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Filter theory question for speaker crossovers



 
 
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  #1  
Old May 21st 05, 01:11 AM
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Default Filter theory question for speaker crossovers

Hi All,

Something that I've been thinking about for a while with the design of
speaker crossovers, but don't have the necessary knowledge to calculate
or figure out, is this:

If you were to take, for example, an 18dB/oct Butterworth high pass/low
pass crossover for a two way system, could you synthesize the same
summed electrical response (and therefore the on axis response) in
terms of amplitude and phase response if you were to lower the Q of the
high pass section, and raise the Q of the low pass section from their
standard 0.707, without changing anything else ?

(In practice you would do this by altering the L/C ratio of the
crossovers in opposite directions by a certain factor)

Why would anyone want to do this ? Recently I've come to the slow
realization of what may be one of the big downsides of having a
crossover in the first place, when doing listening/measurements between
a full range driver, and that same full range driver crossed over
normally with a tweeter.

Some classes of high pass and low pass filter have ringing at their
crossover frequency whose phase is opposite to their complementary
filter - so for example a symetrical high pass/low pass filter can have
quite bad ringing at the crossover frequency if you take only one
section on its own, but when the output of the two filters are summed
together (accoustically) the ringing is largely negated.

(My filter theory isn't strong enough here to know WHICH kinds of
filter this applies to so hopefully someone can butt in here and
correct me)

It occurs to me that this cancellation of ringing only occurs on axis,
and that even to the side on the horizontal axis this cancellation
effect will be incomplete due to the different horizontal dispersion of
the large driver vs the small one it is crossing over to.

The end result, particularly if there is a large difference in
dispersion between the two drivers as is often the case, is that the on
axis response may contain very little ringing at the crossover
frequency, and sound fine, but the ambient sound field in a typical
reflective/reverberant room due to the off axis power response of the
speaker near the crossover frequency will be predominately that of the
high pass section, as the smaller driver has the widest dispersion.

With the output from the low pass section unable to balance the output
from the high pass section in these off axis directions, the ringing
will not be canceled.

The ambient sound field may contain undesirable artificats of ringing
and in fact I think I can sometimes hear this characteristic in some of
the tests I've done.

Assuming that making the dispersion of the drivers more similar is not
an option, it occured to me why not make the Q of the high pass section
lower, so that the output of the high pass section which is dominating
the ambient sound field near the crossover frequency is free of
ringing, (or reduced) and then increase the Q (and/or do whatever other
correction is necessary) of the low pass filter to give the same or
nearly the same summed on axis response.

Because the driver connected to the high pass section is bound to have
much wider dispersion, you're not going to have a situation where the
higher Q low pass section is heard on its own - at any angle you can
hear that significantly, the output from the highpass will be audible
too.

Has anyone tried something like this ? Any gaping holes in my idea ?

Regards,
Simon

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  #2  
Old May 21st 05, 07:08 AM
dangling entity
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Default

Wow, that's quite a mouthful! ...but how can we be concerned about
this when we got this "am I going to heaven?" issue to mull over???
Just kidding, ya. I'm looking forward to hear some responses to your
topic, as well.

  #3  
Old May 21st 05, 11:54 AM
Arny Krueger
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Default


> wrote in message
oups.com...
> Hi All,
>
> Something that I've been thinking about for a while with

the design of
> speaker crossovers, but don't have the necessary knowledge

to calculate
> or figure out, is this:
>
> If you were to take, for example, an 18dB/oct Butterworth

high pass/low
> pass crossover for a two way system, could you synthesize

the same
> summed electrical response (and therefore the on axis

response) in
> terms of amplitude and phase response if you were to lower

the Q of the
> high pass section, and raise the Q of the low pass section

from their
> standard 0.707, without changing anything else ?


No. While you can play with Q's to get small areas of the
response curve with similar slopes, over the ranges
required, the basic properties of the filters come to the
forefront.



  #4  
Old May 21st 05, 01:10 PM
Greg Berchin
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On 20 May 2005 17:11:51 -0700, wrote:

>>Has anyone tried something like this ? Any gaping holes in my idea ?


http://www.aes.org/publications/preprints/search.cfm, search for
preprint #5010, from the 107th Convention, in 1999.

Greg Berchin
  #5  
Old May 30th 05, 05:26 AM
[email protected]
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Arny Krueger wrote:
> > wrote in message
> oups.com...
> > Hi All,
> >
> > Something that I've been thinking about for a while with

> the design of
> > speaker crossovers, but don't have the necessary knowledge

> to calculate
> > or figure out, is this:
> >
> > If you were to take, for example, an 18dB/oct Butterworth

> high pass/low
> > pass crossover for a two way system, could you synthesize

> the same
> > summed electrical response (and therefore the on axis

> response) in
> > terms of amplitude and phase response if you were to lower

> the Q of the
> > high pass section, and raise the Q of the low pass section

> from their
> > standard 0.707, without changing anything else ?

>
> No. While you can play with Q's to get small areas of the
> response curve with similar slopes, over the ranges
> required, the basic properties of the filters come to the
> forefront.


I'm not sure that you follow what I'm asking. I'm not asking for the
individual responses of the filters to be the same, as that is
obviously impossible - if they're different, they're different.

What I'm asking is if there is a way to achieve the same summed
response from a different combination of high/low pass filters, where
ONE of the individual sections has a better transient response at the
expense of the other.

My example was to take an 18dB/oct Butterworth, and alter things so
that the high pass section has an improved transient response at the
expense of a worse transient response for the low pass section, but
with the same (or similar) transient response as the original design
for the summed response.

Surely this is not so different from a subtraction based crossover
where one half is a standard filter and the other slope is derived from
a difference signal ? (Although admitedly, that approach is limited to
active designs...)

Any takers ?

Regards,
Simon

  #6  
Old May 30th 05, 05:28 AM
[email protected]
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Hi Greg,

Since those preprints are not free to download, can you tell me in what
way it is relevant to my question ? Or whether it is just vaugely
related.

Regards,
Simon

  #7  
Old May 30th 05, 02:23 PM
Greg Berchin
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On 29 May 2005 21:28:41 -0700, wrote:

>Since those preprints are not free to download, can you tell me in what
>way it is relevant to my question ?


Well, I figured that the title -- "Perfect Reconstruction Digital
Crossover Exhibiting Optimum Time Domain Transient Response in All
Bands" -- would be a good hint.

In your original post, you said:

>could you synthesize the same
>summed electrical response (and therefore the on axis response) in
>terms of amplitude and phase response if you were to lower the Q of the
>high pass section, and raise the Q of the low pass section from their
>standard 0.707, without changing anything else ?


[...]

>Some classes of high pass and low pass filter have ringing at their
>crossover frequency whose phase is opposite to their complementary
>filter


[...]

>It occurs to me that this cancellation of ringing only occurs on axis,


[...]

>With the output from the low pass section unable to balance the output
>from the high pass section in these off axis directions, the ringing
>will not be canceled.


In the AES paper, I address exactly this problem. First, the lowpass
and highpass filters are perfectly complementary -- that is; their
responses sum to unity magnitude and linear phase (pure delay) at all
frequencies. Second, their responses are in-phase at all frequencies,
so there are no off-axis anomalies. Third, ringing is eliminated
because the filter upon which this system is based is Gaussian (or a
Bessel approximation to Gaussian).

>Has anyone tried something like this ? Any gaping holes in my idea ?


Basically, it lends itself only to digital signal processing, because
there are time delays inherent in the technique. Implementing pure
delay in analog electronics is difficult.

Greg Berchin
  #8  
Old May 31st 05, 07:26 AM
[email protected]
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Greg Berchin wrote:
> On 29 May 2005 21:28:41 -0700, wrote:
>
> >Since those preprints are not free to download, can you tell me in what
> >way it is relevant to my question ?

>
> Well, I figured that the title -- "Perfect Reconstruction Digital
> Crossover Exhibiting Optimum Time Domain Transient Response in All
> Bands" -- would be a good hint.


Hi Greg,

My apologies, I didn't realise that YOU were the author of the paper
you were refering to ;-) Somehow I didn't connect 2 and 2
together...thanks for your email, I'll give the article a good read.

>
> In your original post, you said:
>
> >could you synthesize the same
> >summed electrical response (and therefore the on axis response) in
> >terms of amplitude and phase response if you were to lower the Q of the
> >high pass section, and raise the Q of the low pass section from their
> >standard 0.707, without changing anything else ?

>
> [...]
>
> >Some classes of high pass and low pass filter have ringing at their
> >crossover frequency whose phase is opposite to their complementary
> >filter

>
> [...]
>
> >It occurs to me that this cancellation of ringing only occurs on axis,

>
> [...]
>
> >With the output from the low pass section unable to balance the output
> >from the high pass section in these off axis directions, the ringing
> >will not be canceled.

>
> In the AES paper, I address exactly this problem. First, the lowpass
> and highpass filters are perfectly complementary -- that is; their
> responses sum to unity magnitude and linear phase (pure delay) at all
> frequencies. Second, their responses are in-phase at all frequencies,
> so there are no off-axis anomalies. Third, ringing is eliminated
> because the filter upon which this system is based is Gaussian (or a
> Bessel approximation to Gaussian).


I don't see how being in phase at all frequencies could eliminate
off-axis anomolies ? Surely going off axis vertically will introduce a
time delay that will cause problems no matter what type of filtering
you use. Or are you only refering to the effects of horizontal off axis
response where the drivers are still equidistant from the listener, but
the narrower dispersion of the larger driver causes an additional
change in the response that causes incomplete summing of the response.
(Which is what my original post was about)

(Note: I havn't read your article yet)

>
> >Has anyone tried something like this ? Any gaping holes in my idea ?

>
> Basically, it lends itself only to digital signal processing, because
> there are time delays inherent in the technique. Implementing pure
> delay in analog electronics is difficult.


Yes I kind of suspected that at the very least it could only be
implemented using an active filter, or possibly even only a digital
filter.

Regards,
Simon

  #9  
Old May 31st 05, 02:03 PM
Greg Berchin
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On 30 May 2005 23:26:36 -0700, wrote:

>I don't see how being in phase at all frequencies could eliminate
>off-axis anomolies ? Surely going off axis vertically will introduce a
>time delay that will cause problems no matter what type of filtering
>you use. Or are you only refering to the effects of horizontal off axis
>response where the drivers are still equidistant from the listener, but
>the narrower dispersion of the larger driver causes an additional
>change in the response that causes incomplete summing of the response.


Consider the "ideal" (but impractical) case, in which the woofer driver
and the tweeter driver have identical characteristics. If the crossover
is in-phase at all frequencies, then as the frequency is increased the
signal will gradually be diverted from the woofer to the tweeter. But
the only difference between the woofer signal and the tweeter signal,
regardless of frequency, will be amplitude. There will be off-axis
cancellation (in the vertical direction if the drivers are stacked; in
the horizontal direction if the drivers are side-by-side), but it will
be predictable and stable.

Now consider the same "ideal" drivers, but with a crossover that puts
the drivers, say, 90 out-of-phase at the crossover frequency.
Depending upon the distance between the drivers, at some locus of
horizontal and vertical angles the drivers will be perfectly in-phase,
resulting in an increase in output at that frequency and those
directions. Similarly, at some other locus of horizontal and vertical
angles the drivers will be 180 out-of-phase, resulting in no output at
all at that frequency and those directions. Furthermore, the crossover
that puts the drivers 90 out-of-phase at the crossover frequency likely
also puts them at different relative phase angles at other frequencies,
so the off-axis interference pattern varies not only with direction, but
with frequency.

To make matters even worse, as you mentioned, the off-axis
characteristics of the woofer and tweeter are never the same. So the
"ideal" situation described above, as bad as it is, is never even
achieved because the off-axis driver responses never sum or cancel
perfectly. In one's living room this may be a minor annoyance. In a
theater or an auditorium or a stadium it is a real problem. In
practical terms, the way to minimize (but not eliminate) the problem is
to ensure that the drivers are in-phase at all frequencies.

Greg
 




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