Active Subtractive XOs

Active Subtractive XOs

Moderater's note: 23-aug-02 This thread is the result of splitting off the subtractive XO posts from a previous thread on a Jordan speaker. It was getting a bit OT from the original thread but was good stuff.

dave (with my moderator hat on)

The whole concept of active subtractive XOs i find very interesting so hopefully this will give the subject a little more visibility.

dave (with just my regular diyAudio cap on)

phase_accurate said:
I intend on using a subtractive crossover consisting of a 2nd order lowpass and a derived 1st order higpass with a Manger broadband driver and an Audio Technology woofer.

I used one of these (based on the old colony boards) in the latter half of the '80s with a set of Quads & a single sub.

I am trying to figure out how to do the same thing with tubes... have some ideas -- need to try them out.

Janneman wrote:
The examples you guys are talking about are passive ones, right?

No, I was trying to convince you to stay active.:)

Even though you were using a passive crossover in front of your amps the final outcome is almost the same (i.e. it has some slight advantages and disadvantages compared to an active filter) as if you had used an active filter.

IMO the main reason (beneath others) why many people prefer single-driver solutions is the high transient accuracy when there is no crossover introducing time-smear.

There are only a few options to implement crossovers that are amplitude and phase accurate ;) :) :cool: .
One of them is the subtractive active filter as described on the Passlabs page.

If you want to go the passive way and stay transient perfect then there are two solutions: either first order (parallel or series) or second order with overlap and equalizing. Discussions on all of these you will find on John Kreskovky's Homepage:


What was your experience with the subtractive crossover ? :) or :( ?
What kind of subtractive crossover do you want to implement with tubes (i.e. which path do you want to make higher order and which one derived 1st order), maybe I can do some brainstorming as well ?


phase_accurate said:

What was your experience with the subtractive crossover ? :) or :( ?
What kind of subtractive crossover do you want to implement with tubes (i.e. which path do you want to make higher order and which one derived 1st order), maybe I can do some brainstorming as well ?

My recollections are positive. It wasn't what you would call a hi-resolution system used in a business environment (Nak Casette, NAD 7020, subtractive XO, ILP module w Tangent PS into a single sealed 12", XO back into 7020 to drive Quad 57s hanging upside down from the ceiling)

At this point both my applications need the 2nd order on the Low Pass.


I've done a little thinking and came to the circuit you will see attached below.

Since I was way too lazy to look for an appropriate model of a triode, I used JFETs for the simulation, since this was the closest thing to a triode that was on hand. It wouldn't be that difficult to adapt it for tubes. Depending upon it's use some input and/or output buffer stages will be necessary.

Whoever tries to implement it in real life has to pay attention to the DC-path between ground and input (i.e. gate/grid). I omitted this in my simulation circuit simply because it is intrinsic to the signal source I used for the simulation. Also the values of resistors # 1, 2, 12 and 13 are a little lower than optimal for maximum headroom.

The lowpass hasn't got any positive feedback, giving a Q of 0.5 approx. This can of course be changed easily.

The lowpass output can be taken from C11 (R19 represents the input impedance of the next stage).

At C10 (which has to be reasonably large !!) the inverted version of the lowpass filtered input signal is taken off and added to the input signal via the two summing resistors R17 and R18. At their summing junction the derived highpass signal is available, although damped by 6dB approx.
If everything were ideal then R17 and R18 would be of same value. But the signal level at J1's drain was a little lower than at it's source so I lowered R17's value a bit. Maybe R17 should be made at least partially adjustable anyway.

At C12 the highpass output can be taken off. The stage around J2 has a gain of 6 dB approx and is delivering an INVERTED output signal (which is still a little low by the fraction of a dB).

The DC Blocking capacitor C10 can be moved to another leg of the summing network, depending on how the DC path at the input is made (from the optimal-signal-summing point of view it's best place would be after the summing point but then the DC current flow through R17 and R18 has to be taken into account ! And don't forget another resistor from gate of J2 to ground when doing this!).

Although this little circuit may not be perfect it is at least a usable starting point.




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Hi Janneman

Although there is a hump in the derived branch of a subtractive crossover the combined response doesn't have a hump. Additionally this hump does NOT come from any form of resonance as would be expected from the first glimpse.
The combined response is both flat in terms of amplitude AND phase !!!
It will of course not be that perfect anymore as soon as drivers are connected to it (with amplifiers in between of course, but their error is marginal compared to the drivers).
The drivers should also be positioned reasonably close.

Most of this is mentioned in the article on the passlabs website.



This is good to chew on -- you have gotten the thing simplier than my sketches to date, but it is quite similar. I like that there is only one follower (getting a cathode follower to sound good takes some care).

As the order of the filtered stage goes up, the bump in the bottom of the derived 1st order filter gets larger -- hence the recommend to restrict them to 2nd & 3rd order.

The addition of an all pass filter in front of the derived part can be used to get higher orders -- and the derived filter becomes the same order as the reference filter.

Jordan stuff


Not wanting to nag, but when I review the pass article, I notice that at the xover both legs of the subtractive xover are 3dB down, for a flat summed curve.
I have trouble correlating that to the two curves (lin and log) that you published, where at xover the sum seems quite a lot larger than in the two passbands. Maybe it is just a matter of axis units or scaling?

Jan Didden
Hi Jan

If you have a look at Nelson Pass' drawings you might see that the two signals are down by different amounts on different drawings.
I assume that this is mainly due to the accuracy of the drawings. I think the most exact ones are those where both branches are down by 2 dBs approx at the crossover point. Thats's what you would see on my simulations as well.
As already mentioned the highpass output is approx half a dB too low. But I didn't want to tweak around too much since levels must be made adjustable anyway to get the whole thing flat in the end.

But for curiosity I increased R13 to the uncomfortable value of 2.36 kOhms in order to get a more accurate gain setting.

Enclosed you will see the results. Again I stored a linear and a log version. The green one is the lowpass output after C11, the red one is the derived output at C12 and the blue one is the summed curve (to be more exact it is the lowpass-signal minus the highpass signal; since the stage around J2 is inverting the phase I had to invert it again before summing it which is the same as to subtract one from the other).

Enclosed is also a simulation of the circuit's response to a rectangular signal.
Again the colors are green for lowpass, red for highpass and blue for summed response. The tilt on the output is due to the highpass function introduced by the coupling capacitors C11 and 12 (wouldn't be necessary when using OP-AMPs).
For those who are not embarrassed to use OP-amps* I would stongly recommend to do so when building subtractive crossovers anyway.
The main point is that you can make use of one of the most interesting properties of these crossovers to full advantage:
As soon as all gain requirements are fullfilled the summed output of these filters will always be flat, regardless of capacitor tolerances. The only thing that has to be quite accurate are the values of the resistors setting the gain and these can be obtained with sufficient tolerances (1%) without any problem.



* I very kindly apologize for sometimes using the words OP-AMP, FEEDBACK and the like :eek: ;)


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Jordan etc

hi phase_accurate,

Well, if I look at your second set of lin curves, I note that the hi- and low-pass at xover are each about 60mV in amplitude, yet the summed response shows flat at about 76mV. I think the crux is in looking at the phase response. Two signals each 60mV can only be summed to 76mV if there is an (appreciable) phase difference between the two. In-phase they would sum to 120mV, fully out-of phase they would sum to 0mV. A quick calculation shows that for the given numbers, the phase difference between the two signals at xover would be around 100 degrees. Do your simulations confirm that?

Jan Didden
Originally posted by phase_accurate in the Intro Forum
It will use a subtractive crossover (called analog computer crossover by John, like the ones introduced on Nelson Pass' homepage, in order to achieve perfect transient AND amplitude response. Although I will use a very standard asymmetric subtractive crossover (3rd order lowpass/1st order highpass) I did some thinking and came to conclusions how symmetrical subtractive crossovers could be made or very simple three-way ones. If at least more than just three persons are interested, then I will of course supply more details on this subject.

I'd be interested in your scheme for a symmetrical subtractive XO. There is a paper in the AES journals (i'll have to dig the paper out to say who by) that adds an allpass filter in front of the derived side of the filter to achieve symmetry.

Hi Dave

I will search for the P-SPICE schematic I once sent to John Kreskovsky. He answered that he had already senn such a proposal somewhere else but but couldn't remember where exactly.
The response of the filter is looking a little similar to John's suggestion using 2nd order filters with overlap and equalisation (I don't remember who - but it is most probably an Australian member of this forum - is selling a crossover design program that supports John's kind of X-over).
My suggestion is using two cascaded subtractive crossovers to achieve the same thing with less capacitors. Additionally it is less susceptible to capacitor tolerances because whatever you do their outputs will always sum flat (assumed that the gains are exact which isn't that hard to achieve if you are not ashamed of using OP-AMPs).

I will post the diagram as soon as I have found it, together with a different solution doing the same.

There are some higher order subtractive filters using an additional allpass. These sum flat as well (in terms of amplitude response) but with the disadvantage that the phase response is as bad as with any ordinary higher order crossovers. I have some literature on these as well and will post info on them as soon as I have time to do so (a famous one is the subtractive LR-4 implementation by Malcolm Hawksford, AES Preprint 2468, or even Elrad 8/95 for those from the German speaking part of the world).
There was also a variant in an audio special issue of Elektor using 2nd order Bessel sections and allpass filters.


O.K. here it is:

For the simulation I used voltage controlled voltage sources and summers and subtractors instead of OP-AMPs or whatever. I think it is not that difficult to imagine how this would be implemented using OP-AMPs. If anybody is having difficulties, let me know then I will redraw it with OP-AMPs.

Enclosed are also simulation results. Highpass in green, lowpass in red and summed response in blue. One can see that the output signals sum flat in amplitude AND phase, therefore also the summed squarewave response is again a squarewave !!!!!
In the transition region they are by approx 90 degrees apart and there is a hump on both outputs, there is also some overlap. Keep in mind that this humps have nothing to do with resonant behaviour (or the sqarewave response would not be as it is). The height and width of the humps can be altered by moving the cutoff-frequencies of the two sub-filters (move apart or overlap).

There is also a possibility for using 3rd order subtractive subfilters giving asymmetric 2nd/3rd order crossovers. While the advantages stay the same the overlap and height of the humps will increase which make them less interesting than the 2nd/2nd order version.




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Transient perfect filters:

The subtractive crossovers discussed in this thread are one of a few possible solutions to filters that give a flat phase- AND amplitude- response. The solutions known to me are the following, with their advantages and disadvantages listed:

1.) First order crossover (passive and active):

A: The least complex solution (at least the filter itself, impedance compensation for passive crossovers are a different story).
D: slopes only 6dB/octave, signals not in phase in crossover region

2.) Second order with overlap and EQ (active-active and passive-active):

A: slopes are 12dB/octave
D: overlap and humps plus signals not in phase in crossover region

3.) “Classic” subtractive crossovers (active)
These are the ones discussed at the beginning of the thread

A: Simple construction, high immunity to capacitor tolerances
D: same as with 2.) but additionally the disadvantage of one branch only having a slope of 6dB/octave

4.) Cascaded subtractive and “advanced filler driver” * (active)
The first one has been discussed in my last post

A: same as with 2.) but additionally higher immunity to capacitor tolerances AND decreased complexity.
D: same as with 2.)

5.) FIR filters (active)
Although there were some attempts to implement FIR filters using allpass sections, in order to work properly, these have to be implemented digitally.

A: These have by far the greatest versatility of all these transient perfect solutions and have steep slopes.
B: Needs DSP skills to design, quite high circuit complexity, in case of analog inputs there will be an additional signal-degrading A/D conversion, in SOME applications the large delay inherent to low crossover frequencies may be a problem.

I stepped into these kind of filters because I was 1.) looking for a solution to properly integrate a woofer and an MSW and 2.) was reading James Watkinson’s series of articles in “Electronics World & Wireless World”. I will most probably use the subtractive topology giving 2nd order lowpass and 1st order highpass response.
Because the wavelength at the crossover frequency (200-250Hz region) is quite large compared to the driver sizes, the phase issue doesn’t matter that much IMO.
I think a small wideband driver that has to be supported at the low end is the most reasonable application for this kind of crossover due to the driver-size/crossover-wavelength ratio. It doesn’t have to be a pricey driver like the MSW at all. Using such a topology the advantages of a small wideband driver can be ex-ploited to the maximum extent (point source character, phase/pulse response) while achieving a good LF response.

In my opinion ANY deviation from the original signal is detrimental to the sound, so we do not only have to maintain low nonlinear distortion and flat amplitude response, we also have to reproduce the wave-SHAPE as accurately as possible.

I am by no means fanatic about that because I know that such sytems also have limitations (mainly in terms of IMD and dynamics). Apart from that these crossover topologies don’t use the amps output power as well as crossovers do whose outputs are in phase in the crossover region (to be correct: they are of course OUT of phase by 360 degrees !!).
If, for instance, I were to design a horn system for reasons of clean and loud reproduction I would go for the crossover topology that exploits this attributes to the maximum extent possible, i.e a higher-order crossover.

* I still have to prepare some drawings to show what I mean by “advanced filler driver”, how it was derived and what can be done with it. So please be patient.


phase_accurate said:

I intend on using a subtractive crossover consisting of a 2nd order lowpass and a derived 1st order higpass with a Manger broadband driver and an Audio Technology woofer.

It could be woth a try since it is not very complicated and it is transient perfect.

Hi Charles,

I've been pondering designing something (active) with the MSW. Do you have the information package by Manger? It is quite informative on the driver itself and on passive designs.

They always use a first order high pass for the MSW and a third order low pass for the woofer. Do you have any idea why? Does the MSW have a mechanical second order high pass function so that the slopes do match?

They state that the MSW is a bending wave driver above 150 Hz and becomes more and more like a conventional driver below.
I've been wondering whether it makes sense to use a steeper low pass. This would limit the LF piston movement and hence lower IMD (FM) Doppler distortion.

They also recommend to have the electrical low pass filter frequency at 350 Hz because this compensates for the increase in sensitivity observed below (looking at their plots of the unfiltered driver, probably in a very large baffle, there LF increase begins at 250 Hz and reaches 5 dB at 160 Hz). The net acoustical transfer frequency would then be 170 Hz they claim. If this is true, it kind of defeats you approach of using a subtractive crossover, doesn't it?