied to the driver, and is typically calculated to be four time the RMS Power. I recommend you dont use Peak Power for anything except bragging to someone who doesnt know anything about sound.

Should I buy the most powerful speakers I can afford?

Probably not – It’s best to get speakers appropriate to your requirement. This is partly due to how speakers work. High power speakers are designed to have a high excursion (thats lots of cone movement) – in order to be able to handle the extra power, they typically have stiffer components, particularly with regard to the suspension. These high power speakers require a certain amount of power to overcome the mechanical resistances of the suspension. Comparing two extreme examples, of say a 100W speaker and a 1000W speaker running bass. The 100W speaker will have a low output for say, the first 5-10W put into it, once you are putting in 50W or so, the speaker will be at half its rated power, and will be (depending on sensitivity) fairly loud, ramp it up to 90-100W and the driver is giving all it can, potentially operating at its most efficient point. Lets suppose you only have a 100W amplifier, the 100W speaker will give you more output than the 1000W speaker. If you put your 1000W woofer on the end of your 100W amplifierm the first 40-50W of power will be used inefficiently, just to overcome the stiffness and resistance of the suspension, ramp it up to 100W, and you are still only tickling the 1000W woofer, you will find that you may need 200W running through the 1000W woofer to be as loud as the 100W woofer. As you keep ramping up the power, the 1000W woofer will ultimately create a lot more sound output than the 100W speaker ever will, but if you only have a small amplifier, you are better off with an appropriately matched driver.

So what if I exceed the power ratings?

You run the risk of overheating the voice coil of the speaker, and causing it to fail – but be careful – just keeping an driver within it’s recommended power rating is no guarantee of longevity. You also need to be away of excursion (often specified using Xmax and Xlim) as you can damage an driver through over-excursion without exceeding the power rating.

What about Power Compression?

Power compression is the little bugbear that can upset your best laid plans, and give you reason to throw the manufacturer’s specifications out the window. Many manufacturers choose to ignore power compression, some actively avoid specifying it or even mentioning it.

The sensitivity (efficiency) manufacturers specify is measured at a power level of 1W at a distance of 1m from the speaker. At 1W, very little heat is lost within the voice coil, so the driver is more effective at converting electricity into sound.

Its very common for loudspeaker voice coils to be wound from copper, which has a positive temperature co-efficient of +0.393% per degree C. It’s quite feasible for the voice coil of a high power speaker to reach 200 degrees Celsius, which could mean a change in the resistance of the wire to increase of 50% or more. Your 8 ohm driver will no longer be an 8 ohm driver, and the nominal impedance could rise to as high as 13 or 14 ohms. At full power, many drivers are no longer operating at their stated impedance, and they generating a lot of heat.

A good quality driver, with low power compression at its full rated power, could be 3-4 dB louder than a driver that suffers badly from power compression. Many modern designs are taking account of this, and making efforts to ensure driver cooling is maximised to counter the effects of power compression.










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Power Compression

Posted By Andy Kos

When selecting speakers, it’s common for people to just look at maximum power handling, and many manufacturers make a point of specifying seemingly unbelievable power handling capacity of 1000W or more. Its quite rare for manufacturers to specify power compression though, and it seems to be often overlooked by system designers.

It seems that loudspeakers to handle what appear to be insanely high levels of power compared to 10 or 15 years ago. Has there been some amazing technological breakthrough? Do we need to re-write the physics text books? No, it’s still just basic physics – so what are the changes?

Firstly, modern materials used in the construction of voice coils are able to withstand significantly higher temperatures before failing.  Why is this important? Well Cone loudspeakers are in fact very inefficient, with even the best transducers only converting around 5% of the electrical energy supplied into sound, the majority of the remainder is converted into heat. So a 1000W bass speaker running at full power may well be converting only 50W into acoustic power, and 950W of heat. Thats like having a 1kw bar heater in your bassbin! That’s a lot of heat, which can cause big problems.

Aside from improving construction materials, manufacturers are also refining designs to maximise heat transfer away from the voice oil, this also contributes to the increases in power handling capacity we are experiencing.

What’s all this got to do with power compression?

Enabling speakers to handle much higher temperatures might seem a good thing, as it increases maximum power handling, but it also has a detrimental effect. Most voice coils are made from copper or aluminium wire, both of which have a positive temperature co-efficient of around 0.4% per °C. What’s the significance of that? You will have heard of superconductors, which operate at extremely low temperatures in order to try to reduce and minimise resistance.  Loudspeaker voice coils  unfortunately work in the opposite way: as the temperature increases, the resistance also increases.

A modern state of the art voice coil is designed to withstand extremely high temperatures, often operating at up to 3000C or more when driven at full power. 0.4% may sound insignificant, but remember this is per °C – at only 2300C the voice coil DC resistance has almost doubled which causes the voice coil impedance to increase accordingly. Some simple maths and you can quickly see that the increase in temperature  can make your 8 ohm speaker start behaving more like a 16 ohm speaker.

So after setting your sound system carefully at the start of the night, an hour in, and it doesn’t sound as loud – you might wonder whats going on. Two things: firstly, your ears have a self defence mechanism: there are 2 tiny muscles in the middle ear that will contract when the ear is exposed to loud sounds. This contraction will reduce the loudness of the sounds reaching the inner ear, thereby protecting the inner ear against exposure to loud noises. This isn’t power compression, but it’s something to be aware of, as you may well be tempted to turn up the volume, I know from experience that a typical DJ will certainly try this, and end up running his mixer into overdrive in the attempt to get more volume.

The second factor is power compression, a typical loudspeaker can lose 3-6 dB of volume once power compression kicks in.

You could think of power compression a bit like the aerodynamics of driving a car. When you start moving, a certain level of power from your engine sets you hurtling forwards at high speed, but as you go faster, wind resistance increases, so you stop accelerating. You need to apply more power to increase speed, but wind resistance keeps increasing too, so you have to apply even more power.

If your amplifiers have headroom, your instincts will make you want to turn them up, to restore the original volume level. To some extent this will work, if you’re familiar with the maths, you’ll see whats going on. Your 8 ohm speaker at room temperature happily accepts 1000W from your amplifier, and gradually reaches an operating temperature of say 250°C. Your resistance has doubled, and your ‘new’ 16 ohm speaker will probably only be receiving around 500W from your amplifier. In a way, as the speaker reaches temperature, it ‘protects itself’ by reducing the power it is operating at, stopping it getting any hotter. If it were to cool a little, the power would increase again, causing it to heat up.

Lets suppose you turn the gain up on your amplifiers, determined to try to push 1000W through your speakers. As you apply more power, you will generate more heat,  perhaps reaching 350°C or more, with your speakers resistance continuing to increase to perhaps 20 or more ohms. Essentially you are fighting a losing battle, as you turn the gain up, the speaker fights back with a higher resistance. You will eventually reach a limit, either your amp will run out of headroom and you cant turn it any louder, or the other possibility, which happens all too often, is your speaker will overheat, and burn out causing catastrophic failure.

Now you know about power compression and the fact that speaker resistance increases with heat, you’ll probably realise that you actually have to push a speaker very hard in order to cause it fail – so if your speaker suddenly fails and you smell burning, the only person to blame is YOU, as you now know better than to try to fight power compression by applying more power.

Now consider what effect power compression will have. 3-6dB loss at full operating power is almost like switching off half your PA system. To achieve the same consistent volume you will need twice as many speakers!

What’s the solution? Either buy speakers with headroom, e.g. if you want to operate at around 500-600W, you might want to consider purchasing speakers rated at 800W or more. At 75% of rated power, the effects of power compression should be much less significant. Also, try to select speakers with improved cooling technology, that suffer less from power compression. Avoiding power compression could make your speakers twice as loud, meaning you could take half as many to the gig!

There are other side effects from the increased levels of heat in a speaker, T/S parameters can vary, bass can sound boomy and mid frequencies can sound muffled. For the best sound quality, its best to try to  minimise power compression effects,




Impedance – FAQs

Posted By Andy Kos

How do I know what impedance load I have?

Most manufacturers will specify impedance, and will include it in the product specifications, often printing it on the speaker itself. If you don’t have this information, you can measure the DC resistance using a multi-meter (please note Resistance is NOT Impedance – find out why here:

You should only measure the resistance of speakers when they are not in use, and not connected to an amplifier. By putting your multi-meter probes on each terminal of the speaker you will get the DC resistance, which can be used as a guide to get the impedance. A DC resistance of 5-6 ohms is normal for a driver with 8 ohm impedance, around  12-13 ohms  is common for  a 16 ohm impedance driver, and  3 ohms DC resistance would be normal for a 4 ohm impedance. You may notice that moving the cone whilst checking the resistance will make the reading change, this is because the voice coil is moving in a magnetic field, which will induce a voltage in the  coil, which in turn will affect the multimeter’s measurement.

Many loudspeaker manufacturers will label the drivers to make identification easier, Eminence for example include a suffix on the drivers, for example the Beta12A is the standard model, and is 8 ohm impedance, the letter A designated 8 ohm impedance. The Beta 12B is 16 ohm impedance, and the Beta 12C is 4 ohm impedance. This same letter designation is used through the range of Eminence speakers.

I have more than one speaker in parallel – what’s the impedance?

First, let’s clarify what we mean by parallel, this is where the electrical paths through the drivers from + to – run in parallel to each other. If you trace a route from + to – you go through either one driver, or the other. The diagram below shows two speakers wired in parallel:


 To wire speakers in parallel, all you have to do is connect the + (positive or red terminal) on each speaker to the + (positive or red terminal) on your amplifier, and the corresponding – (minus or black terminal) on the speaker to the – (minus or black terminal) on your amplifier. If you plug several speakers into one amplifier, unless you have unusual cabling, this would be the standard way you would run several speakers off one amplifier.

Its normal to put speakers of the same impedance in parallel with each other, mismatching impedances isn’t a great idea unless you have a fairly advanced knowledge of speaker systems and are doing this for a specific purpose.

So what does this do to the impedance?

The impedance of each speaker stays the same, but the impedance load the amplifier sees will change. In the diagram above, if the two speakers were both 8 ohm impedance, the load the amplifier would see is 4 ohms. To think of this in simple terms, you could think of one loudspeaker as a busy road with a specific amount of traffic travelling along it, if you have two roads, the traffic can travel along either road, which presents less ‘resistance’ to the same amount of traffic. With a basic knowledge of maths, and using this analogy of two routes between start and finish, you can guess what the resistance of two parallel 8 ohm drivers would be, it’s half that of one 8 ohm driver, and is 4 ohms.

The formula for calculating parallel resistances is as follows:


R1, R2, R3, are the individual resistances, the formula works for as many, or as few resistances there are in parallel, for two drivers in parallel, you use R1 and R2 only, for three drivers you use R1, R2 and R3.

RT is the total parallel resistance. For equal parallel resistances, the formula becomes very simple, as the table of parallel 8 ohm impedances shows:

No drivers Parallel Impedance Fraction
1 8 ohms 1/1
2 4 ohms 1/2
3 2.6 ohms 1/3
4 2 ohms 1/4
5 1.6 ohms 1/5
6 1.3 ohms 1/6

As you can see, 3 drivers gives a combined parallel impedance of one third of the original impedance of 8 ohms, and 4 drivers gives a combined parallel impedance of one quarter of the original impedance.

Very few amplifiers will run happily into impedances below 2 ohms, and there is a strong possibility you can damage the amplifier by plugging too many speakers into it. Some amplifiers will not work safely below 4 ohms, so it’s quite important to ensure you have the correct load on your amplifier.

How do I wire speakers in series?

The term series where things are arranged in sequence implies how you would arrange speakers in series, as per the diagram below you can see that the positive (+) terminal of the first speaker is connected  to the positive (+) of the amplifier as normal, but the negative  (-) terminal goes the the positive terminal of the second speaker. The last speaker in the series has it’s negative (-) terminal connected to the negative (-) terminal of the amplifier.


Series impedances work opposite to parallel, going back to the comparison with traffic, if your busy road has traffic lights in it, every extra set of traffic lights adds more resistance to traffic flow. In the same way, each loudspeaker in series adds to the impedance. To calculate the total impedance, simply add together the individual impedances, as shown in the table below. In most instances, its rare to have more than 2 drivers wired in series, as the increase in impedance will mean most amplifiers are able to deliver very little power to the drivers.

No drivers Series Impedance
1 8 ohms
2 16 ohms
3 24 ohms
4 32 ohms

 If we get less power, what’s the point of connecting drivers in series?

If you just have one pair of speakers, there isn’t much point, but it gets interesting when you have multiples of speakers. If for example you have four speakers, that are 8 ohms, and you want to run all four speakers off one amplifier, you could wire all four in parallel, to give a 2 ohm load, or all 4 in series to get a 32 ohm load. But what if your amplifier wont work below 4 ohms?

The solution is simple, a series-parallel combination:



Assuming all drivers are 8 ohms, some simple maths and you can see that each of the two series combinations has an impedance of 16 ohms. Two 16 ohm impedances in parallel have an overall impedance of 8 ohms. What this allows you to do is use four speakers where you would previously have only used one, giving you a significant increase in power handling.

Variations of series-parallel configurations are common in guitar speakers,  4 x10″ and 4 x 12″ cabinets are common, with different wiring to suit specific applications and impedance requirement. Many guitar cabinets utilise 16 ohm drivers in order to achieve the desired results.

Its sometimes advised that its best to avoid using series configurations with speakers, due to the fact that that you have two coils or inductors which can induce unwanted voltage and cause distortion. Series configurations are rarely used in hifi or studio systems.








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Why does my 8 ohm speaker read 6 ohms when I measure it on a multimeter? It must be faulty right?


I’ve heard this so many times I’ve lost count, but there is a difference between impedance and resistance. When you measure resistance with a multimeter you are measuring DC resistance. The DC resistance is determined by the copper (or sometimes aluminium) wire in the voice coil of the speaker, and is actually as the name suggests; resistance to the passage of electric current through the copper. The key point here is that the electrical current travels in one direction only, and is fixed and does not change.

Impedance is equivalent to resistance, but for circuits where the voltage and current change, such as in a loudspeaker. An extra factor comes into play, which is the fact the the loudspeaker is based on a coil of wire. This coil of wire acts as an inductor. Without getting too involved in the science part of this, its sufficent to know the inductor creates an additional ‘reactance’ to alternating signals, which when added to the DC resistance of the voice coil, gives the overall Impedance.

To complicate matters further, the Impedance varies with frequency, so the 8 ohms specified for loudspeakers is not totally accurate, it is referred to as ‘nominal impedance’ – a kind of ‘average’ impedance figure that can be used for typical calculations involving loudspeakers. The graph below show a typical 18″ subwoofer, the impedance is shown on the scale on the left hand side.


For purposes of being able to run your own sound system, or building your own speakers, it’s sufficient to accept the manufacturer’s quoted impedance as being correct for your application. You don’t need to be concerned with the finer points of impedance unless you get into more serious aspects of speaker design, and if you’re at that level, I highly doubt you will have bothered read this far, as you will know all of this already!


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Some of the basics of crossovers have been covered in this article: – here we will go into a little more detail of how passive filters work, and give you the tools to design your own.

Crossovers and Filters

Lets’s start with a reminder of the basics, a crossover is a combination of high pass and low pass filters which split the signal into bands. The most basic crossover is a 2-way crossover, which splits the signal into 2 bands. Common configurations are 3-way and 4-way, which allow better matching of speakers with their appropriate operating range. 5-way active crossovers are not uncommon in large format PA systems in order to help cover as wide a frequency range as possible, as effectively as possible, to maximise various factors such as quality, dispersion, volume, as required by the design criteria. It is possible to keep splitting the audio range into smaller and smaller bands, but this can become an exercise of diminishing returns.

The Basic Building Blocks: Capacitors and Inductors

Capacitors: A Capacitor  has a high ‘resistance’ (commonly known as reactance) to low frequency signals, and a low ‘resistance’ to high frequency signals. When combined with a resistor, you get a filter circuit, as shown in the diagram below.

high_pass_1st_order copy

If you’ve ever looked at  a high pass filter , and taken notice of the components, you might be wondering why you don’t have a resistor, its because the resistor in the above circuit is your loudspeaker. This is something to be aware of when using passive filters, that the filter DOES NOT work independently of the loudspeaker, the loudspeaker forms part of the circuit. If you change the load resistance from 8 ohms, to 4 ohms or 16 ohms, you change how the filter circuit works.

The diagram below shows the relative magnitude of the signal at point V1 with 0dB in the diagram indicating full signal. V1 is the Voltage that will be applied to the loudspeaker (R1). The cut off frequency in the diagram is 1kHz. We use dB scale for audio purposes due to how we perceive  differences in volume of sound, a doubling or halving of magnitude is a significant enough change to be noticeable.


The filter has a cut-off frequency, commonly known as FC. Below the cut-off frequency, the capacitor has a high resistance, effectively blocking the signal. The purple line represent the magnitude of the signal that will pass through the filter. You can see that as the frequency reduces, the magnitude of the signal passing through the capacitor reduces.  The point where the purple line crosses -3dB is at  the cut off frequency, where the capacitor ‘resistance’ will be approximately equal to the resistor in the circuit.  With the capacitor and resistor being roughly equal, the system will work as a voltage divider, with approximately half the input voltage across the capacitor, and half the voltage across the resistor (loudspeaker). FC is sometimes known as the -3dB point, where -3dB indicate half magnitude.   Beyond the cut off frequency the capacitor reactance reduces, allowing higher frequency signals to pass unhindered. At these higher frequencies a ‘pure’ capacitor would have no effect on the passage of signals whatsoever, unfortunately pure capacitors are theoretical, and impossible to manufacture – any capacitor used in a filter circuit will also have a small constant resistive component and some inductance also – these contribute to distortion within the  signal, as well as power losses. Higher quality capacitors are designed to be closer to a ‘pure’ capacitor and minimise losses and distortion within the capacitor.

Calculations for 1st order High Pass Filters

The resistance value (measured in ohms), and the capacitance (measured in farads)  determine the cut-off frequency as per the following formula:



In our examples above , R1 is 8 ohms, and C1 is 20uF (microfarads). To use the formula above you need to use the capacitor value in farads, 20 uF = 0.000020 farads. Pi is  the mathematical constant, you can use pi to 2 decimal places (3.14) for purposes of calculating filters. If you put the numbers into the formula, you’ll get FC of 994Hz.

As mentioned previously, the loudspeaker impedance forms a part of the circuit, if you try the formula you will notice that increasing the impedance from 8 ohms to 16 ohms will halve the cut-off frequency and reducing the impedance from 8 ohms to 4 ohms will double the cut off frequency.  This is why you should only use a passive crossover or filter with the correct impedance load it has been designed to operate at.

We can change the formula to make it more useful, as we usually know what cut-off frequency we want, and what the resistance (impedance) is, but what we need to calculate is what value capacitor. This formula will yield the correct results:

C Formula

You must use FC in Hertz, and NOT kiloHertz to get the correct answer.

If you’re not so keen on maths, you can use our calculator to help (kHz/uF units are handled automatically)

 A first order filter is generally sufficient as a tweeter protector in an active system. You can add a capacitor in series to protect against DC Faults and/or accidental connection to a bass amplifier. You should make Fc of the capacitor  one octave lower than the Crossover Frequency on your active crossover to avoid any problems. One octave lower is exactly half the freqency, so if your compression drivers are operating from 2kHz upwards, your tweeter protector should be selected to operate at 1kHz. The calculator above will give suitable results for this application. Some people would argue that is is better to use a 2nd order filter, due to the phase shift caused by the filter (We’ll discuss this in another article).

Multiple Capacitors:

When using capactiors in filter circuit, you should  be aware that  capacitors in series/parallel sum differently to resistances, in fact the rules for capacitors are opposite to how series/parallel resistances combine. Two equal resistors in parallel will halve the overall resistance, however two capacitors in parallel sum together. So two 10 microfarad capacitors in parallel are equivalent to one 20 microfarad capacitor. Two resistors in series, sum together to increase the resistance, capacitors in series give a smaller overall capacitance:  two 10 microfarad capacitors in series will give an overall capacitance of 5 microfarads. Putting capacitors in parallel is a handy way of making up capacitance values that are not easily available off the shelf. You wouldn’t normally put capacitors in series in a filter circuit.

1st Order High Pass Filter: 

A single capacitor when used with a loudspeaker, forms the most basic High Pass Filter, which is known as a 1st order filter. However, capacitors on their own are not enough to form crossovers, we also need inductors.

Inductors: Most commonly these are coils of wire, copper is most commonly used as it has a low DC resistance.  In fact a straight copper wire would be what you normally use to connect up your speakers, so how does it form part of a filter? When current flows through a wire, an electromagnetic field forms around the wire, in a straight wire this field does not easily interact with other parts of the wire, so the effects are negligible, however, winding the wire into a coil creates a larger magnetic field. This magnetic field induces a voltage in the wire which opposes the current flow that creates it, this is often known as back EMF (electro motive force)  So every time there is a change in current, the inductor creates a back EMF to try to stop the change in current.

An inductor has a low resistance to low frequencies. An inductor’s lowest resistance is it’s DC resistance,  you can think of DC as a 0Hz signal.  Inductors allow DC to pass, as once current is established, there is generally no change in current. Inductors block or resist AC, or alternating current, and an audio signal can be regarded as a form of AC.

The circuit below shows an inductor and a resistor, forming a simple low pass filter.


Again, the R1 is the loudspeaker,  and L1 represents an inductor.  For our example, we will make L1 equal to 1.27mH (milliHenries), which is written as 0.00127 H. With an 8 ohm loudspeaker for R1 we get the following frequency response:

low pass graph

Inductors behave like resistors for purposes of summing their values. Two inductors in series sum together to create an equivalent bigger inductance in much the same way as two resistors in series are equivalent to a higher resistance. The formula for calculating the cut-off frequency is therefore different to the one for capacitors:


You can test the formula for our example, where R = 8 ohms, and L = 0.00127 Henries. You will get an answer very close to 1000Hz.

Re-arranging the formula makes it more useful, allowing the required inductance to be calculated for a desired cut-off frequency.

L Formula

In that same way as it has not been possible to create the ‘perfect’ capacitor, there has also not been an ‘ideal’ inductor created to-date. The nearest that has been achieved is a  supercooled inductor. All real world inductors have a series resistance created by the copper (or other metal) wire used to make the coil. This series resistance generates some heat, and causes losses in the circuit. Using an inductor with thinner wire will create more losses, so it’s best to choose an inductor with the thickest wire thats available and affordable in order minimise losses.

single inductor in series with a loudspeaker forms the most basic Low Pass Filter, this is known as a 1st order filter. A low pass filter (an inductor) and a high pass filter (a capacitor) together form a crossover, splitting the sound two ways, with the bass passing through the low pass, and the treble passing through the high pass.

Simple 1st Order Crossover:

crossover circuit 1

R1 represents a tweeter, operating at higher frequencies only, and R2 represents a woofer, operating at lower frequencies only. To create the above circuit, we have simply combined the circuits for the separate low pass filter and high pass filter. We’ll continue with the same component values of 20uF and 1.27mH, which will give the same cut-off frequency, and we’ll combine the two frequency responses into one graph.


The blue line represents the frequency response of the low pass filter, and the purple line the frequency response of the high pass filter. You’ve probably already realised the significance of the crossover frequency, where the purple and blue lines ‘cross over’ each other and the  graph probably starts looking quite familiar if you’ve ever looked into how crossovers work in the past. If nothing else, you should notice that the point where the two lines cross is at -3dB (half magnitude), if you sum the two responses together you are back at 0dB. So at the crossover frequency, both the woofer and tweeter should be producing the same sound, but each at half magnitude.

In a typical crossover, adding together the bass response and treble response should give you a flat response across the whole frequency spectrum – except there is a problem, inductors and capacitors cause phase shift, and a 1st order filter causes a 90° shift – inductors and capacitors cause phase shift in opposite directions, which would mean the bass and treble are directly out of phase with each other. Near the bottom of the frequency spectrum, you’ll have bass only, coming out of your woofer. At the top, you will have treble only, coming out of your tweeter. To some extent, it doesnt matter if these are out of phase with each other, as they are independent of each other and do not interact, however, around the cut off frequency, both the woofer and tweeter are creating the same frequencies, and if they are directly out of phase with each other, they can cancel each other out – bad news for creating a flat frequency response. With first order filters, this is fairly significant.

If you’re not sure what phase is, or what this means with respect to sound – we’ll cover this in a different article to be published at a later date.

The other problem with 1st order filters is that they are not that effective at splitting the sound, they reduce the magnitude of the stop band by only 6dB per octave, it can take two or more octaves to reduce the sound passed sufficiently, this means that quite a lot of treble still leaks into the bass, and a fair bit of bass leaks into the treble. For better quality sound, it is desirable to restrict frequencies to appropriate speakers, and to do this we need to use higher order filters. For passive crossovers, 2nd order filters are generally regarded as sufficient, occasionally with 3rd order filters used on the high pass only, to help protect tweeters from unwanted bass frequencies.

So how do we make a 2nd order filter?

If this is all new to you, you might think that you can just put two 1st order filters in series to create a 2nd order filter – in some parts of electronics this will work, passive RC filters  can be cascaded to create higher order filters. With loudspeaker filters, the R is the loudspeaker, and you only have one of them, and it’s part of the circuit, so we have to be a bit more clever.

Its not possible to just use two capacitors in series, as these are just equivalent to one capacitor with a different capacitance. Two capacitors in series will just change the cut off frequency, it wont give you a 2nd order filter

To make a 2nd order order high pass filter, we start with our capacitor, but we then add a low pass filter (inductor) in parallel with our loudspeaker, as per the diagram below.

2nd order High Pass

Frequencies below the cut off frequency are blocked by the capacitor, whats interesting is what happens around the cut-off frequency. With a correctly selected inductor, at the cut off frequency, the inductor blocks high frequencies, so these are forced to go through the loudspeaker, but the inductor allows frequencies at or below the cut off frequency to pass – creating a short cut , bypassing the loudspeaker. The result of the capacitor and working together at the cut-off frequency is to increase the slope from 6db/octave to 12 db/octave, a significant improvement.

1st and 2nd order High Pass

The purple line is the response from a 1st order High Pass Filter, and the blue line the response from a 2nd order High Pass Filter. Both are Butterworth filters. The 1st order filter is a 20uF Capacitor on its own, the 2nd order filter is a 14uF capacitor and a 1.8mH inductor.

You’ll notice the point the responses pass through the -3dB point remain the same for both filters. Selecting the correct values of capacitance and inductance is important for this to work correctly. Where both inductor and capacitor are active around the cut off frequency, the values of the inductor and capacitor have to be adjusted to make the filter operate in a desirable manner. The maths starts getting more involved, and unless you want to get into the finer points of crossover design, its probably easiest just to use one of the crossover calculators that are available online (we will be making ours live very soon)

In more advanced designs, it is possible to tweak the values  to give a different Q. In a Butterworth filter the Q is 0.707, and these are the most commonly used filters in passive crossovers.

Amongst other things, different Q filters alter the shape of the ‘knee’, or bend, where the filters response changes from the stop band to the pass band. Changing the shape of the slope around the cut off frequency can have a significant impact on how the low pass and high pass signals sum. A shallower softer slope (such as a Bessel filter with a Q of 0.5) can result in a ‘hole’ in the response. An optimal slop, such as Linkwitz-Riley or Butterworth aims to keep the overall summed response flat across the crossover frequency. High Q filters, such as Chebychev are rarely used, as these  will tend to give peaks in the frequency response, as well as other undesirable effects.

Higher order filters:

We can continue adding capacitors and inductors alternately to create higher order filters, as per the diagrams below:

3rd order high pass


C2 is added to make a 3rd order High Pass Filter.

4th order high pass

and then L2 is added to create a 4th order high pass filter.

In passive loudspeaker crossovers its rare to see filters higher than 4th order, and even 4th order filters are not very common due to the increased cost of additional components.

Higher order Low pass filters can also constructed in a similar manner to high pass filters, with the components working in a similar manner as high pass filters. In a 2nd order low pass filter, the capacitor acts as a bypass across the loudspeaker, creating a short-cut for high frequencies to skip past the loudspeaker. Where inductors and capacitors are efffectively ‘opposites’ of each other for purposes of passive filtering, to create a low pass filter, the positions of the inductors and capacitors within the circuit are swapped over. The diagram below shows a 2nd order low pass filter.

2nd order Low PassYou can follow the same pattern to work out the configuration of 3rd order and 4th order low pass filters.

Depending on the crossover design, you use corresponding low pass filter and high pass filters to achieve the desired result. If you’re new to this, I would suggest sticking to 2nd order filters on both the low pass and high pass section.

Beyond Passive crossovers?..

If you’ve understood all of this, you should now know how passive filters and crossovers work. Many early active crossovers used the same principles, but using just RC filters with op-amps in order to split the signal before it reaches the power amplifier stage. Many early active crossovers had fixed frequencies, and could not be easily adjusted, a common means of customisation was to have plug in modules, with different capacitors and resistors relating to different configurations of frequency. Innovations in circuit design and improvements in component availability allowed variable frequency active crossovers to be built, back in 1990s, I recall the Rane AC23 becoming available, this was regarded as a high quality, but affordable variable frequency active crossover, I seem to recall they cost around £300, which back in the mid 90s wasnt cheap! A few years later, designs similar to this started becoming commonplace in the industry, and are now used in virtually all variable frequency analog active crossovers that are commercially available today, with prices now in the £50-£100 range.

The revolution in digital processing has now surpassed this, and  most people prefer digital signal processing for active crossovers, mainly due to the massively increased versatility.

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With current technology, it’s  impossible to have a single transducer that is able to reproduce the entire audio spectrum effectively, different types of loudspeaker driver are better suited to different speakers. Typically those handling lower frequencies are cone drivers, and commonly known as woofers. Drivers handling higher frequencies are usually much smaller, and are often known as tweeters. In many basic speakers its common to have a woofer and a tweeter in order to cover as wide a range of the audio spectrum as is possible.

A crossover is a device which splits sound/music into two or more frequency bands. In the case of a basic two-way system there would be two bands, one band covered by the woofer, and one by the tweeter.

Why can’t we just put a Woofer and Tweeter in parallel without a crossover?

Tweeters can not handle bass frequencies, lots of bass into a tweeter would destroy it. Tweeter must have high frequencies only, limited to the frequencies the tweeter is designed to handle.

In a very simple speaker, you could just use a high pass filter in series with a tweeter, in parallel with the woofer. The high pass filter would remove damaging bass frequencies and keep the tweeter operating safely.

For purposes of simplicity, all diagrams will be simplified, and a 1st order filter is assumed to be in use. A 1st order filter does not require a connection to negative (-) and can be simply put in series as per the diagram. Any filter 2nd order or higher will require a connection to negative from the filter, which will be explained in more detail in another article:

Simple speaker with Passive High Pass Filter in series with tweeter:


HPF in the diagram is the High Pass Filter, which must be fitted in series with the Tweeter in order to protect it.

For basic speaker designs, this solution may sometimes be acceptable, but you need to be aware of the fact that below the filter frequency, the impedance of the circuit will be 8 ohms, as the amplifier will only see the woofer as the load, but at high frequencies, the amplifier will deliver power to both the woofer and the tweeter, this will present a 4 ohm load to the amplifier at higher frequencies. (8 ohm impedance of woofer and tweeter assumed in this example)

If you only intend to put one cabinet on the output of the amplifier, this wont present a problem, but if you use multiple cabinets you may find the overall impedance drops too low, which is undesirable.

Many woofers are also very inefficient at reproducing high frequencies, whilst they will readily allow power from the amplifier, they wont necessarily turn that power into anything useful, in effect wasting the power from the amplifier.

The final thing to consider is that some woofers really dont sound good outside their designed operating range, so whilst putting high frequencies signals through the woofer wont damage it, the woofer may just sound completely horrible when it tries to produce those frequencies.

The Solution? 

The solution is to put a Low Pass Filter (or LPF) in series with the Woofer, this filters out high frequencies, so that the woofer is only producing sounds that are in its operating range.

2-way crossover

The above diagram shows a passive LPF in series with the woofer, and a passive HPF in series with the tweeter.

A matched LPF and HPF that usually share the same cut-off frequency form a system known as a crossover. With a simple two-way system, crossover frequencies of between 1200 Hz and 3000 Hz are common, depending on the components used.

The cut off frequency is the point in the audio spectrum at which the filter begins to take significant effect, in the case of a Low Pass Filter, frequencies significantly below the cut-off frequency should be passing through unaffected. Just slightly below the cut-off frequency the filter begins to take effect, and starts blocking. The cut-off frequency is generally regarded as the point where the signal is at -3dB, and is in the middle of the ‘knee’ or bend in the response graph. Just above the cut-off frequency, the level begins to drop off rapidly, blocking higher frequency signals from passing. The HPF filter works the opposite way around.


By aligning the cut-off frequencies to be the same on the HPF and LPF circuits, the system impedance will stay more or less the same over the audio spectrum. Overlapping the cut-off frequencies of passive filters will cause the impedance to drop in the overlapped range. Leaving a gap between the cut-off frequencies will cause the impedance to rise in the gap.

It is possible to create more elaborate passive crossovers, such as three way crossovers that split the sound into bass, mid and treble. For smaller applications, such as hifi or studio speakers this is fairly common, but this becomes less common in high power PA speakers, as the component costs can increase significantly and in some instances it becomes difficult to source parts that can handle sufficient power

So far, we have only tackled passive crossovers..

So what is an active crossover? and whats’s the difference?

Passive crossovers do not have their own power source, all they can do is block the signal, they are regarded as passive as they can not increase it or amplify it. Passive crossovers/filters are placed between the amplifier and the speaker driver(s).

Active crossovers work quite differently. DO NOT ever fit an active crossover between the amplifier and driver, they are designed to go BEFORE the amplifier.

An active crossover will split the signal at line level, before it reaches the amplifier. The amplifier will then only amplifier the desired frequency band and deliver those frequencies to the speaker. This is a better solution, as it is more efficient – any passive crossover will have losses in it due to the components used to do the filtering. The losses amount to wasted power. Also, in cheaper crossovers, distortion can be introduced from cheaper components. Low losses and minimal distortion can be achieved with passive crossovers, but the cost of components can become astronomical, making active crossovers a better solution. There are also physical limitations with what can be achieved with passive crossovers, and as the overall system power is increased, passive crossovers become a less desirable solution.

There is a significant difference with using active crossovers, you need more amplifiers.

By splitting the signal BEFORE the amplifier, you then need a separate amplifier for each frequency band. In the case of a two-way system you will need two amplifiers, for a three-way system you will need three amplifiers.

Each amplifier will only be used to run speakers within a specific frequency band, as per the diagram below.


An active crossover also gives a much greater level of control over the system, with a typical crossover allowing boost or gain of each frequency band, and adjustable crossover frequencies. Some more advanced active crossover also allow variation of filter type (Butterworth, Linkwitz-Riley, Bessel, etc) to give precise control over the system configuration.

For large HIGH POWER systems, active crossovers are the preferred solution, with a separate amplifier for each band.

For small-medium size systems, a hybrid crossover solution is common. A 2-way active crossover is used to split bass from the mid and high frequencies, this requires one amp for Bass, and one for mid-high. The Mid-High cabinet then utilises an internal passive crossover to split between Mid and Treble. This solution is something of a compromise, it doesn’t quite give the total control of a fully active system, but it reduces the number of amplifiers needed, by not requiring a dedicated HF amplifier, and also simplifies cabling a little – eliminating the need for four core cable to run to the mid-high cabinet. This is a very common solution, as it provides a good balance of versatility and cost.



 Whats best active or passive?

Its generally regarded that active crossover solutions are best, for a number of reasons:

1. Passive crossovers are always lossy, even the best passive crossovers lose some power within the crossover, primarily due to the DC resistance of the inductors.

2. Sound quality. Passive crossovers using cheaper components can often suffer from sound quality issues, to achieve better sound quality costs often escalate with passive crossovers.  Generally, active crossovers offer better sound quality than passive crossovers.

3. Active crossovers allow for a more accurate predictable response, there is always some manufacturing tolerance with inductors and capacitors with variation of values of +/- 5% being common. This can often mean (more so with cheaper components) that no two passive crossovers will produce exactly the same response, so if your system comprises of numerous speakers, they could all be producing a different sound around the crossover frequency.

4. Better control. With active crossovers its much easier to balance different frequency bands. Its common with passive crossovers to require attenuation of high frequencies, through the use of attenuation resistors. With an active crossover you can just reduce the gain.

5. Easier scalability. Active crossovers make it easier to increase the size of your system, you can simply add more amplifiers and more speakers, and run them off the same signal from your crossover.



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To save you time, we’ve put together a calculator for one of the most common passive crossovers, a 2nd order Butterworth. You can configure the Impedance of the woofer and tweeter, and the crossover frequency.

C1, C2, L1 and L2 correspond to the relavant capacitors and inductors in the diagram below:

2nd order Crossover medium

Where Vin is connected to the positive terminal of your amplifier, and 0V is the negative terminal. The dots on the circuit signify where components/wires are connected. L2 connects to the input, and NOT to 0V, hence the ‘loop’ in the wire in the diagram.





New improved version of the crossover calc this now includes a graphical plot of the frequency response. Due to the size of the graphics, the form below will submit to a full page version of the calculator. You can select 1st order or 2nd order slopes, with the option of Linkwitz-Riley on 2nd order. We will add 3rd order and 4th order in due course. This calculators works two ways, you can enter the frequencies and impedances and calculate the component values, or you can enter the component values to get the crossover frequencies and see the frequency response. This version also allows different impedance and frequency between Low Pass and High Pass, as well as different slopes. So you could for example have the Low Pass section with a 8 ohm woofer, crossing over at 1200 Hz, and the High Pass at 16 ohms crossing over at 1800 Hz. Combinations like this are becoming increasingly common, as using a 16 ohm HF driver often negates the need to put attenuation in the HF part of the circuit. Also, a typical 1600Hz Butterworth crossover can often have a peak in response around the crossover frequency, particularly if the HF driver is highly efficient – offsetting the crossover frequencies may seem counter-intuitive as it might appear you are leaving a hole in the response, but often the coupling between LF and HF counteracts this. If you already have a crossover, you can simulate the response using the lower part of the controls. Please check you have component values correct, Capacitors should be specified in microFarads (uF) and Inductors in milliHenries (mH). Most pre-built crossovers will have capacitor values printed on the components, unfortunately very few divulge the Inductor values, to get these you will need an appropriate measurement meter.

2nd order Crossover Calc
To get the component values for a crossover, enter the impedances and crossover frequencies for the high pass and low pass sections and then click ‘CALC’
Low Pass Fc:
Woofer Impedance: Ohms
High Pass Fc:
Tweeter Impedance: Ohms
To see the response and crossover frequencies for known component values, enter these in uF and mH in the boxes below and click ‘CALC’
C1: uF
L1: mH
C2: uF
L2: mH