This is my first post here, so howdy all. I have a burning question in need of an answer. As of late I have been seeing the term "elliptical crossovers" being bantered around but haven't been able to find anything in the way of what an elliptical crossover actually is. So I was hoping someone here might be able to enlighten me on this matter. What is it? How does it differ from your standard 1st - 4th order run of the mill crossovers? What is gained?
I've been designing/building my own speakers for HiFi home systems as well as building high end systems in cars since the early 80's so I'm fairly competent when it comes to such matters but I don't know what it means to be elliptical.
So if someone could let me in on the secret, I'd appreciate it.
I've been designing/building my own speakers for HiFi home systems as well as building high end systems in cars since the early 80's so I'm fairly competent when it comes to such matters but I don't know what it means to be elliptical.
So if someone could let me in on the secret, I'd appreciate it.
It's a filter that's steeper than his colleagues at the same order. The name comes from the elliptical function it's based on.
The advantage is, the steepness is increased compared to a
you keep the advantages of a less steep filter (supposedly more 'harmonic' transition from one driver to the other, it is supposed to sound more homogene) to a steeper filter (steeper slope, keeps the tweeter from getting power and excursion of the lower frequencies, which means you can xo it lower and/or use it with more power).
The disadvantages are obvious, if you look at the linked paper:
- filter overswing
- bad summation, results in unlinearity
- strong phase shift
- impedance can get very low quickly in a passive crossover because of the strong interaction/influence of the impedance of the drivers ->
- difficult to implement passive
- higher number of parts
- semi-obsolete active since the use of cascaded filters or EQing in a DSP became much cheaper
In short: No free lunch today.
No. That wouldn't be an elliptical filter anymore.
Generally, you 'can' only get n-order filter, every order adding a 6dB/octave steeper slope. In praxis the acoustical slope is much more important because of the driver response. And a lot of filters (passive) look a lot different from the standard calculated filter. You can adjust the filter slope by varying the parts values and achieve a lot of different filters and reach similarities to most filter types but it's often much better not to create a mass-grave of crossover parts. I would not use anything steeper than 18dB (3rd order) on a passive crossover since you have to pull the impedance response flat before in many cases. More often than not it sounds much less homogene, even if you use a dsp. The drivers got their 'own mind', you have to account for that and the resulting sound is much more important than to follow a certain filter philosophy.
This is a topic that I am familiar with, since I have tried to massage some elliptical filters into crossovers in the past (and it worked!).
Crossovers are basically a combination of a highpass filter and a lowpass filter such that their outputs sum to unity gain.
OK then, so what is an elliptical filter?
A true elliptical class filter is constructed only from high-pass-notch, or low-pass-notch responses (for even order). If the filter is odd order there is ONE first order high or low pass response in series with the rest. That's it. If there is anything else in there then it's NOT an elliptic filter.
Elliptical filters are a class of filters that have one or more notches (referred to as zeros of the filter function) in the response. The notches create ripple in the response, and one parameter of elliptical filters is how "deep" these ripples are (in dB) and the depth can be zero dB (see below).
The notches/zeros can be located both above and/or below the corner frequency of the filter. This creates the subclasses of Chebyshev type I and II, where (for type I) there are no zeros/notches in the stopband or (for type I) there are no zeros/notches in the passband. When there are notches in both stopband and passband you have a full elliptical filter. When I say "there are no notches in the stop/pass band I strictly mean that the depth of the notch has been set to 0dB.
Why are elliptical filters of interest?
This class of filters provides the steepest possible rate of attenuation for a given order. This makes them useful when you want to keep the amount of circuitry to a minimum (e.g. for a analog active filter). On the other hand (again for an analog active filter) elliptical filters even of modest order require pole Q's that can quickly get large, and component tolerances make it difficult to accurately control the overall response. This is not a problem at all with DSP implementations, however, since you can calculate the filter in a (relatively) mathematically precise manner and get the exact response you desire.
The Chebyshev type II subclass of elliptical filters is the most useful for audio work because the passband has zero ripple, and the rolloff from the passband to the stop band is similar to (but steeper than) a Butterworth filter. As a result, the high and low pass filters can be made to work together with less pain than for other elliptic filter types.
In general for audio work, the unmodified elliptical filters are not useful because the highpass and lowpass pair do NOT sum to unity at the crossover point and instead you get a sharp peak or dip there. Instead you must resort to "tweaking" the filter response by separating high and low pass filters, changing the Q of certain stages, etc. This process is to the best of my knowledge not well understood and is largely trial-and-error. I used it to come up with some 5th-8th order crossovers based on a few elliptical filter starting points and the result can be a nice in-phase response that sum with very little ripple. But sometimes it just can't be made to work well.
Some well known "elliptic" or "Cauer" filters add on other stages. For example the "NTM" (Thiele) crossover uses one high/low-pass notch, a second order high/low pass function, plus two first order high/low pass functions. The order is therefore FIXED at 6th order due to the types of filters used. Contrary to what is claimed, that is NOT an elliptic filter by any stretch of the imagination. The other one that comes to mind is the Hardman filter. This uses a combination of one high/low-pass notch plus a second order high/low pass function. Like the NTM filter, the order is therefore fixed at four and it's not a true elliptical filter. THe NTM and Hardman filters are described in Chapter 5 of Douglas Self's book "The Design of Active Crossovers", and he has worked up some circuit examples for them.
It seems that the term "elliptic" became commonly used to refer to any filter with a notch in it, but that is a more than loose definition. The elliptic filters are very tightly and mathematically defined functions that are not open to interpretation and modification.
Crossovers are basically a combination of a highpass filter and a lowpass filter such that their outputs sum to unity gain.
OK then, so what is an elliptical filter?
A true elliptical class filter is constructed only from high-pass-notch, or low-pass-notch responses (for even order). If the filter is odd order there is ONE first order high or low pass response in series with the rest. That's it. If there is anything else in there then it's NOT an elliptic filter.
Elliptical filters are a class of filters that have one or more notches (referred to as zeros of the filter function) in the response. The notches create ripple in the response, and one parameter of elliptical filters is how "deep" these ripples are (in dB) and the depth can be zero dB (see below).
The notches/zeros can be located both above and/or below the corner frequency of the filter. This creates the subclasses of Chebyshev type I and II, where (for type I) there are no zeros/notches in the stopband or (for type I) there are no zeros/notches in the passband. When there are notches in both stopband and passband you have a full elliptical filter. When I say "there are no notches in the stop/pass band I strictly mean that the depth of the notch has been set to 0dB.
Why are elliptical filters of interest?
This class of filters provides the steepest possible rate of attenuation for a given order. This makes them useful when you want to keep the amount of circuitry to a minimum (e.g. for a analog active filter). On the other hand (again for an analog active filter) elliptical filters even of modest order require pole Q's that can quickly get large, and component tolerances make it difficult to accurately control the overall response. This is not a problem at all with DSP implementations, however, since you can calculate the filter in a (relatively) mathematically precise manner and get the exact response you desire.
The Chebyshev type II subclass of elliptical filters is the most useful for audio work because the passband has zero ripple, and the rolloff from the passband to the stop band is similar to (but steeper than) a Butterworth filter. As a result, the high and low pass filters can be made to work together with less pain than for other elliptic filter types.
In general for audio work, the unmodified elliptical filters are not useful because the highpass and lowpass pair do NOT sum to unity at the crossover point and instead you get a sharp peak or dip there. Instead you must resort to "tweaking" the filter response by separating high and low pass filters, changing the Q of certain stages, etc. This process is to the best of my knowledge not well understood and is largely trial-and-error. I used it to come up with some 5th-8th order crossovers based on a few elliptical filter starting points and the result can be a nice in-phase response that sum with very little ripple. But sometimes it just can't be made to work well.
Some well known "elliptic" or "Cauer" filters add on other stages. For example the "NTM" (Thiele) crossover uses one high/low-pass notch, a second order high/low pass function, plus two first order high/low pass functions. The order is therefore FIXED at 6th order due to the types of filters used. Contrary to what is claimed, that is NOT an elliptic filter by any stretch of the imagination. The other one that comes to mind is the Hardman filter. This uses a combination of one high/low-pass notch plus a second order high/low pass function. Like the NTM filter, the order is therefore fixed at four and it's not a true elliptical filter. THe NTM and Hardman filters are described in Chapter 5 of Douglas Self's book "The Design of Active Crossovers", and he has worked up some circuit examples for them.
It seems that the term "elliptic" became commonly used to refer to any filter with a notch in it, but that is a more than loose definition. The elliptic filters are very tightly and mathematically defined functions that are not open to interpretation and modification.
Edot: CL beat me to it. Still, might as well leave it up.
Broadly speaking as far as crossovers are concerned, when eliptical filters are mentioned, people typically mean a 'conventional' filter of xzy electrical order with a zero pole notch added to accelerate the initial rolloff rate to a desired higher acoustic order. With careful adjusting of the filter coefficients you can use it to track a given high order acoustical slope (e.g. LR6, BW7, LR8 &c.) with a reduced number of components for ~the first octave of the rolloff. You then have the characteristic bounce-back and ~2nd order rolloff above / below (as appropriate to high or low pass filters) that point, but typically speaking by that point the driver should already be heavily attenuated.
I have seen crossovers with any kind of zero [or near zero] pole notch described as 'eliptical', even if it's simply stamping on a stopband resonance rather than affecting the rolloff in the transition band, which is stretching the definition a bit too far IMO; that said with crossovers it's not a hard and fast definition, since the term is not being used strictly in the first place.
Broadly speaking as far as crossovers are concerned, when eliptical filters are mentioned, people typically mean a 'conventional' filter of xzy electrical order with a zero pole notch added to accelerate the initial rolloff rate to a desired higher acoustic order. With careful adjusting of the filter coefficients you can use it to track a given high order acoustical slope (e.g. LR6, BW7, LR8 &c.) with a reduced number of components for ~the first octave of the rolloff. You then have the characteristic bounce-back and ~2nd order rolloff above / below (as appropriate to high or low pass filters) that point, but typically speaking by that point the driver should already be heavily attenuated.
I have seen crossovers with any kind of zero [or near zero] pole notch described as 'eliptical', even if it's simply stamping on a stopband resonance rather than affecting the rolloff in the transition band, which is stretching the definition a bit too far IMO; that said with crossovers it's not a hard and fast definition, since the term is not being used strictly in the first place.
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Well, most filters ring, the question is how much. GD can be higher than some, but this very much depends on the specifics of the design -it's not a fixed quantity where one can say 'any filter described as "eliptical" has a given amount that is higher than xyz present in other types'. For e.g., in some cases it may be lower than the equivalent built up in a conventional ladder network (while also saving components, insertion losses and money).
That being said, they're far from a panacea; purely IMO, assuming we're using the term to refer to filters that use a zero pole notch to accelerate the initial rolloff rate, then their primary use is to heavily attenuate a driver before it gets into trouble e.g. major breakup modes, rather than 'just' trying to notch those out. If you don't have those -the balance of advantage probably tips toward more conventional topologies tracking lower order slopes.
GD can be higher than some, but this very much depends on the specifics of the design -it's not a fixed quantity where one can say 'any filter described as "eliptical" has a given amount that is higher than xyz present in other types'. For e.g., in some cases it may be lower than the equivalent built up in a conventional ladder network (while also saving components, insertion losses and money). That being said, they're far from a panacea; purely IMO, assuming we're using the term to refer to filters that use a zero pole notch to accelerate the initial rolloff rate, then their primary use is to heavily attenuate a driver before it gets into trouble e.g. major breakup modes, rather than 'just' trying to notch those out. If you don't have those -the balance of advantage probably tips toward more conventional topologies tracking lower order slopes.
All righty then. To all who responded I say thank you. It does seem a bit clearer now. The paper that Indigio linked to helped a lot. I see how an elliptical filter might come in handy in car audio to improve staging and make the tweeters in the A pillars coalesces with the mids/woofers in the doors. Of course today it is so much easier with DSP in a vehicle that no one is hardly using passive XO's any more. Here is a site that really puts a lot into the whole elliptical thing. These guys actually make some pretty good stuff and they are in my city just a few miles from mt house.
CDT Audio Crossovers
CDT Audio Crossovers
It's this kind of BS that you hear associated with crossover filters that have one or more notches:
This is from that car audio site you linked to above.
Let's do the math: 24dB/oct (4th order) plus 6db/octave (first order) makes 10th order? Hmmmm, sounds like that "new math" to me. It's just a 5th order (as they mention in the first paragraph) with a notch.
What actually happens is that, where the steepest part of the response drops into the notch, the slope approaches "60dB/oct" but only for a very short frequency range. It really is nothing like a 10th order crossover. That is just the marketing hype that they try to toss around to make it sound "superior" to those who do not have any understanding about what they are talking about! It's about on par with other claims of certain "elliptical" crossover embodiments I have seen.
This is from that car audio site you linked to above.
Let's do the math: 24dB/oct (4th order) plus 6db/octave (first order) makes 10th order? Hmmmm, sounds like that "new math" to me. It's just a 5th order (as they mention in the first paragraph) with a notch.
What actually happens is that, where the steepest part of the response drops into the notch, the slope approaches "60dB/oct" but only for a very short frequency range. It really is nothing like a 10th order crossover. That is just the marketing hype that they try to toss around to make it sound "superior" to those who do not have any understanding about what they are talking about! It's about on par with other claims of certain "elliptical" crossover embodiments I have seen.
Elliptical crossovers can be useful if you are working with a metal driver. The notch filter takes our the sharp breakup mode of the metal driver but also 'assists' with the roll off.
The SEAS L18 works well with this kind of crossover. With just a baffle step inductor and a notch you can have a 2k crossover which has excellent phase (depending on choice of tweeter).
The SEAS L18 works well with this kind of crossover. With just a baffle step inductor and a notch you can have a 2k crossover which has excellent phase (depending on choice of tweeter).
Well, if you look at the first linked paper and analyze the graph..
It's over 35dB/oct, can't tell exactly how much because the plot stops there at the bottom. That's a lot more than a 5th order (30dB) filter. I'm really not fond of that filter (slopes aren't symmetrically, linearity bad, phase jumps etc) but you have to give it to the filter, it's 'effective', that's why I compared it with higher order filters.
I don't like the bumps in the response either and I would probably never use that filter anyway, it simply isn't a clean crossover topology. It reads ~-30dB on these humps. Many speakers got the distortion higher than that on dynamic music passages. And on low parts, it's below audibility. There sure are a lot of technical uses that do not tolerate such a behaviour, on audio the bumps doesn't necessarily matter much.
The filter got a lot of disadvantages more which weight heavier, (at least IMO). And in audio, I don't see much (or any) real advantages. With a passive crossover you can hardly (if ever) use it, active it isn't flexible/variable at all (unlike easily 'trimable' other filter types) and with DSPs being cheap, much more flexible and to get a 'clean' higher order filter or same order filter and a bit EQing will often work better, I can't really see the use of it.
I see it the same. It's technobabble for people which are impressed easily because they can't recognize the drawbacks of that filter type and just go for 'it's different from all the others, it must be better'.
Attachments
Hi iamjackalope,
The so called elliptic function filter is not new as far as filter types are concerned as you will see in the link bollow.
NTM Crossovers
IMO, this paper provides an excellent explanation of how the elliptical filter works. Please note that although the author has shown the magnitude and phase response of this type of crossover, they are simulations of the electrical performance of his schematic and not the acoustic response to which they should be applied.
Hope this helps.
Peter
The so called elliptic function filter is not new as far as filter types are concerned as you will see in the link bollow.
NTM Crossovers
IMO, this paper provides an excellent explanation of how the elliptical filter works. Please note that although the author has shown the magnitude and phase response of this type of crossover, they are simulations of the electrical performance of his schematic and not the acoustic response to which they should be applied.
Hope this helps.
Peter
Quite.
If you're going to use an elliptic filter variation (and I'm assuming here we're using the term to describe a filter with a zero pole notch to increase the initial rolloff rate) then you need to do so properly. Far too often people talk about them as though they are somehow exempt from basic principles of crossover design. They really aren't. To properly implement for hi-fi purposes, you have to treat them just like you would any other crossover topology and adjust the filter coefficients so that for the first octave the combined filter + driver response is tracking a given acoustical slope, be it LR6, BW7, LR8 or whatever. In addition to this, you have to pay some attention to the characteristic stopband ripple & and ensure the 'bounce back' doesn't come up too high in level: -40dB would be a reasonable 'maximum permissible', give or take. Preferably give.
If you're going to use an elliptic filter variation (and I'm assuming here we're using the term to describe a filter with a zero pole notch to increase the initial rolloff rate) then you need to do so properly. Far too often people talk about them as though they are somehow exempt from basic principles of crossover design. They really aren't. To properly implement for hi-fi purposes, you have to treat them just like you would any other crossover topology and adjust the filter coefficients so that for the first octave the combined filter + driver response is tracking a given acoustical slope, be it LR6, BW7, LR8 or whatever. In addition to this, you have to pay some attention to the characteristic stopband ripple & and ensure the 'bounce back' doesn't come up too high in level: -40dB would be a reasonable 'maximum permissible', give or take. Preferably give.
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The depth of the maximum "bounceback" (as you call it) in the stopband is actually an adjustable parameter of an elliptic filter. There is a tradeoff between order, depth of bounceback, and the frequency response interval between where the response leaves the passband and where the first notch is located (the transition region). For a given order you can reduce the level of the the highest bounceback depth but to do that you must make the transition region wider.
Here is a plot that illustrates these regions in the filter response:
You can tell this is an even order elliptic filter because the tops of all the "bouncebacks" are at the same level. This is a characteristic of all even order elliptic filters with stopband notches (e.g. elliptic and Chebyshev type II). If this was an odd order elliptic filter, the tops of the bouncebacks would trend downwards at 6dB/oct due to the additional first order stage required to achieve the odd order.
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Yes, I am aware of that, and its characteristics, as I'm obliged to work with them frequently. I even mentioned (well, alluded to if you want pedantry) the fact that it is adjustable when noting that attention must be paid to it when working with them.
Re the terminology, unfortunately the term 'elliptic[al]' appears to have been widely adopted to describe any filter with a near zero pole notch used to increase the initial roll-off, and sometimes even for a filter with any kind of notch at all. Technically speaking incorrect, but however much you, I or anyone else (including PLB, judging by the 'so called' preface in his post) may dislike the term being used in that way, you're never going to change it; it's too widely used. Which doesn't make it any the less irritating I agree. About the one consolation is that it's far from alone, or the worst example of misnomers in audio.
Re the terminology, unfortunately the term 'elliptic[al]' appears to have been widely adopted to describe any filter with a near zero pole notch used to increase the initial roll-off, and sometimes even for a filter with any kind of notch at all. Technically speaking incorrect, but however much you, I or anyone else (including PLB, judging by the 'so called' preface in his post) may dislike the term being used in that way, you're never going to change it; it's too widely used. Which doesn't make it any the less irritating I agree. About the one consolation is that it's far from alone, or the worst example of misnomers in audio.
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Wow. This is quite a response. Thanks to everyone who has posted in this thread. I have got a good general understanding of what an elliptical crossover is now. Correct me if I'm wrong. An elliptical filter is a low pass notch filter combined with a high pass notch filter for even order and for odd order there is a series filter before the notch. They are used for very steep slopes that roll off quickly but they are a pain in the *** to get right and have limited real world usage because true elliptical filters don't sum to unity. There are usually better alternatives
Er, wrong on most counts I'm afraid. Let's try again.
First: as far as loudspeaker crossovers go, the term 'elliptic filter' typically (although technically incorrectly) refers to any filter, whether a high, low or bandpass, that has a notch used to increase the roll off rate of the drivers.
That out of the way, notched filters are not in themselves especially difficult to implement, but many people for some reason get stuck on the name and don't adjust the filter coefficients to track a filter slope that does sum flat. The same people would never, in a million years, do that with a different filter topology. The primary use for crossovers is indeed to achieve a rapid driver rolloff tracking a desired slope -if they have limited usage it's largely because most of the time very high order acoustical slopes (say, > 4th order) are unnecessary, however these are achieved. Sometimes these high order slopes are useful, such as when working with metal cone drivers that have significant breakup modes, but in most other cases they aren't required, so there is no particular reason to employ notched / 'elliptical' filters (or a very lengthy ladder network).
First: as far as loudspeaker crossovers go, the term 'elliptic filter' typically (although technically incorrectly) refers to any filter, whether a high, low or bandpass, that has a notch used to increase the roll off rate of the drivers.
That out of the way, notched filters are not in themselves especially difficult to implement, but many people for some reason get stuck on the name and don't adjust the filter coefficients to track a filter slope that does sum flat. The same people would never, in a million years, do that with a different filter topology. The primary use for crossovers is indeed to achieve a rapid driver rolloff tracking a desired slope
-if they have limited usage it's largely because most of the time very high order acoustical slopes (say, > 4th order) are unnecessary, however these are achieved. Sometimes these high order slopes are useful, such as when working with metal cone drivers that have significant breakup modes, but in most other cases they aren't required, so there is no particular reason to employ notched / 'elliptical' filters (or a very lengthy ladder network).
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