(c) copyright Robert B. Richards 2014
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I've been researching, designing and building speaker systems since about 1967 as a hobbyist, and worked professionally in the Audio field on several occasions in the 1980's and 90's (see Who's Bob section of website or my Resume). I don't know it all (nobody does), but I have a lot of practical experience and may be better at explaining things than many others in some cases. I view every speaker system I do as an experiment. I'll often throw in something unusual just to see how it works (open baffle, various cabinet shapes, different crossover network types, etc.). Theory is very useful, but there's no substitute for practical learning experience, especially when it comes to understanding acoustics. Designing an excellent speaker system can be very complicated, and that's part of what I like about it as a hobby. It challenges and inspires me. Having said that, it's not real hard to design and build an "average" speaker system that most people will be plenty satisfied with.
When I set out to build a set of speakers, I first evaluate the room they will be put in, and decide tentatively where I'll put the speakers and how much space I'm willing to give up for them. Should they be bookshelf speakers? Should they be towers? Taller is usually better but how tall am I willing to put up with? Should they be open baffle speakers which need to be placed at least 3 feet away from any walls in order to work right? Should they be floor to ceiling Line Arrays? Should I hang them from the ceiling? Am I going to want more than two speakers for surround sound? Should they have separate woofer cabinets to handle the bass? Where would those go? Is there room for many poweramps so I can use active crossovers? Is efficiency an issue? Do I want to optimize them for a sweet spot with the best possible stereo imaging, or do I want the best sound regardless of where in the room anyone sits? How loud do I want them to go? It's wise to get clear on these kind of questions before starting down the path. A very great speaker can sound pretty bad in the wrong room.
One of the best arrangements I've ever heard was Bruce Penney's satellite speakers hanging from the ceiling (100HZ on up), aimed downward at he couch, which was roughly 10 feet out from the sofa, which had a tapestry on the wall behind it to absorb some of the acoustic energy. These "satalites were tri-amp'd (2 five inch KEF drivers D'Appilito style with a 1.5 inch phenolic upper-mid dome and a 3/4 inch Celestion dome super tweeter between them). Below 100HZ was handled by two large woofer cabinets (JBL 15 inch woofers with JBL 15 inch passive radiators). The system as a whole was 4 way, with 4 pole active crossovers and active EQ. Other great speakers were the DBX Soundfield tower designed by Mark Davis. Although these had to be placed at least 3 feet from any walls, they sounded great anywhere in the room. And then there's my brothers McIntosh ML-1 speakers from 1972 that have always impressed me (a 4 way bookshelf speaker designed by Roger Russel). Just when you're sure the speakers make all the difference, you find rather modest set of speakers sounding unfairly good, due to how they interact with the listening room acoustics.
One of the best sounding speakers I ever made (1976 - sorry no photo), was two 8 inch full range speakers and a Marantz 2 inch cone tweeter in a box made of 1 inch think oak. One 8 inch ran active, and the other had a shorted voice coil and a fairly heavy washer glued to the front of the voice coil. This second 8 inch driver was acting as an electronically damped (due to the shorted voicecoil) passive radiator. The one pole passive crossover network divided the spectrum at about 2kHZ. The cabinet internal volume was about right for just one 8 inch woofer, and was packed with fiberglas insulation for damping of internal resonances. I gave them to my dentist friend as payment for work he did for me, and years later I went to see him and was astounded at how good they sounded, hanging from the ceiling in his dental office.
Other speakers that impressed me include some Ampex bookshelf speakers made in the 1960's that had just a 6 inch woofer in a closed box and a 2 inch cone tweeter, which were actually placed on a bookshelf surrounded by shelves of books (which is excellent acoustically). On one occasion I heard four Radioshack 3 way bookshelf speakers sound amazingly pleasant (placed on the floor - which rarely sounds best). They were wired "cross-coupled"; the left front was wired to the right rear and vice versa. Another memorable experience was two 6 x 9 inch coaxial ceiling speakers in a large hair salon (spaced rather far apart), which gave an amazingly enveloping stereo effect over a rather large area. The way a speaker interacts with the room acoustics is quite arguably the weakest link in any reproduction process. Either way, it's of HUGE importance.
My pages on this and other audio projects are pretty deep in theory, fancy tecchniques, etc. I don't mean to make it seem like a beginner can't have fun doing a simple version of a speaker system. Without a calibrated mic and pink noise generator, a speaker builder is left somewhat guessing at what to do for a crossover network. The math can get you close to accurate in many cases. Without a method of determining the optimal speaker cabinet internal volume, again you take a guess based on any info you can scrounge up. But that was me for the first several years of building speaker systems. All I had was a volt/ohm meter and a soldering iron. Not much more. I was 12. Those syetms weren't great, but they were good enough for teenagers almost constantly listening to rock and blues music with friends dropping in often.
The first thing for a beginner to know is that any tweeter needs to have a capacitor in series with it, or it will probably get damaged. Tweeters can't handle bass frequencies at all. The first time I took apart a friends stereo to find out what a crossover is, it was just a 4uF non-polar capacitor wired in series with the tweeter. The woofer frequecy response rolled off mechanically at the high end, as would be seen on it's frequncy response graph, thereby showing where the tweeter should start making noise in frequncy, which is set by the capacitor. A better crossover would have a coil in series with the woofer, so it's frequency response would roll off more cleanly, and merge/integrate better with the tweeter. The second thing a newbie should know is that frequency response is perhaps the most important thing about a speaker. You want something pretty close to equal amplitude over all frequencies from about 30HZ - 18kHZ ideally. This is referred to as a flat frequency response. In the real world, most listening room acoustics will mess this up a lot.
One of my first decent speaker systems (1967 - I was 12) was just a 12 inch woofer in a fairly large cabinet the size of which we just guessed at, and a "dual cone" 6 inch full range driver in a sub-enclosure acting as midrange and tweeter. I filled the cabinet and sub-enclosure with regular fiberglass to minimize internal resonance issues after noticing that all good speakers had this. I tried a few different capacitors for the mid/tweeter in the vicinity of 4uF - 10uF to see what sounded best, and that was it. Years later I found out the formula for calculating the size of the tweeter capacitor, and I was was thrilled. Also coil math, higher order crossover circuit math, etc. Years later when I started working for Tektronix, I got in with the EE's who had built triamp speaker systems and learned all about that. Now I'm 65 years old and still doing it; building speaker systems for fun. So don't let my picky/nerdy opinions scare you away from this potentially fun hobby.
Where to start... Most musicians I've ever known have very little idea how to get the best sound. They depend on professional sound engineers to make it good, or just copy what other musicians are having good luck with. They rarely complain about someone processing/enhancing their sound to make it more enjoyable. Many purists don't like to tamper with what the recording/mixing engineer created. Some of them don't believe in having tone controls... That's rediculous. The purpose of music is to feel good. Good tone controls can make a big improvement in the enjoyability in most cases.
Directional microphones have what's called "proximity effect" which means the frequency response (amplitude vs. frequency) varies with distance from the mic. When there is more than one mic recording anything, there will be comb filter effects due to crosstalk when the signals are combined electrically in the mixing process. This is why recording studios often have acoustic absorptive walls between each musician in a band to minimize this crosstalk, and use directional mics (cardioid, hyper cardioid, etc.). Sound sources are usually recorded in mono, and then the recording engineer uses fancy electronics to create a sense of stereo soundfield. Orchestral recordings are usually recorded in some variation of "true stereo", but also have the crosstalk/comb filter effects to deal with, among other issues. Most mixing boards use amplitude panning for stereo effect image placement, and ignore the fact that the ear-brain mechanism senses image location by timing comparisons rather than just amplitude comparisons below about 1kHZ. They ignore this fact largely because the playback system will typically have "inter-aural crosstalk", which blurrs our ability to localize an audio image below 1kHZ based on timing cues anyway. There's the Bob Carver method of inter-aural cancellation (electronic), and the Polk Audio version (acoustic) each of which I've researched and built and like, but both require the listener to have their head exactly centered, and approximately the correct distance out from the speakers, and minimal room acoustic issues especially laterally, for that to work well. These methods of inter-aural crosstalk cancellation also cause the center image to be weak sounding.
David Griesinger, formerly of Lexicon, may be one of the most adept experts at recording music in stereo or any variations of surround sound. He has many papers available for reading on the web.
One of the most damaging parts of the reproduction process is how the acoustics of the recording studio and/or playback listening room affect the signal getting to your ear. It's often damaging to the point of making me wonder why I go to so much trouble to make my speakers as perfect as I can.
Many recording studios do what they can to have no acoustics. They build what approximates an "anechoic chamber" so there will be minimal room reflections which cause comb filter effects, and imaging variables. Other studios use a room that is acoustically "dead" at one end, and reverberant or "live" and the other end of the room for effect. Reverb and many other digital processor sound effects have become very sophisticated and are used most of the time these days, to "sweeten" the otherwise "dead" sound. There are those who try for maximum "fidelity" (flat response and no "sweetening" processing), and then there's the other 99% who design for most pleasurable audio experience, whatever it takes. Maximum technical "fidelity" is a good default or starting point in either case, but rarely yields a truly great bottom line experience by itself. More on that later.
In a typical listening room, there are many reflections, each causing a comb filter effect when combined with the direct signal path at your ear, and/or with each other. Those are different than room resonance ringing effects. Both are often substantial issues. At the higher frequencies above about 500HZ, there are so many reflections creating comb filter effects, that the nulls or cancellations created by one reflection combining with the direct path at your ear is largely filled in by other reflection paths, that will have cancellations at other frequencies. Because of the frequency resolution of the ear-brain mechanism, these comb filter effects above roughly 500HZ largely average out and can liven the sound a bit (very short term reverb). Side wall reflections add a sense of spaciousness to the sound, but this spaciousness is always the same for any recording, so it could get tedious to listen to over time in some cases. It can also blurr or dominate any stereo imaging cues embedded in the recording, if there are any. Proximity of the speaker to the room boundaries (walls or large hard furniture), will have a large effect on the frequency response of the speaker, from the point of view of the listening position, especially in the lower frequency range (generally below about 700HZ). Many speakers are designed to depend on this room boundary reinforcement of low frequencies, while other speakers are designed to be used several feet from any walls. The latter will need to use what's called "baffle step correction" EQ, to compensate for the lack of reinforcement below somewhere typically around 700HZ (depending on several variables).
Published speaker driver frequency response graphs are done in the "professional" world with the driver mounted on a large wall, facing into an anechoic chamber (acoustically dead - no reflections at all). That arrangement is called an "Infinite Baffle", because the energy coming out of the back of the speaker driver is never able to get into the anechoic chamber where the calibrated mic is. Although there's a lot to be said for this method of standardization, this is not necessarily very similar to how these same drivers will be used in the real world. Acoustic energy diffracts, or bends, at the lower frequencies, but not so much at the higher frequencies. This means that the wall in that anechoic testing chamber will reinforce the lower frequencies significantly more than the front surface of a typical speaker cabinet (due to its size), especially if it's intended to be positioned several feet out from any walls.
Most rooms that have many hard parallel surfaces and corners will ring at various frequencies. Ringing has both a start up time, and a decay time. A quick transient may not last long enough to cause significant obvious audible room ringing, but a sustained note in music is likely to. If your measurement system uses transient type test signals such as pink noise or a single short pulse (which theoretically has equal energy at all frequencies), you may not see the effects of room ringing, because of the required start up time of the room resonance. If you instead use tone bursts in a gaussian envelop (or any variation of that), you'll be able to see the effects of room and driver resonance (ringing). Real world music is usually made up of both transients and sustained tones, so it's best to look at how a room reacts to each when considering tradeoffs.
Either extreme, (too many room reflections and/or ringing vs. a "dead" room approximating an anechoic chamber) is considered less desirable. I agree with Linkwitz where he basically says that the acoustics of an average living room with all the typical furnishings is actually about as good as it gets. It's impossible to create a "perfect" reproduction system for many reasons. It's always about choosing the best set of tradeoffs for a given situation. On the bottom line, a room with good acoustics is a room that is pleasant to listen in. It has many reflections, but they all average out pretty much over most frequencies, and liven up the sound a bit, but not too much.
This is the frequency range of bass, where most of the warmth comes from. Personally I love low bass. It's often the biggest difference between good speakers and great speakers. It's presence will have a significant "psycho-acoustic" effect on how you perceive the upper frequencies. Virtually all percussive instruments have significant energy in this range, not just a "bass" instrument. It's been said that the sense of depth in the soundstage is highly dependent on the bass response going low enough. "Good bass" in my opinion, is a speaker that is acoustically somewhat flat down to about 40HZ. "Great bass" goes down to 30HZ flat within a few dB. Below that is arguably even better, but many recordings that actually have energy that low are often EQ'd by the recording engineer for the "typical speaker" or "studio monitor", which means they've exaggerated the very low end in order to compensate for the rolloff of the typical commercial speaker system. This can be too much with a speaker that measures acoustically flat down to 20HZ (my experience). Because of this, I find that 30HZ is actually a better place to extend to. It takes significantly more amplifier power and cone surface area to function well down to 20HZ rather than just 30HZ. Plus, the lower frequencies go through walls and bother neighbors more if that's an issue. Movie theaters use concrete block walls to try to isolate bass leakage between rooms in a multiplex theater building, because nothing else can do the job. It's about mass at bass frequencies. All the conventional acoustically absorptive materials do little or nothing at bass frequencies. They start to work in the midrange frequencies and are usually great at the high frequencies.
Due largely to the way the ear works, most of the energy in a typical piece of music will be in the bass frequencies, which usually means large amounts of speaker cone movement. Because of this, it's arguable that the best place for a crossover frequency would be at around 80 - 800 HZ depending on a bunch of variables. Most bi-amp or tri-amp systems that I've seen choose a crossover frequency in this range. A single driver doing the whole frequency range will have significant audible FM (frequency modulation) distortion of the higher frequencies when a bass note or drum hits. Plus, that bass note may cause the poweramp to clip (distort), and it will trash the entire frequency range for that moment. With bi-amping, only the woofer would distort, and the rest of the frequency range would very likely stay clean. I prefer a 4 pole active crossover to separate the woofer from the rest of the drivers, and also use active EQ to make a woofer in a sealed box be acoustically flat down to 30HZ at the listening chair, with a fairly steep drop off below that (so the driver doesn't get damaged as easily and you don't waste a bunch of the amplifier power on sound you don't need or want). This method give me the tightest and cleanest bass, due to the consistent mechanical damping of the woofer cone over frequency, by the air inside the closed box baffle.
M&K made an active woofer that I used to have (Volkswoofer 3B) that had both a 4 pole 125HZ active rolloff, and active EQ making the woofer somewhat acoustically flat down to 20HZ. It also had an adjustment that would roll off everything above 50HZ at a one pole rate (6db/octave). I thought it sounded great in the rooms I was living in at the time (several - I moved a lot in those days), and the optional 50HZ pre-rolloff adjustment came in handy when dealing with typical room acoustics problems. My room had a big resonance at 100HZ. That tweak reduced that problem down to nothing significant. Much less "boomy" sounding. Great idea.
Enclosure types: Folded Transmission Line baffles are way too big and heavy, so not practical IMO. Vented or ported boxes have good physical damping of the woofer cone at the frequency they are tuned for (usually around 50HZ), but the physical damping gets weak on either side of that "tuned" frequency, so using active EQ to make the woofer acoustically flat at the listening position down to 30HZ can cause vented woofers to "bottom out" (coil gets mashed and/or deformed), thereby permanently damaging the driver, so active EQ is not generally recommmended for vented box designs. Venting a box (or using "passive radiators) is sort of the cheaper way to get lower bass, and some vented box designs sound pretty good. Personally I feel that being able to use active EQ is a huge plus, so I'm a big fan of closed boxes and active EQ for the woofers. The bass will be flat to a very low frequency, and have good damping all the way down (tight bass), consistent over frequency. Plus, the closed box can be substantially smaller than a typical vented box will need to be, for a given speaker driver size.
It's arguable that getting bass to be relatively flat at the listeners chair is one of the hardest things to achieve, due to room acoustics, thereby typically causing bass and lower midrange frequencies (typically up to about 400HZ) to sound "boomy". Both room resonance and comb filter effects are typically particularly bad in this frequency range. But getting this challenge conquered can be one of the most satisfying improvements one can make on any speaker system situation. Some people have resorted to having 4 different woofer cabinets placed around their listening room, so some of these problems average out. The floor to ceiling vertical line array crowd claims they have no problems with this kind of thing. Getting the woofers further from any room boundaries may help significantly. Every room is different, so a lot of experimenting goes on when the best sound is desired. Active EQ can be helpful for this, but generally only fixes things for one location in the room, and can actually make it worse in other locations in the room. Active EQ should only ever be used to attenuate peaks in the frequency response, and not used to try and pump up cancellations due to comb filter effects in the accumulated frequency response at the listening chair.
This range of frequencies is where the fundamental frequency energies of human voice and most musical instruments are. The exact character of the sounds is more determined by the higher frequencies. Telephones are designed to do well from about 300HZ to 3kHZ, for maximum voice intelligabililty. When designing a baffle for drivers in this frquency range (and higher), it's wise to consider the size of the half-wavelengths, relative to the baffles internal dimensions, because of the possibility of significant internal cabinet resonances, which will re-emerge thru the speaker diaphrams. Cabinet internal absorbtive materials are likely to make a huge difference in this, and the higher frequency range. For example, the half wavelength of 1kHZ is roughly 6 inches, which isn't far from an internal dimension of some speakler baffles. 500HZ half-wavelength is about a foot.
David Griesinger, formerly of Lexicon, is one of my favorite audio engineers. In one of his papers he talks about how typical room acoustics will actually effectively reduce the sense of separation as you go down in frequency, below about 800HZ. He also notes that this is the opposite of what you want, for a truly enveloping sense of soundstage. Many researchers have noted that we perceive stereo image location primarily by timing comparisons below about 1kHZ, rather than amplitude comparisons above about 1kHZ. This opens the can of worms known as "Inter-aural crosstalk". Up to the frequency where the half wavelength is shorter than the distance between our ears (around 1kHZ), we perceive stereo image location by timing or phase comparisons left to right (and vice versa). Above that frequency, the ear-brain mechanism has no way of knowing which period of waveform it's comparing, so it switches over to amplitude comparisons from about 1kHZ on up (because of the distance between the ears, compared with the distance of the half wavelength).
In real life, any sound will be perceived by both ears. The further ear will hear the sound with a slight delay (in the general vicinity of 125uS) relative to the ear with the more direct acoustic path, and with a relative frequency response rolloff due to the head being in the way. When this happens only once, the ear-brain mechanism knows how to perceive the location of the sound at all frequencies. If it happens a second time, but with a different time delays, because it's reproduced through a set of speakers that allow for a second inter-aural crosstalk, the ear-brain mechanism will get confused and to a large degree lose the ability to sense image location at the frequencies below about 1kHZ. It will still sense image location at the frequencies above about 1kHZ, which is why the stereo effect sounds as good as it does.
What happens in the real world is that the listening room reflections will to some degree regenerate a sense of "space" in the lower midrange. The reflections of the lstening room can create a false but somewhat effective "rejuvination" of these "blurred" timing cues. It's effective because they happen in 3-D, rather than the 2-D that a stereo is technically capable of. Some aspects of our perception of sound and image location are a continuously updated learned thing. By moving our head slightly, we get more clear on the location of certain sounds, because our brain knows how to analyze the differential.
My open baffle dipole speakers generate a second signal mostly on the Z axis (front to back) in the lower midrange that would have about a 6mS delay (reflection off the front wall of my room), which makes embedded reverbs in a recording come to life with a sense of 3-D nature. So, those pesky room acoustics that are usually a problem are actually giving me back part of what I lost with the inevitable inter-aural crosstalk which creates a second set of timing cues. It's fake but it works to a significant degree in a typical listening room (not in small rooms). What I found equally interesting is that because my open-baffle dipole speakers generate that delayed reflection off the front wall of my living room with a 6mS delay (towers 3 feet from the wall), The Carver Holographic Generator technique of inter-aural cancellation with its 125uS delay works very well (for a very confined listening position). The ear-brain mechanism perceives different amounts of delay very differently. These two delays don't seem to interrupt each other at all. Open baffle speakers also have substantial cancellation of lower mid frequencies at the sides (90 degrees off axis), so side wall reflections are minimized in the typical listening room, thereby helping the inter-aural cancellation method do its job.
There's a page on David Griesingers website where he talks about the benefit of using a circuit that reduces the L+R signal as you go down in frequency, from about 600HZ, which compensates for what the typical room acoustics and/or inter-aural crosstalk does. It gives the listener a more "enveloping" sound experience that is arguably more accurate.
This frequency range is where the ear is most sensitive, 3-4kHZ usually being the peak of sensitivity for most people (see Fletcher-Munson curves or equivalent). Due to the size of the wavelengths, image location is perceived primarily by amplitude comparisons left to right and vice versa, rather than timing or phase comparisons. The ear is also most sensitive to distortions and abrupt differential phase changes in this frequency range. Since most playback systems will have the interaural crosstalk issue (headphones avoid that), this is the range that typically allows us to perceive the stereo effect well. This suggests that the frequency response of the upper mid drivers should be very well matched to each other in order to get the best stereo effect (sense of soundstage depth and width - separation of individual instruments, etc.). It could be argued that this range is better off having fewer room reflections that could cause the acoustic "signature" of the left speaker to be significantly different from that of the right speaker at the listening location.
Most hard cone woofers and lower midrange drivers (aluminum, Kevlar, etc.) have substantial cone resonance's in this range of frequencies. That may create an elevated sense of presence or immediacy, but could get tedious to listen to over time. Because a resonance causes ringing, such a resonance could be more "coloring" than a calibrated mic and pink noise test might indicate. Because of the size of the wavelengths in this range (roughly 2 inches to 1 foot), the internal dimensions and shape of the speaker driver enclosure will have a substantial effect on the sound. A sphere with a driver diaphragm at the edge is arguably the best enclosure shape situation, but has a substantial baffle step issue since the outside of the enclosure would not reinforce the lower frequencies (1kHZ and below) very much at all (not like the large flat wall in an anechoic chamber where the published frequency response graphs are typically made). Since acoustic energy is very directional in the higer frequencies, the outside front of the baffle is not a huge issue here, although it will have some effect. You could use waveguide technology to reduce room acoustic effects to get better matching and thereby imaging accuracy, but at the expense of off axis response. Better sweet spot, but arguably less accurate sound to everybody else in the room (outside of the sweet spot). Wider dispersion in this frequency range will typically give you a more spacious sound due to side wall room reflections, and a more even sound for listeners sitting off to one side a bit, but any generated sense of ambience from room reflections is fake (not in the recording), if that matters.
My research suggests that above about 6kHZ, we perceive image location on the up and down or Y axis almost as much as the X axis (left to right). This is where the wavelengths are so short (less than an inch or two) that the shape of the outer ear plays a part in decoding image location. This is the frequency range that will get somewhat absorbed by many objects in the typical living/listening room, and may therefore sound confined relative to the sounds in the other frequency ranges, especially off axis. This may be one of the main reasons why some high-end speaker systems have a rear firing tweeter, or a tweeter array, or even a tweeter facing straight up. A tweeter array runs the risk of creating significant audible comb filter effects as you move your head around, depending on how it's implemented. The rear firing tweeter requires that the speaker be out from the wall some distance so it can be effective (not necessarily the full 3 feet as mentioned above). Sigfried Linkwitz pointed out that the most important part of a tweeters frequency response is actually the lower frequencies, because most adults barely hear anything above about 12-14kHZ, and are particularly sensitive in the upper midrange (1kHZ - 5kHZ), where many tweeters operate. I agree with him on that point. In the past, the bigger challenge was to design a good tweeter that could actually perform well up to the limits of human hearing (20kHZ). Now days most tweeters are pretty flat to 20kHZ, and now it's the lower frequencies of the tweeter that are arguably the bigger issue. Many dome tweeters are said to have "coil tilt" when hit with a transient, causing excessive I.M. distortion (Lynn Olson talks about this), which being at frequencies where the ear is most sensitive manages to be something to worry about. Most metal dome tweeters usually have pretty substantial resonance issues just above the audio frequency range, roughly 24-27kHZish. It's been said that this causes discomfort to humans over time, and is highly likely to cause discomfort for dogs and cats who typically hear well up into the 60kHZ+ range. So I avoid those. Personally I think ribbon tweeters sound the best above about 5kHZ, but they're usually relatively directional, which is less desirable in that frequency range unless you live alone and always sit in the sweet spot. There are some ribbons that are relatively small on both axis, that may well be a top contender (Fountek 1.5 inch for example).
Very few tweeters perform real well below about 2kHZ with a 1 or 2 pole crossover. In a two way system with a 8 inch woofer, a one inch dome tweeter and a crossover at about 2kHZ, there will be a significant dispersion change right at the frequencies where the ear is most sensitive. At 2kHZ a five inch woofer (or midrange driver) has usually become significantly directional in its dispersion (a rolloff in the off-axis frequency response), and the 1 inch dome will have a significantly wider dispersion at that frequency. Room acoustics can make this into a big deal. The response of the acoustic energy bouncing off walls before reaching your ear will have this anomaly. It's not usually a huge problem, but it can be, since that's the frequency range where the ear is most sensitive. This should be considered in any speaker design process.
At the higher frequencies, the large cone driver (woofer or midrange driver) will often emit most of it's energy from the center of the cone, rather than the whole cone (depending on the driver), and thereby not be quite as directional as theory might suggest based on the rim to rim dimensions. Different cone shapes can help reduce this problem as well. Many 2 way systems would be better off with a one pole crossover, so the abruptness of the off axis frequency response change would be more gradual over frequency. This may cause an increase of distortion in the tweeter, so the crossover frequency may be better off being a little higher. It's a tradeoff situation. Speaker system design is all about tradeoffs.
Active crossovers (which are placed ahead of the power amps for each driver) are very accurate, predictable, very low distortion. Passive crossovers are inefficient, difficult to calibrate, coils can be fairly expensive, and are the most common type in the commercial speaker market. Passive crossovers are very sensitive to source and load impedance. A low feedback tube poweramp can throw off how the crossover works pretty significantly in many cases. Speaker drivers come with a "nominal" impedance rating, that often varies quite a bit over frequency. This must be taken into account when calculating the size of the reactive components in a passive crossover netowrk.
Virtually all transistor poweramps have an output impedance that is measured in milliohms (usually less than a tenth of an ohm), due to the very high negative feedback they use. A low feedback tube poweramp (often favored by many hard-core audiofiles) often has an output impedance of between 1 ohm and 8 ohms. Higher order passive crossover networks can be a nightmare to get right, due to the changing impedance's of the drivers over frequency, and the interaction between the crossover coils, capacitors and any resistors. You change the value of one part, and it throw off how other parts work. Higher order means cutoff rates higher than 6dB/octave or "1 pole". A 4 pole active crossover circuit (24dB/octave rolloff rate) is relatively easy to build. Only a handful of people in the whole world are foolish enough to try to do a 4 pole passively. Speaker companies claiming to have a 2, 3 or 4 pole passive crossover are often using the mechanical acoustic rolloff of a given driver as one or two of the effective poles, which can work OK depending on the drivers, but using a driver right up to where it rolls off can bring some nasty distortion issues to the front (slewing and/or ringing) in some cases that I've seen when looking at tone burst test signals.
My approach for active crossovers and/or EQ circuits is to take an existing circuit from anywhere (Linkwitz website for example), stick it in a circuit analysis program (such as SPICE), scale the key part values to get the exact frequency and amplitude characteristics I want, verify the changes with the SPICE program, build it, verify it on the bench, hook it up to the system, set relative levels using a calibrated mic and pink noise, and I'm probably done enough. The higher slope rates mean drivers don't need to operate in areas of frequency where they don't work well, and phase related issues at the crossover frequencies (lobing, combfilter effects, group delay anomalies) are damaging over a much smaller percentage of frequency range (half octave instead of several octaves).
Select drivers that have a relatively flat frequency response over the range you want to use them. Think about power handling capability and off axis resonse. This should be helpful in choosing where in frequency you want to roll off one driver and bring in the next.
Measure the frequency response and impedance curve of each driver if possible. Published specs and graphs can be fairly accurate, but I consider them to be approxiamte. Impedance usually varies significantly with frequency, and is likely to throw off any calculations for crossover part values substantially if you just use the "nominal" impedance rating. A five inch woofer I had was nominally rated at 8 ohms, but measured 15 ohms at 5kHZ (where it started mechanically rolling off), where I had planned to cross it over to a tweeter. My calculations would have been WAY off if I had not measured the impedance at 5kHZ. Published graphs are better than nothing, but are always questionable.
Assuming you have reliable numbers to work with, you calculate the part values starting with efficiency matching resistors since they will directly affect the calculations of the reactive components (L's and C's). Then calculate the reactive part values based on the combination of the efficiency matching resistors and the impedance of the drivers at the crossover frequencies. The reactive parts (L and C) will roll off the frequency response based on what they see, looking out into the circuit. Then build the passive crossovers keeping coils well separated from each other and far away from speaker magnets. Put it all together and measure the result with the calibrated mic and pink noise (or if you want to get fancy use tone bursts in gaussian envelops).
You could be done there, in a perfect world. You could be lucky and it may sound fine.
I highly recommend designing the physical crossover such that you can pull off a jumper to turn off each driver, so you can look at each drivers acoustic output separately with the calibrated mic and pink noise. What I always find is that the drivers don't turn on and off at quite the frequency I had calculated them to. Does this matter much? It can. With a one pole crossover, you generally wire the drivers (woofer and tweeter) in phase with each other because there's only a theoretical 90 degree phase shift at the crossover frequency between the drivers, due to the reactance of the crossover parts (coils and caps), unless you are using a driver right up to where in frequency it mechanically rolls off. The reactance of the drivers will often add or subtract from that theoretical phase shift some. If the actual phase shift at the crossover frequency goes beyond 90 degrees, then swapping the phase of one driver relative to the other will result is a smaller acoustic cancellation at the crossover frequency when the output of the two drivers add in the air (at your ear). If there's an overlap in the two frequency bands due to a sloppy crossover calibration, the amplitude response may not show it as a major anomoly (compared with other anamolies), but the differential phase can be way off, and cause lobing effects that can do serious damage to stereo imaging in the crossover frequency region.
This may not be a huge problem, but worth paying attention to in the final cal'd mic tests. At any crossover frequency, there will be a beaminess that moves up and down (if the drivers are arranged vertically) due to phase shift introduced by the reactive components, as you sweep a sine wave through the crossover region of frequency. You'll get that effect when everything is accurate, but with an overlap (woofer rolls off at 4kHZ and tweeter rolls up at 2kHZ for ex.), it's worse. It will cause this varying beaminess to occur over a wider range of frequency (maybe 3 octaves instead of 2). Room acoustics will grab this and run with it (make it worse). If the crossover is in the upper-midrange frequencies, as it often is, and one side does it differently than the other (likely), stereo effect imaging will be compromised significantly.
So you build the whole thing based on your measurements and calculations, and then using the jumpers to verify that each driver is rolling off as it was designed to do with your crossover network. When it's wrong, you modify some part values to get it close enough (but changing any part value in a passive crossover will affect the function of every other part in that circuit). After you get satisfied with the amplitude response of each driver, you put all the jumpers back on and look for nulls in the acoustic response at each of the crossover frequencies. Now you reverse the phase of the tweeter to see if the null is deeper or shallower. Shallower is what you want. Predicting which phase will work best is difficult, since the mechanical characteristics of the drivers may introduce phase shift, and that may even be affected by the enclosure as well. The 4 pole active crossover has such a tight rolloff, you don't need to care as much about crossover region anomalies. In the case of a 1 or 2 pole passive crossover, you'll have 2 or 3 octaves being significantly damaged by the accuracy of the crossover. If you go into mass production of a speaker system with a passive crossover, you have to worry about tolerance's of all parts involved, including the drivers themselves. Having said all of this, there are many speaker systems out there with passive crossovers that sound VERY good.
I used to think that building an active crossover and having to get more poweramps was definitely more hassle than just going the passive crossover route. In the case of a small 2 way speaker I'd go with passive. If I wanted a truly full range speaker system (good low bass too) that could go fairly loud, I'd bi-amp). Maybe I'm more picky than most people.
Some engineers use hard cone woofers and/or midrange drivers for better resolution, but they all have the severe resonance in the upper midrange frequencies. They often use what's called a "Zobel" filter in the passive crossover network to null out the problem resonant frequency. That's good on paper, but what if the driver characteristics drift over time such that the Zobel null is off a bit in frequency?! Although seemingly not likely, you could end up with a peak right next to a null. I know people who believe you need to "break in" a driver by running high power sinewaves through it for many days continuously, before the specs become pretty much stable over time. I hope they are wrong. I haven't personally verified whether that actually makes a significant difference, but it does raise the question. It could affect the low end FR of the driver, but seems unlikely to me to be much of an issue. I ignore it.
Highpass filter: Xc = 1 / ( 2 pie time freq. times C in farads), or C = 1 / ( 2 times pie times freq times Xc). Xc is the impedance as seen by the capacitor.
Lowpass filter: XL = 2 pie times freq times L in henries, or L = XL / (2 times Pie times frequency. XL is the impedance as seen by the coil.
I always use the cheapest coils since I don't believe that having expensive extra heavy gauge flat wire made with special metals makes any real difference.
Ferrite core inductors (properly designed and rated) should be fine, and will be less reactive with other nearby coils.
Measure the DC resistance of any crossover coil and add that to the impedance of the driver and any efficiency matching resistors, when calculating what the crossover frequency will actually be.
Coils can be very sensitive to magnetic fields and can crosstalk with each other. Keep them several inches away from each other and speaker magnets.
Since driver impedance varies with frequency, and is often pretty far different than the rated "nominal" impedance at the frequency you want to have the crossover at, the final result can be pretty far off if you don't take that into account.
A 2 pole passive crossover is even more sensitive to this, so I won't encourage the 2 pole here. Many so-called 2 pole passive crossovers are actually using the mechanical acoustic rolloff of the driver as one of the poles.
Connect a sinewave generator to the poweramp, and set the generator to the frequency in question. Wire a 50 ohm (or so) variable resistor in series with the driver. This can (and should be) be done at a very low power level. Adjust the pot such that the voltage drop accross the driver is the same as the voltage drop across the resistor. Unhook the pot and measure it with a DC ohm meter. Done. This is mostly accurate, but if you're at a frequency where the impedance is changing fast over frequency, the final result can be a bit off, but this gets you about as close as you can get on paper. The crossover components are sensitive to the impedance at the crossover frequency, but also the impedance anywhere near that same frequency. Final testing with a pink noise signal and a calibrated mic and RTA (spectrum analyzer) will show if this is still an issue.
Again, pink noise as a test signal is transient in nature, so although it's apparently the more common and popular test method for looking at the frequency response of speakers using a calibrate mic and any variation of a real time analyzer display device, it won't show you much about resonant conditions in the speaker itself or the room acoustics, like tone bursts can. This is because a resonance has a start up time and a decay time. It's full significance can only be seen if it gets stimulation for long enough to reach it's peak level.
McIntosh and AR back in the old days (1960's and 70's) dug a hole in the ground outside in a field, away from any building, put the speaker system cabinet in the hole aimed straight up, positioned a calibrated mic several feet above it, and called that their anechoic chamber for verifying the frequency response of the speaker. If it's not too windy and there's very little noise around from other sources, that's pretty legitimate (although it ignores baffle step response). Taking measurements inside your living room is highly unlikely to be legitimate. I've learned this the hard way a few times. Yes there is sophisticated equipment and /or software that after hours and hours of set up and verification, may give you good enough results indoors (gated or windowed bursts for mid and high frequencies, and close mic for bass - then merging the two graphs). In a production environment this test equipment makes sense once all idiosyncrasies are understood and taken into account. For a one-off hobbyist project I'd go for the shovel.
There are those who consider their ears to be one of the best ways to judge a speaker. None of the Engineers I worked with a Dolby Labs agree with that. The audio memory is very weak, the characteristic of the ear varies over time and temperature, and the slightest change in listening room acoustics and/or visuals can sway one's opinion. Inner ear air pressure is a normal condition that varies over time, and changes your perception significantly (according to an Audiologist I talked with). The brain somewhat adapts to this, but it's a variable that's hard to take into account with any accuracy. If you compare speakers in different rooms you'll be way off due to the effects of the room acoustics. Test equipment has it's limitations too (mostly in how it's used), so the ear does have it's place in the process, but as a secondary tool. More for judging how a speaker interacts with the room acoustics after all other efforts are done.
I thought this was the coolest thing ever, since it showed not only the steady state frequency response but also any ringing over frequency on the Z axis (time), when the driver is turned off abruptly. But then I found out how these darn things work (Linkwitz explained it clearly, as opposed to all other Engineers I talked with about it). At the highest frequencies the CSD graph can be relatively accurate, but below about 1kHZ the time window on the Z axis is often shorter than the period of the frequency being analyzed (approx. 1 mS in the case of 1kHZ). So the method of computation is thrown off completely and the results are erroneous. The way this should have been done is to use tone bursts every 6th octave (with gaussian or equiv. burst envelops), so there would always be several cycles of each frequency to be analyzed and displayed.
In a dedicated theater room, there can be a good place for each speaker to be, and room for side and rear speakers to be larger and have a good low frequency response. David Griesinger points out in some of his papers that side and rear speakers will be much more effective and enjoyable if they have a good frequency response in the lower midrange and bass frequencies. In a typical living room, it's often much harder to find a place for all these extra speakers, and they will often need to be small speakers that barely make it down to 100HZ. Is it still worth it? It might be. BUT, if you've got five surround speakers running and you're watching TV, and the commercials come on, it can be extremely annoying. I've kinda gone full circle on this. It's rare that I actually want to be surrounded by sound. It can be rather consuming. There's a time and place for it.
The linkwitzlab.com website is huge and full of good info on everything related to audio reproduction. One of the best website on audio there is, but may be a bit long winded and overly detailed for most people. Perhaps a bit biased toward OB speakers.
David Griesinger is another expert on anything to do with recording techniques (especially binaural recording), surround sound issues, or reproduction of audio in general. One of the best there is. He's been called the pioneer of electronic reverb synthesis, and was one of the main brains behind Lexicon products for many years. Google his name and read his many papers.
Zaphaudio is another website that I have a lot of respect for.
Roger Russel, formerly of McIntosh, now retired, has a great website that among other things will educate you on line array speakers, which he totally believes in and produces now in his retirement. In the right room, this could be the way to go. Google his name.
diyaudio.com has many interesting discussions on everything audio, and many of the contributors are highly educated professionals, but be careful what you believe. Many contributors are not very well educated, but still love to spew their opinions.
One of the most recognized books on the subject is, The Loudspeaker Design Cookbook, by Vance Dickason.
Apparently Madisound offers passive crossover design help for any drivers you might pick. If they actually measure the impedance of the drivers at the crossover frequencies, that would be the way to go for most builders.
Using published impedance graphs is way better than just using the "nominal" impedance ratings. They may or may not be very accurate though.
The worse place to learn is virtually any periodical, since their highest priority is making their advertisers happy. A salesman at a Hi-fi shop is also very questionable, since they are under pressure to get rid of the products that no one else wanted, or push products like "high-end" speaker wire that can cost many hundreds of dollars (even thousands) more than it should, and make no significant difference at all. I use 16 Guage AC line cord wire bought at the hardware store for about 50 cents a foot, unless the wire is more than about 20 feet long. When preparing speaker cables, it's very wise to saturate the bare wire ends (twisted) with solder, so over time the various strands stay in good electrical contact with each other. I have actually seen this be a big problem (with 50 year old cables).
Linkwitz has been using the OPA2134 dual opamp in all of his analog circuitry for many years. I heard his Orion speakers pushed hard with a very high quality recording of an orchestra, and thought they had the best midrange and treble of any speaker I've ever heard. Since I fully respect his technical abilities I've been using the OPA2134 opamps for the last decade or so, with no regrets at all. While there may be opamps that look better on paper, I think it's a waste of time to pretend that any other opamp is going to sound audibly any better. It's going to be about the circuit as a whole, not the opamp. TL072 opamps are probably fine for most people, and are cheaper. 5532 opamps are great too, but have a lower input Z (bipolar input transistors as opposed to Fets), which could throw off high Z filter circuits a bit.
For cap values less than about 10uF, I use polypropylene or polystyrene caps if possible. They have extremely low dielectric distortion. You don't need the expensive versions. Metal film resistors hiss less and should be used in front end or low level circuitry.
These tips will make a much bigger improvement in circuit operation than the difference between an OPA2134 and any opamp that anyone thinks is better for audio. Not using these techniques properly is IMO why many people think they hear a difference in opamps that are supposedly better than an OPA2134. They might have intermittent or spurious supersonic oscillations occurring with some opamps and not others, and not realize it. Rf energy fed into an opamp (or any audio circuit) is likely to get detected and/or cause slewing related distortions which will cause intermodulation (I.M.) sum and difference distortion products. The sum products can cause slewing, and the difference products are likely to generate noise and distortion in the audio frequency range. Digital sources are more likely to have some Rf energy in them, so the Rf filter at the input makes good sense. In the guitar amp world, guitars make great antennas for picking up all kinds of Rf energy, and delivering it to the amp circuit to be detected, creating significant distortions. All of my amplifier circuits have passive RC rolloff components at the input, before getting to the first amplifying device.