Question regarding 1st order xover between tweeter and mid?

[NewInTown]

I am working on a "1st order" xover for a 3way seas - 27TFFC, 15MCA and 22RNX. Based on my measurement, even without any xover, at around 3KHz, the phase difference between the tweeter and mid is already at 60degree. If I only add a cap to the tweeter, and an inductor to the mid, the phase is 180 degree. I ended up having to invert the mid which not only match the tweeter phase, but also match the mid and woofer phase as well.
With the mid inverted, the phase of all drivers tracked very well.
Does anyone have an example of how the tweeter and the mid is crossed without having to invert the polarity?
I attached the measurement and simulation below.

[Evil Twin]

You have not given any indication of the relative acoustic origins of the drivers. This is one of the many challenges for first order networks- if you have mounted all of the drivers on one baffle, you are going to have difficulties, especially if a true pulse capable speaker is your goal. Mounting the drivers in a way such that their true acoustic origins are in the same plane is basically mandatory unless you're doing a digital crossover and can apply time delay selectively to different drivers to arrive at roughly the same condition.

Having successfully designed and built pulse coherent speakers about 40 years ago, I would also advise you to be very careful in your driver choices, as the excursion and performance requirements are substantial.

[NewInTown]

You have not given any indication of the relative acoustic origins of the drivers. This is one of the many challenges for first order networks- if you have mounted all of the drivers on one baffle, you are going to have difficulties, especially if a true pulse capable speaker is your goal. Mounting the drivers in a way such that their true acoustic origins are in the same plane is basically mandatory unless you're doing a digital crossover and can apply time delay selectively to different drivers to arrive at roughly the same condition.

Having successfully designed and built pulse coherent speakers about 40 years ago, I would also advise you to be very careful in your driver choices, as the excursion and performance requirements are substantial.

The mid and tweeter are mounted on a slanted baffle so that the acoustic center of both drivers are aligned. The offset is about 22mm, but even then that should not made enough difference as to the 180degree out of phase of the two drivers. I don't really think having the acoustic center aligned is enough. There have to be some other variables. You mention intentionally introduce delay but wouldn't that be the same as inverting the phase of the drivers? Either you invert the phase of the drivers or you invert the phase of the electrical signal going to it? Someone had mention using an all pass filter but I am not sure that is a workable solution.
So my question is does anyone have an actual example of a 1st order passive xover for the mid and tweeter? My guess is you have to have special made tweeter and mid for these. Nowaday, having drivers that can handle the large overlap is not really a problem. The problem I think is having the phase aligned without having the invert the polarity.

[Juhazi]

NIT, looks like you will get acoustically a Duelund-type 3-way system, just invert the polarity of the midrange! SEAS 27TFFC should handle the task.

http://www.diy-audio.narod.ru/litr/duelund-filter.pdf

[5th element]

I was just about to say. You have drummed up some reasonably nice looking graphs but have you optimised the acoustic responses to provide proper 1st order slopes?

As Juhazi alludes to, the acoustic and electrical responses are not the same thing. You can have a 1st order electrical filter (as you have above) but the resultant acoustic response (drivers natural response + the electrical filter) looks quite different.

I'm assuming that XSim allows you to set target responses? Try over laying a 1st order target response for your given xover frequencies.

1st order filters are notoriously difficult to get right. They require drivers with exceptional bandwidth and power handling/excursion capabilities.

Looking at your raw measurements, for example, both the tweeter and midrange start showing reasonable intrinsic roll offs around 2kHz. In the tweeter this is far more pronounced, but the mid trends in a similar direction. These natural roll offs might not be huge (in the case of the mid) but they will still modify the shallow 1st order electrical roll off by something significant so care has to be taken.

This is one of those situations where driver selection is of the utmost importance. Jon mentions this but it is worth repeating!

For example, lets take a look at this small format Scanspeak neo dome tweeter, the 602010, as borrowed from Zaph...



As you can see this tweeter essentially extends all the way down to 500Hz as pretty much a flat line.

If we compare this to SEAS 27TDFC...



Both tweeters are very capable, but clearly are very different beasts, compare their low end roll offs. This doesn't mean that one is more capable than the other, it's just that the parameters have been optimised differently. A tweeter is, after all, just a small sealed box loudspeaker and the scan has been optimised in a different direction. The scan speak is quite unusual, but if you ignore its price, you can easily see how it would lend itself far better to 1st order networks as its own frequency response would modify the electrical filters response by far less than something like the SEAS.

The same can be said for the SEAS midrange driver that you have chosen. Even on the SEAS website the gentle roll off above 2kHz is present and this will modify your 1st order electrical in a detrimental way. But something like the Scanspeak 10F...



This is as flat as a pancake from 200Hz to over 10kHz.

Now granted the 10F is going to be excursion limited on the low end so you would definitely need to watch what you do there.

It is absolutely worth pointing out here that a true first order system is only 1st order for as much bandwidth as your drivers can maintain. This is true for any loudspeaker/filter order but what exactly do I mean by this?

Typically you have a few regions that describe what a filter does.

1) The pass band - this is the range of frequencies that a filter, or driver, can be said to be 'playing' or allowed to pass.
2) The stop band - this is the range, beyond which, the filter, or driver, can be said to be, realistically, not playing or allowing things to pass.
3) The transition band - this is the range that covers the area between the stop and pass band. It is less commonly referenced because most digital filtering, these days, tends to be brick wall and thus very steep. But when concerning loudspeakers, especially low order ones, is quite important.

So how to these relate to the above and what defines the stop band?

With digital filters the term 'stop band rejection' is sometimes used to basically describe how much of the original signal is rejected by the stop band region of the filter. This is important when the entire point of a filter is to block out digital hash that would otherwise compromise the linearity of your system, but a similar comparison can be drawn to loudspeakers.

A prime and very obvious example to this would be a metal cone loudspeaker. Metal cones ring like the liberty bell and this ringing needs to be kept out of band. With something as aggressive as a metal cone resonance, most designers would want the ringing to be attenuated by at least 40dB, preferably by 48dB. So in this case you could say you want to design your 'stop band' to approach 48dB by the time the driver rings.

Less obviously is simply the typical range, beyond which, one could say a well behaved loudspeaker + its filter is essentially 'quiet'. In other words, when two drivers are crossed over, how much stop band attenuation do I need before I can say one driver isn't having any influence to the overall integration of the crossover any more? A rough value for this is usually said to be around 24dB.

So with well behaved drivers, we need ~24dB worth of rejection from the filter, so we can say that we have transitioned from the pass band and into the stop band.

The transition band is the most important area of a multiway loudspeaker because it's this region that contains all of the driver overlap. It is the region where your phase alignment comes into play and where your crossover order/slope shapes have all of their impact.

The transition band can be very narrow, such as in high order filters or very wide, such as in low order filters.

If we take the 24dB figure for the transition band, then a properly implemented 4th order filter would require 1 octave to reach the stop band.

A 2nd order filter would therefore require 2 octaves and a 1st order filter 4 octaves.

A 4 octave transition band is huge. Which brings me back to what I said above...

It is absolutely worth pointing out here that a true first order system is only 1st order for as much bandwidth as your drivers can maintain. This is true for any loudspeaker/filter order but what exactly do I mean by this?

If we take the scanspeak tweeter, I linked above, as an example. It is essentially a flat line from 500Hz up to 20kHz. For the sake of this example 500Hz would be considered to be its lower end limit, but what we want is roughly 4 octaves higher. In this case we're looking at 8kHz. In other words we'd need to place our first order filter at 8kHz for it to maintain a transition band wide enough to be truly first order down to a sensible stop band attenuation figure of 24dB.

The scanspeak tweeter has exceptionally good bandwidth down low. And would maintain true first order slopes far more easily than other tweeters. But lets say we wanted to cross over at 4kHz instead. This is a much more sensible figure. If we do this though we're looking at only having ~18dB of rejection by the time we hit 500Hz. As the tweeter rolls off naturally below this those last (and least important) 6dB are going to be steeper than true first order. Or looked at another way you'll only 3 octaves of true first order integration. If we lower the crossover point to 2kHz, then we're only going to have 12dB of rejection before we hit 500Hz etc and 2 octaves of true first order integration.

For comparisons sake the 2nd order filter would require 2 octaves to hit our target of 24dB for the stop band and given the same scanspeak tweeter you can accomplish this with a 2kHz xover.

As you can see true first order systems are not to be taken lightly and virtually all are quite heavily compromised in one way or another. None, at least that I can think of, would be able to maintain true first order filter slopes in a transition band wide enough to reach 24dB of attenuation, but loudspeaker design is all about compromises.

Aiming for 4 octaves is essentially impossible. 3 octaves would be ridiculously hard a decent compromise would be something between 2-3 octaves.

One could say that with a DSP and limitless power you could bang any loudspeakers on axis frequency response to fit a true first order acoustic slope but this wouldn't be advisable. First of all we don't have limitless power and DSPs have limits in terms of the overall system gain structure, so applying tons of boost quickly becomes a problem. Not only this but applying boost places huge demands on your drivers and if approached passively (such by raising the Q of a filter) can lower system impedance terribly low.

EQ, in any shape or form, has to be applied carefully and thoughtfully. For example, the gentle roll off of the SEAS midrange above 2khz, you could easily EQ/shape this so that the acoustic response followed a true acoustic first order target, but after 10kHz, where it falls like a stone, forget about it!

From the above you can see why true first order loudspeakers are rarely done. In fact I would argue that a true first order loudspeaker can't even be done properly but can perhaps be done to a decent level of satisfaction.

[NewInTown]

I was just about to say. You have drummed up some reasonably nice looking graphs but have you optimised the acoustic responses to provide proper 1st order slopes?

As Juhazi alludes to, the acoustic and electrical responses are not the same thing. You can have a 1st order electrical filter (as you have above) but the resultant acoustic response (drivers natural response + the electrical filter) looks quite different.

I'm assuming that XSim allows you to set target responses? Try over laying a 1st order target response for your given xover frequencies.

1st order filters are notoriously difficult to get right. They require drivers with exceptional bandwidth and power handling/excursion capabilities.

Looking at your raw measurements, for example, both the tweeter and midrange start showing reasonable intrinsic roll offs around 2kHz. In the tweeter this is far more pronounced, but the mid trends in a similar direction. These natural roll offs might not be huge (in the case of the mid) but they will still modify the shallow 1st order electrical roll off by something significant so care has to be taken.

This is one of those situations where driver selection is of the utmost importance. Jon mentions this but it is worth repeating!

For example, lets take a look at this small format Scanspeak neo dome tweeter, the 602010, as borrowed from Zaph...



As you can see this tweeter essentially extends all the way down to 500Hz as pretty much a flat line.

If we compare this to SEAS 27TDFC...



Both tweeters are very capable, but clearly are very different beasts, compare their low end roll offs. This doesn't mean that one is more capable than the other, it's just that the parameters have been optimised differently. A tweeter is, after all, just a small sealed box loudspeaker and the scan has been optimised in a different direction. The scan speak is quite unusual, but if you ignore its price, you can easily see how it would lend itself far better to 1st order networks as its own frequency response would modify the electrical filters response by far less than something like the SEAS.

The same can be said for the SEAS midrange driver that you have chosen. Even on the SEAS website the gentle roll off above 2kHz is present and this will modify your 1st order electrical in a detrimental way. But something like the Scanspeak 10F...



This is as flat as a pancake from 200Hz to over 10kHz.

Now granted the 10F is going to be excursion limited on the low end so you would definitely need to watch what you do there.

It is absolutely worth pointing out here that a true first order system is only 1st order for as much bandwidth as your drivers can maintain. This is true for any loudspeaker/filter order but what exactly do I mean by this?

Typically you have a few regions that describe what a filter does.

1) The pass band - this is the range of frequencies that a filter, or driver, can be said to be 'playing' or allowed to pass.
2) The stop band - this is the range, beyond which, the filter, or driver, can be said to be, realistically, not playing or allowing things to pass.
3) The transition band - this is the range that covers the area between the stop and pass band. It is less commonly referenced because most digital filtering, these days, tends to be brick wall and thus very steep. But when concerning loudspeakers, especially low order ones, is quite important.

So how to these relate to the above and what defines the stop band?

With digital filters the term 'stop band rejection' is sometimes used to basically describe how much of the original signal is rejected by the stop band region of the filter. This is important when the entire point of a filter is to block out digital hash that would otherwise compromise the linearity of your system, but a similar comparison can be drawn to loudspeakers.

A prime and very obvious example to this would be a metal cone loudspeaker. Metal cones ring like the liberty bell and this ringing needs to be kept out of band. With something as aggressive as a metal cone resonance, most designers would want the ringing to be attenuated by at least 40dB, preferably by 48dB. So in this case you could say you want to design your 'stop band' to approach 48dB by the time the driver rings.

Less obviously is simply the typical range, beyond which, one could say a well behaved loudspeaker + its filter is essentially 'quiet'. In other words, when two drivers are crossed over, how much stop band attenuation do I need before I can say one driver isn't having any influence to the overall integration of the crossover any more? A rough value for this is usually said to be around 24dB.

So with well behaved drivers, we need ~24dB worth of rejection from the filter, so we can say that we have transitioned from the pass band and into the stop band.

The transition band is the most important area of a multiway loudspeaker because it's this region that contains all of the driver overlap. It is the region where your phase alignment comes into play and where your crossover order/slope shapes have all of their impact.

The transition band can be very narrow, such as in high order filters or very wide, such as in low order filters.

If we take the 24dB figure for the transition band, then a properly implemented 4th order filter would require 1 octave to reach the stop band.

A 2nd order filter would therefore require 2 octaves and a 1st order filter 4 octaves.

A 4 octave transition band is huge. Which brings me back to what I said above...



If we take the scanspeak tweeter, I linked above, as an example. It is essentially a flat line from 500Hz up to 20kHz. For the sake of this example 500Hz would be considered to be its lower end limit, but what we want is roughly 4 octaves higher. In this case we're looking at 8kHz. In other words we'd need to place our first order filter at 8kHz for it to maintain a transition band wide enough to be truly first order down to a sensible stop band attenuation figure of 24dB.

The scanspeak tweeter has exceptionally good bandwidth down low. And would maintain true first order slopes far more easily than other tweeters. But lets say we wanted to cross over at 4kHz instead. This is a much more sensible figure. If we do this though we're looking at only having ~18dB of rejection by the time we hit 500Hz. As the tweeter rolls off naturally below this those last (and least important) 6dB are going to be steeper than true first order. Or looked at another way you'll only 3 octaves of true first order integration. If we lower the crossover point to 2kHz, then we're only going to have 12dB of rejection before we hit 500Hz etc and 2 octaves of true first order integration.

For comparisons sake the 2nd order filter would require 2 octaves to hit our target of 24dB for the stop band and given the same scanspeak tweeter you can accomplish this with a 2kHz xover.

As you can see true first order systems are not to be taken lightly and virtually all are quite heavily compromised in one way or another. None, at least that I can think of, would be able to maintain true first order filter slopes in a transition band wide enough to reach 24dB of attenuation, but loudspeaker design is all about compromises.

Aiming for 4 octaves is essentially impossible. 3 octaves would be ridiculously hard a decent compromise would be something between 2-3 octaves.

One could say that with a DSP and limitless power you could bang any loudspeakers on axis frequency response to fit a true first order acoustic slope but this wouldn't be advisable. First of all we don't have limitless power and DSPs have limits in terms of the overall system gain structure, so applying tons of boost quickly becomes a problem. Not only this but applying boost places huge demands on your drivers and if approached passively (such by raising the Q of a filter) can lower system impedance terribly low.

EQ, in any shape or form, has to be applied carefully and thoughtfully. For example, the gentle roll off of the SEAS midrange above 2khz, you could easily EQ/shape this so that the acoustic response followed a true acoustic first order target, but after 10kHz, where it falls like a stone, forget about it!

From the above you can see why true first order loudspeakers are rarely done. In fact I would argue that a true first order loudspeaker can't even be done properly but can perhaps be done to a decent level of satisfaction.

Thanks for the information and it was quite a read. I learned a lot from your post. You're last statement I would agree given what I've known of first order. There will be some intrinsic phase delay between the tweeter and the mid that it's impossible for them to line up. There may be some tweeter or mid driver they have such a wide operating frequency range that their phase can better line up, but I am not sure if they do no compromise on the sound quality. I look at the Tang Bang driver and it almost seems to good to be true. I mean it is perfectly flat all the way to 20kHz. I wonder if its sound quality could be an issue.
As for phase aligning, I could include an all pass in the signal path of either the tweeter or the mid but I am not sure it will make the sound better, it may be different and it may as well able to reproduce the square wave but the fix may be worse than the problem itself.

But anyway, I think I finally had my xover to a point where I am satisfy with it. It is slightly on the laid back side, but a little more upfront the sibilance is more than I would like. I really like the sound. The sound is quite a bit more immersive, the soundstage is more enveloping. I mean the vocal is almost at my nose and the back of the soundstage is way back there. The sound has better transient and more present.
I think part of the reason the 1st order have a good sound because the simplicity of the xover. It allows the amp to have better control of the load. Assuming you only have an 8ohm resistive load on the amp output and you run a square wave and measure the quality of this square wave output. Now connect a large inductor in series to the 8 ohm then measure the square wave again. Now connect another capacitor to ground to mimmic a 2nd order filter, then connect another inductor for 3rd. order and so on. Each time the output square wave will deviate if only slightly with more and more complex component add to the load. Another argument is that whether 1st order is more "efficient". I think it's true that in the absolute sense, 1st order is not more efficient and efficiency is a function of driver instrinsic efficiency and cabinet size. But I think 1st order will result in better transient and therefore have more perceived dynamic which some people attribute to efficiency. I do notice my 1st order filter have better bass speed. All amplifiers have some type of feedback (although some manufactures claim no global feedback, but there are always some type of feedback in the forward path) and more complex load will introduce more phase lag in the amplifier feedback loop hence the time domain will suffer.

My speakers are based on Troels PMS design that is a combination of 3rd and 2nd order which is actually very good. I rework the xover to 1st order. Compared the two, they both have similar sound but the 1st order is little more musical, better present, more immersive soundstage, more perceived bass.

[NewInTown]

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