# x-over impedence question

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Anonymous

Apologies if there is an FAQ site that covers this....

My question is in regards to xover calculations and the fact they are
based on the nominal impedence of the driver.

Where available, is it more appropriate to use the actual impedence
of the driver at the x-over point, rather than the nominal impedence?

A simple example:
Driver: Vifa P17-00-08
x-over: 6db Butterworth at 4kHz

Calc using the nominal impedence (8 ohms) => 0.318 mH
Calc using actual impedence at 4kHz (~16 ohms) => 0.637 mH

....and of course similar differences occur with higher order x-overs.

Cheers
Nick

Anonymous

ozNick wrote:
> Apologies if there is an FAQ site that covers this....
>
> My question is in regards to xover calculations and the fact they are
> based on the nominal impedence of the driver.
>
> Where available, is it more appropriate to use the actual impedence
> of the driver at the x-over point, rather than the nominal impedence?
>
> A simple example:
> Driver: Vifa P17-00-08
> x-over: 6db Butterworth at 4kHz
>
> Calc using the nominal impedence (8 ohms) => 0.318 mH
> Calc using actual impedence at 4kHz (~16 ohms) => 0.637 mH
>
> ...and of course similar differences occur with higher order x-overs.

The problem is not that the impedance at the crossover point is not
the same as the nominal impedance, that's an easy problem to solve.
The problem is that the impedance at the crossover point is not
RESISTIVE. A first order network cannot be made to work properly at
all into a typical driver load, no matter what impedance value you
assume.

To illustrate, a first order low-pass network using a series
inductor works because the relative impedance of the series
inductor increases as a first order function of frequency,
while that of the assumed resistive speaker impedance is constant
with frequency. But the driver presents an impedance which is
also a function of frequency, though a more complex function
that that of an inductor. The result is that it is impossible
to obtain the desired first order response out of such a network.

That's the entire point of conjugate impedance matching networks,
or so-called "zobels." They provide an impedance which is the
complex conjugate of the driver impedance over a sufficiently wide
range of frequencies that the result is a resistive impedance,
one which is reasonably independent of frequency. Once that's
accomplished, normal passive networks can be made to work fine.
Anonymous

Arny Krueger wrote:
> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
> news:xxppsy1f4k0.fsf@usrts005.corpusers.net
> > dpierce@cartchunk.org writes:
> >> [...]
> >> That's the entire point of conjugate impedance matching networks,
> >> or so-called "zobels." They provide an impedance which is the
> >> complex conjugate of the driver impedance over a sufficiently wide
> >> range of frequencies that the result is a resistive impedance,
> >> one which is reasonably independent of frequency. Once that's
> >> accomplished, normal passive networks can be made to work fine.
> >
> > Dick,
> >
> > It is these tidbits of gold that make me hope you keep on
> > posting to these newsgroups as long as I can read.
>
> The other half of the story is that one can design effective
> crossovers without zobels. You generally end up going to higher
> order filters to get the desired slopes.

Without a working definition "effective crossover," I'd have to
say, no, you cannot.

If, as an example, I want a 2nd order low pass function with
Butterworth or Bessel or such transfer function using passive
ladder filter topology then, no, absolutely not: you can't get
there given the impedance presented by electrodynamic drivers.

> Zobels are conceptually simpler. They also can work.

And, quite specifically, they are the ONLY game in town if what
you want to achieve is a specific class of transfer functions.

> But, they aren't the only way.

Then please show us how one can obtain the same transfer function
of an nth order filter using an n+m order filter. Remember, in
the absence of a working definition of "effective crossover,"
I'm using the definition that it means achieving a specific
transfer function. To the point, can you show that, given the sort
of impedance presented by a typical electrodynamic woofer, that it
is possible to obtain a 1st order low pass, a 2nd or 3rd order
low-pass with Butterworth properties using a higher order filter?
An "effective corssover" just doesn't have a slope of "x", it
has a specific target transfer function.

> As active crossovers become more widely used, Zobel technology
> will largely disappear.

Please, Arny, it's hardly "Zobel technology." The freakin' patent
expired over 60 years ago.
Related resources
Anonymous

dpierce@cartchunk.org writes:
> [...]
> That's the entire point of conjugate impedance matching networks,
> or so-called "zobels." They provide an impedance which is the
> complex conjugate of the driver impedance over a sufficiently wide
> range of frequencies that the result is a resistive impedance,
> one which is reasonably independent of frequency. Once that's
> accomplished, normal passive networks can be made to work fine.

Dick,

It is these tidbits of gold that make me hope you keep on
posting to these newsgroups as long as I can read.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124
Anonymous

"Randy Yates" <randy.yates@sonyericsson.com> wrote in message
news:xxppsy1f4k0.fsf@usrts005.corpusers.net
> dpierce@cartchunk.org writes:
>> [...]
>> That's the entire point of conjugate impedance matching networks,
>> or so-called "zobels." They provide an impedance which is the
>> complex conjugate of the driver impedance over a sufficiently wide
>> range of frequencies that the result is a resistive impedance,
>> one which is reasonably independent of frequency. Once that's
>> accomplished, normal passive networks can be made to work fine.
>
> Dick,
>
> It is these tidbits of gold that make me hope you keep on
> posting to these newsgroups as long as I can read.

The other half of the story is that one can design effective crossovers
without zobels. You generally end up going to higher order filters to get
the desired slopes.

Zobels are conceptually simpler. They also can work. But, they aren't the
only way.

As active crossovers become more widely used, Zobel technology will largely
disappear.
Anonymous

Arny Krueger wrote:
> <dpierce@cartchunk.org> wrote in message
> > Arny Krueger wrote:
> >> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
> >> news:xxppsy1f4k0.fsf@usrts005.corpusers.net
> >>> dpierce@cartchunk.org writes:
> >>>> [...]
> >>>> That's the entire point of conjugate impedance matching
networks,
> >>>> or so-called "zobels." They provide an impedance which is the
> >>>> complex conjugate of the driver impedance over a sufficiently
wide
> >>>> range of frequencies that the result is a resistive impedance,
> >>>> one which is reasonably independent of frequency. Once that's
> >>>> accomplished, normal passive networks can be made to work fine.
> >>>
> >>> Dick,
> >>>
> >>> It is these tidbits of gold that make me hope you keep on
> >>> posting to these newsgroups as long as I can read.
> >>
> >> The other half of the story is that one can design effective
> >> crossovers without zobels. You generally end up going to higher
> >> order filters to get the desired slopes.
>
> > Without a working definition "effective crossover," I'd have to
> > say, no, you cannot.
>
> In the face of intellectual narrowness of this kind, I've got to
retire from
> the discussion.
>
> Dick you've got some kind of hidden agenda going here - one where
some
> things that route signals among drivers based on frequency are
crossovers,
> and for reasons you've gratuitously added after I made my statement,
others
> aren't.

Your interpretation of my words is, to say the least, bizzarre.

> IOW, you seem to be claiming that unless signals are routed in
> accordance with a narrow list of rules that may be known only to you,
one
> doesn't have an effective crossover.

Bullshit, in a word.

I asked a simple question: if a particular transfer function is
required, one example OF MANY being a 2nd order butterworth low pass,
you simply CANNOT get there using passive filters and a non-resistive
filter termination.

You countered that an "effective crossover" can be constructed using
higher order networks to achieve the same slope. Talk about narrow-
mindeness, my friend: a crossover is NOT solely constrained nor
fully described by its slope. I am sure you know that, yes?

Again, can you show that any given transfer function that can be
can be achieved by a higher order crossover into a non-resistive
termination. That is the crux of the discussion, it seems. Let's
not talk about "effective crossover" or other such ill-defined
terms. Let's keep everything very simple: I'll provide you with
a transfer function for a resistive terminated filter, and your
job is to come up with a higher order filter that has the same
transfer function into a non-resistive termination that typifies
the sort of impedance found in electrodynamic loudspeakers.
SAME TRANSFER FUNCTION. Pick ANY transfer function you want,
ANY transfer function that is implementable with a passive filter
topology. Not some "secret" function that you erroneously accuse
me of keeping hidden from you, ANY TRAFSRE FUNCTION AT ALL.

The sole requirement is for you to show that you can achieve the
same transfer function into a non-resistive termination using
a higher order filter.
Anonymous

<dpierce@cartchunk.org> wrote in message
> Arny Krueger wrote:
>> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
>> news:xxppsy1f4k0.fsf@usrts005.corpusers.net
>>> dpierce@cartchunk.org writes:
>>>> [...]
>>>> That's the entire point of conjugate impedance matching networks,
>>>> or so-called "zobels." They provide an impedance which is the
>>>> complex conjugate of the driver impedance over a sufficiently wide
>>>> range of frequencies that the result is a resistive impedance,
>>>> one which is reasonably independent of frequency. Once that's
>>>> accomplished, normal passive networks can be made to work fine.
>>>
>>> Dick,
>>>
>>> It is these tidbits of gold that make me hope you keep on
>>> posting to these newsgroups as long as I can read.
>>
>> The other half of the story is that one can design effective
>> crossovers without zobels. You generally end up going to higher
>> order filters to get the desired slopes.

> Without a working definition "effective crossover," I'd have to
> say, no, you cannot.

In the face of intellectual narrowness of this kind, I've got to retire from
the discussion.

Dick you've got some kind of hidden agenda going here - one where some
things that route signals among drivers based on frequency are crossovers,
and for reasons you've gratuitously added after I made my statement, others
aren't. IOW, you seem to be claiming that unless signals are routed in
accordance with a narrow list of rules that may be known only to you, one
doesn't have an effective crossover.
Anonymous

<dpierce@cartchunk.org> wrote in message
> Arny Krueger wrote:
>> <dpierce@cartchunk.org> wrote in message
>>> Arny Krueger wrote:
>>>> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
>>>> news:xxppsy1f4k0.fsf@usrts005.corpusers.net
>>>>> dpierce@cartchunk.org writes:
>>>>>> [...]
>>>>>> That's the entire point of conjugate impedance matching networks,
>>>>>> or so-called "zobels." They provide an impedance which is the
>>>>>> complex conjugate of the driver impedance over a sufficiently
>>>>>> wide range of frequencies that the result is a resistive
>>>>>> impedance, one which is reasonably independent of frequency.
>>>>>> Once that's accomplished, normal passive networks can be made to
>>>>>> work fine.
>>>>>
>>>>> Dick,
>>>>>
>>>>> It is these tidbits of gold that make me hope you keep on
>>>>> posting to these newsgroups as long as I can read.
>>>>
>>>> The other half of the story is that one can design effective
>>>> crossovers without zobels. You generally end up going to higher
>>>> order filters to get the desired slopes.
>>
>>> Without a working definition "effective crossover," I'd have to
>>> say, no, you cannot.
>>
>> In the face of intellectual narrowness of this kind, I've got to
>> retire from the discussion.
>>
>> Dick you've got some kind of hidden agenda going here - one where
>> some things that route signals among drivers based on frequency are
>> my statement, others aren't.
>
> Your interpretation of my words is, to say the least, bizzarre.

As is your interpretation of mine, Dick.

>> IOW, you seem to be claiming that unless signals are routed in
>> accordance with a narrow list of rules that may be known only to
>> you, one doesn't have an effective crossover.

> Bullshit, in a word.

It's BS that you made Dick, up based on an odd interpretation of what I
said.

> I asked a simple question: if a particular transfer function is
> required, one example OF MANY being a 2nd order butterworth low pass,
> you simply CANNOT get there using passive filters and a non-resistive
> filter termination.

That's not a question, its an assertion. It is perfectly obvious to anybody
who can read that this is not a question. Where do you get off Dick calling
what I said bizarre, when you can't even properly call an assertion an
asssertion, but instead call it a question?

> You countered that an "effective crossover" can be constructed using
> higher order networks to achieve the same slope.

The phase "same slope" is your words, not mind, Dick. Just another example
of how inappropriate you've been. I never said same slope. You said same
slope. So now you're arguing with yourself, while claiming that you're
arguing with me.

> mindeness, my friend: a crossover is NOT solely constrained nor
> fully described by its slope. I am sure you know that, yes?

I'm not your friend Dick, I'm your victim. I never said that a crossover is
solely constrained nor fully described by its slope. Your claims are
becoming more bizarre by the moment.

> can you show that any given transfer function that can be
> derived from a passive ladder type filter into a resistive load
> can be achieved by a higher order crossover into a non-resistive
> termination.

Never said that, never intend to. More bizarre behaviour on your part, Dick.

>That is the crux of the discussion, it seems.

There is no discussion between us, Dick. You're making up issues and then
arguing with them. Weird!

> Let's not talk about "effective crossover" or other such ill-defined
> terms.

I'm glad to see that you are willing to admit that I did use the phrase
"effective crossover", Dick. That's *all* I meant to say. Guess what, it's
as vague as I intended it to be!

> Let's keep everything very simple: I'll provide you with
> a transfer function for a resistive terminated filter, and your
> job is to come up with a higher order filter that has the same
> transfer function into a non-resistive termination that typifies/
> the sort of impedance found in electrodynamic loudspeakers.

Not my job.

> SAME TRANSFER FUNCTION. Pick ANY transfer function you want,
> ANY transfer function that is implementable with a passive filter
> topology. Not some "secret" function that you erroneously accuse
> me of keeping hidden from you, ANY TRAFSRE FUNCTION AT ALL.

Not what I said.

> The sole requirement is for you to show that you can achieve the
> same transfer function into a non-resistive termination using
> a higher order filter.

Not anything that I was interested in getting involved with!
Anonymous

Randy Yates wrote:
> dpierce@cartchunk.org writes:
> > [...]
>
> > that typifies the sort of impedance found in electrodynamic
> > loudspeakers.
>
> Dick, could you please provide such a transfer function? I'm
> interested in seeing how this plays out.

Okay.

First step, let's assume a 2.5 kHz 2nd order crossover, We'll
pick Butterworth properties but since other alignments are simply
derived by different coefficients in the transfer function, this
topology will have the same properties.

Assume an 8 ohm resistive load impedance, we end up with the
following SPICE circuit that does that job admirably:

L1 1 2 0.72MH
C2 2 0 5.63UF

Now, let's substitute a realistic load for that resistor.
Here's a SPICE equivalent circuit of a 5" woofer/midband that
matches the measured impedance over the range of 20Hz to 20 kHz
to within about 3% worst case deviation:

.SUBCKT wmsample 1 10
Re 1 2 5.97
Cmes 2 3 221.53UF
Lces 2 3 22.68MH
Res 2 3 28.03
Lvc1 3 4 0.32MH
Rs1 3 4 5.0
Lvc2 4 5 0.14MH
Rs2 4 5 18.0
Lvc3 5 6 0.12MH
RRR1 6 10 0.5
LRR 6 10 5MH
.ENDS

The resulting circuit, then would look like:

L1 1 2 0.72MH
C2 2 0 5.63UF

However, the actual response is substantially different than
the desired response. Let's look at the results covering the
two or so octaves surround the crossover point:

1040 Hz -0.13 dB -1.48 dB
1110 -0.17 -1.55
1190 -0.22 -1.6
1280 -0.29 -1.62
1370 -0.37 -1.62
1470 -0.49 -1.59
1580 -0.63 -1.53
1690 -0.82 -1.44
1810 -1.05 -1.3
1940 -1.34 -1.12
2080 -1.7 -0.893
2230 -2.12 -0.625
2390 -2.63 -0.318
2560 -3.22 0.0
2740 -3.89 0.32
2940 -4.64 0.54
3150 -5.47 0.57
3380 -6.37 0.28
3620 -7.32 -0.42
3880 -8.33 -1.53
4160 -9.37 -2.94
4460 -10.4 -4.54
4780 -11.6 -6.23
5120 -12.7 -7.92
5490 -13.8 -9.6
5880 -15 -11.2
6300 -16.2 -12.9

The first column represents frequency, the second column is
the magnitude response of the ideal network into the resistive
load, the third is the same network into the driver load. Clearly,
it does not come close to the desired response.

Now, let's redo it only using simple and approximate first-order
conjugate. Please bear with me as this is a first cut with NO
tweaking or optimization of the conjugate whatsoever. The only
thing that was changed was the values of the crossover to deal
with the fact that the speaker load with the conjugate is 6.88
ohms.

1040 Hz -0.127 dB -0.222 dB
1110 -0.167 -0.273
1190 -0.219 -0.33
1280 -0.287 -0.397
1370 -0.375 -0.479
1470 -0.489 -0.585
1580 -0.634 -0.721
1690 -0.819 -0.896
1810 -1.05 -1.12
1940 -1.34 -1.4
2080 -1.7 -1.75
2230 -2.12 -2.16
2390 -2.63 -2.65
2560 -3.22 -3.22
2740 -3.89 -3.86
2940 -4.64 -4.57
3150 -5.47 -5.34
3380 -6.37 -6.17
3620 -7.32 -7.06
3880 -8.33 -8
4160 -9.37 -8.98
4460 -10.4 -10
4780 -11.6 -11.1
5120 -12.7 -12.1
5490 -13.8 -13.3
5880 -15 -14.4
6300 -16.2 -15.6

Now, more interesting then the absolute numbers is the deviation
from the ideal response, shown here:

1040 Hz 1.35 dB 0.10 dB
1110 1.38 0.11
1190 1.38 0.11
1280 1.33 0.11
1370 1.25 0.10
1470 1.10 0.10
1580 0.90 0.09
1690 0.62 0.08
1810 0.25 0.07
1940 -0.22 0.06
2080 -0.81 0.05
2230 -1.50 0.04
2390 -2.31 0.02
2560 -3.23 0.00
2740 -4.21 -0.03
2940 -5.18 -0.07
3150 -6.04 -0.13
3380 -6.65 -0.20
3620 -6.90 -0.26
3880 -6.80 -0.33
4160 -6.43 -0.39
4460 -5.86 -0.40
4780 -5.37 -0.50
5120 -4.78 -0.60
5490 -4.20 -0.50
5880 -3.80 -0.60
6300 -3.30 -0.60

The first column lists frequency, the second is the deviation
from desired response in the straight, non-conjugate network
while the third column shows the deviation from the desired
response using the conjugate-compensated network.

What we can onserve is that the worst case deviation is less
than 1 dB from ideal. And in the octave centered around 2500
Hz, the error is within +0.07, -0.26 dB. That is, again, with
no attempt whatsoever to optimize.

So, I'm suggesting this is a benchmark: is it possible to
design a passive network, higher than second order, that does
not use a conjugate impedance compensating network, that achieves
an equal or better match to the desired response than what's
shown in this example of a conjugate-compensated network?

Now, as one who does this for paying clients, the requirement
is to provide a transfer function that matches the requirements
of the driver. That is the ONLY "effective crossover" that will
work. That means a specific transfer function, whatever that
transfer function may be. It's not a crossover that's effective
for me, or effective for you, but one which is effective for the
specific application. It is the driver and system target repsonse
that dictates the required transfer function.

Indeed, I am not stating, as I have been accused, of

"claiming that unless signals are routed in accordance with
a narrow list of rules that may be known only to you, one
doesn't have an effective crossover"

rather, I am stating:

"unless the signals are routed in accordance with the narrow
list of rules dictated by the design constraints imposed by
the specific requirements of the speaker, the characteristics
of the driver and so forth, one, very definitely, does NOT
have an effective crossover."
Anonymous

The fact is, everybody can do what the hell they want, and that's the beauty
of it. Nothing is "bizarre" or "effective".

Everything is childish.

So why don't you both stop flaming the s**t out of each other and debate

Thank you.

Hugo

"Arny Krueger" <arnyk@hotpop.com> wrote in message
news:gYOdnZ7PHuJe9arfRVn-pQ@comcast.com...
> <dpierce@cartchunk.org> wrote in message
> > Arny Krueger wrote:
> >> <dpierce@cartchunk.org> wrote in message
> >>> Arny Krueger wrote:
> >>>> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
> >>>> news:xxppsy1f4k0.fsf@usrts005.corpusers.net
> >>>>> dpierce@cartchunk.org writes:
> >>>>>> [...]
> >>>>>> That's the entire point of conjugate impedance matching networks,
> >>>>>> or so-called "zobels." They provide an impedance which is the
> >>>>>> complex conjugate of the driver impedance over a sufficiently
> >>>>>> wide range of frequencies that the result is a resistive
> >>>>>> impedance, one which is reasonably independent of frequency.
> >>>>>> Once that's accomplished, normal passive networks can be made to
> >>>>>> work fine.
> >>>>>
> >>>>> Dick,
> >>>>>
> >>>>> It is these tidbits of gold that make me hope you keep on
> >>>>> posting to these newsgroups as long as I can read.
> >>>>
> >>>> The other half of the story is that one can design effective
> >>>> crossovers without zobels. You generally end up going to higher
> >>>> order filters to get the desired slopes.
> >>
> >>> Without a working definition "effective crossover," I'd have to
> >>> say, no, you cannot.
> >>
> >> In the face of intellectual narrowness of this kind, I've got to
> >> retire from the discussion.
> >>
> >> Dick you've got some kind of hidden agenda going here - one where
> >> some things that route signals among drivers based on frequency are
> >> crossovers, and for reasons you've gratuitously added after I made
> >> my statement, others aren't.
> >
> > Your interpretation of my words is, to say the least, bizzarre.
>
> As is your interpretation of mine, Dick.
>
> >> IOW, you seem to be claiming that unless signals are routed in
> >> accordance with a narrow list of rules that may be known only to
> >> you, one doesn't have an effective crossover.
>
> > Bullshit, in a word.
>
> It's BS that you made Dick, up based on an odd interpretation of what I
> said.
>
> > I asked a simple question: if a particular transfer function is
> > required, one example OF MANY being a 2nd order butterworth low pass,
> > you simply CANNOT get there using passive filters and a non-resistive
> > filter termination.
>
> That's not a question, its an assertion. It is perfectly obvious to
anybody
> who can read that this is not a question. Where do you get off Dick
calling
> what I said bizarre, when you can't even properly call an assertion an
> asssertion, but instead call it a question?
>
> > You countered that an "effective crossover" can be constructed using
> > higher order networks to achieve the same slope.
>
> The phase "same slope" is your words, not mind, Dick. Just another example
> of how inappropriate you've been. I never said same slope. You said same
> slope. So now you're arguing with yourself, while claiming that you're
> arguing with me.
>
>
> > mindeness, my friend: a crossover is NOT solely constrained nor
> > fully described by its slope. I am sure you know that, yes?
>
> I'm not your friend Dick, I'm your victim. I never said that a crossover
is
> solely constrained nor fully described by its slope. Your claims are
> becoming more bizarre by the moment.
>
>
>
>
> > can you show that any given transfer function that can be
> > derived from a passive ladder type filter into a resistive load
> > can be achieved by a higher order crossover into a non-resistive
> > termination.
>
> Never said that, never intend to. More bizarre behaviour on your part,
Dick.
>
> >That is the crux of the discussion, it seems.
>
> There is no discussion between us, Dick. You're making up issues and then
> arguing with them. Weird!
>
> > Let's not talk about "effective crossover" or other such ill-defined
> > terms.
>
> I'm glad to see that you are willing to admit that I did use the phrase
> "effective crossover", Dick. That's *all* I meant to say. Guess what, it's
> as vague as I intended it to be!
>
> > Let's keep everything very simple: I'll provide you with
> > a transfer function for a resistive terminated filter, and your
> > job is to come up with a higher order filter that has the same
> > transfer function into a non-resistive termination that typifies/
> > the sort of impedance found in electrodynamic loudspeakers.
>
> Not my job.
>
> > SAME TRANSFER FUNCTION. Pick ANY transfer function you want,
> > ANY transfer function that is implementable with a passive filter
> > topology. Not some "secret" function that you erroneously accuse
> > me of keeping hidden from you, ANY TRAFSRE FUNCTION AT ALL.
>
> Not what I said.
>
> > The sole requirement is for you to show that you can achieve the
> > same transfer function into a non-resistive termination using
> > a higher order filter.
>
> Not anything that I was interested in getting involved with!
>
>
Anonymous

> >
> > > Let's keep everything very simple: I'll provide you with
> > > a transfer function for a resistive terminated filter, and your
> > > job is to come up with a higher order filter that has the same
> > > transfer function into a non-resistive termination that typifies/
> > > the sort of impedance found in electrodynamic loudspeakers.
> >
> > Not my job.
> >
> > > SAME TRANSFER FUNCTION. Pick ANY transfer function you want,
> > > ANY transfer function that is implementable with a passive filter
> > > topology. Not some "secret" function that you erroneously accuse
> > > me of keeping hidden from you, ANY TRAFSRE FUNCTION AT ALL.
> >
> > Not what I said.
> >

It's time for Arny to back up the check he's been writing all this
time. I never claimed to be an engineer; let's see if Arny is.
Anonymous

There we go. Actual proof.

Thank you.

Hugo

<dpierce@cartchunk.org> wrote in message
>
> Randy Yates wrote:
> > dpierce@cartchunk.org writes:
> > > [...]
> >
> > > that typifies the sort of impedance found in electrodynamic
> > > loudspeakers.
> >
> > Dick, could you please provide such a transfer function? I'm
> > interested in seeing how this plays out.
>
> Okay.
>
> First step, let's assume a 2.5 kHz 2nd order crossover, We'll
> pick Butterworth properties but since other alignments are simply
> derived by different coefficients in the transfer function, this
> topology will have the same properties.
>
> Assume an 8 ohm resistive load impedance, we end up with the
> following SPICE circuit that does that job admirably:
>
> L1 1 2 0.72MH
> C2 2 0 5.63UF
>
> Now, let's substitute a realistic load for that resistor.
> Here's a SPICE equivalent circuit of a 5" woofer/midband that
> matches the measured impedance over the range of 20Hz to 20 kHz
> to within about 3% worst case deviation:
>
> .SUBCKT wmsample 1 10
> Re 1 2 5.97
> Cmes 2 3 221.53UF
> Lces 2 3 22.68MH
> Res 2 3 28.03
> Lvc1 3 4 0.32MH
> Rs1 3 4 5.0
> Lvc2 4 5 0.14MH
> Rs2 4 5 18.0
> Lvc3 5 6 0.12MH
> RRR1 6 10 0.5
> LRR 6 10 5MH
> .ENDS
>
> The resulting circuit, then would look like:
>
> L1 1 2 0.72MH
> C2 2 0 5.63UF
>
> However, the actual response is substantially different than
> the desired response. Let's look at the results covering the
> two or so octaves surround the crossover point:
>
> 1040 Hz -0.13 dB -1.48 dB
> 1110 -0.17 -1.55
> 1190 -0.22 -1.6
> 1280 -0.29 -1.62
> 1370 -0.37 -1.62
> 1470 -0.49 -1.59
> 1580 -0.63 -1.53
> 1690 -0.82 -1.44
> 1810 -1.05 -1.3
> 1940 -1.34 -1.12
> 2080 -1.7 -0.893
> 2230 -2.12 -0.625
> 2390 -2.63 -0.318
> 2560 -3.22 0.0
> 2740 -3.89 0.32
> 2940 -4.64 0.54
> 3150 -5.47 0.57
> 3380 -6.37 0.28
> 3620 -7.32 -0.42
> 3880 -8.33 -1.53
> 4160 -9.37 -2.94
> 4460 -10.4 -4.54
> 4780 -11.6 -6.23
> 5120 -12.7 -7.92
> 5490 -13.8 -9.6
> 5880 -15 -11.2
> 6300 -16.2 -12.9
>
> The first column represents frequency, the second column is
> the magnitude response of the ideal network into the resistive
> load, the third is the same network into the driver load. Clearly,
> it does not come close to the desired response.
>
> Now, let's redo it only using simple and approximate first-order
> conjugate. Please bear with me as this is a first cut with NO
> tweaking or optimization of the conjugate whatsoever. The only
> thing that was changed was the values of the crossover to deal
> with the fact that the speaker load with the conjugate is 6.88
> ohms.
>
> 1040 Hz -0.127 dB -0.222 dB
> 1110 -0.167 -0.273
> 1190 -0.219 -0.33
> 1280 -0.287 -0.397
> 1370 -0.375 -0.479
> 1470 -0.489 -0.585
> 1580 -0.634 -0.721
> 1690 -0.819 -0.896
> 1810 -1.05 -1.12
> 1940 -1.34 -1.4
> 2080 -1.7 -1.75
> 2230 -2.12 -2.16
> 2390 -2.63 -2.65
> 2560 -3.22 -3.22
> 2740 -3.89 -3.86
> 2940 -4.64 -4.57
> 3150 -5.47 -5.34
> 3380 -6.37 -6.17
> 3620 -7.32 -7.06
> 3880 -8.33 -8
> 4160 -9.37 -8.98
> 4460 -10.4 -10
> 4780 -11.6 -11.1
> 5120 -12.7 -12.1
> 5490 -13.8 -13.3
> 5880 -15 -14.4
> 6300 -16.2 -15.6
>
> Now, more interesting then the absolute numbers is the deviation
> from the ideal response, shown here:
>
> 1040 Hz 1.35 dB 0.10 dB
> 1110 1.38 0.11
> 1190 1.38 0.11
> 1280 1.33 0.11
> 1370 1.25 0.10
> 1470 1.10 0.10
> 1580 0.90 0.09
> 1690 0.62 0.08
> 1810 0.25 0.07
> 1940 -0.22 0.06
> 2080 -0.81 0.05
> 2230 -1.50 0.04
> 2390 -2.31 0.02
> 2560 -3.23 0.00
> 2740 -4.21 -0.03
> 2940 -5.18 -0.07
> 3150 -6.04 -0.13
> 3380 -6.65 -0.20
> 3620 -6.90 -0.26
> 3880 -6.80 -0.33
> 4160 -6.43 -0.39
> 4460 -5.86 -0.40
> 4780 -5.37 -0.50
> 5120 -4.78 -0.60
> 5490 -4.20 -0.50
> 5880 -3.80 -0.60
> 6300 -3.30 -0.60
>
> The first column lists frequency, the second is the deviation
> from desired response in the straight, non-conjugate network
> while the third column shows the deviation from the desired
> response using the conjugate-compensated network.
>
> What we can onserve is that the worst case deviation is less
> than 1 dB from ideal. And in the octave centered around 2500
> Hz, the error is within +0.07, -0.26 dB. That is, again, with
> no attempt whatsoever to optimize.
>
> So, I'm suggesting this is a benchmark: is it possible to
> design a passive network, higher than second order, that does
> not use a conjugate impedance compensating network, that achieves
> an equal or better match to the desired response than what's
> shown in this example of a conjugate-compensated network?
>
> Now, as one who does this for paying clients, the requirement
> is to provide a transfer function that matches the requirements
> of the driver. That is the ONLY "effective crossover" that will
> work. That means a specific transfer function, whatever that
> transfer function may be. It's not a crossover that's effective
> for me, or effective for you, but one which is effective for the
> specific application. It is the driver and system target repsonse
> that dictates the required transfer function.
>
> Indeed, I am not stating, as I have been accused, of
>
> "claiming that unless signals are routed in accordance with
> a narrow list of rules that may be known only to you, one
> doesn't have an effective crossover"
>
> rather, I am stating:
>
> "unless the signals are routed in accordance with the narrow
> list of rules dictated by the design constraints imposed by
> the specific requirements of the speaker, the characteristics
> of the driver and so forth, one, very definitely, does NOT
> have an effective crossover."
>
Anonymous

dpierce@cartchunk.org writes:
> [...]

> that typifies the sort of impedance found in electrodynamic
> loudspeakers.

Dick, could you please provide such a transfer function? I'm
interested in seeing how this plays out.
--
% Randy Yates % "My Shangri-la has gone away, fading like
%% Fuquay-Varina, NC % the Beatles on 'Hey Jude'"
%%% 919-577-9882 %
%%%% <yates@ieee.org> % 'Shangri-La', *A New World Record*, ELO
Anonymous

Well, rather than continue to engage in an acrimonious
content-free debate, I thought I'd break with tradition and
actually directly address the original poster's question with
actual data, to wit:

> My question is in regards to xover calculations and the fact
> they are based on the nominal impedence of the driver.
>
> Where available, is it more appropriate to use the actual
> impedence of the driver at the x-over point, rather than
> the nominal impedence?

Let's explore exactly that possiblity. Using the example from
last night's post, I re-ran the experiment using a variety of
conditions. In all cases, the target is a 2nd order low pass
with Butterworth (that means maximally flat amplitude response
in the passband) using a simple ladder-type (meaning series
inductor, shunt capacitor) filter. Here are the conditions of
each experiment (netlists are shown in SPICE notation for
convenience):

CASE 1
Assume the driver presents an 8 ohm, purely resistive load,
and values calculated on that basis, with the result being:

L1 1 2 0.72MH
C2 2 0 5.63UF

CASE 2
Using the driver model presented previously with the
crossover values caculated for 8 ohm resistive load:

L1 1 2 0.72MH
C2 2 0 5.63UF

CASE 3
Using the driver model, recalculate the crossover values
using the actual impedance of 11.3 ohms at the crossover
frequency of 2500 Hz:

L1 1 2 1.02MH
C2 2 0 3.98UF

CASE 4
Using the driver mode, employ a simple 1st order impedance
conjugate and use value appropriate for the resulting load
impeance:

L1 1 2 0.62MH
C2 2 0 6.54UF
Rcc 2 3 10
Ccc 3 0 10UF

The data is tabulated below. The first column denotes the
frequency, with points being calculated every 1/10th octave from
2 octaves below to 2 octaves above the target crossover point of
2500 Hz. The second column shows the desired response.

>From there, each column is shown in pairs, the first of the pair
is the actual log magnitude response (Gm, in dB) of the
experimental filter, while the second is the deviation (err, in
DB) from the desired target response. (Please note that the
table is best read using a fixed-width font.)

-------------------------------------------------------------
FREQ CASE 1 CASE 2 CASE 3 CASE 4
Gm Gm err Gm err Gm err
------ -------- ------------ ------------ ------------
625 -0.02 -0.66 -0.64 -1.4 -1.38 0.13 0.15
670 -0.02 -0.78 -0.76 -1.61 -1.59 0.08 0.11
718 -0.03 -0.91 -0.88 -1.81 -1.78 0.03 0.06
769 -0.04 -1.03 -0.99 -2.02 -1.98 -0.02 0.02
825 -0.05 -1.15 -1.1 -2.22 -2.17 -0.06 -0.01
884 -0.07 -1.26 -1.19 -2.42 -2.35 -0.11 -0.04
947 -0.09 -1.36 -1.27 -2.6 -2.51 -0.16 -0.07
1020 -0.12 -1.45 -1.34 -2.78 -2.67 -0.21 -0.09
1090 -0.15 -1.52 -1.37 -2.94 -2.79 -0.26 -0.1
1170 -0.2 -1.58 -1.38 -3.08 -2.88 -0.31 -0.11
1250 -0.26 -1.62 -1.36 -3.21 -2.95 -0.37 -0.11
1340 -0.34 -1.63 -1.29 -3.31 -2.97 -0.45 -0.11
1440 -0.45 -1.61 -1.16 -3.4 -2.95 -0.55 -0.1
1540 -0.58 -1.56 -0.98 -3.46 -2.88 -0.67 -0.09
1650 -0.75 -1.47 -0.72 -3.49 -2.74 -0.83 -0.08
1770 -0.97 -1.35 -0.38 -3.5 -2.53 -1.04 -0.07
1890 -1.24 -1.19 0.05 -3.48 -2.24 -1.3 -0.06
2030 -1.57 -0.98 0.6 -3.43 -1.86 -1.62 -0.05
2180 -1.97 -0.72 1.25 -3.35 -1.38 -2.01 -0.04
2330 -2.45 -0.43 2.02 -3.25 -0.8 -2.48 -0.03
2500 -3.01 -0.1 2.91 -3.13 -0.12 -3.02 -0.01
2680 -3.65 0.22 3.87 -2.99 0.66 -3.63 0.02
2870 -4.38 0.48 4.86 -2.86 1.52 -4.32 0.06
3080 -5.18 0.59 5.77 -2.76 2.42 -5.07 0.11
3300 -6.05 0.42 6.47 -2.75 3.3 -5.88 0.17
3540 -6.99 -0.13 6.86 -2.88 4.11 -6.75 0.24
3790 -7.98 -1.11 6.87 -3.22 4.76 -7.67 0.31
4060 -9.01 -2.43 6.58 -3.83 5.18 -8.64 0.37
4350 -10.1 -3.98 6.12 -4.73 5.37 -9.64 0.46
4670 -11.2 -5.65 5.55 -5.88 5.32 -10.7 0.5
5000 -12.3 -7.34 4.96 -7.22 5.08 -11.8 0.5
5360 -13.4 -9.03 4.37 -8.69 4.71 -12.9 0.5
5740 -14.6 -10.7 3.9 -10.2 4.4 -14.0 0.6
6160 -15.8 -12.3 3.5 -11.8 4.0 -15.2 0.6
6600 -16.9 -13.9 3.0 -13.4 3.5 -16.3 0.6
7070 -18.1 -15.4 2.7 -14.9 3.2 -17.5 0.6
7580 -19.3 -16.9 2.4 -16.4 2.9 -18.7 0.6
8120 -20.5 -18.4 2.1 -17.9 2.6 -19.9 0.6
8710 -21.7 -19.8 1.9 -19.4 2.3 -21.1 0.6
9330 -22.9 -21.2 1.7 -20.9 2.0 -22.4 0.5
10000 -24.1 -22.6 1.5 -22.3 1.8 -23.6 0.5
--------------------------------------------------------------

Now let's briefly analyze the results.

CASE 2
This is the network designed for an 8 ohm load used with the
actual driver. Here, we see that overall, we have a deviation
overall of -1.38 to +6.86 dB from target response (total
range of 8.24 dB), and within the 2 octaves centered on the
target crossover frequency, the deviation is -1.36 to +6.86
dB (range of 8.24 dB).

CASE 3
This is the network with values reworked assuming an 11.3 ohm
resistive load. In this case, the overall deviation from
target is -2.97 dB to 5.37 dB (range of 8.34 dB), and is the
same for the 2 octaves centered around the target crossover
point.

CASE 4
This is the network which incorporates the conjugate
impedance correction and has crossover values adjusted to the
actual load presented, approximately 6.88 ohms. The deviation
from target response is now -0.11 to 0.6 dB overall (range of
0.71 dB), and within -0.11 to 0.5 dB (range 0.61) over the 2
octave span centered on the target crossover point.

>From this we can directly answer the original question:

> Where available, is it more appropriate to use the actual
> impedence of the driver at the x-over point, rather than
> the nominal impedence?

It would seem that, at least for the 2nd order low pass case,
the answer is most definitely no, it is not more appropriate.
The range of error is essentially the same, the maximum errors
just occur at somewhat different frequencies.

Using the expedient of a complex impedance conjugate, even a
simple first order, non-optimized conjugate, gets us much closer
to the desired target response. Indeed, the deviation resulting
from this quick experiment is actually less than can be
reasonably expected from sample-to-sample variations in drivers
of the same model.

Two contentious phrases were introduced in this discussion,
phrases that were absent a working definiton, those being
"effective crossover" and "desired slope." I will, for the
purpose of clarification, propose a definition for each:

effective crossover: A crossover function that meets the
requirements and constraints set by the driver properties
and the desired system target response. An effective
crossover must provide the transfer function necessary to
achieve the full target system response, given the drivers
used in that system.

desired slope: the slope of the amplitude vs. frequency
response that is defined by the required crossover transfer
function needed to meet the target system response.

There was a derived phrase of "same slope" which caused a rather
innappropriate amount of semantic bickering. However, it can be
shown that "same slope" is, in the current context, identical to
"desired slope," in the sense that the slope required is the
"same" as that defined by the "desired" crossover transfer
function.

It was asserted that:

"one can design effective crossovers without zobels [by]
going to higher order filters to get the desired slopes."

Using the very practical working constraints that the "desired
slope" is the slope defined by the specific transfer function
needed to achieve the target system response I syill, in the
absence of any evidence to the contrary, say no, it is not. The
basis of the assertion quoted is that a transfer function of,
say,

1
--------------------
as^3 + bs^2 + cs + 1

results in the same transfer function (because it is, after all,
the tranbsfer function that defines whether the crossover is
effective or not, a point not yet credibly challenged) as:

1
-------------
ms^2 + ns + 1

Now, the two WILL be the same IFF a=0, b=m and c=n, but that
simply reduces the third-order transfer function to a second
order transfer function.

The "desired slope" of a crossover is not just the slope in the
stop-band, it's the slope at every point in the overall
operating bandwidth of the filter. And the slope is merely one
parameter of the complex transfer function of the system, it is
merely the derivative of response WRT frequency.

To date, no evidence has been provided that if the "desired
slope" is that afforded by a passive resistive terminated filter
of a specific transfer function, that a higher order transfer
function can provide that "desired slope."
Anonymous

<dpierce@cartchunk.org> wrote in message

> "unless the signals are routed in accordance with the narrow
> list of rules dictated by the design constraints imposed by
> the specific requirements of the speaker, the characteristics
> of the driver and so forth, one, very definitely, does NOT
> have an effective crossover."

That's perfectly obvious. That you would try to pass it off Dick, as a
correction to what I said shows how completely you've missed my point. My
point all along is that effective crossovers can be and have long been built
without Zobels.
Anonymous

"Arny Krueger" <arnyk@hotpop.com> writes:

> <dpierce@cartchunk.org> wrote in message
>
> > "unless the signals are routed in accordance with the narrow
> > list of rules dictated by the design constraints imposed by
> > the specific requirements of the speaker, the characteristics
> > of the driver and so forth, one, very definitely, does NOT
> > have an effective crossover."
>
> That's perfectly obvious. That you would try to pass it off Dick, as a
> correction to what I said shows how completely you've missed my point. My
> point all along is that effective crossovers can be and have long been built
> without Zobels.

Arny,

I think there's a conceptual error here on your part. In order
to see what I mean, let's make a few definitions and work with them.

In the case where a Zobel network is not used but rather just a crossover,
denote the driver's transfer function by D(s), the crossover impedance
transfer function C(s), and the overall (composite) desired transfer function
H(s). Then necessarily we have the following situation:

H(s) = C(s) * D(s).

If we solve for the crossover function, then

C(s) = H(s) / D(s). [1]

Now in the case where a Zobel network is used, denote the Zobel network's
transfer function as Z(s). Then we design the Zobel network so that

Z(s) = 1 / D(s).

Then the composite response of our "desired" response H(s) and the
Zobel network, i.e., our overall crossover response, is

C(s) = H(s) * Z(s)
= H(s) / D(s). [2]

Note that [1] and [2] are identical.

What this simple analysis implies is that, no matter how you
implement the functionality, the inverse driver response 1 / D(s)
is a part of the composite response if one requires a specific
desired transfer function H(s). Whether you consider the Zobel
as part of the crossover network or not, this inverse must be
present in order to obtain the desired response.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124
Anonymous

"Randy Yates" <randy.yates@sonyericsson.com> wrote in message
news:xxpk6o7vihj.fsf@usrts005.corpusers.net
> "Arny Krueger" <arnyk@hotpop.com> writes:
>
>> <dpierce@cartchunk.org> wrote in message
>>
>>> "unless the signals are routed in accordance with the narrow
>>> list of rules dictated by the design constraints imposed by
>>> the specific requirements of the speaker, the characteristics
>>> of the driver and so forth, one, very definitely, does NOT
>>> have an effective crossover."
>>
>> That's perfectly obvious. That you would try to pass it off Dick, as
>> a correction to what I said shows how completely you've missed my
>> point. My point all along is that effective crossovers can be and
>> have long been built without Zobels.
>
> Arny,
>
> I think there's a conceptual error here on your part. In order
> to see what I mean, let's make a few definitions and work with them.

Wrong, Randy, you seem to totally misunderstand. I made a statement about
practicality, and observable facts related to that which is customary use.
As soon as anybody tries to turn this into a detailed technical discussion,
they've missed the point.

Have you ever surveyed the crossover circuits of a large groups of
well-regarded loudspeakers? Can you give an informed percentage of those
that have zobels versus those that don't? How about a statistically
reliable number relating to which in general sound better or are more
sucessful comercially or technically?

Would a speaker with zobels necessarily have flatter response than one that
didn't? Remember, the designers of both speakers have free choice of
*everything*.
Anonymous

"Arny Krueger" <arnyk@hotpop.com> writes:

> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
> news:xxpk6o7vihj.fsf@usrts005.corpusers.net
> > "Arny Krueger" <arnyk@hotpop.com> writes:
> >
> >> <dpierce@cartchunk.org> wrote in message
> >>
> >>> "unless the signals are routed in accordance with the narrow
> >>> list of rules dictated by the design constraints imposed by
> >>> the specific requirements of the speaker, the characteristics
> >>> of the driver and so forth, one, very definitely, does NOT
> >>> have an effective crossover."
> >>
> >> That's perfectly obvious. That you would try to pass it off Dick, as
> >> a correction to what I said shows how completely you've missed my
> >> point. My point all along is that effective crossovers can be and
> >> have long been built without Zobels.
> >
> > Arny,
> >
> > I think there's a conceptual error here on your part. In order
> > to see what I mean, let's make a few definitions and work with them.
>
> Wrong, Randy, you seem to totally misunderstand.

I understand that you said

> >> My point all along is that effective crossovers can be and
> >> have long been built without Zobels.

This is a matter of record and not up for debate.

I went on to show that one cannot implement a desired response in
a crossover network without inverting the driver's response, which
is precisely what a Zobel does.

Either refute what I showed (via the logic of or the definition of
terms used therein) or recant. Those are the only two options if you
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124
Anonymous

"Randy Yates" <randy.yates@sonyericsson.com> wrote in message
news:xxp1xafvdld.fsf@usrts005.corpusers.net
> "Arny Krueger" <arnyk@hotpop.com> writes:
>
>> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
>> news:xxpk6o7vihj.fsf@usrts005.corpusers.net
>>> "Arny Krueger" <arnyk@hotpop.com> writes:
>>>
>>>> <dpierce@cartchunk.org> wrote in message
>>>>
>>>>> "unless the signals are routed in accordance with the narrow
>>>>> list of rules dictated by the design constraints imposed by
>>>>> the specific requirements of the speaker, the characteristics
>>>>> of the driver and so forth, one, very definitely, does NOT
>>>>> have an effective crossover."
>>>>
>>>> That's perfectly obvious. That you would try to pass it off Dick,
>>>> as a correction to what I said shows how completely you've missed
>>>> my point. My point all along is that effective crossovers can be
>>>> and have long been built without Zobels.
>>>
>>> Arny,
>>>
>>> I think there's a conceptual error here on your part. In order
>>> to see what I mean, let's make a few definitions and work with them.
>>
>> Wrong, Randy, you seem to totally misunderstand.
>
> I understand that you said
>
>>>> My point all along is that effective crossovers can be and
>>>> have long been built without Zobels.
>
> This is a matter of record and not up for debate.
>
> I went on to show that one cannot implement a desired response in
> a crossover network without inverting the driver's response, which
> is precisely what a Zobel does.
>
> Either refute what I showed (via the logic of or the definition of
> terms used therein) or recant. Those are the only two options if you

Since my original statement was not made as a formal statement of fact, I
decline on the grounds of irelevance.

I suggest that one and all read the following:

http://www.searchlores.org/schopeng.htm

More specifically, item number one.
Anonymous

"Arny Krueger" <arnyk@hotpop.com> wrote in message

My
> point all along is that effective crossovers can be and have long been
built
> without Zobels.

Of course they have. And will continue to be. Sometimes a Zobel is the best
option, sometimes it's not. It's quite possible, for example, to build an
effective 4th order low pass crossover using just an inductor and a cap.

Stephen
Anonymous

"Stephen McLuckie" <stephen.mcluckie@pinniger1.plus.com> wrote in
message news:39qs87F63mjd2U1@individual.net
> "Arny Krueger" <arnyk@hotpop.com> wrote in message
>
> My
>> point all along is that effective crossovers can be and have long
>> been built without Zobels.
>
> Of course they have. And will continue to be. Sometimes a Zobel is
> the best option, sometimes it's not. It's quite possible, for
> example, to build an effective 4th order low pass crossover using
> just an inductor and a cap.

Congratulations for observing something that is apparently invisible to
several august members of this group.
Anonymous

> > ... Either refute what I showed (via the logic of or the definition of
> > terms used therein) or recant. Those are the only two options if you
>
> Since my original statement was not made as a formal statement of fact, I
> decline on the grounds of irelevance.
>
> I suggest that one and all read the following:
>
> http://www.searchlores.org/schopeng.htm
>

My opinion of whoever abides by the rules suggested on that page is one of
stupidity and closed-mindedness.

Hugo
Anonymous

Dude, can I use this as my mid-term in electronics?

<dpierce@cartchunk.org> wrote in message
> Well, rather than continue to engage in an acrimonious
> content-free debate, I thought I'd break with tradition and
> actually directly address the original poster's question with
> actual data, to wit:
>
> > My question is in regards to xover calculations and the fact
> > they are based on the nominal impedence of the driver.
> >
> > Where available, is it more appropriate to use the actual
> > impedence of the driver at the x-over point, rather than
> > the nominal impedence?
>
> Let's explore exactly that possiblity. Using the example from
> last night's post, I re-ran the experiment using a variety of
> conditions. In all cases, the target is a 2nd order low pass
> with Butterworth (that means maximally flat amplitude response
> in the passband) using a simple ladder-type (meaning series
> inductor, shunt capacitor) filter. Here are the conditions of
> each experiment (netlists are shown in SPICE notation for
> convenience):
>
> CASE 1
> Assume the driver presents an 8 ohm, purely resistive load,
> and values calculated on that basis, with the result being:
>
> L1 1 2 0.72MH
> C2 2 0 5.63UF
>
> CASE 2
> Using the driver model presented previously with the
> crossover values caculated for 8 ohm resistive load:
>
> L1 1 2 0.72MH
> C2 2 0 5.63UF
>
> CASE 3
> Using the driver model, recalculate the crossover values
> using the actual impedance of 11.3 ohms at the crossover
> frequency of 2500 Hz:
>
> L1 1 2 1.02MH
> C2 2 0 3.98UF
>
> CASE 4
> Using the driver mode, employ a simple 1st order impedance
> conjugate and use value appropriate for the resulting load
> impeance:
>
> L1 1 2 0.62MH
> C2 2 0 6.54UF
> Rcc 2 3 10
> Ccc 3 0 10UF
>
> The data is tabulated below. The first column denotes the
> frequency, with points being calculated every 1/10th octave from
> 2 octaves below to 2 octaves above the target crossover point of
> 2500 Hz. The second column shows the desired response.
>
> >From there, each column is shown in pairs, the first of the pair
> is the actual log magnitude response (Gm, in dB) of the
> experimental filter, while the second is the deviation (err, in
> DB) from the desired target response. (Please note that the
> table is best read using a fixed-width font.)
>
> -------------------------------------------------------------
> FREQ CASE 1 CASE 2 CASE 3 CASE 4
> Gm Gm err Gm err Gm err
> ------ -------- ------------ ------------ ------------
> 625 -0.02 -0.66 -0.64 -1.4 -1.38 0.13 0.15
> 670 -0.02 -0.78 -0.76 -1.61 -1.59 0.08 0.11
> 718 -0.03 -0.91 -0.88 -1.81 -1.78 0.03 0.06
> 769 -0.04 -1.03 -0.99 -2.02 -1.98 -0.02 0.02
> 825 -0.05 -1.15 -1.1 -2.22 -2.17 -0.06 -0.01
> 884 -0.07 -1.26 -1.19 -2.42 -2.35 -0.11 -0.04
> 947 -0.09 -1.36 -1.27 -2.6 -2.51 -0.16 -0.07
> 1020 -0.12 -1.45 -1.34 -2.78 -2.67 -0.21 -0.09
> 1090 -0.15 -1.52 -1.37 -2.94 -2.79 -0.26 -0.1
> 1170 -0.2 -1.58 -1.38 -3.08 -2.88 -0.31 -0.11
> 1250 -0.26 -1.62 -1.36 -3.21 -2.95 -0.37 -0.11
> 1340 -0.34 -1.63 -1.29 -3.31 -2.97 -0.45 -0.11
> 1440 -0.45 -1.61 -1.16 -3.4 -2.95 -0.55 -0.1
> 1540 -0.58 -1.56 -0.98 -3.46 -2.88 -0.67 -0.09
> 1650 -0.75 -1.47 -0.72 -3.49 -2.74 -0.83 -0.08
> 1770 -0.97 -1.35 -0.38 -3.5 -2.53 -1.04 -0.07
> 1890 -1.24 -1.19 0.05 -3.48 -2.24 -1.3 -0.06
> 2030 -1.57 -0.98 0.6 -3.43 -1.86 -1.62 -0.05
> 2180 -1.97 -0.72 1.25 -3.35 -1.38 -2.01 -0.04
> 2330 -2.45 -0.43 2.02 -3.25 -0.8 -2.48 -0.03
> 2500 -3.01 -0.1 2.91 -3.13 -0.12 -3.02 -0.01
> 2680 -3.65 0.22 3.87 -2.99 0.66 -3.63 0.02
> 2870 -4.38 0.48 4.86 -2.86 1.52 -4.32 0.06
> 3080 -5.18 0.59 5.77 -2.76 2.42 -5.07 0.11
> 3300 -6.05 0.42 6.47 -2.75 3.3 -5.88 0.17
> 3540 -6.99 -0.13 6.86 -2.88 4.11 -6.75 0.24
> 3790 -7.98 -1.11 6.87 -3.22 4.76 -7.67 0.31
> 4060 -9.01 -2.43 6.58 -3.83 5.18 -8.64 0.37
> 4350 -10.1 -3.98 6.12 -4.73 5.37 -9.64 0.46
> 4670 -11.2 -5.65 5.55 -5.88 5.32 -10.7 0.5
> 5000 -12.3 -7.34 4.96 -7.22 5.08 -11.8 0.5
> 5360 -13.4 -9.03 4.37 -8.69 4.71 -12.9 0.5
> 5740 -14.6 -10.7 3.9 -10.2 4.4 -14.0 0.6
> 6160 -15.8 -12.3 3.5 -11.8 4.0 -15.2 0.6
> 6600 -16.9 -13.9 3.0 -13.4 3.5 -16.3 0.6
> 7070 -18.1 -15.4 2.7 -14.9 3.2 -17.5 0.6
> 7580 -19.3 -16.9 2.4 -16.4 2.9 -18.7 0.6
> 8120 -20.5 -18.4 2.1 -17.9 2.6 -19.9 0.6
> 8710 -21.7 -19.8 1.9 -19.4 2.3 -21.1 0.6
> 9330 -22.9 -21.2 1.7 -20.9 2.0 -22.4 0.5
> 10000 -24.1 -22.6 1.5 -22.3 1.8 -23.6 0.5
> --------------------------------------------------------------
>
> Now let's briefly analyze the results.
>
> CASE 2
> This is the network designed for an 8 ohm load used with the
> actual driver. Here, we see that overall, we have a deviation
> overall of -1.38 to +6.86 dB from target response (total
> range of 8.24 dB), and within the 2 octaves centered on the
> target crossover frequency, the deviation is -1.36 to +6.86
> dB (range of 8.24 dB).
>
> CASE 3
> This is the network with values reworked assuming an 11.3 ohm
> resistive load. In this case, the overall deviation from
> target is -2.97 dB to 5.37 dB (range of 8.34 dB), and is the
> same for the 2 octaves centered around the target crossover
> point.
>
> CASE 4
> This is the network which incorporates the conjugate
> impedance correction and has crossover values adjusted to the
> actual load presented, approximately 6.88 ohms. The deviation
> from target response is now -0.11 to 0.6 dB overall (range of
> 0.71 dB), and within -0.11 to 0.5 dB (range 0.61) over the 2
> octave span centered on the target crossover point.
>
> >From this we can directly answer the original question:
>
> > Where available, is it more appropriate to use the actual
> > impedence of the driver at the x-over point, rather than
> > the nominal impedence?
>
> It would seem that, at least for the 2nd order low pass case,
> the answer is most definitely no, it is not more appropriate.
> The range of error is essentially the same, the maximum errors
> just occur at somewhat different frequencies.
>
> Using the expedient of a complex impedance conjugate, even a
> simple first order, non-optimized conjugate, gets us much closer
> to the desired target response. Indeed, the deviation resulting
> from this quick experiment is actually less than can be
> reasonably expected from sample-to-sample variations in drivers
> of the same model.
>
> Two contentious phrases were introduced in this discussion,
> phrases that were absent a working definiton, those being
> "effective crossover" and "desired slope." I will, for the
> purpose of clarification, propose a definition for each:
>
> effective crossover: A crossover function that meets the
> requirements and constraints set by the driver properties
> and the desired system target response. An effective
> crossover must provide the transfer function necessary to
> achieve the full target system response, given the drivers
> used in that system.
>
> desired slope: the slope of the amplitude vs. frequency
> response that is defined by the required crossover transfer
> function needed to meet the target system response.
>
> There was a derived phrase of "same slope" which caused a rather
> innappropriate amount of semantic bickering. However, it can be
> shown that "same slope" is, in the current context, identical to
> "desired slope," in the sense that the slope required is the
> "same" as that defined by the "desired" crossover transfer
> function.
>
> It was asserted that:
>
> "one can design effective crossovers without zobels [by]
> going to higher order filters to get the desired slopes."
>
> Using the very practical working constraints that the "desired
> slope" is the slope defined by the specific transfer function
> needed to achieve the target system response I syill, in the
> absence of any evidence to the contrary, say no, it is not. The
> basis of the assertion quoted is that a transfer function of,
> say,
>
> 1
> --------------------
> as^3 + bs^2 + cs + 1
>
> results in the same transfer function (because it is, after all,
> the tranbsfer function that defines whether the crossover is
> effective or not, a point not yet credibly challenged) as:
>
> 1
> -------------
> ms^2 + ns + 1
>
> Now, the two WILL be the same IFF a=0, b=m and c=n, but that
> simply reduces the third-order transfer function to a second
> order transfer function.
>
> The "desired slope" of a crossover is not just the slope in the
> stop-band, it's the slope at every point in the overall
> operating bandwidth of the filter. And the slope is merely one
> parameter of the complex transfer function of the system, it is
> merely the derivative of response WRT frequency.
>
> To date, no evidence has been provided that if the "desired
> slope" is that afforded by a passive resistive terminated filter
> of a specific transfer function, that a higher order transfer
> function can provide that "desired slope."
>
Anonymous

Stephen McLuckie wrote:
> It's quite possible, for example, to build an effective 4th
> order low pass crossover using just an inductor and a cap.

A "4th order crossover" is one whose transfer function is a 4th order
complex polynomial.

Can you show us how a single inductor and capacitor combine to
form a 4th order filter according to this widely accepted
definition of filter order?
Anonymous

"Hugo Lalumiere" <hlalumiere@videotron.ca> wrote in message
news:CG7_d.55065\$nT2.2449275@weber.videotron.net
>>> ... Either refute what I showed (via the logic of or the
>>> definition of terms used therein) or recant. Those are the only two
>>
>> Since my original statement was not made as a formal statement of
>> fact, I decline on the grounds of irelevance.
>>
>> I suggest that one and all read the following:
>>
>> http://www.searchlores.org/schopeng.htm
>>
>
> My opinion of whoever abides by the rules suggested on that page is
> one of stupidity and closed-mindedness.

Anonymous

<dpierce@cartchunk.org> wrote in message
>
> Stephen McLuckie wrote:
> > It's quite possible, for example, to build an effective 4th
> > order low pass crossover using just an inductor and a cap.
>
> A "4th order crossover" is one whose transfer function is a 4th order
> complex polynomial.
>
> Can you show us how a single inductor and capacitor combine to
> form a 4th order filter according to this widely accepted
> definition of filter order?

A 2 mH inductor and a 10uF cap will produce a fourth order crossover
(Butterworth, if I remember rightly) at around 2kHz on many typical 6.5 inch
speakers as well as correcting for the response step caused by the baffle.
The trick doesn't work very well at frequencies higher than this, but for a
crossover around 2 kHz it's usually worth a shot.

If you want a mathematical analysis of why it works, I can't help.

Stephen
Anonymous

On 17 Mar 2005 04:31:41 -0800, dpierce@cartchunk.org wrote:

>Can you show us how a single inductor and capacitor combine to
>form a 4th order filter according to this widely accepted
>definition of filter order?

A final 4th order filter can be designed by including the driver(s) in the
design. However the LC part will be second order at best.
Anonymous

1. Carry your opponent's proposition beyond its natural limits;
exaggerate it. The more general your opponent's statement becomes,
the more objections you can find against it. The more restricted
and narrow your own propositions remain, the easier they are to
defend.
2. Use different meanings of your opponent's words to refute his
argument. Example: Person A says, "You do not understand the
mysteries of Kant's philosophy. Person B replies, "Of, if it's
mysteries you're talking about, I'll have nothing to do with them.
3. Ignore your opponent's proposition, which was intended to refer
to some particular thing. Rather, understand it in some quite different
sense,
and then refute it. Attack something different than what was asserted.
agree to them in no definite order. By this circuitous route you
Example, if the opponent is a member of an organization
or a religious sect to which you do not belong, you may employ the
declared opinions of this group against the opponent.

I mean, come on....

Hugo

"Arny Krueger" <arnyk@hotpop.com> wrote in message
news oydnQboCdYk4aTfRVn-iw@comcast.com...
> "Hugo Lalumiere" <hlalumiere@videotron.ca> wrote in message
> news:CG7_d.55065\$nT2.2449275@weber.videotron.net
> >>> ... Either refute what I showed (via the logic of or the
> >>> definition of terms used therein) or recant. Those are the only two
> >>
> >> Since my original statement was not made as a formal statement of
> >> fact, I decline on the grounds of irelevance.
> >>
> >> I suggest that one and all read the following:
> >>
> >> http://www.searchlores.org/schopeng.htm
> >>
> >
> > My opinion of whoever abides by the rules suggested on that page is
> > one of stupidity and closed-mindedness.
>