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Multi-Way Conventional loudspeakers with crossovers

Introduction to designing crossovers without measurement
Introduction to designing crossovers without measurement
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Old 29th May 2011, 12:11 AM   #1
AllenB is offline AllenB  Australia
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Default Introduction to designing crossovers without measurement

This tutorial is designed to get you started and tweaking a decent crossover… whether you're new to crossovers, or have built speakers before and are looking for a design method that relies on listening and doesn't require measurements.

This is a simple but effective crossover. With it you will achieve a much higher quality of crossover than possible using basic online calculators, and there is enough explanation to enable you to take it to the next level. Math has been kept light.

For illustration, I will be assuming a dome tweeter and a mid sized mid/woofer but with a little common sense this tutorial can apply to more than just two-way systems using typical drivers. (A follow up (post #82) for three-way systems).


Post 2 - Choosing the crossover frequency - Part 1
Post 3 - Choosing the crossover frequency - Part 2
Post 4 - Directivity
Post 5 - Choosing the level
Post 6 - Baffle step diffraction
Post 7 - The design process - why the following stages are necessary

Post 8 - Flattening the woofer's impedance
Post 9 - Flattening the tweeter's impedance
Post 10 - The woofer's crossover
Post 11 - The tweeter's crossover

Post 12 - Phase and diffraction
Post 13 - Tweaking the woofer
Post 14 - Tweaking the tweeter
Post 15 - Tweaking the system

You'll need to achieve these goals…
As this tutorial covers more than you may need, here is a list of the essential steps in case you don't plan on reading all of it.

1. Choose a crossover frequency based on your drivers

2. Choose the tweeter level (how loud it should be)

3. Flatten the impedances

4. Add the crossovers

…then on to tweaking. The rest of this tutorial helps in understanding how it works which will make the tweaking process more successful.

The goal of a crossover
Is to blend the sound from the two drivers (woofer and tweeter) so they work together as one. It may need to make the drivers as loud as each other, to divide the frequencies between them, and to correct or sidestep the limitations each driver will have.

Crossovers will not cut the drivers off suddenly at some frequency. There is a more gradual roll-off, somewhat like rolling a treble or bass control down. This means the drivers will be working together near the crossover frequency.

Last edited by AllenB; 8th September 2014 at 09:14 AM.
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Old 29th May 2011, 12:12 AM   #2
AllenB is offline AllenB  Australia
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You will firstly need to choose a crossover frequency that gets the best out of the drivers. If we choose too high a frequency, we risk poor sound from the woofer, and poor matching to the tweeter. If we choose too low a frequency we risk distortion and power handling issues with the tweeter.

Get some spec sheets
If you haven't already, collect the specifications for each of the drivers which you'll likely find at the manufacturers website. (if not, read on… but there'll be more on what to do at the end of this section.)

A spec sheet should show a bunch of numbers relating to things such as - how much power it can handle, how big is the cone and how far does it travel, how loud it plays compared to other speakers etc…

The spec sheet should also show a graph with a couple of lines plotted on it. One line will show how the speaker produces sound by plotting how loud the speaker will play at each frequency. The other will show how the speaker behaves electrically by plotting how it conducts electricity at each frequency.

Woofers - choosing where to cross
If you look at the woofer's frequency response plot shown below, you will see that the woofer has a peak in its response at 4kHz (4,000 Hertz) just before it rolls off above 7kHz. In other words, it will play too loud at these frequencies. This peak is not uncommon for a woofer but it will not always be obvious when looking at some plots.

It is the region of cone breakup, and it is the result of the cone flexing when working at these frequencies. Woofers don't normally sound good here and it is best to cross them over below this point which prevents them receiving as much energy at these frequencies.

A rule of thumb is to leave at least an octave (or two) between the crossover point and the cone breakup. An 'octave' means a doubling or a halving in frequency, so in the case of the woofer shown below, our crossover should probably be at or below 2kHz.
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Last edited by AllenB; 29th May 2011 at 12:14 AM.
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Old 29th May 2011, 12:14 AM   #3
AllenB is offline AllenB  Australia
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If you look at the spec sheet for the tweeter below, you'll see one spec named "fs". This is the resonance frequency of the tweeter (550Hz in this case) and you shouldn't cross this low. The response plot below (image 2) shows that the tweeter can't produce useful sound this low in frequency although the dome or cone will still move about freely if you ask it to. You can overdrive a tweeter if not careful. This may produce distortion, or cause damage.

The rule of thumb here is to cross the tweeter an octave above, and preferrably two octaves above the resonance frequency. In our case, this means our crossover should be higher than 1,100Hz and if possible 2,200Hz.

The best crossover frequency for this example set of drivers
With the woofer's maximum of 2kHz and the tweeter's minimum of 1100Hz, the crossover should be somewhere in this range. I would tend towards 2kHz as this way, when the volume is turned up the tweeter shouldn't be the first thing to strain (as it probably would if we chose 1100Hz for the crossover frequency). Sometimes a woofer will have particularly bad cone breakup and a tweeter may be known to handle a low crossover frequency so the option may be there to take yours lower as required.

If you can't get specs…
…then your crossover will be based largely on trial and error (unless you can measure the drivers or find out from someone else) First you'll need a starting point. If the rated impedance is not written on the driver, you can estimate this by measuring the resistance with a multimeter (on the speaker terminals) and multiplying this by 1.25 and rounding to the nearest whole number.

When choosing a crossover point, most dome tweeters will happily work down to 5kHz, and some down to 2kHz or less. You should choose a high crossover frequency to start with as this will reduce the risk of damage. Once you learn the capabilities of the drivers through listening, you can lower the crossover frequency as this will stop the woofers working at their upper extremes where they may not sound as good. Generally, smaller woofers can be crossed over at higher frequencies.
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Old 29th May 2011, 12:15 AM   #4
AllenB is offline AllenB  Australia
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Note -- The first time crossover builder may want to skip to the next section…this is here only to make a point about driver selection, and is slightly technical.

At higher frequencies, a woofer will be producing less sound off to the sides (off-axis). Its forward (on-axis) sound may measure good and flat across the frequencies we want it to produce, and this may seem to be all that matters.

The attached image shows a plot for a 6" full range driver showing the on-axis response (top line), 30 degrees off-axis (dotted) and 60 degrees off-axis showing the driver is becoming directional at around 2kHz. The total sound (from all angles) reverberates around the room and comes back to the listening position. The on-axis sound is most important but the total sound is also an issue.

A dome tweeter radiates over a wider angle near the crossover as the dome is smaller. If a crossover was set above a few kHz in this case, and we based it solely on the on-axis frequency response, there would be less total sound from the woofer just below the crossover. This could contribute to tonal problems and may cause the tweeter to stand out rather than blending in.

All the same, there are good reasons to use a woofer into this upper region where the design specifically calls for it, usually where a tweeter with controlled directional qualities is used.
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Old 29th May 2011, 12:17 AM   #5
AllenB is offline AllenB  Australia
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This is how loud the speaker will play compared to how much power you give it, and is called it's sensitivity. This is normally how loud the driver will be if we feed it with one Watt, after screwing it to a large flat baffle and setting the microphone back one metre from it.

As we need to set the tweeter to be around as loud as the woofer, we first need to discover how loud the woofer will be. Our tweeter needs to already be at least as loud as the woofer because we will be reducing the tweeter's level, not the woofer's.

Discovering the woofer's level
Looking at the woofer specs (image 1), we see that the sensitivity is listed as 87.5 dB/W/m. Looking at the woofer graph you'll see that much of the plotted response is at that level except for the cone breakup region (image 2).

This will be the level of our example system. If you choose to do some baffle step compensation (next post), this will come down further.

Setting the tweeter level
Later, we will use resistors to make the tweeter more quiet until it matches the woofer level. You should write down the published tweeter sensitivity specification as well as the chosen system level (in dB).
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Old 29th May 2011, 12:19 AM   #6
AllenB is offline AllenB  Australia
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Note -- The first time crossover designer may want to skip this section as it is slightly technical and is not an essential part of the basic crossover. It is addressed in the system tweaking section and can be worked on later with little trouble.

What is the problem?
If we were to mount a speaker in the middle of a solid wall, none of the sound would be able to go behind it, but if we mount it on a narrow baffle some of the sound wraps around the sides and goes off in other directions. The higher frequencies will stay in front, and the lower ones will wrap around the cabinet. (This is a matter of wavelengths being larger at lower frequencies.) If we were to measure the response from on-axis, it may seem as if the lower frequencies have gone quiet by up to 6dB (see the attached graph).

The common reaction to this is to use the crossover to cut the woofer's upper response down by 6dB to match the bass as shown in the image. The problem with this approach is that even though the lower frequencies seem to have disappeared, they haven't. They are still in the room. If we try to fix the on-axis response we may be creating a new problem of overall balance. Still, baffle step compensation is a useful tool that may prove useful with some speakers.

It is feasible to do a partial compensation and I would suggest trialling this kind of compensation in small steps.

What to do
If you decide to do any baffle step compensation, you will be lowering only the woofer's higher frequencies. You then need to lower the tweeter by the same amount.

There are three ways to do this. Firstly, if you use a narrow baffle, your baffle step will happen at a higher frequency nearer to the crossover. You might simply set your woofer's crossover to a lower frequency (make the inductor larger) which can offset the rising response.

Secondly, you can use extra components in your crossover, as will be discussed later…

…and thirdly, you can design a speaker that doesn't require compensation, (not something I will cover here), or just leave it for now and tweak it later after listening tests.
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Old 29th May 2011, 12:21 AM   #7
AllenB is offline AllenB  Australia
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Default THE DESIGN PROCESS - Why the following stages are necessary

Note -- If you are looking for a 'cookbook' approach, feel free to skip this section. It is a discussion post, and is slightly technical but recommended. It covers the interactions between the crossover and the speaker, and how to approach the design process. (I will be ignoring baffle step compensation here as it can be dealt with separately, isn't always necessary, and would needlessly complicate the following sections).

The first image below shows the example published woofer and tweeter response, with the desired final response. Now, it should be clear that the woofer and tweeter need to be treated differently… something you wont get following standard formulas.

In order to achieve this target response you'll want to make the individual responses look like the second graph shown below (around the crossover region). For this no-measurement crossover, I am going to use a first order electrical filter on the woofer and a second order electrical filter on the tweeter. Although these are not equal, it is more important that the drivers cross well acoustically and this combination typically works well.

This has the advantage of being a fairly straightforward crossover, whilst offering a fair range of control over the responses, and enough protection for the tweeter. Even for a 'measured' style crossover, this format is a common final result. I encourage you to think 'outside the box' once you get the feel for it… for the time being without measurement it may be prudent to start with something like this.

This is the final hurdle to cross before we can get down to designing the crossover itself. First though a short explanation of the word impedance. For our purposes, impedance is the same as resistance except that it applies to alternating current like music signals. Impedance can be a combination of plain resistance, inductance, and capacitance. The difference being that resistors behave the same at all frequencies but inductors and capacitors have a varying effect that shows greater influence at higher or lower frequencies.

A crossover is electrical, and when you put one on to a speaker, the impedance plot shows how the speaker will be 'seen' by the crossover. An example impedance plot is shown as the third image below, and it is fairly typical.

The problem here is that the crossover will have a varying effect as the impedance of the driver varies (i.e: the impedance will present a lighter or heavier load to the crossover depending on the frequency, which may upset the balance).

How to deal with the impedance issue
Without measurements, we are not as free to design a crossover that works directly around this issue, but this won't be a problem as we can approach it another way. We will first correct the impedances which then frees us to apply more standard crossovers successfully. This means flattening the impedance plots near the crossover region, which makes the speakers 'look' more like resistors, which are predictable and consistent.
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Old 29th May 2011, 12:22 AM   #8
AllenB is offline AllenB  Australia
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We'll need to use one resistor and one capacitor (per woofer). The first image below shows the before and after impedance plot (grey/yellow). The impedance is now the same at all frequencies around the proposed crossover. The second image shows the schematic (electrical) diagram so far.

Working out the values
Looking at the specs (image 3) you'll see one called either 're' or 'Rdc'. When working out the value for the resistor in this circuit you should multiply this value by 1.25. For our example this is 5.5 x 1.25 Although this equals 6.875, there is no easy to find resistor of this value, but 6.8 ohms will do nicely.

For the capacitor, look for a spec called "Le" which for our example is 0.4mH (that is 0.4 milli, also known as 0.0004). Take your value of Le and divide it by R squared. For example, our resistor was 6.8 ohms, and 6.8 squared is 46, so 0.0004 divided by 46 gives us a value for our capacitor of 8.7uF, which is close enough to the easy to find value of 8.2uF.
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Old 29th May 2011, 12:24 AM   #9
AllenB is offline AllenB  Australia
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In this section, you need to choose a value to use as the tweeter's impedance in an upcoming section, as well as choosing a resistor to add to the tweeter circuit.

Adding the resistor
The tweeter has an impedance peak at its resonance like the white curve shown in the first image below, at 550Hz. If we don't take care of this it may cause the tweeter to play loud around the resonance as our crossover will be less predictable. It may also reduce power handling.

The simple way to deal with this is to put a resistor in parallel with the tweeter. The entire impedance will be reduced, but the peaks will be reduced by the greatest amount. The smaller the value of resistor the more effective it will be but don't go too low… you may lower the total impedance too much which some amps won't like. (It isn't so bad if you plan to add some series resistance later, as will be shown in the crossover section.)

The first image below shows the effect (from top to bottom) of no resistor, a 20 ohm resistor, and a 10 ohm resistor. This will be a matter of trial and error for your tweeter. The circuit so far is shown in the second image.

If you are interested in taking this further or have a difficult tweeter, you can look at resonance peak filters. One of these could remove the peak altogether.

The new impedance
We'll need to know what the impedance is now, in order to work out the values to use later in the crossover. Estimating the 'typical' impedance value near the crossover frequency will be good enough for our purposes, and is not too difficult.

This example tweeter is a 6 ohm tweeter. Looking at the white curve on the plot below (which is the published curve from the spec sheet), the impedance goes to around 6 ohms at 2kHz, where our crossover will be. This impedance 'dip' region is not uncommon for the chosen crossover point because it happens above the resonance where we often choose to cross. For an 8 ohm tweeter we might assume it will be 8 ohms at this point (it isn't really that critical as long as we don't do anything unusual or assume too much).

Because the two blue plots in the image below will not be given on the spec sheets, we need to figure in the effect of the resistance we put in parallel with the tweeter, and this is how to do it. Start with the rated impedance of the tweeter (such as 8 ohms but in this example it is 6 ohms). Multiply this by the resistor you put in parallel, then divide this by the amount you get when you add the two. For example, a 6 ohm tweeter and a 10 ohm parallel resistor…. (6 x 10)/(6 + 10). This equals 3.75 ohms. Write your value down.
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Old 29th May 2011, 12:25 AM   #10
AllenB is offline AllenB  Australia
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What we will need here is an inductor. This is a coil of wire that has the property of impeding the flow of high frequency energy whilst letting the low frequencies pass. The final basic woofer crossover is shown in the image below (…more in the tweaking section).

Choosing the inductor value
Since we have flattened the impedance, we can use the standard formula to find the starting value of inductance. First take the driver's rated (nominal) impedance and divide this by 6.3 times the crossover frequency. For example, 8 ohms divided by (6.3 x 2000Hz). In other words, 8/12600 which equals 0.000635 This is also written as 0.635m and the nearest easily available value of inductor should be 0.68mH, which will make a good starting value.

The second image below shows the frequency response of the woofer with and without the crossover. It isn't quite there yet, but in a later post on tweaking I will discuss how changing the values of each of the three woofer crossover components gives us a finer control over the woofers response.
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