What I am going to present here is an old incarnation of my transient-„perfect“ crossover topology. I will try a more refined one in the future so I decided to let this one out to the public.
What I basically did is the electroacoustical approximation of the responses of the two branches of an asymmetrical subtractive crossover with a 2nd order highpass and a 1st order lowpass. Higher orders are theoretically possible but they don’t have advantages only.
The basic linear transfer function of a transient perfect crossover of the order N has the same numerator and denominator. That is actually the source of the infamous humps of subtractive crossovers. They don’t have the same cause as the humps of a transfer function with high Q-values – as it is often misunderstood.
But these humps are responsible for increased power needs, flat slopes around the crossover frequency (for very high orders they tend to get shallower than 6dB/octave !) and lobing.
So the lower the order, the less one runs into these problems. It is theoretically possible to cross any driver combination with such crossovers of arbitrary order - but doing it with a midwoofer/tweeter combination is not for the faint - hearted.
One of the most suitable topologies is therefore the fullrange (or wideband) + woofer topology because of 3 reasons:
1.) The wavelength at the crossover frequency is quite large relative to the physical dimensions involved (-> lobing !).
2.) The “tweeters” involved are more forgiving in terms of shallow crossover slopes.
3.) People using wideband/fullrange drivers often care more about transient accuracy than the “multiway fraction”.
So I thought it was a natural to post it here in the fullrange forum.
It is possible to do more accurate approximations than the one presented here but they would tend to be more complicated and need more accurate driver modelling. But everyone is free to do so. Since the circuit is quite simple it can easily be tried out on a breadboard if one has a second amp to use.
What we do to begin with is taking the response of the aforementioned subtractive crossover. As highpass function we take a 2nd order filter with a Q of 0.5. The actual crossover frequency wouldn’t be the pole frequency (where there is already a 6 dB drop compared to 3 dB for the Butterworth case) but about one octave higher. Both drivers are down by about two dB at the crossover frequency. For higher-order filters the relative level at the crossover point might be higher than 1 - just to mention one of the disadvantages of higher order subtractive crossovers.
So the original transfer function we are going to use will be:
H(s) = (1 + sT/0.5 + s^2*T^2) / (1 + sT/0.5 + s^2*T^2 )
This is then split into two parts:
H(s) = (1 + sT/0.5 ) / (1 + sT/0.5 + s^2*T^2 ) + s^2*T^2 / (1 + sT/0.5 + s^2*T^2 )
Giving the highpass function
Hh(s) = s^2*T^2 / (1 + sT/0.5 + s^2*T^2 )
And the lowpass function
Hl(s) = (1 + 2*sT) / (1 + sT/0.5 + s^2*T^2 )
As one can see the lowpass section is actually the sum of a 2nd order bandpass and a 2nd order lowpass. That’s where the 1st order slope and the hump of the lowpass come from. Another method to generate this transfer function is to multiply a 2nd order lowpass with the sum of unitiy gain and the output of a differentiator. It is the latter that we are going to do.
Enclosed you see the simulated responses of the topology we are going to approximate. It is shown for a highpass pole-frequency of 100 Hz.
More to come !!
What I basically did is the electroacoustical approximation of the responses of the two branches of an asymmetrical subtractive crossover with a 2nd order highpass and a 1st order lowpass. Higher orders are theoretically possible but they don’t have advantages only.
The basic linear transfer function of a transient perfect crossover of the order N has the same numerator and denominator. That is actually the source of the infamous humps of subtractive crossovers. They don’t have the same cause as the humps of a transfer function with high Q-values – as it is often misunderstood.
But these humps are responsible for increased power needs, flat slopes around the crossover frequency (for very high orders they tend to get shallower than 6dB/octave !) and lobing.
So the lower the order, the less one runs into these problems. It is theoretically possible to cross any driver combination with such crossovers of arbitrary order - but doing it with a midwoofer/tweeter combination is not for the faint - hearted.
One of the most suitable topologies is therefore the fullrange (or wideband) + woofer topology because of 3 reasons:
1.) The wavelength at the crossover frequency is quite large relative to the physical dimensions involved (-> lobing !).
2.) The “tweeters” involved are more forgiving in terms of shallow crossover slopes.
3.) People using wideband/fullrange drivers often care more about transient accuracy than the “multiway fraction”.
So I thought it was a natural to post it here in the fullrange forum.
It is possible to do more accurate approximations than the one presented here but they would tend to be more complicated and need more accurate driver modelling. But everyone is free to do so. Since the circuit is quite simple it can easily be tried out on a breadboard if one has a second amp to use.
What we do to begin with is taking the response of the aforementioned subtractive crossover. As highpass function we take a 2nd order filter with a Q of 0.5. The actual crossover frequency wouldn’t be the pole frequency (where there is already a 6 dB drop compared to 3 dB for the Butterworth case) but about one octave higher. Both drivers are down by about two dB at the crossover frequency. For higher-order filters the relative level at the crossover point might be higher than 1 - just to mention one of the disadvantages of higher order subtractive crossovers.
So the original transfer function we are going to use will be:
H(s) = (1 + sT/0.5 + s^2*T^2) / (1 + sT/0.5 + s^2*T^2 )
This is then split into two parts:
H(s) = (1 + sT/0.5 ) / (1 + sT/0.5 + s^2*T^2 ) + s^2*T^2 / (1 + sT/0.5 + s^2*T^2 )
Giving the highpass function
Hh(s) = s^2*T^2 / (1 + sT/0.5 + s^2*T^2 )
And the lowpass function
Hl(s) = (1 + 2*sT) / (1 + sT/0.5 + s^2*T^2 )
As one can see the lowpass section is actually the sum of a 2nd order bandpass and a 2nd order lowpass. That’s where the 1st order slope and the hump of the lowpass come from. Another method to generate this transfer function is to multiply a 2nd order lowpass with the sum of unitiy gain and the output of a differentiator. It is the latter that we are going to do.
Enclosed you see the simulated responses of the topology we are going to approximate. It is shown for a highpass pole-frequency of 100 Hz.
More to come !!
Attachments
The drivers one is going to use should be reasonably well behaved within their passband. Irregularities and baffle-step should be EQed out. This is shown as EQw and EQf. The woofer should at least be usable up to about 5 to 10 times the crossover frequency.
The 2nd order highpass function for the fullrange is achieved by simply using an LTF in order to push the pole-frequency upwards to the pole-frequency fx and achieve a Qtc of 0.5.
There are two problems that remain: 1) There is not much protection at the low end (though still a big improvement over real fullrange usage) and 2.) the phase-shift of the woofer can play havoc with proper SPL summation.
A simple and effective means for 2.) is the use of a highpass filter Hw in the fullrange branch that mimics the low-end response of the woofer and that also intrinsically improves 1.). For a closed box this would be a 2nd order highpass and for a reflex box a 4th order highpass respectively.
Though I am not sure if one wants to use a reflex box for a “transient-perfect” loudspeaker !
A little more complicated is the situation for the woofer.
As already mentioned we can achieve the required lowpass transfer function with a 2nd order lowpass, a summing stage and a differentiator.
But when doing this we have to take the woofer’s upper frequency limit Fu into consideration. We do therefore truncate the lowpass function at the upper frequency limit of the woofer by the use of the two resistors Rsl. This is of course only an approximation but it is better than doing nothing at all. The best thing would be to use a dual gang pot for these when experimenting. It can then be replaced by fixed resistors later on. Also R can be substituted by a dual gang pot during fine-tuning of the circuit.
The differentiator function does have to be truncated as well - otherwise we run the risk that this crossover branch has very high gain at high frequencies. This is done at a frequency between 10 and 30 times the crossover frequency by the use of Rsd (and therefore chose Rsd 10 to 30 times smaller than R).
The other reason not to try to achieve 1st order behaviour of the woofer/xover combination up to infinity: The fullrange driver’s response starts to fall off at a finite frequency and we would not want the woofer to try to compete with the HF response of the fullrange !!!
The differentiator’s feedback path can be used for gain setting with R1 and/or baffle step correction if needed.
The circuit presented may not give the flattest possible response (and the formulae are only coarse approximations) but it is one of the cheapest entry tickets to the world of transient-perfect loudspeakers.
Enclosed you’ll see the block diagram:
The 2nd order highpass function for the fullrange is achieved by simply using an LTF in order to push the pole-frequency upwards to the pole-frequency fx and achieve a Qtc of 0.5.
There are two problems that remain: 1) There is not much protection at the low end (though still a big improvement over real fullrange usage) and 2.) the phase-shift of the woofer can play havoc with proper SPL summation.
A simple and effective means for 2.) is the use of a highpass filter Hw in the fullrange branch that mimics the low-end response of the woofer and that also intrinsically improves 1.). For a closed box this would be a 2nd order highpass and for a reflex box a 4th order highpass respectively.
Though I am not sure if one wants to use a reflex box for a “transient-perfect” loudspeaker !
A little more complicated is the situation for the woofer.
As already mentioned we can achieve the required lowpass transfer function with a 2nd order lowpass, a summing stage and a differentiator.
But when doing this we have to take the woofer’s upper frequency limit Fu into consideration. We do therefore truncate the lowpass function at the upper frequency limit of the woofer by the use of the two resistors Rsl. This is of course only an approximation but it is better than doing nothing at all. The best thing would be to use a dual gang pot for these when experimenting. It can then be replaced by fixed resistors later on. Also R can be substituted by a dual gang pot during fine-tuning of the circuit.
The differentiator function does have to be truncated as well - otherwise we run the risk that this crossover branch has very high gain at high frequencies. This is done at a frequency between 10 and 30 times the crossover frequency by the use of Rsd (and therefore chose Rsd 10 to 30 times smaller than R).
The other reason not to try to achieve 1st order behaviour of the woofer/xover combination up to infinity: The fullrange driver’s response starts to fall off at a finite frequency and we would not want the woofer to try to compete with the HF response of the fullrange !!!
The differentiator’s feedback path can be used for gain setting with R1 and/or baffle step correction if needed.
The circuit presented may not give the flattest possible response (and the formulae are only coarse approximations) but it is one of the cheapest entry tickets to the world of transient-perfect loudspeakers.
Enclosed you’ll see the block diagram:
Attachments
Hi Hartono
No it isn't - it is most likely by John Kreskovsky. I don't have this article but I assume it is dealing with this:
http://www.geocities.com/kreskovs/CrossoverdocN.html
regards
Charles
No it isn't - it is most likely by John Kreskovsky. I don't have this article but I assume it is dealing with this:
http://www.geocities.com/kreskovs/CrossoverdocN.html
regards
Charles
Forgot to mention - here ist the measured step response of my Manger/Audiotechnology combination using this x-over toplology:
http://www.diyaudio.com/forums/showthread.php?postid=1139711#post1139711
And here is the QUAD ESL 63 for comparison:
http://stereophile.com/floorloudspeakers/416/index11.html
Regards
Charles
http://www.diyaudio.com/forums/showthread.php?postid=1139711#post1139711
And here is the QUAD ESL 63 for comparison:
http://stereophile.com/floorloudspeakers/416/index11.html
Regards
Charles
Hartono said:
It may have been my "phase coherent crossovers", which you
can dowload from www.passlabs.com/np under the name "pcxvr"
which are tiff images of the Audio Amateur pages.
Funny you should mention this as I've been working with them
lately with Lowther drivers and woofers with good results
ps you will note from the 1982 vintage, there were no AP
systems or computer graphics - all those curves were generated
and drawn by hand.
Hi Mr. Pass,
Your article seems to predate the AudioXpress article! the bottom of the page indicate SpeakerBuilder. Thanks for the information.
"all those curves were generated
and drawn by hand"
you must be very good at mathematics !!!
ps: on the last page there's classified advertising, 1 word cost 25 cents.......interesting, wonder how much it cost today on AX.
Hartono
Your article seems to predate the AudioXpress article! the bottom of the page indicate SpeakerBuilder. Thanks for the information.
"all those curves were generated
and drawn by hand"
you must be very good at mathematics !!!
ps: on the last page there's classified advertising, 1 word cost 25 cents.......interesting, wonder how much it cost today on AX.
Hartono
I have noticed that an increasing number of people are now building FAST systems using one of the readily available DSP xover platforms. Some of these folks might be interested in a crossover topology offering improved transient response.
While it is of course possible to build almost any kind of "wild" xover topology with most DSPs, things don't look as easy if one wants to use the convenient SW tools that come with many of these DSP modules. These usually don't allow the use of subtraction and each way has to be configured as a "straight chain of filters".
The transfer functions of asymmetrical 2nd/1st and symmetrical 2nd/2nd order subtractive crossovers can still be modelled using these tools however.
Within the following few posts I will show how this could be achieved.
There is no free lunch however. The quite shallow slopes are one of the downsides, the other one is the lobing behaviour. The latter can be eased up a little by using close driver spacing or D'Appolito arrangements.
Regards
Charles
While it is of course possible to build almost any kind of "wild" xover topology with most DSPs, things don't look as easy if one wants to use the convenient SW tools that come with many of these DSP modules. These usually don't allow the use of subtraction and each way has to be configured as a "straight chain of filters".
The transfer functions of asymmetrical 2nd/1st and symmetrical 2nd/2nd order subtractive crossovers can still be modelled using these tools however.
Within the following few posts I will show how this could be achieved.
There is no free lunch however. The quite shallow slopes are one of the downsides, the other one is the lobing behaviour. The latter can be eased up a little by using close driver spacing or D'Appolito arrangements.
Regards
Charles
There are two problems that remain: 1) There is not much protection at the low end (though still a big improvement over real fullrange usage) and 2.) the phase-shift of the woofer can play havoc with proper SPL summation.
A simple and effective means for 2.) is the use of a highpass filter Hw in the fullrange branch that mimics the low-end response of the woofer and that also intrinsically improves 1.). For a closed box this would be a 2nd order highpass and for a reflex box a 4th order highpass respectively.
Though I am not sure if one wants to use a reflex box for a “transient-perfect” loudspeaker !
Hi,
I fail to see how adding to the high bass roll-off of the fullrange
with additional high pass filters would help, surely the phase
shifts would be made worse.
No wait a minute, perhaps your really do mean the woofers alignment
being applied to the FR, but that runs into the rather serious problem
of the FR's own bass alignment well before you get to the woofers.
You would need to LT the FR to the woofers alignment, and
that is no recipe for improving its protection at the low end.
I guess it depends on the two drivers in the FAST and the
x/o frequency, but it doesn't strike me as a general way
of doing things for all combinations of FAST drivers.
rgds, sreten.
You don't LT the FR to the woofer's alignment. You LT the FR to the desired acoustical highpass slipe that you want to target. You then add another highpass filter to the FR in order to add the same phase-shift as the woofer to to the FRs (out of band) response and at the same you increase protection at those frequencies.
In some cases you might simply use the FRs natural rolloff as acoustical crossover, sometimes you would need a parametricc EQ for lowering the Qtc to 0.5. Each case has to be looked at separately. And there are cases where it simply wouldn't work.
Regards
Charles
In some cases you might simply use the FRs natural rolloff as acoustical crossover, sometimes you would need a parametricc EQ for lowering the Qtc to 0.5. Each case has to be looked at separately. And there are cases where it simply wouldn't work.
Regards
Charles
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In the schematics you can see how the baffle-step correction can be included in the feedback path of the woofer xover. For the FR this has to be added in one of the known fashions. And yes - it will further take something away from the steepnes of the achievable highpass but that's how life is. With the FR driver (Manger) that I used I could do without BS correction on the FR because it has a rising response towards the lower end which can be abused for BSC.
If a third-order highpass function was called for I can do the maths as well but be aware that this would mean some more overlap in the XOVER area.
Regards
Charles
If a third-order highpass function was called for I can do the maths as well but be aware that this would mean some more overlap in the XOVER area.
Regards
Charles
I will have to re-read the "old part" because it wasn't meant that way but maybe I was unclear with what I wrote.
What I basically did was "building" a 2nd order highpass using EQing of the FRs natural low-end response as the highpass part of the crossover. It is clear that this works much better if the EQed response has a higher cutoff frequency than the natural response of the FR than vice-versa.
The next step was to build a transfer function that approximates the lowpass function of the subtractive crossover and at the same time taking into consideration the woofer's non-idealities at its upper end to some degree.
The third step was to add the woofer's phase response to the FR by the use of a highpass filter. This is admittedly taking place at a frequency range where the FR doesn't contribute to total SPL that much anymore but it would still be contributing in a undesirable fashion du to taking place quite close to the xover frequency. This highpass would not even have to be a very exact replica of the woofer response. And in some cases it might be done by dimensioning some coupling caps accordingly.
Regards
Charles
The thread that you link to is dealing with another beast of crossover than what is dealt with here.
Here we are dealing with the classic constant-voltage crossovers that don't use any form of subtractive delay simply because of two reasons: They can't be built easily using analog methods (although I know at least one practical example which is a "mass grave" of allpass filters) or digitally using these DSP crossovers that are configured by the use of a convenient but restricted GUI.
Last year I was playing around with a crossover that is an approximation of a subtractive-delay crossover which is generating the highpass without subtraction and therefore needs less component accuracy while always guaranteeing a 3rd order rolloff in the stopband. The way I did this guarantees flat group dealy only until about one octave above the crossover frequency. But total group delay is smaller than LR2 or LR4 and both drivers are connected in the same polarity. If flat group delay is desired up to higher frequencies then this could be achieved with an allpass based group-delay EQ. But this would only make sense for the usual mid/tweeter crossover frequencies. Otherwise the EQ would be too long for practical purposes.
The xovers shown here are useful for orders up to three IMO. That would allow 2nd/1st, 3rd/1st and 2nd/2nd. Otherwise overlap etc would become too large.
Edit: Forgot to get into the crossover order discussion. I am totally aware that a second order acoustical rolloff doesn't exactly mean perfect driver protection. But a speaker built this way would still offer more protection for an FR than running it full-range without crossover - let alone the much increased LF capabilities of a FAST compared to a FR alone.
Regards
Charles
Here we are dealing with the classic constant-voltage crossovers that don't use any form of subtractive delay simply because of two reasons: They can't be built easily using analog methods (although I know at least one practical example which is a "mass grave" of allpass filters) or digitally using these DSP crossovers that are configured by the use of a convenient but restricted GUI.
Last year I was playing around with a crossover that is an approximation of a subtractive-delay crossover which is generating the highpass without subtraction and therefore needs less component accuracy while always guaranteeing a 3rd order rolloff in the stopband. The way I did this guarantees flat group dealy only until about one octave above the crossover frequency. But total group delay is smaller than LR2 or LR4 and both drivers are connected in the same polarity. If flat group delay is desired up to higher frequencies then this could be achieved with an allpass based group-delay EQ. But this would only make sense for the usual mid/tweeter crossover frequencies. Otherwise the EQ would be too long for practical purposes.
The xovers shown here are useful for orders up to three IMO. That would allow 2nd/1st, 3rd/1st and 2nd/2nd. Otherwise overlap etc would become too large.
Edit: Forgot to get into the crossover order discussion. I am totally aware that a second order acoustical rolloff doesn't exactly mean perfect driver protection. But a speaker built this way would still offer more protection for an FR than running it full-range without crossover - let alone the much increased LF capabilities of a FAST compared to a FR alone.
Regards
Charles
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