"A Basic Guide to Crossovers" and other things

[flakko 1]

I found this very interesting and decided to post it here to save yall precious clicking time. I probably understood like 65% of the material, but get the basic idea.

All of this info is taken from here :

http://www.diymobileaudio.com/forum/showth...ht=coustic+xm-6

Mod edit: Thank you to MiniVanMan from DIYMA for putting this together.

"There have been a lot of questions of late on the differences between active and passive crossovers. I'm sure with the influx of people on this board there's some confusion over what's what when crossovers are mentioned and how they're employed.

So, while this is in no way a comprehensive tutorial on crossovers, it's a beginning. Especially for those just cutting their teeth on audio.

Feel free to add, as hopefully this will grow, and feel free to correct me for anything I've said.

Okay, as promised here goes.

CROSSOVERS!!!!

First, this whole topic can be confusing in the respect that there is so much debate on this subject. Some guys swear by 24 db Linkwitz-Riley filters, while another guy can write an entire doctoral thesis for his PhD on how the 6 db Norman Bates filter is superior. So what does it all mean, 6 db, 24 db, Linkwitz-Riley, Butterworth, L-Pad, Zobel, blah, blah, blah, blah, blah.....?????????

Let's start simple. High Pass, Low Pass and Band Pass. I just need to mention this just to be sure everybody stays on the same page, and even understands the very, very, very, very, very, basics. High Pass means only frequencies above the crossover point, or sometimes referred to as the cutoff frequency, are played. For example, a 2000 hz high pass will only play frequencies above 2000 hz. Low Pass means only frequencies below the crossover point are played. For example, a 2000 hz low pass means only frequencies below 2000 hz will be played. BandPass plays frequencies between two points by utilizing both a high pass and low pass in the same filter network. So, for example you could have a midrange driver only playing 200 hz to 4000 hz.

***** Note - Before everybody and their grandmothers jump on me, let me cover myself. Because I say that a high pass will only play frequencies above a certain point, does not mean I don't understand that the frequencies below that point are still played, just cut me some slack. I'll get to that point later.

Next are slopes! Slope is the name associated with the numbers, 6 db, 12 db, 18 db, and 24 db. These are the most common, and I'm sure you've all seen them. What they actually mean, is "X" db drop off after the cutoff frequency per octave. So, to translate, let's take a 2000 hz "High Pass" I said above that a 2000 hz "High Pass" will only play frequencies above 2000 hz. That's not entirely true, as you may have gathered by my "Note" above. Okay, first you need to understand what an "Octave" is. An Octave is half, or double of a given frequency. 1000 hz to 2000 hz is an octave, as is 5000 hz to 10000 hz. So a 6 db per octave slope, cut at 2000 hz will yield a 6 db dropoff of output at 1000 hz, and 12 dbs by 500 hz, etc. Now understand that a 3 db gain is double the output, and 3 db loss is half the output. A "Low Pass" at 2000 hz using a 6 db slope would yield a 6 db drop of output by 4000 hz. Clear as mud???? Good!

Why are these numbers important? Well let's take a tweeter for example. You'll toodle around on this site and see many people talk about "Fs" or "Resonant Frequency". As a general rule that we use around here, we like to say that when picking tweeters, use double the "Fs" of the tweeter to determine lowest crossover point for a 12 db slope. This is in direct conjunction with how much power you can expect your tweeter to handle. So for example we'll take a tweeter with an Fs of 1500 hz. This tells us that we can safely use this tweeter at 3000 hz with a 12 db per octave slope. Now anybody that's been around speakers knows that it's not the high frequencies that blow speakers. It's the low ones. Just look at subwoofers. You might be able to get that 10" sub to play 20 hz, but you might start hearing some nasty clunky sounds when you try to get that sub to play 20 hz with double is rated power. The same can be said for a tweeter. So how do we get the tweeter to play closer to its Fs? Raise the slope of the crossover. A 24 db drop, when a 3 db drop is half the output is considerable. I'm not doing the math. You do it if you actually want to figure out how many halfs of halfs that is. Anyway, because 24 dbs is a lot more than 12 db, you can drive your tweeter closer to it's Fs. Same can be said of midbass drivers. You want your 7" midbass driver to play flat to 60 hz, but it's got an Fs of 40 hz. Well, you'd probably better use a 24 db slope.

Getting muddier, and muddier, isn't it??

Now on to Linkwitz-Riley, Butterworth, etc.

You'll usually see a name associated with a crossover. It's usually Linkwitz-Riley, or Butterworth, or even Bessel, or some fairly exotic ones. So, a crossover is a crossover right? WRONG!! With the case of passive crossovers, not knowing the difference can be very detrimental if you're trying to design one. Let's talk about what happens at the crossover point. We'll use our 2000 hz example again. If you have one driver playing 2000 hz, and another driver playing 2000 hz, and both are putting out the same amount of output, that would be effectively doubling the output, correct? Double the output is a 3 db gain. So, if you have one speaker playing flat to 2000 hz, and the other is playing flat to 2000 hz, then at 2000 hz, you'll have a summing of frequencies and effectively a 3 db gain in output. Maybe not so desireable, or maybe it is. Depends on the drivers and the application of the drivers. Well, this is actually the basic design behind a 12 db Butterworth crossover. It's simple and uses one crossover point to calculate the values for the components of your network. Only hitch is the 3 db gain at the crossover point. So, how do we get rid of that 3 db gain. Well, maybe by offsetting the frequencies a bit. Let's say 1850 hz for the low pass, and 2150 for the high pass (these are arbitrary numbers). Since they're not technically overlapping at this point, then the summing of the frequencies is only happening AFTER the output has started to go down. (I use calculators to determine this stuff so please don't ask me to do any math). With the right calculations, you can determine what sums will create a flat response. This is what a Linkwitz-Riley filter does. A Bessel filter will yield a 1.2 gain, and if you want to do the math, you can probably create your own filter network and apply your name to it. Then you can write a long diatribe about how great your filter that has a .82564345 db gain is, and how it will revolutionize the audio world.

"Man, are you sure this is mud, it smells more like....

Now to put this all together.

There are some common statements on this board. "Go active, the results are better". "I'm new to car audio, and am unsure about tuning an active setup". "Passives are way too hard to get right, you're better off going active." etc, etc, etc....

So, let's take a car application. You have a choice. That shiney new Diamond Hex set looks really sweet and you can get a great deal on it, or you can do it the hard way, and get an active crossover, some new shiney Seas drivers, and another amp. Well, with all this information you now have, please tell me how Diamond Audio knows how their components will be installed in your vehicle. Did they use a 12 db butterworth filter in their crossover? Doesn't that mean there's a 3 db gain at the crossover point. If I put these in kicks, on-axis, will that give me a nasty peak at the crossover point? If I put the midbass in the doors though, maybe the fact they're off-axis will be compensated for a bit by the butterworth design....

This is why we're advocates of active processing. It doesn't matter what kind of filter it is. As long as you can change it and experiment on the fly to get what sounds best. There's no math that needs to get things all muddled up.

However, if you really want to design a passive crossover go for it. Remember home audio uses the passive with great success. Their environment, however, is MUCH more controlled than ours."

[flakko 1]

"A crossover consists of two or more filters designed to split the desired frequency range into parts. Each part then being assigned a dedicated drive unit (speaker). A 2-way crossover has two filters: a high pass and a low pass, and is usually used to integrate a mid-bass and a tweeter.

Each filter then has several characteristics, one of which is it's slope (or roll-off), measured in decibels per octave (dB/oct). An octave being a factor of 2 of the original frequency. Thus 1kHz has octaves at 500Hz and 2kHz.

The rate of roll-off is always a factor of 6 (for ease of circuit design and calculation). The most popular types being 6dB/oct, 12dB/oct, and 24dB/oct. Further to the numerical rate of roll-off, filters are often asigned an 'order' number. Order numbers are again a factor of 6, thus a 1st order filter equates to 6dB/oct (1*6), 2nd order 12dB/oct (2*6), and 4th order 24dB/oct (4*6).

The other important filter characteristic is the filter point (crossover point where necessary). The filter point is that chosen at the design stage and equates to the 'half-power point', or the frequency where output is -3dB (-3dB equating to a 50% reduction in power). *** This assumes the filter design uses -3dB, some designs are -6dB at the filter point ***.

For example: a 1kHz high pass filter. In it's most basic sense everything above 1kHz passes, everything below is discarded. That's not particularly accurate. The frequencies below 1kHz are not discraded, rather they are attenuated according to the rate of roll-off of the filter. Assuming 6dB/oct: The output from the filter is -3dB at 1kHz, an octave later (500Hz) the output is -9dB (ie the output is already -3dB, and the filter reduces that by a further -6dB). Another octave lower (250Hz) and the output will be -15dB. If the filter were 2nd order, 12dB/oct, the output would be -15dB within the space of an octave, ie at 500Hz. -15dB equates to over 95% reduction in power.

This should indicate the importance of high order filters, especially within high power systems, and especially with tweeters. With a 6dB/oct filter, low mid-bass frequencies will still be entering the tweeter. And even though the output is considerably reduced, if enough power is available, the percentage reduction may not be enough to stop tweeter damage.

Just for reference:

-3dB = 50% reduction, or a factor of 2

-6dB = 75% reduction, or a factor of 4

-12dB = 93.75% reduction, or a factor 16

-18dB = 98.4375% reduction, or a factor 64

-24dB = 99.609375% reduction, or a factor 256"

[flakko 1]

"The way two drivers combine at the crossover frequency depends on the magnitude and phase at the crossver frequency, where both drivers are playing the same frequency. Strictly speaking, of course, it's the acoustic phase that matters. But let's say that the two drivers are equidistant to your ears, so we'll just focus on electrical phase for now.

If two drivers have the same amplitude, and are 0 degrees out-of-phase, the combination will be 6dB hotter in amplitude. If two drivers have the same amplitude, and are 90 degrees out-of-phase, the combination will be 3dB hotter in amplitude. If two drivers have the same amplitude, and are 180 degrees out of phase, the combination will perfectly cancel.

And now for a couple popular ones:

First order, 6dB per octave. Each driver is down 3dB at the xover frequency, and each driver experiences a 45 degree phase shift at the crossover (but in opposite directions). So the relative phase between the drivers is 90 degrees at the xover frequency. This means the drivers will have a combined response that's 3dB hotter ... and each was down 3dB at xover, meaning a combined result that's perfectly flat. This is a good thing ... but the shallow roll-off/up renders this solution almost useless (or at least not real popular anymore).

The 12dB Butterworth Alignment provides 12dB roll off/up for each driver, and each driver amplitude is down 3dB at the crossover frequency. Each filter "order" also provides 45 degrees of phase shift at the crossover frequency ... so the woofer will experience a negative 90 degree phase shift (second order), while the tweeter will experience a positive 90 degree phase shift (second order). This means that the drivers are naturally 180 degrees out-of-phase at the crossover frequency. This is kind of a bad thing, because it means a deep cancellation null at the crossover (again, we're assuming same distance from each driver to your ear). To solve it, many people wire the tweeter out-of-phase at the crossover. This puts the drivers back to a 0 degree phase relationship (inversion provides exactly 180 degree phase shift), which will result in a +3dB amplitude bump (since each one was down 3dB). Can be addressed by underlapping xover freqs a bit.

The 24dB Linkwitz-Riley was discovered by the challenge to find a crossver where each driver would be down 6dB at the crossover ... instead of the typical 3dB ... and each driver would experience a 180 degree phase shift (in opposite directions, of course) ... meaning a "perfect", 6dB summation at the xover. It was discovered that the cascade of 2 second-order butterworths satisfy all requirements, while also providing a relatively steep roll-off/up."

"Any linear filter is completely characterized by two things : it's MAGNITUDE response versus frequency, and it's PHASE response versus frequency. Together, these two functions define the COMPLETE FREQUENCY RESPONSE fo the filter. Oftentimes, we are more interested in the first derivative of the phase response, giving rise to a new function of frequency called the GROUP DELAY ... which will also, of course, be a function of frequency.

A "Butterworth" response is also known as Maximally Flat Magnitude. Mathematically, it is determined by setting as many derivatives as possible ... of the filter's MAGNITUDE function ... equal to zero at DC (for a low-pass filter). The resulting low-pass shape will have a MAGNITUDE response that is as FLAT as possible ... until it kinda starts to rolloff, of course Applicable to low-pass, high-pass and band-pass of course. This filter has a phase response that, while not as good as our next candidate, still isn't "bad".

A "Bessel" response is also known as Maximally FLat Group Delay. Mathematically, it is determined by setting as many derivatives as possible ... of the filter's GROUP DELAY function ... equal to zero at DC (for a low-pass filter). The resulting low-pass shape will have a GROUP DELAY response that is as FLAT as possible. Applicable to low-pass, high-pass and band-pass of course. The magnitude response will still look low-pass (or whatever you want), but will not roll-off as quickly or sharply as the Butterworth.

The transient time domain behavior of any filter ... including both of these, and any other linear system ... is completely determined by the COMPLETE frequency response (magnitude and phase, or group delay). The Bessel is generally considered to be a bit "better" ... less overshoot, less ringing for higher orders ... because it's phase is better behaved. But the Butterworth isn't bad, and given it's sharper roll-off, it's generally preferred for most crossover designs.

Excepting, of course, the Linkwitz-Riley. From a simple filter perspective, it's simply a cascade of two Butterworth responses. It won't be as flat as a true Butterworth of equal order, but it's strength is the way the two drivers combine at crossover, as discussed above."

[flakko 1]

Figuring out which frequency to crossover drivers:

"I'm going to use a couple of examples, and some response graphs to help you understand this.

I'll start with the Peerless Exclusive 7". Scroll to the bottom of the PDF where the response chart is.

http://www.madisound.com/pdf/peerless/830883.pdf

You'll notice the "blue", "red" and "green" response graphs. Labeled at the bottom you'll see "On Axis", "30 Degrees", "60 Degrees" respectively.

Looking at the graph you can see that the upper end response of the driver lowers dramatically the further off axis you play them at. Now if your driver side door sits 60 degrees off-axis of your listening position (which most doors fall in that area) then you can get a good idea of what the upper end response will be. In this case the graph shows about 1750 hz before it starts to collapse, and is probably useable up to about 2200 hz.

Your passenger side driver will yield a considerably higher response due to it be much closer to on-axis than the driver side, so you might start to hear some bias from the passenger side should you try to run the set up to 3500 hz.

Now let's look at the Vifa MG 4" midrange

http://www.madisound.com/pdf/vifa/mg10md09-04e.pdf

Here you'll notice that on-axis response is great. Near 15k flat, with extension up to 20k. Npdang tested this driver and mentioned that it can almost be used without a tweeter. By the response graph we can see that.

However, now let's say we're building some kick pods, and due to some reason, we can't get them completely on-axis, but rather 30 degrees off-axis is the best we can do. You'll see that the 30 degree off-axis response graph basically tells us we can use these midranges up to about 5k before any real degradation of response. Pretty nice.

Now, for low end response. For tweeters, the general rule of thumb is twice the Fs (Resonant Frequency) at 12 db. A higher slope (i.e. 18 or 24 db) can get you closer to the Fs, but we'll use 12 db for now.

Let's first look at the most common tweeter on this board... The LPG

http://www.madisound.com/pdf/lpg.pdf

The Fs of this tweeter is 1850 hz. Doubled that is 3700 hz. Now, try coupling that with a 7" driver mounted in a door 60 degrees off-axis, and you have quite a gap between 2000-3700 hz. Almost a full octave. Now to be fair, let's look at the upper end extension. The on-axis, 30 and 60 deg graphs look almost flat up to 20k. Very nice. These can be mounted in some sail panels firing horizontally across your front stage and you can get great results from them.

Next is the Seas Neo tweeter.

http://www.madisound.com/pdf/seas/h1396.pdf

Here is a tweeter with a much lower Fs. 1170 hz, using our rule, can be crossed at 2340 hz. The specs say 2500, so we're pretty close. With a 24 db slope you could get 2200 hz out of them. These would be much better to mate with a set of Exclusives mounted 60 degrees off-axis. However, their top end is nowhere near that of the LPGs. You can definitely see that these would lack the top end "sparkle" that so many people refer to when talking about the LPG's. These will be much more neutral and laid back on the top end. Not a bad thing, as a lot of music doesn't go any higher than 15k. You will also notice a huge difference between on and off-axis. A major consideration when considering how to mount them.

These are just some suggestions on how to "guess" at appropriate crossover points. The graphs give you a good idea of how to tell how a driver will perform in a given installation. These graphs in no way indicate how a driver will sound, nor how they will perform at the upper and lower limits of their capabilities."

[flakko 1]

Frequencies in music (good for eqing):

"Understanding Frequency - What does What

A lot of you know that I am a bit of an sq fiend, I am one of the few people on here that often turns of the sub just to check it's still running...I personally like sub bass as an anchor for the low end and to add warmth to the music. To me, mid and midbass is the key.

Mid and Midbass IS critical. let's look at the frequency response of some instruments and see where all the action is. I am not going to go into the the differences of Fundemental and Harmonic frequencies, and how they interact (I can if need be), this is more of an overview of what frequencies make up what.

For those of us who listen to acoustic music, apposed to synthesised dance music, for want of a better description, I shall take some drums, bass guitar, electric guitar, and vocals.

I shall work through the frequencies rather than the instruements, as this will allow us to see where there are complimentary frequencies (different instruments produce the same sound).

50hz (usually sub bass)

this freq is where all the boom is, if you want more boom on foot drums and bass guitar, boost, to reduce, cut.

100hz( usually mid bass)

this is the hard bass sound, it gives drums that solid feel, boosting here will harden the drums/bass guitar, as well as adding warmth to guitars. A cut will reduce boom on guitar and add clarity.

200hz (either midbass/mid)

Boost to add warmth to vocals and guitar, reduce to clean up vocals

400hz (usually mid / large Horn)

Boost to bass in general, reduce to decrease cardboard sound low drums.

800hz(usually mid/horns)

Boost to add clarity and Punch to bass, this is the one that digs you in the ribs , cut to reduce tinnyness to guitars

1.5khz (mid/tweet/horns)

Boost to add clarity to bass guitar, reduce to impreve dullness of guitar

3khz (mid/tweet/horns)

Boost to increase pluck on bass guitar, attack on guitar and high drums, increases clarity of vocals.

Cut to reduce breathy sound on vocals.

5khz(mid/tweet/horns)

boost for vocal presence, low drum attack, piano attack, and guitars, reduce to distance background.

7khz(usually tweet/horn)

boost, more attack on low drums, percussion and bring life to dull vocals, also sharpen elctric guitar

Cut to reduce siblance

10khz (tweet/horn)

increase to brighten vocals/guitar and piano

cut to reduce siblance

15khz (tweet/horn)

increase to brighten vocals/guitar and piano highs

Right, looking down this list we can see that if we want a good solid bass line ( add @100hz), that's not boomy (cut @ 50hz), with good punch (add @ 800hz), with good attack ( boost at 5-7khz), most of the action is in the midbass and midrange area, with only boominess being in the sub area.

This also highlights one of the main benefits of horns( the huge range they cover).

Understanding these frequencies also allows for fine tuning things like stage height (more attack of drums gives perception of a higher stage), and adding depth, ( make background sounds more distant)"

[flakko 1]

about level matching:

"Okay, now that you’ve had some time to absorb all the previous information, I’m going to step it up a little bit.

Let’s first look at the challenges we face in building any kind of speaker system.

First is level matching. It’s very difficult to find a tweeter and a woofer that have the exact same sensitivities, and will operate at the same volume given the same power.

Second is impedance variations. As you move through a speakers frequency response the impedance varies. As you get towards the upper end of response the impedance starts to rise considerably. This is demonstrated in the following graph. This a factor of inductance of the voice coil.

As you can see, the impedance is rising the higher you go. This causes a drop in output. A Zobel will level that out, giving you a flatter response.

Third is spikes and dips that cause your response to be something other than flat.

Let’s start in order here. Level matching is done using an L-Pad. Generally, the tweeter is much more sensitive than the woofer. So the tweeter needs to be attenuated. The L-Pad circuit can be introduced into your passive crossover. It can be done 2 ways. First is fixed. If you know the amount of attenuation, you can get the appropriate resistors and build the network right into the crossover. The problem with this is if you don’t get it right, you need to completely redo it. The second way is to use a variable L-Pad. Parts Express has these and in a car audio application using passive crossovers they are a MUST in my opinion.

http://www.partsexpress.com/webpage....Group_ID=1 96

The drawback is you need to build around the L-Pad and mount it somewhere that is accessible. However, it does allow you to adjust your tweeter to compensate for different mounting locations. These are what upstage kits, like CDT use.

Next is the Zobel network. The Zobel network compensates for the rise in impedance due to voice coil inductance. Pretty much enough said.

Third, and this is where crossovers start to get REALLY tricky, and even I’m a little fuzzy in this area. Depending on your baffle, mounting locations, varying distances of voice coils, your response will be something other than flat. If your baffle is too narrow, (as in a tower speaker) your mid drivers can experience a spike in response of around 6db starting at around 100 hz and flattening off at around 1k hz. This is called baffle step. You use baffle step compensation to, well, “compensate” for it. I’m not going to go into it a whole lot, and baffle step is just one example of how a speaker reacts to it’s environment. I will say that there is a compensation circuit that will cover just about every peak, and dip.

What does this all mean? It means that you can drive yourself CRAZY trying to build the perfect crossover for any application. There’s a point of diminishing returns when a crossover just becomes too over-engineered. It’s safe to say that a decently built crossover will contain 3 parts, the actual crossover network, the L-Pad, and the Zobel. The other networks don’t really come into play until you NEED them. Baffle step can be fairly accurately predicted, but other “notch” type filters are usually used to compensate for something unpredicted and unwanted. It’s possible to “notch” out a peak caused by a Butterworth type crossover at the crossover point, but it’s just better, if it’s a problem to pick a different alignment.

LEAP is great, as are a lot of other programs out there. LEAP allows you to build your crossover ‘to the enclosure’ for the best possible results. LEAP can only be effective when the surrounding variables of a driver are controlled. For example, the difference between a well built speaker enclosure, and a door frame. LEAP can predict and design a crossover to compensate for the way the speaker will react within a given enclosure by simply inputting the dimensions. LEAP is going to “leap” out of your computer and kick the snot out of you if you try to enter door frame parameters.

So, if you are looking to go the passive crossover route, you can pretty easily design a crossover as long as you know which speakers you’re going to be using. You add your three essential items and voila you have a working crossover. However, based on the above information that’s all you’ll get. You won’t get any kind of compensation for the way the speakers will react in the car. And believe me, they will react BADLY.

So, what do we do to compensate for these unknown and highly erratic, unpredictable peaks and dips in our frequency response? We EQ them out. An equalizer will do everything that a notch filter will do, and is effectively an “Active Notch Filter”. We couple the EQ with an Active Crossover, and you get a system that is highly adjustable and can correct for the many, less than desirable, effects your car will have on your system. Add Time Alignment and you can achieve results comparable to a cheap home audio setup (given that you spend $1000.00 on high quality speakers).

By going active, we’re essentially, trying to take the “car” out of the “car audio”. Active processing is also used in home audio and is highly desired by many audiophiles out there. However, in my opinion, the difference between a well built tower with a passive crossover and an active setup in home audio is not nearly as dramatic as an active to passive setup in car audio."

whew. iz done. other info can be seen over in the link given

[b5i8 0]

So, what do we do to compensate for these unknown and highly erratic, unpredictable peaks and dips in our frequency response? We EQ them out. An equalizer will do everything that a notch filter will do, and is effectively an

[bdawson72 0]

Whew!

Good read though, I needed it

[Jybfan04 1]

Great read.. I plan on reading this several times to fully grasp the concepts discuss in this tutorial.

[JimJ 11]

I thought it was a little oversimplified and generalized in places, but OK.

[DevilDriver 28]

I thought it was a little oversimplified and generalized in places, but OK.

Perhaps even "Basic"?

I had been working on a similar version when MiniVanMan posted this so I unfortunately wasted a fair bit of time. There are a couple of things I'll try to add later when I have time.

[///M5 2,833]

That is a lot of prose for basic, but I must admit I haven't read it. Why, see the first part of the last sentence.