Phase-alignment based method of designing multi-way speakers
After reading already famous article by AllenB I decided to write alternative tutorial for those who'd like to take completely different path. I'd like to thank him for inspiration to do so!
INTRODUCTION: „For great sounding multi-way driver relative phase must be equal at all frequencies. Period.”
Typical approach in loudspeaker design is provided in many articles as follows: choose drivers, choose baffle, choose crossover point and filter orders, apply corrections. Phase is too difficult to understand, so lets omit that.
This one will be different as it will deal with phase alignment in the first place and only then all other things. This almost step-by-step guide is aimed for reader familiar with basic loudspeaker building principles, having moderate experience but still struggling with consequences of typical approach. I hope this article will be somewhat helpful or at least wake a challenge to try it and compare with previous results. So lets start with
BAFFLE STEP DIFFRACTION: use wide (~60cm) front baffle. Therefore LF roll-off will start under 300Hz where room modes start to help. This way you may avoid electrical compensation at all. Use two LF drivers instead of one as it will make matching even easier, especially with bipole push-push type design (one LF driver facing backwards, both in-phase) and give you additional LF sensitivity usually lacking in regards to tweeter. Gains: no need to introduce large inductance for electrical baffle-step compensation and to ruin transient response and sensitivity. Increased sensitivity for LF band; need for attenuation of tweeter level is reduced.
ACOUSTIC PHASE ALIGNMENT AND DIRECTIVITY: using shallow waveguide for tweeter will align acoustic centers by placing them on the same vertical axis and hence aligning acoustic phase (nothing complex here) plus it gives improved HF dispersion pattern. Gains: much wider listening sweet spot, airiness, less reflections from walls. Trade-off: slight roll-off of top HF frequencies (usually above 12k) and more pronounced 2k-4k region. So seek for HF driver with upward increasing frequency response if you want to compensate for that. Even with „normal” drivers I find benefits much more pronounced than this trade-off.
By placing HF driver on top of LF driver’s baffle within its own baffle will give you some space to fine-tune it's position after all further steps are done (so you'll end with what you started but on different precision level as you'll have speakers phase-aligned also electrically). See fig 29-31 here to get the general idea of acoustic phase misalignment side-effects. Make sure there is smooth transition without pronounced „step” between baffles. Also, HF baffle will benefit from thin soft damping material separating it from higher order vibrations coming from LF baffle so HF baffle and waveguide won’t be amplifying them.
To reduce LF driver beaming at 1-3kHz region rounded baffle corners with at least 10cm radius will be beneficial. Hard to build (at least from wood), that's for sure. Even if tweeter is capable and crossed low (below 1.5kHz) and have a very large waveguide (at least 30cm) round corners for LF baffle will give some dispersion benefit for midrange.
FLATTENING THE WOOFER'S IMPEDANCE: rule of thumb is to flatten with Zobel only to a some degree. Lets have it in detail. By using Zobel we get woofer impedance (and electrical phase response) ruler flat at its HF region. HF driver isn't impacted by LF driver’s Zobel so its impedance will be raising. Its phase will be shifted in the same region: Z and phase curves are following each other like twin-sisters. With flat LF impedance due Zobel at its max individual responses of both drivers in this region will be gradually getting out of phase in regards to each other ending with maximum phase difference up to 45 degrees at top end of frequency range. This will introduce unwanted additional HF cancellation and "lifelessness" in upper midrange as usually observed. That's why its usually suggested to tune R value for Zobel "by ear" by gradually increasing its value, usually without explaining the reasons why it should be done.
When we increase R value compared to „flat” version LF driver impedance curve starts to raise from being flat. With some optimal R value its phase curve will mirror that of HF driver. If phase nulls before impedance raise for both drivers luckily or deliberately are placed on the same frequency then with some particular R value of LF driver's Zobel they will get very close to being exactly in-phase at the whole top end high frequency region. Therefore individual driver responses will sum together nicely instead of response being gradually attenuated with increasing frequency as in case with totally Zobel-flattened LF impedance.
So we have are obvious gains here - electric phase gets aligned and there is less loss of HF energy for combined output (if any). Also, by increasing Zobel's R HF roll-down gets less steep for LF driver just because of less degree of shelved 1-st order filtering. It can be hard to find the best R value without seeing measured Z and phase curves, still with good ear it is possible to get pretty close. Do it by ear this time :)
FLATTENING THE TWEETERS IMPEDANCE: same as previous, except in this HF resonance region we'd like to see HF driver impedance as flat as possible as it overlaps with usually flat impendance (and phase curve) of LF driver in this very sensitive region both for ear and for crossing. Due wild phase swing peaks and dips in combined response are expected on both sides of tweeter resonanse frequency unless we flatten it by damping it with a notch filter (RLC series filter parallel to HF driver). This is the second part of key to getting drivers phase aligned (now in midrange region). RLC values can be calculated if you know Fo and Qes of the HF driver. Unfortunately these values may often be quite far from factory specs so results can be very erratic. I'd suggest to get free version of impedance analyzer (for example LIMP, part of ARTA software suite), solder five resistors according to LIMP manual, connect to sound card inputs and headphone output to see the actual Z curve. Play with R, L and C values. Start with R as average Z multiplied by 2 (16Ohms for 8Ohm driver), C ~5uF, L around 0.6uH. Change the values, measure again and see where it leads until you find the right values for flat Z curve around driver's resonance. Or calculate values according to methodology described here. Now when you have involved impedance measurement box, redo LF driver Z measurement after you flatten HF drivers resonance as phase shift may have been changed and LF Zobel will need to be corrected again to match the HF's phase.
Actually most efficient sequence would be to start with flattening tweeter’s resonance and then tuning Zobel for woofer. But it is always fun to see how close you could get by ear compared to measured optimal value, so if you want, take this little extra side-step first to test your ear :)
Note: Z flattening will also change rolloff slope of HF driver towards low frequencies. Usually it will get less steep and start somewhat earlier extending response more towards low frequencies. Depending on selected LF driver it may be beneficial for driver integration and transient response.
Should you use Zobel for HF driver to get its impendance straight? No, this will just lead to significant reduction of the upper HF output. But yes definitely in case you decide to add supertweeter to extend your HF range. In this case you’ll need to make notch filter for supertweeter to damp its resonance, then add and tune Zobel for HF driver to match supertweeter’s Z and also re-tune Z for woofer to match the same. In other words - get all "tails" tied together. This can bee seen as hint on how to align more than two-way speakers in general.
Series resistor (if any) must be put only after the hi-pass filter, and the filter component values must be corrected for combined resistance. If possible avoid using series resistor unless HF driver impedance is significantly higher and you want to match these to each other. Redo LF driver Z measurement after you implement series resistor to be sure that phase curves still match. If attenuation level must be even higher then calculate L-pad type of attenuation circuit. It means some resistance to be added parallel to HF driver (and flattening notch filter) most probably leading to overdamped resonance as the result. So after calculated L-pad is applied return to Z measurement and increase value of R in RLC filter to get back to flat Z around HF drivers resonance.
PHASE COHERENCE: must be achieved at this point! Will be fine tuned at the end.
CROSSOVERS: now that woofer and tweeter have flattened impedance and phase curves in crossover region it is easy to ruin it all by combining even and odd order filters for the drivers to match the different steepness of natural roll-off slopes of drivers. Don't. Orders must be the same type for both drivers as each order turns phase by 90 degrees. Doing the opposite would create obvious phase misalignment again. Its a good idea to start with finding naturally matching drivers that have natural roll-offs at about the same frequency with similar steepness so you can use same filter orders on both sides.
Regarding tweeter polarity: in case of both being 1-st order we have to invert the tweeter polarity as we have summed relative phase shift of 180 degrees. With both being 2-nd order – don’t invert (180+180=360=0). With third – invert again (270+270=540=180). With fourth - don't (even hope to build one correctly passively). Generally all filter orders higher then the first are said to negatively impact driver's transient response. Never measured it by myself, still i find first order filter to be the most pleasant sounding. With sensitive drivers (>93dB/2.83V) you can achieve decent sound levels without getting too close to cone breakup.
Crossing point: now when we have completely tamed HF driver’s resonance I see only few things that may prevent you from crossing even as low as at HF driver’s resonance frequency - distortion values typical for chosen HF driver and natural LF roll-off due small cone size. Isn’t that cool for a two-way anyway?
If you cross actively use 4-th , 6-th or 8-th order Linkwitz-Riley phase-aligned filters.
PHASE COHERENCE – FINE TUNING. Switch on pink or white noise generator for one of the drivers (or use radio hiss between stations), go to listening position and ask someone to marginally adjust tweeter’s position in regards to LF driver by moving it forward or backwards. The moment the speaker disappears you know that you have achieved probably the best you can make out with your with particular drivers, speaker enclosure and filter components. Repeat it with the second speaker. Connect the first one again and pull out your most loved records. Review tonal balance, airiness, imaging, presence.. you name it.
TWEAKING: any additional notch filters or series resistors applied for individual drivers after we have done phase alignment will ruin it. Still you can apply them to whole speaker as it will impact both drivers and their relative phase alignment will be kept unchanged, but absolute (total) phase change doesn't matter. So if you feel like having any irregularities in combined frequency output you can add baffle step shelving filter (parallel LR in series with the speaker) to compensate for lack of bass response and/or additional notch filter (series RLC parallel to speaker) to flatten obvious response peaks. But before you do that see if you can’t resolve these by mechanically improving drivers (by damping their baskets, etc) or just by changing speaker placement in room.
LISTENING: I'd say that without any measurement it is extremely difficult to detect the problems and get to their source.
First, your ear doesn't lie, but your brain most probably does.. at least for some time. Excitement of „new sound” compared to "old" will mask some of less pronounced problems. Still if there are problems, your brain will get tired by listening for longer periods, several hours are usually enough.
Second, your mind will adapt. You may like the sound for a week of lots of listening. After one weak break you may perceive your system tuning quite differently, perhaps less pleasant. Plus your speakers will typically sound differently in the morning (more harsh) than in the evening. So do the testing at time of of typical listening and take brake for at least one day in between sessions.
Third, your perception is loudness dependent. So test your system almost at the same sound level which you chose to be your typical listening level. If you like to do it on different levels then calibrated loudness correction must be put in place matched to sensitivity of your system and with input signal RMS (average loudness) leveled from one musical piece to another.
Also different compression levels and different tonal balance of recording techniques of different times will sound very different. That’s all too gets very complicated, I agree, but that’s about how we are built by nature and that’s how musicians’ and studio gear have evolved over time. Still I believe each of us can reach one’s „sweet spot” of necessary corrections combined and get our ears pleased.
EPILOGUE: This particular approach to loudspeaker design as a whole is new to myself. It came to me as the concept and became a method quite recently. Some parts of it have been covered in great detail by several authors. I devote this method to my grandfather which would have turned 98 today. He had „golden hands” and taught me patience working with lots of materials. Many thanks to him! And also thanks to Rod Elliott and Siegfried Linkwitz whose much more elaborate articles basically led me to create this very simplified one, and who found a time to answer me some of the questions personally.
That's about it! Questions, corrections and additions are welcome.
nice explanation of how to use a zobel on a woofer, and a good logical sequence, but the minimalist in me asks why not omit the zobel & the notch filter on the tweeter & simply tweak the crossover components to acheive the same result?
I don't at all disagree with your basic approach. It does bring a lot of the best practices to the forefront in an effort to manage driver to driver differences through their overlap ranges. This should help a lot of folks step it up a little.
I take a practical exception to your introduction statement. It would be wonderful. It would be a big advance. But you are not going to do it without independent DSP control of each driver. All of the drivers would have to be coaxial. This is now technically possible with coaxial drivers, and tools like UE. However if you did achieve it, where are you going to get source material that is still phase correct? Even my measurement mics are not of uniform phase. Fortunately, SoundEasy accepts a plot. Phase is totally disregarded through the entire recording process. The best we can hope for is to not be too ugly through the crossover regions.
My basic sequence is just a little different:
Profile the drivers.
Use my DCX to model something close enough to determine the amount of padding you want on the tweeter.
I use a single series resistor for padding.
Now re-profile it and go back to the DCX to be sure you get the overall balance correct.
I build the woofer zobel and re-profile the driver. That will get me a test box.
Determine if baffle step compensation will be needed. As yo say, with as large baffle and a three way carefully selected crossover, it can often be avoided.
Do the same for the mid.
Add in whatever notch filters you find necessary. I am very interested in deep filters at driver breakup points.
Now you have complex compensated drivers in separate boxes. Stack them up and proceed with the actual passive crossover design. I like your idea of using noise for offset listening testing.
I find I do not like the electrical crossover to exceed second order. With clever driver to crossover selection as you point out, this can achieve something close to fourth order acoustic. This works fine unless you are looking for really high power, but switching to multiple drivers is a better approach for that anyway. I tend to pad the tweeter about 2 dB lower than measurements would suggest. It may have more to do with my rooms, but di-pole or bi-pole have never worked for me.
Pete, I like your quote. Clever man. Miss-guided, but astute.
PeterMck, thanks for your question!
The simple answer is obvious: because drivers behave far from ideally within their resonance region (at Fo).
First, the more pronounced tweeter resonance is (low Qes) the more "wild" is phase swing that should be aligned against usually smooth phase response of LF driver at this region. So we can expect response ripple on both sides of crossover due partial cancellations and sums of combined output. Correcting these will actually increase complexity of filter, but non-correction will give some sub-optimal response.
Second, directivity of tweeter gets wide at it's Fo which can give very unpleasant harshness especially in-room combined with reflections from walls. Combined near- and far-field frequency response may seem be pretty fine and give false impression of overall correctness unless we measure directivity or far-field only and therefore see the whole picture.
What we can do alternatively to damping the resonance?
Generally it could be somewhat corrected with creating artificial response dip at tweeter's resonance. Which means creating notch filter, which in turn will do the same - damp the tweeter's resonance at some degree. So we're actually back to damping. If instead of correcting only the tweeter we apply notch to whole speaker, then relative phase shift between drivers (and other issues, more about them further) will stay the same and we will make the system to sound right to a much lesser degree. In analogy from car world it would probably be like taking out the dampers from suspension and placing them under driver's seat.
Decision to go with 4-th or higher active filtering these negative side effects will lead to significantly reducing them if we are crossing reasonably high, like 2kHz with Fo being 1kHz. So octave lower would give us 24dB suppression. Additionally, HF driver’s resonance probably will be damped by being directly connected to amplifier [to what degree? How much amplifier will "like" it? Will it work for correcting phase twist? What about transient response and impact of more pronounced at resonance back-EDS and its soaking into feedback?]. So amplifier qualities will probably play more significant role here. Hard to measure and compare as we all mostly have different amps :) Plus simplicity is lost again due additional gear needed. Second possible issue with this approach is directivity. LF driver at its last octave up to the crossover point will be most probably "beaming". In contrary to that HF driver will typically have its widest dispersion pattern here (with flare-like effect at its resonance). Combining that means highly risking to seriously distort overall directivity around crossover's frequency (here is nice visualization of possible outcome in Fig12). So directivity issues may have to be resolved with this approach unless a) drivers are crossed very low (around 1kHz) and very steep; this generally means more expensive HF speakers with low Fo, or b) if crossed at recommended octave above then shallow waveguide applied to LF driver may sort things up a bit towards better overall directivity. Still it may be a bit complex to construct. This is the way of how better end of pro-grade monitors are usually designed.
A drawback of resonance damping is obvious – lost output from Fo to about and octave higher. But at the same time if waveguide is used it is regained at about the same level – (something that had to be corrected with parallel RC filter connected in series, so moving towards simplicity here). Also, more output is gained from Fo to an about octave lower (the latter very much depends on HF driver’s dimensions) which may provide smoother driver integration especially with LF driver Zobel-corrected (to partial degree). Plus slight hornloading of HF waveguide also will give higher output at the same excursion level hence less distortion. All this is easily measurable. Plus better directivity - a bit harder to measure, still quite possible with DYI rotating panel and ARTA software with included automation scripting). True, finding and matching good waveguide could be somewhat difficult. Also top-end will have some roll-off, and adding supertweeter or horn-EQ seems the only valid options here. As mentioned already in the article, judging by ear I didn’t find this roll-off being very noticeable.
So that's my opinion why resonance-damping approach isn't making things more complex, I’d say rather contrary as here we fight with the root-cause of typical issues. I hope you can put a good use of it, or, at least give it a try.
It is rubbish when tossed in as an absolute requirement without any proof.
As a diy forum there is always a lot of idealism involved here in discussing speakers and how they should perform. Since diy types don't need to make a living with their designs they can proclaim what the ideal criteria are and pursue them to the very ends.
If we want to advance the art, though, we need to really research what can and can not be heard. Even with highly audible criteria there are thresholds of audibility and we need to figure out what those are and not waste time and money pushing performance well beyond the thresholds of "good enough". (To do so generally means we are make do in other performance areas where we might not yet be to the threshold of inaudibilty.
Many studys have been done on phase audibility and there is a general consensus that minor phase errors are not audible. Of course extreme phase errors will be audible, but errors of less than a foot or a mSec in time are generally not heard except with some specialized test tones.
I realize that there is great appeal to having a speaker that will pass a square wave, conversly, to have one with poor square wave response and say "it doesn't matter" takes a lot of will power for some.
I always refer others to the listening tests of Toole. He found that a lot of speakers could sound quite fine if the designer concentrated on on-axis and near on-axis flatness and smoothness. Power response, phase response, and some distortion characteristics could be surprisingly non-ideal and not downgrade rank ordering in his tests.
Worth your reading his book.
Yes, and how about it ? Your pontificating on a subject you don't really grasp.
Duelund may be worth investigating, as well as the fact the final acoustic
phase response is the only thing that matters, zobels and impedance
correction circuits only impinge that if they are strictly necessary.
The fact is your understanding of the issues are limited, so are mine, but
less so, but I don't expound you need to do "this and that" necessarily.
There is nothing new in your original post.
Fact is typically for a two way the acoustic phase response is manipulated
by making the x/o slopes slightly assymetric to account for different driver
acoustic centres, to control the optimum listening axis, for example.
And as Charlielaub has pointed out, if your original premise doesn't make
any sense, which it doesn't, being impossible, what follows cannot either.
And it doesn't. It doesn't follow and it doesn't make any sense.
(You can't backtrack and say you actually meant something
else, when your main premise is stated as fact - period.)
Close to rubbish components given what is technically feasible ? I've no
idea what you imagine are good technically unfeasable components.
(in fact I do - for ideal components - but they don't exist and never will.)
If you want to tell people the way it is, you need to know your onions ....
A small remark regarding the introductory statement - it's in quotes, so it's not mine. I took it as a guideline for a challenge to try to get as close as possible and find whether there is a truth in it.
Thanks for all the opinions so far, lets summarize what we have in to do list:
Building loudspeaker with acoustically aligned drivers and two types of filters - one using phase alignment method and second using traditional method. Then making:
- comparative F response on-axis and off-axis measurements;
- blind listening tests.
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