Why we use 1st order crossovers

A microphone in reverse could best describe the role of a loudspeaker

 A crossover is an electrical filter circuit, located inside your speaker cabinet, usually close behind the speaker wire connections.

It receives the music signal from the amplifier and then filters it to pass the relevant frequencies to each drive unit of the speaker. Our 1st order crossover has a capacitor to pass high frequencies to the tweeter and an inductor to pass low frequencies to the woofer.

Crossovers are described as having an 'order', 1st order, 2nd order, 3rd and 4th. The number denotes the strength of the filter, with 1st being the weakest and 4th the strongest.

A 4th order filter, for a woofer, would feature 4 components, typically 2 inductors and 2 capacitors. 

A 3rd order filter, for a woofer, would feature 3 components, typically 2 inductors and 1 capacitor.

A 2nd order filter, for a woofer, would feature 2 components, typically 1 inductor and 1 capacitor.

A 1st order filter, for a woofer, would feature 1 component, typically 1 inductor.

Inductors and capacitors are 'reactive' components, changing their electrical characteristics as each frequency arrives.

This reactance is the reason they are used. Inductors filter out high frequencies. Capacitors filter out low frequencies.

 

Each of these components share the same value of filter power. For each octave they will lower the signal by 6dB, (-6dB).

1 inductor. . . . . . . . . . . . .   (which is a 1st order filter ) that starts to filter at 500Hz will then lower 1000Hz by -6dB and lower 2000Hz by -12dB, 4000Hz by -18dB and 8000Hz by -24dB. 

1 inductor with 1 capacitor (which is a 2nd order filter ) that starts to filter at 500Hz will then lower 1000Hz by -12dB

and lower 2000Hz by -24dB, 4000Hz by -36dB and 8000Hz by -48dB.

3rd = 1000-18dB, 2000-36dB, 4000-54dB, 8000-72dB

4th = 1000-24dB, 2000-48dB, 4000-72dB, 8000-96dB

    

It all seems quite functional, harmless and unimportant, the crossover is hidden away and we don't see it working. Loudspeaker manufacturers rarely mention them in their specifications, usually just quoting the single crossover frequency and not stating the strength/order of crossover filters used. Reviewers normally take a cursory look using the limited information from the user manual, and like the majority of us, do not really want to know how or what filter is being used.

 

To a loudspeaker designer the choice of filter tells them a great deal before the listening begins.  

The question then arises 'What good or harm will be done to the music with each type of filter ?'

When your music arrived at the speaker it was in pretty good shape. Everything arrived on time, in the correct order and each sound started and stopped precisely where it was meant to. It was correct in transients, amplitude, time and phase.

The speaker drive units, tweeter and woofer, now need all the help they can get from the crossover to maintain the original structure of the music because within the transients, amplitude, time and phase are the triggers that help your ear and brain decide how realistic the music appears to be.

I'm sad to say that once the music has passed through the crossover (capacitors and inductors) it emerges with changes to the transients, amplitude time and phase. Every original key part of the musical structure has been altered or moved from its original position. 

Speaker manufacturers do not like talking about their crossover designs very much and if they do talk it is only to focus on the one strength it may possess such as time coherence or phase coherence, power handling or that it is a simple, minimalist design. They would rather talk about the materials used in the drivers, a bespoke component or how the new speaker betters the previous model and generally aspects that are more obvious for the buyer to see and understand.

Crossovers are, however, the single most influential component in determining how the loudspeaker will reproduce the original music signal. They deserve more attention and understanding because they set the parameters for the drivers and ultimately how they will operate as a 'single' unified force in reconstructing the original signal. 

 

We use 1st order crossover filters for the tweeter and woofer drive units in our speakers. We do this because the music reproduced appears very natural, easy to listen to and understand with effortless detail and a realistic timbre coupled to solid imaging of the sound stage.

 

At 3 Square Audio we are very experienced listeners of music playback systems (36 years and still going strong) and we definitely know how we want our speakers to replay music but only slowly are we beginning to understand why 1st order gives us ALL the properties we want. It is a crossover that can help the speaker drive units, more than any other, work as a team.

In brief it outputs a -45 degree vector to the tweeter and a +45 degree vector to the woofer. This is as good as it gets for the speaker drive units, a signal that sums to unity with a combined phase shift of zero.

Below is a visual version of how the music 'reads' when it exits a crossover, that is not 1st order.

Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.

The above text shows how the timing and order of information has been corrupted but has sufficient structure for the brain to do corrective work and make sense of it.

 

The text errors get worse still at the crossover point between the woofer and tweeter. A 2nd order crossover will turn half of the letters upside down while 4th order would not invert any letters or change their order but instead duplicate the first and last letter of each word i.e. ffirstt aandd llastt lletterr ooff eeachh wwordd.

Almost all loudspeaker manufacturers use 2nd, 3rd, or 4th order crossovers and very often a combination, such as 2nd on the woofer and 3rd on the tweeter. 

A 1st order crossover will not change the order of letters, invert or duplicate them. They will exit the crossover in the same order they entered it. The letters would look tilted, half leaning forward 45 degrees and half leaning back 45 degrees but not upside down, duplicated or in the wrong order.

It is this time/order coherence 'locked' to its phase coherence that allows the brain to turn down its corrective work, relax and perceive the music signal as more natural and lifelike.

With 1st order we have managed to do the least amount of harm to the music and passed to the tweeter and woofer the closest version of the original. 

1st order

4th order

This page is still a work in progress. Below are a collection of pieces discussing crossover design which you may find interesting in the meantime

The output of a crossover network is a vector sum with real and imaginary components in polar coordinates. What you have in a 1st order at the crossover freq is one vector at .707, +45, and the other at .707, -45, which adds to unity in vector space with a combined phase shift of zero. But because the vectors rotate together with frequency, they are always 90 degrees apart, and they always add to unity voltage and zero phase in vector space, no matter what the frequency.

To say it differently, the combined output of the two drivers is always unity at zero phase, even though the two vectors are always 90 degrees apart. This is difficult to conceptualize, but the math behind it is relatively simple.

For obvious reasons, this is called a constant-voltage minimum-phase transfer function, and the first-order is the only crossover type that has this characteristic. I should note that this presumes identical drivers mounted very closely together and resistive loading, which is hard to achieve in the real world. But with some effort, one can come close, and the effort is well rewarded in the listening.

One of the major advantages of the first-order crossover, which isn't mentioned often enough, is the fundamental simplicity of the network. Every increase in crossover order is accompanied by a proportional increase in the number of network elements, and the audibility of this problem is severe. Even a single high-quality inductor or capacitor in the signal path is audibly degrading when compared to none at all, which is why so many people decide to live with the severe compromises present in single-driver speakers. It's hard to describe this effect until you play around with it-- my best description is that it "sucks the life out of the music". And the higher the slope, the worse this problem gets. Not very scientific, I agree, but the degree to which this is true is stunning when you hear it.

Also, I would take issue with the research quoted by Joseph. One of the basic facts about second-order crossovers is that they require at least one of the drivers to operate in inverted electrical phase, to avoid a null in frequency response at the crossover frequency. This inversion alone is enough to utterly destroy the integrity of the musical signal, and any comparisons to fourth-order crossovers at that point are completely meaningless. Since no one in their right mind would use second-order networks in the first place, it doesn't say much that fourth-order sounds better than second-order. This paper, like a lot of quoted research, might be true in its own limited environment, but it doesn't even begin to tell the whole story in the real world.

The main drawback to first-order networks, as stated above, is the need for very wide bandwidth and very high quality drivers, with no severe "breakup modes". Thankfully, these are available at a price from Scan Speak and Audio Technology, among others.

 

As I described in the recent Time Coherence thread, the phase shifts by 90 degrees, yes, for each additional order of crossover, as you state above.

But do know that the correct expression to use is that the phase DIFFERENCE is changed by 90 degrees for each additional order- at the CROSSOVER FREQUENCY. Those are important distinctions.

You see, the problem caused by higher-order crossover circuits is that this phase difference is ALWAYS CHANGING as one moves away from the crossover point- a DIFFERENT time delay is being imposed on each and every frequency.

This ever-changing phase difference (ever-changing time delay) CANNOT be corrected with any additional circuit.

The math also shows, without question, that this ever-changing phase difference/time-delay distortion cannot be "fixed" by inverting the tweeter's polarity.

Flipping a tweeter's wires from + to - serves only to flatten the frequency response, when one measures using continuous sine-wave test tones or continuous pink noise.

Those are both unchanging signals, without beginning nor end (and therefore carry no information). These test signals do not indicate anything about WHEN things happen- about the time-delay distortions that are occuring, frequency-by-frequency. When the tweeter's wires are reversed, the resulting transient response has only a "different kind" of inaccuracy, even though one will like "the tone balance better".

Only a first-order crossover has a CONSTANT PHASE DIFFERENCE at every frequency above, at, and below the crossver point. That means there is Zero change in phase between them, so the signals out of the high- and low-pass sections are "in Phase", always, on every frequency.

And all of that means, finally, that first-order circuits are the only ones that pass all their signals through with the SAME time delay, so all of those emerge in the same time-order in which they entered. This is called time-coherent behaviour. So you get the original transient, one not smeared out in time.

A speaker that is designed to deliver a time-coherent output is automatically "phase coherent". The converse is not true, as you may know: A phase-coherent speaker is not necessarily a time-coherent speaker. In fact, if you see the advertisement claim phase coherency, you can bet that the speaker is not time coherent. One has to put something in an ad!

On the Tannoys, their "phase distortions" (time-delay distortions) are rather mild. In my experience, once those varying delays are removed (which cannot be in Tannoys), the difference you'd hear is at least the difference between an average mic and an outstanding one. By the way, neither a phase- or time-coherent behaviour can be directly inferred by looking at the electrical phase of a speaker's impedance curve.

That the Tannoy's phase distortion is tolerable for you, is because it is unconsciously ameliorated in those studios by their mic selection, mic technique, the type and tone of the echo/reverb mixed in, the settings of the tone controls on the mic's channel, and by the EQ applied to the monitor system. And in pop music, the phase shift problems are also "danced around" by the sounds created by compressors, limiters, de-essers, and other tools. I speak from many years of recording experience, and of designing speakers with all these different crossovers (and using many others that had all sorts of their own time-domain distortions).

 


Sean, the answers to what you ask in your first two paragraphs lie in Karls' contribution, and the information you present in your last three paragraphs is correct. Yes, we are trying for a linear phase response across the board, which is not possible as you approach the frequency extremes, without digital correction (which has not, in my experience, been applied correctly to any speaker). There will be some thoughts on that on our new website by the time it is published, and if not, in the weeks following.

Skrivis, I think some of the reason Stereophile does not draw any conclusions is related to what Paul Candy says about that in his sixmoons.com review of our Callisto speakers, about alienating most of their speaker manufacturers. Part of it (again, in my opinion) is that their tests only extend down through the mid and tweeter crossover range, never down into the woofer/mid crossover range, which is where more of the music lies.

Finally, one must know what time-coherence really sounds like, perhaps by going to hear live music up close and personal, for hundreds of hours. Ever hear a string quartet practice for weeks in one's living room, and then get up and walk around them? Or a bluegrass band, or a wind band, or a Fender Twin Reverb, or a soprano, or a Steinway played with expert hands? From four feet away? How about experiencing a 100-voice chorale, on stage from 20 feet? Across weeks of rehearsals? I know this is what a speaker designer needs to do.

Those are not common experiences for anyone, let alone to have spent hundreds of hours in studios learning what the mic hears and how the studio must alter its sound, so that we think it is a) pleasing, and b) realistic.

Golix,
You say "Also a speaker which has the drivers on a vertical axis can only be phase coherent at one point in space. This of course is a purely geometrical problem independent of any electrical feature."
True. And in a two-way speaker, that point can be aligned to anywhere via tilting the speaker and with a small change in your ear height for the final touch.

For a three way, one has to move the top two drivers relative to the woofer. Our Continuum 1 three-way offered adjustable driver positions in 1995, and was reviewed in Audio Ideas Guide in `97. That adjustability has become a standard feature in all our three-way designs, and for several new models coming into production over the next many weeks. We call this "adjusting the Soundfield Convergence(tm)".

Golix, please do reconsider your notion that
"Basically a phase coherent speaker is one that is not only [coherent] in time but also in phase; a time coherent speaker is one that's [coherent] in time but not in phase."

To be correct, that should read nearly the opposite:
"Basically a phase coherent speaker is one that is ONLY coherent in phase; a time coherent speaker is one that's coherent in time AND in phase. All the math, all the physics supports that.

And we speaker designers get to screw that up! Nowhere in the recording chain, nor in the playback chain is the timing split between highs and lows, or the polarity, or both. This is purely a speaker phenomenon/distortion. One can learn to recognize that, the way an amplifier designer can hear if someone's amplifier needs a bigger transformer- it's a unique sound distortion.

Thus, Golix, please understand that while those Tannoys are indeed smoothly phase coherent, they are not time coherent. A step function would show this: Perfection in a step function looks like the plus-half of a single square wave, rising up quickly, leveling off and then going on forever- like a single stair step. There would be no ringing or rounding over at the initial corner, and the top would stay level forever, never returning to zero.

In that Tannoy, the first energy to arrive from that step-input is upwards-going, as it should be. A moment later, the late-arriving, inverted-polarity tweeter shoves (sucks) that initial positive air-pressure-increase down into the negative-air-pressure portion of the graph.

The tweeter's dome then returns to rest from its full "-" excursion, because the crossover cannot pass the "DC" to tell it to "hold your position, albeit sucked in". The air pressure then returns to the positive from the midrange tones' positive-pressure continuing to arrive.

Finally, no speaker ever then "levels off" and holds that air-pressure "positive" interminably, because the room leaks that pressure away. So the step droops back to zero, even though you see the woofer still shoved "out".

With regard to our measurements- we have those measurements supplied by the driver manufacturers, such as MorelUSA, taken in their chambers. But those measurements are usually taken in a half-anechoic chamber. Go to the Scanspeak website here:

http://www.d-s-t.com/link/scs/data/d2008_851200c.htm
and click the frequency response graph to see their measurement setup.
Can anyone say that is a realistic test of the direct sound from a tweeter? You will see a picture come up of a woofer mounted in this fully-reflective wall of that test chamber- their tweeters are tested in that same position.

For our own testing, we are still in the analog days here, not for want of trying to go digital, so I cannot show you hard copy. I will be working to present this information on our website as we continue to grow.

I can tell you that our anechoic chamber is outdoors when required from 200Hz on up, which covers the woofer/mid crossover region. Testing indoors, in an average room, is fine for looking what happens from 800Hz on up. There are also certain ways to combine very nearfield measurements, that I must decline to describe, which obviate the need for a chamber.

Digital test-gear has not shown us what we need to know any more accurately, and I have extensively used/leased all of the well-known systems available. I do know that it is easier to perform many more misleading tests in the digital domain. One has to scrutinize for many problems, with very specific measurements, either by analog or digital means. There is no one, or two, or three measurements, or even "dozens", that tell anyone how a speaker will actually sound. It takes many more than that, with an experienced ear listening for suspected deviations that physics is pointing out, and a working knowledge of what "a suspected (and/or measured) deviation or problem" should sound like.

In analog measurements, we look directly at the `scope. In particular, we look at the moment of first arrival of a burst of 4-8 cycles of a single sine-wave tone, taken all the way up the frequency scale. Perfection in time-arrival means that each of those tone bursts, at each frequency tested, starts upwards from the zero-axis at the very same L-R position on the `scope face.

The Tannoys would show a left-to-right motion of that starting point (which is the time delay creeping in) in the crossover range, and then the tone burst smoothly flips upside down in the tweeter range. Ours stand still from 200Hz to 8kHz, and always have the same polarity.

What does +/-2 degrees mean at 200Hz? It is +/- 1/180th of a 200Hz wave's period, or +/- 1/180th of 1/200th of a second, or +/- 0.3millseconds, which is readable on a `scope face. This, for the lower midrange, amounts to a front-to-rear shift of the mid-driver's location by +/- 0.4 inches, relative to the woofer. I can hear when the focus becomes as sharp in that crossover range as it is away from that range. So has every person for whom I have demo'd this.

The audible change from moving that mid back and forth, even an eighth of an inch, cannot be explained by wave-cancellation math, nor can it be explained by any change in the cabinet-face or wall-surface reflections in my designs.

We hear the difference as a loss of sharpness, or definition, of a sound's location from front-to-rear. Depth is time delay, and the sharpness of the image begins at its front-most element (the singer's mouth). If that initial location is smeared from front-to-rear, then the depth "behind" that voice is also smeared over by that initial information, and the depth itself is also smeared in time.

This is all information audible by WHEN it arrives. If that initial location is smeared, we also hear a loss of attack, which is a leading-edge phenomenon- another time-domain aberration. There exist many more ways the ears can guide time-domain measurements, and vice versa.

For the 8kHz point, that +/- 2 degrees amounts to a spatial shift of +/- one one-hundredth of an inch- tough to measure: One can easily have the microphone inadvertently jiggling from floor vibrations, by that small amount. It can be heard however, as an overall clarity of the top end, because there are a lot of frequencies nearby that 8kHz- notably the ones all the way down to 4kHz- only one octave, one "undertone" away.

I can hear when the ribbon supertweeter in our previous Imago flagship-design is a 1/32nd of an inch too close or too far away- it was crossed over from the Dynaudio dome tweeter at 8500Hz:
What moment did the stick strike a small bell or a triangle (which creates a very sharp and brief transient) relative to when did that instrument's actual tones emerge? They should have begun after the stick hit and then was removed from the metal body, right? Yet, the timing can be warped just enough so that one hears the stick-hit occurring AFTER the tones start. Now that is an un-natural sound anyone can identify! And the time-delay from this small offset of that supertweeter? Millionths of a second.

The same thing happens when judging the firmness of the felt on a mallet on a tympani or vibraphone. Or no felt at all- just the sound of hard wood, or a large-diameter mallet head or a small one. They each make their own sound, which a time-coherent speaker easily reveals, even in the midst of an entire orchestra reaching its crescendo around them.

In the usual mid-to-tweeter crossover range, achieving precise focus lets us hear exactly when the singer's tongue leaves the roof of her mouth- important to her shaping that note. Or to the definition of any other instrument that requires half-mid and half-tweeter, such as tambourine, trumpet, guitar, piano...it's a long list that includes non-instrument wideband-sounds, such as applause and film "noises". Then include the distinctive sound of each one's ambience directly behind those events- there is much to listen for, that leads to more musicianship being heard.

Also, it is possible for nearfield, tweeter-only measurements to have a standing wave build up between the microphone and the tweeter's dome, on sinewave tones, which totally fouls up anything we are trying to measure. Changing that test-tone's frequency by just a few percent, or moving the microphone back just a 1/4 of an inch, makes a huge change in the sound pressure level at the microphone (again, on a sine wave).

This is somewhat related to the how the notion of first-order speakers having comb-filtering effects comes about- from applying the math, and measuring, with specific single tones. Which do not occur in music, especially if that particular frequency lies between the tones of the musical scale. I do agree with all of what Karls goes on to say in his post right above, including his analysis of lobing. However, I find lobing is exaggerated when the cabinet-face, or even the area right around the tweeter, is contributing many reflections.

Comb filtering, from simple, "fewest possible drivers", first-order speakers, is not apparent to me, or at least objectionable on music. The ultimate audible test was comparing what is heard out of a speaker's mid/tweeter crossover range, with what is heard in that tone range from a small, say 6" square, electrostatic panel, or a plasma tweeter. We have done that, and found no significant differences that we can say were from the comb-filtering effects that must indeed arise from having two drivers producing the same range.

Multiple drivers in the same tone range present a lot of different frequencies to cancel out, because those six tweeters, for example, each arrive later than the one nearest your ear. That leads directly to lobing, which is a frequency-dense form of comb filtering. What you want to call it depends on how you measure it.

Stereophile thoroughly tested our original Diamante model in April 1994, and showed how its step response aligned quite well between mid and tweeter as the microphone was moved down to their time-coherent axis. JA was really nice to us by also showing how the corresponding step response also changed (for the better) as that time-coherence was achieved. He then showed how the overall phase response measured, which was pretty good. Ten years later, our deviation from zero is far less. Also, the Diamante tweeter's tone balance on that "best" axis was not flat for him, because at 50" away, the tweeter was well above the mic (the mic was far off the tweeter's axis). In the same issue, examine the B&W Silver Signature two-way monitor's step response. Not even close to being a step at all...The Diamante review is not archived on-line, unfortunately. Maybe those measurements are- I have not searched for those in JA's database he graciously offers.

Returning for a moment to the use of tone-bursts: One can also look at the envelope shape of each burst, from which many things can be seen, such as cones and cabinets flexing. If there is cone-breakup/ringing, then that energy was stolen from the initial input of energy into the cone. That is something that can be seen at the beginning of the envelope, as the output failed to reach full height on the very first cycles. The cone flexing absorbed that energy, only to give it back later. Of course the cone could be highly damped, then it never gives it back as audible sound, but just leaves the initial dynamic-rise blunted. Too "laid back" you would hear. Think about the dynamic response heard from soft plastic cones...

One can see a returning echo from inside the cabinet, after the end of the pulse, which can be fixed. A flex in a cabinet wall can be detected, and that can be stiffened. A reflection off the cabinet-face can be seen, and that can be absorbed or avoided. One does not need an anechoic chamber to perform those tests.

There is digital hope for us: This Summer, I look forward to working with Agilent Technologies in developing a system that will do what we need. A few years ago, the computing power was also not available for certain tests I have always wanted to make in the digital domain. Now it looks like it is.

My apology that this is so long, but I do not see this basic information published elsewhere. When (and if) you re-read it, it does seem to fit together. There were also a lot of good questions posed one after the other. Arnie of Audiogon, thank you so much for publishing this.

Applejelly:
You ask, "Even if a stereo system from source to speaker was perfectly able to preserve the original waveform, what are we trying to preserve? I know very little about the recording process, but I can bet many an album has been processed by recording engineers in ways that destroys the phasing of the instruments used to make the music."

The answer, yes, they destroy the phasing, just as you say. But please note that no studio effect ever splits the time-coherence of the signal anything like a speaker can. You are indeed trying to preserve the "original waveform", for nothing more than to reduce another audible distortion we don't need to hear. I hope that helps, because yours is a valid question. Karls, I would say that time coherence not only helps great recordings, but is very necessary to avoid "chewing up" distorted recordings. Think about how "distorted distortion" would sound.

Applejelly, you also ask, "And is the sound outside the sweet spot worse for time coherent designs?". Yes and no. It is better than severely phase-shifted speakers, because when you stand, you are not moving spatially as far off alignment as the other crossovers delayed the signals. And by direct comparison, the other speakers are scrambled even sitting down, and so your added "positional" phase shift does not add that much more. Karls says something on this, above.

You hear the difference on first-order speakers precisely because you have at least a focal point to compare, as you physically move away from it. I know that with proper attention to the speaker's design, at ten feet or more away, it does not feel like your head must be in a vise- I know now that is one artifact of the drivers "not quite being in full alignment- just very close". As that broadband alignment is widened and sharpened, the sweet spot relaxes.

About the highs going away when you stand? That is what happens with a particular design you heard. This is not indigenous to "being a first-order speaker", but only "that particular first-order speaker" you auditioned. What one can say with certainty is that when you stand, you always hear less depth to the image.

Also, you did hear the tweeter's sound emerge first, which is not natural, but it is emerging first by far less of a time "advance" than what higher-order speakers do. And if it emerges even more "too soon" when you stand up (still less "too soon" than with high-order speakers), then it can reach a relative location that lets it cancel the mid's output in the range above the mid's crossover point, and that means "less highs."

Thanks for the compliment, Suits_me. I don't think I have made any mis-statement, but please let me know if I foul up. Since this is my profession, I deeply feel I owe every bit of science, and knowledge of the sound of real music, and of how studios work, and how we hear, to my designs and our customers.

Thanks to all for reading through this. I hope you found it worth your time. I wish that I had someone tell me all of this when I started designing in 1973! My hope is that someone young picks up the ball and runs with it, to see what we have from them in thirty years, `cause it probably won't be from me! It is part of what is behind my mention of a "Foundation" in sixmoons' Callisto review's Q&A at its end. Also there are all the topics I consider important to a speaker's design, before we even strap on a crossover.