[genericaudioperson]

Hello,

Is there a common technique for hooking up more than the standard two
speakers to a power amp? If you had a powerful amp, you could run
four speakers. But I'm not sure if you use a simple Y cable, or if
you need a signal conditioning device of some sort to do it properly.

It makes me wonder how a live concert can take a stereo feed off of a
mixing console, and then send it to multiple power amps and multiple
speakers. There must be some sort of standard process to make the
signals rout properly without drop-off and hiss.

[William Sommerwerck]

You can connect as many speakers as you like to an amplifier output. You
simply have to be sure that the combined impedance is not lower than what
the amplifier is rated to drive.

[Richard Crowley]

"genericaudioperson" wrote from Gooooooooooogle Groups ...
Is there a common technique for hooking up more than the standard two
speakers to a power amp?

Is two speakers "the standard"?
The standard for what, exactly?

Can you run more than (x) speakers from a power amp?
Yes, you can run as many as the amplifier will safely drive.

Is there a "common technique" for connecting multiple speakers?
No. It depends on exactly what the specific amplifier and
speakers are.

If you had a powerful amp, you could run four speakers.

If you had a powerful (enough) amp you could run 500 speakers
(or substitue whatever number you wish.)

But I'm not sure if you use a simple Y cable,

No, it is not done with cable adapters. It is more sophisticated than that.

If you have a specific configuration in mind, you could explicitly
reveal what it is. Otherwise you are asking a hypothetical question
for which there are thousands of possiible answers, most of them
likely meaningless or even confusing to you.

or if
you need a signal conditioning device of some sort to do it properly.

Signal conditioning devices have nothing to do with driving multiple
speakers from an amplifier(s).

It makes me wonder how a live concert can take a stereo feed off of a
mixing console, and then send it to multiple power amps and multiple
speakers. There must be some sort of standard process to make the
signals rout properly

There is usually more (and sometimes less) than "a stereo feed".
Larger venues typically don't bother with "stereo" because most
of the audience would hear only one side and miss the other.

The outputs from the mixing console are sometimes just fed in
parallel to multiple amplifiers (which have high-impedance,
"bridging" inputs). Or sometimes using distribution amplifers
and/or frequency crossovers, etc.
And in larger venues, using equipment which compensates for
time alignment betweeen multiple sets of speakers, etc. etc.

without drop-off and hiss.

Dunno what you mean by "drop-off"?

As for hiss, typical professional equipment has enough dynamic
range to run signals well above the levels where you would hear
hiss. Besides, even with no audience in them, large venues have
enough residual noise to mask most hiss unless you have you ear
within a few inches of the speaker. (and you wouldn't want it there
for long when they send any kind of signal through it.)

[Laurence Payne[_2_]]

On Sat, 29 Nov 2008 15:18:15 -0800, "Richard Crowley"
wrote:

his usual screed of contempt to an inexpert question

Richard, are you the Grinch?

[Richard Crowley]

"Laurence Payne" wrote...
"Richard Crowley" wrote:

his usual screed of contempt to an inexpert question

Richard, are you the Grinch?

Perhaps we should set up news:alt.flame.richard for you so the rest
of us can discuss audio topics here.

[genericaudioperson]

This is interesting. So when you add speakers, the impedance drops.
And then you have to do some sort of math to figure it out. It's
intersesting that there is a low amount of impedance you are trying to
avoid. Usually "overload" means a large number (for us mortals who
don't know what we're doing).

It must be a splitter cable. If the amp only has two outputs, and you
are trying to run 4 enclosures, then you need to mult the signal with
a Y-cable or something like that. That sounds like something that is
not on the cable wall at Guitar Center, which means I don't know how
to use it
:-). Maybe it's behind the counter in the voodoo area.

[Chris Hornbeck]

On Sat, 29 Nov 2008 17:09:24 -0800 (PST), genericaudioperson
wrote:

This is interesting. So when you add speakers, the impedance drops.
And then you have to do some sort of math to figure it out.

Impedances add up the same way as resistances; parallel two
impedances, and the result is the product over the sum, just
like resistors.

But maybe a better way for you to think about the issue is
to think in terms of current. Each speaker cabinet will need
to draw some current from the amplifier. The current drawn
by both cabinets is a simple sum, just like you'd expect.


It's interesting that there is a low amount of impedance you are trying to
avoid. Usually "overload" means a large number (for us mortals who
don't know what we're doing).

It's actually a large amount of current that you're needing to
avoid, because the amplifier will balk at trying to supply it.


The reason that there isn't a simple, single answer to your question
isn't that it's complicated or that you're not smart enough to
understand it - it's that the numbers aren't available. Speakers
are a complicated load and amplifiers are a complicated source.
There are rules of thumb and sometimes actual experience of a
particular setup, but God dwells in the details, and she's not
telling, often as not.


All the best fortune,
Chris Hornbeck

[Michael R. Kesti[_3_]]

genericaudioperson wrote:

This is interesting. So when you add speakers, the impedance drops.
And then you have to do some sort of math to figure it out. It's
intersesting that there is a low amount of impedance you are trying to
avoid. Usually "overload" means a large number (for us mortals who
don't know what we're doing).

It is interesting and a source of confusion because a lower impedance
presents a larger load. So, an amplifier "spec" that reads "minimum
load: 4 ohms" is somewhat ambiguous!

It must be a splitter cable. If the amp only has two outputs, and you
are trying to run 4 enclosures, then you need to mult the signal with
a Y-cable or something like that. That sounds like something that is
not on the cable wall at Guitar Center, which means I don't know how
to use it
:-). Maybe it's behind the counter in the voodoo area.

There are many ways to go about distributing amplifier outputs to speakers.
One is, as you say, a slitter ( "wye" or, more commonly 'Y') cable. This
implies the use of 1/4" phone jacks which, although popular, are poorly
suited for amplifer to speaker applications.

A step up is banana plugs (http://en.wikipedia.org/wiki/Banana_plug) and
and binding posts (http://en.wikipedia.org/wiki/5_way_binding_post).
Some banana plugs are stackable and make connecting multiple speakers in
parallel as simple as plugging one connector into the back of others.

Pro sound systems often use custom built rack panels with connectors
that allow convenient and versatile patching and connecting speakers to
the amplifiers mounted in the rack(s). The Speakon connector
(http://en.wikipedia.org/wiki/Speakon) is superior in many ways and is
popular with the pros.

--
================================================== ======================
Michael Kesti | "And like, one and one don't make
| two, one and one make one."
mrkesti at hotmail dot com | - The Who, Bargain

[Mark]

On Nov 29, 10:50*pm, "Michael R. Kesti"
wrote:
genericaudioperson wrote:
This is interesting. *So when you add speakers, the impedance drops.
And then you have to do some sort of math to figure it out. *It's
intersesting that there is a low amount of impedance you are trying to
avoid. *Usually "overload" means a large number (for us mortals who
don't know what we're doing).

It is interesting and a source of confusion because a lower impedance
presents a larger load. *So, an amplifier "spec" that reads "minimum
load: 4 ohms" is somewhat ambiguous!

It must be a splitter cable. *If the amp only has two outputs, and you
are trying to run 4 enclosures, then you need to mult the signal with
a Y-cable or something like that. *That sounds like something that is
not on the cable wall at Guitar Center, which means I don't know how
to use it
:-). *Maybe it's behind the counter in the voodoo area.

There are many ways to go about distributing amplifier outputs to speakers.
One is, as you say, a slitter ( "wye" or, more commonly 'Y') cable. *This
implies the use of 1/4" phone jacks which, although popular, are poorly
suited for amplifer to speaker applications.

A step up is banana plugs (http://en.wikipedia.org/wiki/Banana_plug) and
and binding posts (http://en.wikipedia.org/wiki/5_way_binding_post).
Some banana plugs are stackable and make connecting multiple speakers in
parallel as simple as plugging one connector into the back of others.

Pro sound systems often use custom built rack panels with connectors
that allow convenient and versatile patching and connecting speakers to
the amplifiers mounted in the rack(s). *The Speakon connector
(http://en.wikipedia.org/wiki/Speakon) is superior in many ways and is
popular with the pros.



so the op's questions is still valid..

the standard methods I know of connect the speakers in paralel...

but if you have too many speakers ___what is the industry standard way
of dealing with this?

I know you may want to use a series parallel connection but I have
never seen a breakout box or other standard device that you can buy at
GC for connecting a group of speakers in a series parallel arrangment,
is there a way or is that just not done?


the other alternative is to use multiple amplifers which I suppose is
the standard solution..

Mark

[Mike Rivers]

genericaudioperson wrote:
This is interesting. So when you add speakers, the impedance drops.
And then you have to do some sort of math to figure it out.

This is basic electricity, something that anyone going beyond a
plug-and-play system should understand.

intersesting that there is a low amount of impedance you are trying to
avoid. Usually "overload" means a large number (for us mortals who
don't know what we're doing).

The lower the impedance, the closer you get to a short circuit. Does
that help you to understand what's going on here?

It must be a splitter cable. If the amp only has two outputs, and you
are trying to run 4 enclosures, then you need to mult the signal with
a Y-cable or something like that.

The reason why it's not a common off-the-shelf item is because hooking
up multiple plug-and-play speakers isn't something that's done very
often - simply because it's often not a good idea to do that. If you
exceed the power rating of the amplifier, usually you'll know it before
you do any damage because you'll hear distortion at a lower volume than
you expect. But if you keep operating it that way, you WILL damage the
amplifier, the speakers, or both.

You MUST know what you're doing in this business if you want to keep
your equipment working. Some speakers are built with two connectors,
making it easy to connect a second speaker in the chain, but the people
who make the speakers don't know what amplifier you're connecting them
to, so just because you CAN hook them up doesn't guarantee that they'll
work.

You should also understand what you're asking when you ask a "will this
work?" question on a forum. In order to give a reasonably good answer,
someone must know the characteristics of the amplifier and speakers that
you're planning to use. Just posting model numbers means that we need to
research the equipment, do some calculations, and make a (not
guaranteed) recommendation. That's a system engineering job, and people
make good money doing that work.

So do your homework before you jump in. Chances are you can figure
things out yourself. You'll get more cooperation and more complete
information if you start with all the details you can pull together.




--
If you e-mail me and it bounces, use your secret decoder ring and reach
me he
double-m-eleven-double-zero at yahoo -- I'm really Mike Rivers
)

[Mike Rivers]

Mark wrote:

but if you have too many speakers ___what is the industry standard way
of dealing with this?

I know you may want to use a series parallel connection but I have
never seen a breakout box or other standard device that you can buy at
GC for connecting a group of speakers in a series parallel arrangment,
is there a way or is that just not done?

The "industry standard" way of dealing with a large number of speakers,
for instance the speakers installed in the ceiling of a factory or
department store, is to use what's known as a constant voltage
distribution system. You'll occasionally see references to a 70.7 volt
output on an amplifier. The way this works is that each speaker has a
transformer with it that determines how much POWER that speaker get. It
works like your house wiring. You can plug in a lamp, a computer, a
toaster, as many things as you want, until you blow the fuse, and
everything gets the same power and enough current to do the work.

As far as an off-the-shelf series/parallel breakout, nope. There are too
many possible combinations of speakers and desired impedance load to the
amplifier that a store couldn't possibly stock all of them. These
arrangements are all custom-wired, and often the speakers are chosen as
part of the design.


--
If you e-mail me and it bounces, use your secret decoder ring and reach
me he
double-m-eleven-double-zero at yahoo -- I'm really Mike Rivers
)

[Richard Crowley]

"Mark" wrote from Gooooooooooogle Groups...
so the op's questions is still valid..
the standard methods I know of connect the speakers in paralel...
but if you have too many speakers ___what is the industry standard way
of dealing with this?

1. Constant-voltage system ("70-volt" et.al.)
2. Series-parallel connections (to maintain total impedance)
3. Multiple amplifiers.
4. likely others also

I know you may want to use a series parallel connection but I have
never seen a breakout box or other standard device that you can buy at
GC for connecting a group of speakers in a series parallel arrangment,
is there a way or is that just not done?

There is a great deal more to sound reinforcment systems than
what is available at your local guitar shop. We don't even know
whether the OP is asking about portable or installed systems?

I once maintained an amphitheatre in a med school where they
had special transducers at each seat for the students' stethoscopes.
The lecturer had recordings of normal and abnormal heart (and
other) sounds which he used to familiarize the future physicians
with what "normal" is supposed to sound like, etc. These 350
transducers were such high impedance that even when all
connected in parallel, they represented 20 ohms combined
impedance.

I also designed and installed a seat-back system in a church
which uses 3x5 speakers on 18-inch spacing, essentially one
speaker per person, to avoid hanging a big bin from the
ceiling to cover the (octagonal) seating area. The system is
used exclusively for speech reinforcement as all the music
is acoustic (starting with the tracker pipe organ and concert
grand piano). Photo at
http://www.rcrowley.com/Rieger/SSDAReiger2.htm
You can barely see the continuous grille at the top of the
pew-back . I should post some closer photos of the detail.

The speakers in each row are all wired in series, and the
rows are wired in parallel. I recruited the choir members
to help install all the speakers, and trained 4-5 of them
how to solder properly. It worked out quite well. Only
one screwdriver through a cone, and very few cold
solder joints upon final inspection (by me).

The speakers are divided into 4 sections, each driven by
an amplifier channel in order to implement time-delay
correction. The total impedance turned out to be something
between 8 and 16 for each section, so they were easily
driven by conventional amplifiers. The 550-seat
auditorium is easily driven (for speech reinforcement) by
~300W total amplifier power which idles along at a fraction
of that power.

The new auditorium just celebrated its 25-year anniversary
and the system still works quite well. The potential gain
before feedback is amazing. :-)

[Les Cargill]

Mike Rivers wrote:
genericaudioperson wrote:
This is interesting. So when you add speakers, the impedance drops.
And then you have to do some sort of math to figure it out.

This is basic electricity, something that anyone going beyond a
plug-and-play system should understand.

intersesting that there is a low amount of impedance you are trying to
avoid. Usually "overload" means a large number (for us mortals who
don't know what we're doing).

The lower the impedance, the closer you get to a short circuit. Does
that help you to understand what's going on here?


alternate explanation

The lower the impedance, the more current. The more current
into a constant load, the more heat*. The more heat, the higher the
probability of failure....

*it's called IR heating - current and resistance....

snip

--
Les Cargill

[Mark]

On Nov 30, 9:30*am, "Richard Crowley" wrote:
"Mark" *wrote from Gooooooooooogle Groups...

so the op's questions is still valid..
the standard methods I know of connect the speakers in paralel...
but if you have too many speakers ___what is the industry standard way
of dealing with this?

1. Constant-voltage system ("70-volt" et.al.)
2. Series-parallel connections (to maintain total impedance)
3. Multiple amplifiers.
4. likely others also



OK I know about 70 volt system for that kind of lower power PA...
I was thinking (and I should have said) in a PA FOH application where
there are a large number of speakers in an array at the FOH.

How do most people manage this.... with custom cables to create a
series parallel connection to the amp or just use a large number of
amps as well or what?

In other words, when I go to a venue and see maybe 24 speakers at FOH
and a rack of maybe 6 amps, I would guess there are 2 speakers in
parallel per side 6x4 = 24... but usually it doesn't work out that
simple, sometimes i see maybe 10 speakers on each side up on cranes,
are these wired together somehow or how is it done?

Mark

[Richard Crowley]

"Mark" wrote...
OK I know about 70 volt system for that kind of lower power PA...
I was thinking (and I should have said) in a PA FOH application where
there are a large number of speakers in an array at the FOH.

How do most people manage this.... with custom cables to create a
series parallel connection to the amp or just use a large number of
amps as well or what?

In other words, when I go to a venue and see maybe 24 speakers at FOH
and a rack of maybe 6 amps, I would guess there are 2 speakers in
parallel per side 6x4 = 24... but usually it doesn't work out that
simple, sometimes i see maybe 10 speakers on each side up on cranes,
are these wired together somehow or how is it done?

Typically, there is a large rack of amplifiers that go with each of those
speaker stacks. In the rack along with the amplifiers is likely also some
sort of active or passive (line-level) signal distribution and/or electronic
(line-level) crossovers which route lows, mids, highs, etc. to separate
amplifier and speaker sections.

[Mark]

Typically, there is a large rack of amplifiers that go with each of those
speaker stacks. In the rack along with the amplifiers is likely also some
sort of active or passive (line-level) signal distribution and/or electronic
(line-level) crossovers which route lows, mids, highs, etc. to separate
amplifier and speaker sections.

ok so far so good...

then only two or maybe three speakers are connected togther in
parallel to each amp output using standard speakon cables etc?

Mark

[Richard Crowley]

"Mark" wrote ...
Richard wrote...
Typically, there is a large rack of amplifiers that go with each of those
speaker stacks. In the rack along with the amplifiers is likely also some
sort of active or passive (line-level) signal distribution and/or
electronic
(line-level) crossovers which route lows, mids, highs, etc. to separate
amplifier and speaker sections.

ok so far so good...

then only two or maybe three speakers are connected togther in
parallel to each amp output

Yes one or two cabinets connected to each amplifier output channel,
etc. This is done as much for redundancy (failure survival) as for
other reasons.

using standard speakon cables etc?

For big racks of amplifiers and big stacks of speaker cabinets, they
more likely use pre-assembled cable harnesses which use larger multi-
pin connectors rather than one-at-a-time Speakons, etc. Not only are
multi-pin connectors faster to deploy (and strike), but they also reduce
accidental mis-connection. Any kind of (pre-engineered) series/
parallel speaker wiring is likely built into the (custom) cable harnesses.

[Arny Krueger]

"genericaudioperson" wrote
in message

Hello,

Is there a common technique for hooking up more than the
standard two speakers to a power amp? If you had a
powerful amp, you could run four speakers. But I'm not
sure if you use a simple Y cable, or if you need a signal
conditioning device of some sort to do it properly.

If you have 4 identical speakers, you can hook them up in series-parallel,
and they will load the amp like just one speaker, but have 4 times the power
handling capacity.

[Scott Dorsey]

genericaudioperson wrote:

Is there a common technique for hooking up more than the standard two
speakers to a power amp? If you had a powerful amp, you could run
four speakers. But I'm not sure if you use a simple Y cable, or if
you need a signal conditioning device of some sort to do it properly.

This is discussed in the Yamaha Sound Reinforcement Handbook. You can
run as many parallel speakers off of an amp as you want, so long as the
total impedance the amplifier sees is higher than it's minimum rated load
impedance.

So if the amp says "4 ohm load or higher" you can put two 8 ohm speakers
per channel, but not three.

It makes me wonder how a live concert can take a stereo feed off of a
mixing console, and then send it to multiple power amps and multiple
speakers. There must be some sort of standard process to make the
signals rout properly without drop-off and hiss.

In the case of the line level signals it's much easier, since the output
impedance is very low and the input impedance is very high. You can
Y with impunity for the most part.
--scott
--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[Scott Dorsey]

genericaudioperson wrote:
This is interesting. So when you add speakers, the impedance drops.
And then you have to do some sort of math to figure it out. It's
intersesting that there is a low amount of impedance you are trying to
avoid. Usually "overload" means a large number (for us mortals who
don't know what we're doing).

Go right now and buy the Yamaha Sound Reinforcement Handbook. It will
answer most of these elementary electrical questions. There is also
a discussion of amp loading in the FAQ for this group.
--scott


--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[Scott Dorsey]

Mark wrote:

OK I know about 70 volt system for that kind of lower power PA...

I once ran a 5KW 70 volt system. And it used to be very common for
70V systems to be used in theatres to deal with the long runs between
the amps in the projection booth and the speakers behind the screen.

I was thinking (and I should have said) in a PA FOH application where
there are a large number of speakers in an array at the FOH.

In most of those applications, the speakers are being individually
processed....each driver has an amplifier connected to it and a DSP
module devoted to that amplifier. All the DSP modules are fed from
the console and there is usually some sort of workstation that allows
the operator to adjust DSP parameters.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[Scott Dorsey]

Arny Krueger wrote:
"genericaudioperson" wrote
in message

Hello,

Is there a common technique for hooking up more than the
standard two speakers to a power amp? If you had a
powerful amp, you could run four speakers. But I'm not
sure if you use a simple Y cable, or if you need a signal
conditioning device of some sort to do it properly.

If you have 4 identical speakers, you can hook them up in series-parallel,
and they will load the amp like just one speaker, but have 4 times the power
handling capacity.

And twice the distortion and some amount approaching twice the frequency
response abnormalities. Remember when you do this, each driver is in series
with a nonlinear load.
--scott
--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[Arny Krueger]

"Scott Dorsey" wrote in message

Arny Krueger wrote:
"genericaudioperson"
wrote
in message

Hello,

Is there a common technique for hooking up more than the
standard two speakers to a power amp? If you had a
powerful amp, you could run four speakers. But I'm not
sure if you use a simple Y cable, or if you need a
signal conditioning device of some sort to do it
properly.

If you have 4 identical speakers, you can hook them up
in series-parallel, and they will load the amp like just
one speaker, but have 4 times the power handling
capacity.

And twice the distortion and some amount approaching
twice the frequency response abnormalities.

Not at all. In theory and in practice, the effective source impedance for
either speaker calculates and measures out to be about half the output
impedance of the source.

Remember
when you do this, each driver is in series with a
nonlinear load.

But, its the identical same nonlinear load. That's one reason why I
specified "4 identical speakers". If they are signficantly different, then
many of the bad things you suggest may happen.

[Misifus[_2_]]

genericaudioperson wrote:
This is interesting. So when you add speakers, the impedance drops.
And then you have to do some sort of math to figure it out. It's
intersesting that there is a low amount of impedance you are trying to
avoid. Usually "overload" means a large number (for us mortals who
don't know what we're doing).

It must be a splitter cable. If the amp only has two outputs, and you
are trying to run 4 enclosures, then you need to mult the signal with
a Y-cable or something like that. That sounds like something that is
not on the cable wall at Guitar Center, which means I don't know how
to use it
:-). Maybe it's behind the counter in the voodoo area.


If you run a splitter cable, basically, the impedance becomes half.
That is only practical if the amp is able to handle the increased
current required by the lowered impedance. That is, roughly, double the
current. Some amps will handle that happily, but many will not. If I
didn't know for certain that the amp was safe with the lower impedance,
I wouldn't try to operate it with the four speakers.

There are many other variables involved and much of the discussion here
has involved them, but this is the general situation.

-Raf

--
Misifus-
Rafael Seibert

Photos: http://www.flickr.com/photos/rafiii
home: http://www.rafandsioux.com

[Mark]

Not at all. In theory and in practice, the effective source impedance for
either *speaker calculates and measures out to be about *half the output
impedance of the source.


Really?

I could see this might be true if the speaker coils were like the
windings of a center tapped transformner, but I don't think they are,
they are not magnetically or acousticaly closely coupled to each other
and the winding resistance is high compared to the self coupling of
each coil...

I don't think the source Z that each speaker sees could be any lower
than the source Z of the amp output ...and is probably higher...

For the sake of discussion, lets assume the source Z of the amp is 0
Ohms. I think each speaker sees a source Z just equal to it's own
source Z for 2 speakers in series. Or for 4 speakers in series
parallel, each speaker sees a source Z equal to 1/3 of its own?
(assumming identical speakers)

But yes each speaker sees exactly 1/2 the VOLTAGE at the amp output..


this IS an interestig question...

Mark

[Chris Hornbeck]

On Mon, 1 Dec 2008 20:03:19 -0800 (PST), Mark
wrote:

But yes each speaker sees exactly 1/2 the VOLTAGE at the amp output..

"Exactly" is the key to the puzzle...


Much thanks, as always,
Chris Hornbeck

[Arny Krueger]

"Mark" wrote in message

Not at all. In theory and in practice, the effective
source impedance for either speaker calculates and
measures out to be about half the output impedance of
the source.

Really?

I could see this might be true if the speaker coils were
like the windings of a center tapped transformer, but I
don't think they are, they are not magnetically or
acoustically closely coupled to each other and the winding
resistance is high compared to the self coupling of each
coil...

It's not necessary that they be coupled. Just do the math with resistors.

I don't think the source Z that each speaker sees could
be any lower than the source Z of the amp output ...and
is probably higher...

Just do tht math.

For the sake of discussion, lets assume the source Z of
the amp is 0 Ohms. I think each speaker sees a source Z
just equal to it's own source Z for 2 speakers in series.
Or for 4 speakers in series parallel, each speaker sees a
source Z equal to 1/3 of its own? (assumming identical
speakers)

You are just waving your hands, and using a weird example of an amp with
zero output impedance.

But yes each speaker sees exactly 1/2 the VOLTAGE at the
amp output..

Follow that thought.

this IS an interestig question...

Seemed intuitively clear to me.

An amplifier driving two identical speakers in series, is like two amps in
series, each putting out half the voltage with half the source impedance,
both in series driving the same 2 speakers in series.

Now, rearrange things so that one speaker and one amp are connected together
in each of two independent systems.

It's all the same.

[Mark]

For the sake of discussion, lets assume the source Z of
the amp is 0 Ohms. *I think each speaker sees a source Z
just equal to it's own source Z for 2 speakers in series.
Or for 4 speakers in series parallel, each speaker sees a
source Z equal to 1/3 of its own? (assumming identical
speakers)

You are just waving your hands, and using a weird example of an amp with
zero output impedance.

It's not necessary that they be coupled. Just do the math with resistors.




OK lets do the math... for a simple case of resistors...
assume two identical speakers in series, each speaker = 8 Ohms.
and assume the speakers behave as resistors
and assume the amp output Z = 1 Ohm
assume all Z's are simply R

In this most simple case the math says each speaker sees a source Z of
the other speaker in series with the amp 8+1 = 9 Ohms...

I think your point was each speaker would see 1/2 Ohm, I don't see
that?

Yes, I see each speaker sees 1/2 the voltage, that is obvious and will
always be true even if the speaker Z varies as a function of frequency
or even if it is non-linear woth amplitude, as long as the two
speakers are identical.

But I don't see the effective source Z being 1/2.

Mark

[Chris Hornbeck]

On Tue, 2 Dec 2008 06:45:26 -0800 (PST), Mark
wrote:

OK lets do the math... for a simple case of resistors...
assume two identical speakers in series, each speaker = 8 Ohms.
and assume the speakers behave as resistors
and assume the amp output Z = 1 Ohm
assume all Z's are simply R

In this most simple case the math says each speaker sees a source Z of
the other speaker in series with the amp 8+1 = 9 Ohms...

I think your point was each speaker would see 1/2 Ohm, I don't see
that?

Yes, I see each speaker sees 1/2 the voltage, that is obvious and will
always be true even if the speaker Z varies as a function of frequency
or even if it is non-linear woth amplitude, as long as the two
speakers are identical.

But I don't see the effective source Z being 1/2.

Whoa!, when did we change from four speakers per channel
to two? Somewhere upstream, fersure.

For four identical speakers in series-parallel, the load
to the amplifier is the same as that of one of the speakers,
and each speaker gets 1/2 the voltage and 1/2 the current
from the amplifier, so sees the same source impedance as
a single speaker.

Somewhere the discussion slipped from four speakers to two,
leading to this confusion.

Much thanks, as always,
Chris Hornbeck

[Mark]

On Dec 3, 12:21*am, Chris Hornbeck
wrote:
On Tue, 2 Dec 2008 06:45:26 -0800 (PST), Mark
wrote:





OK lets do the math... for a simple case of resistors...
assume two identical speakers in series, each speaker = 8 Ohms.
and assume the speakers behave as resistors
and assume the amp output Z * = 1 Ohm
assume all Z's are simply R

In this most simple case the math says each speaker sees a source Z of
the other speaker in series with the amp 8+1 = 9 Ohms...

I think your point was each speaker would see 1/2 Ohm, I don't see
that?

Yes, I see each speaker sees 1/2 the voltage, that is obvious and will
always be true even if the speaker Z varies as a function of frequency
or even if it is non-linear woth amplitude, *as long as the two
speakers are identical.

But I don't see the effective source Z being 1/2.

Whoa!, when did we change from four speakers per channel
to two? Somewhere upstream, fersure.

For four identical speakers in series-parallel, the load
to the amplifier is the same as that of one of the speakers,
and each speaker gets 1/2 the voltage and 1/2 the current
from the amplifier, so sees the same source impedance as
a single speaker.

Somewhere the discussion slipped from four speakers to two,
leading to this confusion.

Much thanks, as always,
Chris Hornbeck- Hide quoted text -


Chris,

the question is not about what load the AMP sees, you are correct what
you said about what load the amp sees but that is not in question, the
question I am discussing is not what load that the amp sees but rather
what does each speaker see as a source Z driving it...this is what
determines the damping factor for the speaker..

in the case of one speaker, the speaker obvisously sees the output Z
of the amp.

The question at hand is what does each speaker see as a driving Z when
two speakers are connected in series.. and it is not a simple
question as it first appears.....

Arny,

I think you are right..for the special case of two identical speakers,
the back EMF generated by each speaker is identical so you cannot use
the simple method of treating the speakers as seperate independent
loads. These are DEPENDENT sources. If you use the simple method of
indepenedent sources, you get the simple wrong answer of 8+1 = 9 Ohms
for the example case above. But I now think this is wrong and you are
right. To calculate the right answer you have to consider that the
two EMFs are not independent but identical so the back EMFs are
identical and you cannot analyze this in the simple way like resistors
but rather have to consider that you have DEPENDENT EMF sources.
Using symmetry as you suggested, I agree you are correct, each
speaker sees a source Z of 1/2 the amp source Z or 1/2 Ohm in this
example, a big difference!

Note this is true only for the special case of INDENTICAL speakers so
that the back EMF is identical and you have DEPENDENT sources. If you
connect two different speakers in series then they are no longer
exactly DEPENDENT sources and the problem gets much more complicated.
My orignal answer of 9 Ohms is correct for totally independent sources
like resistors.

thanks for the interesting discussion

Mark

[William Sommerwerck]

This long and currently pointless (or at least meandering) thread began when
someone largely ignorant of the most-basic electronics theory asked a
question he probably had no real interest in the answer for.

I see this over and over. People trying to be helpful spend huge amounts of
time answering questions that are covered in library books. There has got to
be a better way to direct people to the information they need.

I rarely ask broad questions, limiting myself to something specific that I
couldn't readily find the answer for. I consider it my own responsibility to
educate myself, and not to abuse other peoples' generosity.

[Scott Dorsey]

William Sommerwerck wrote:
This long and currently pointless (or at least meandering) thread began when
someone largely ignorant of the most-basic electronics theory asked a
question he probably had no real interest in the answer for.

I see this over and over. People trying to be helpful spend huge amounts of
time answering questions that are covered in library books. There has got to
be a better way to direct people to the information they need.

That IS what the FAQ is for, isn't it?
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[Mark]

On Dec 3, 9:31*am, "William Sommerwerck"
wrote:
This long and currently pointless (or at least meandering) thread began when
someone largely ignorant of the most-basic electronics theory asked a
question he probably had no real interest in the answer for.

I see this over and over. People trying to be helpful spend huge amounts of
time answering questions that are covered in library books. There has got to
be a better way to direct people to the information they need.

I rarely ask broad questions, limiting myself to something specific that I
couldn't readily find the answer for. I consider it my own responsibility to
educate myself, and not to abuse other peoples' generosity.

yes the original question from the OP was basic...

the secondary question re the impact series/parallel connection has on
speaker damping factor is not basic and is not covered in any book I
have seen...

if you find this long and pointless, please feel free to not
participate...

thanks

Mark

[GregS[_3_]]

In article , Mark wrote:
On Dec 3, 9:31=A0am, "William Sommerwerck"
wrote:
This long and currently pointless (or at least meandering) thread began w=
hen
someone largely ignorant of the most-basic electronics theory asked a
question he probably had no real interest in the answer for.

I see this over and over. People trying to be helpful spend huge amounts =
of
time answering questions that are covered in library books. There has got=
to
be a better way to direct people to the information they need.

I rarely ask broad questions, limiting myself to something specific that =
I
couldn't readily find the answer for. I consider it my own responsibility=
to
educate myself, and not to abuse other peoples' generosity.

yes the original question from the OP was basic...

the secondary question re the impact series/parallel connection has on
speaker damping factor is not basic and is not covered in any book I
have seen...

if you find this long and pointless, please feel free to not
participate...

This is long, as I may quote....sorry...I'm leaving part 2 out.


Damping: Loudspeakers In Series
Dick Pierce
Professional Audio Development

1 INTRODUCTION

An entire mythology surrounds the notion of damping in
loudspeakers. We have separately treated the oft-cited and
nearly useless "damping factor" specification in a separate
article. Here, we discuss much of the myth surrounding the
behavior of loudspeakers connected in series and the
seemingly intuitive effect on damping tat results. Of late,
this topic is relevant or several reasons.

First, we have seen a gain in use of multiple-woofer
systems, exemplified by the popular, so-called "D'Appolito"
configuration (often the woofers are connected in parallel,
but there are applications where a series connection could
be appropriate as well). Second, we have observed an
unfortunate trend in consumer electronics, especially in
home theater receivers. More and more, these receivers have
skimped on power supply and/or output stage design and are
quite unable to drive the lower impedances oft found in
today's speakers. The question often arises whether speakers
can be hooked in series, thus raising the impedance.

The answer often given to both of these scenarios is "Oh,
no, you can't do that. The damping of each speaker will be
severely reduced because of the series impedance of the
other speaker!

As you might have guessed, we're going to show why this is
wrong. We'll do this by taking an analytical approach, and
test our analysis by actually measuring actual systems.

2 WHAT IS DAMPING?

The term "damping" is has a very specific and unambiguous
definition: technically, it is a measure of how quickly
energy is removed from a resonant system. This definition
stands despite attempt to co-opt the term for otherwise
imprecise and often incorrect uses(1). It is a measure of
how quickly a resonant or oscillatory system is brought
under control by removing energy that would otherwise keep
the resonance going.

Energy is stored in reactive elements. These include masses
and compliances (or springs) in the mechanical world, and
inductances and capacitances in the electrical world.
Mechanically, energy of a mass is the kinetic energy due to
the motion of a mass. The kinetic energy of a moving mass
equal to the mass times the velocity squared. In a spring or
compliance, the energy is stored as potential energy in the
compression or extension. The potential energy is equal to
the spring constant times the compression or extension
squared).

Electrically, kinetic energy is in the magnetic field around
an inductor created by the current flowing through the
inductor. The energy is equal to the inductance times the
current squared. In a capacitor, it's the potential energy
in the electric field caused by the impressed voltage on the
plates of a capacitor, equal to the capacitance times the
voltage squared.

Energy is removed through loss mechanism, such as frictional
losses in the mechanical domain or ohmic losses in the
electrical. These losses convert energy to heat, and once
that happens, the energy is no longer available.

In loudspeakers, there is a direct measure of the ratio of
energy stored to energy lost, and that is the so-called "Q"
factor. And we find that in most loudspeakers, there are two
predominant loss mechanisms, each with there own Q
measurement. The due to mechanical losses is designated as
Qm, while that for electrical losses is designated as Qe(2).
We can calculate these factors knowing the energy storage
and losses mechanisms involved

The mechanical Qm results from the energy storage in the
moving mass of the cone and the frictional losses in the
suspension. It is calculated thus:

Mm
Qm = 2 pi F ----
Rm

where is the F resonant frequency of the system in Hertz, Mm
is the mechanical mass of the system and Rm is the
frictional loss in the system. Increase the mass, and more
energy is stored in the system. Increase the friction, and
more energy is dissipated from the system

The electrical Qe of the system results, again, from the
energy stored in the moving mass, but now dissipated by the
electrical resistance in the system. It is calculated as:

Mm
Qe = 2 pi F ------- Re
2 2
B l

Here, B represents the magnetic flux density in the voice
coil gap, l is the length of wire in the magnetic field, and
Re represents the DC resistance of the voice coil.

We can also speak, of course, of the total Q, or Qt, of the
system due to the combined mechanical and electrical
damping, and it's calculated by the familiar formula:

Qm * Qe
Qt = ---------
Qm + Qe

The lower the Q, the more damped the system is. The higher
the Q, the less damped.

3 THE INTUITIVE PREMISE

Here's the claim: putting speakers in series is a bad idea
because the series resistance of one speaker destroys the
damping of the other. Why, even the equation for electrical
Qe above says so: having two voice coils in series doubles
the voice coil resistance (assuming the voice coils are the
same, for simplicity). So it must logically follow that
adding two speakers in series must severely destroy the
damping, and the equation above shows that it should double.

It makes intuitive sense. It even seems to appeal to
technical authority. But will it stand up to analytical and
empirical scrutiny? Is this, perchance, another widely held
belief that might not be so?

4 ANALYSIS

We'll consider the case where we are connecting two of the
same thing in series, be it two identical woofers in an
enclosure or two identical speakers in series. We're using
identical woofers or systems to make the analysis
simpler(3).

Let's first look at the effects of two speakers in connected
together in the mechanical domain. It might seem obvious,
but since no electrical effects are considered in the
mechanical domain, it makes no difference on the mechanical
damping or Qm whether two speakers or two woofers are
connected in series or parallel. Indeed, it doesn't even
make any difference if they aren't connected at all
electrically.

In the mechanical case, we have doubled the moving mass Mm
to 2*Mm to (we have twice as many cones, after all), but we
have also double the amount of frictional Rm loss from to
2*Rm as well (twice as many surrounds and spiders, too).
Plugging these changes into the equation for mechnaical
damping, we find:

2 Mm
Qm = 2 pi F ------
2 Rm

We can simplify: in the equation 2/2 is equal to 1, and we
thus end up with:

Mm
Qm = 2 pi F ----
Rm

This equation, describing the effect on Qm of connecting two
speakers in series, is precisely the same equation for the
case of a single speaker by itself.

Now, let's look at the electrical damping or Qe. Here, we
have, indeed, doubled the resistance Re to 2*Re (the voice
coils are hooked in series), but we have also doubled the
moving mass from Mm to 2*Mn as well and we've also double
the length of the voice coil wire from l to 2*l sitting in
the magnetic field as well. Now, let's plug all those
factors of two into the equation for electrical Q:

2 Mm
Qe = 2 pi F ---------- 2 Re
2 2
B (2l)

The next step expands and combines terms:

2 Mm
Qe = 2 pi F --------- 2 Re
2 2
B 4 l

In another step, let's accumulate all these new factors (2
from the doubling of mass, 2 from the doubling of the voice
coil resistance, and 4 from the square of the doubling of
the length of the wire) together for the numerator and the
denominator:

4 Mm
Qe = 2 pi F - ------- Re
4 2 2
B l

And, since the fraction 4/4 is equal to 1, we can reduce
this equation to:

Mm
Qe = 2 pi F ------- Re
2 2
B l

Again, this result, showing the Qe electrical of two
speakers connected in series, is identical to the case of
just a single speaker.

Thus the analysis clearly shows that the damping is not
severely compromised by connecting two systems or drivers in
parallel, because the measures of damping, Qm and Qe,
remains the same for both the mechanical and electrical
domains, and thus the total also remains the same. Q.E.D.

5 EMPIRICAL SUPPORT

The intuitive premise makes one clear prediction: the
damping is seriously compromised by placing two speakers in
series. This must be manifested by a substantial increase in
the Q factors of the speaker. Specifically, the premise
predicts that the electrical Q factor should be much
greater. How much greater is not clear, because the premise
is woefully short of analytical precision. But let's say
that we should see at least a doubling of the electrical Q.
And since the electrical damping predominates in most
speakers, the total Q should be similarly affected.

On the other hand, our analysis above predicts that the Q
factors should remain essentially unchanged. Such an
unambiguous difference makes this discussion an ideal
candidate for falsification by experiment(4).

For the first experiment, I selected two woofers, a pair of
Seas PR17RC 6 1/2" woofer-midrange drivers. I measured the
relevant parameters, the DC resistance, resonance and the
mechanical, electrical and total damping of each separately,
and then with the two connected in-phase in series to see
the effect on damping of such a series connection. The
actual results are shown in Table 1:

Measurement Prediction
Parameter A B A+B Analytical Intuitive
------------------------------------------------------------
Resonance F 71.20 69.03 70.1
DC resistance Re 5.72 5.70 11.42

Damping
Mechanical Qm 1.29 1.33 1.32
Electrical Qe 0.88 0.92 0.91 ~0.90 1.80
Total Qt 0.52 0.54 0.55 ~0.53 1.06
-----------------------------------------------------------
Table 1: Driver Measurements

The data would seem to strongly support the analytical
method's predictions, and refute those of the intuitive
model. That's fine for single speakers, and this result has
been validated in numerous home-built systems using multiple
drivers in series. It might be a different question, though,
for complete speaker systems, often the situation found in
some installations.

So, I went to my storage room and grabbed a pair of rather
ordinary bookshelf speakers, some ancient ones made by the
old H. H. Scott company. I could well have used any two
speakers, but there were handy and fully functional. I
measured the resonant frequency, the DC resistance of the
voice coil, and the relevant Q factors for each speaker
alone, and the two in series. Along with these numbers, I
also present the predictions made by the two competing
theories, the "intuitive" premise, and the "analytical"
theory described above. The results are shown in Table 2.

Measurement Prediction
Parameter A B A+B Analytical Intuitive
------------------------------------------------------------
Resonance F 110.5 113.7 112.6
DC resistance Re 6.86 6.87 13.90

Damping
Mechanical Qm 2.77 3.06 3.15
Electrical Qe 1.02 1.09 1.14 ~1.06 2.28
Total Qt 0.75 0.80 0.83 ~0.80 1.6
------------------------------------------------------------
Table 2: Speaker System Measurements

It would seem that the empirical data strongly supports our
analytical model, and strongly refutes the intuitive
premise. Q.E.D.

1 FREQUENCY RESPONSE ERRORS

One problem with two speakers in series is that the
frequency dependent impedance variations of one will upset
the frequency response of the other, and vice versa. As it
turns out, this is not the case as well.

Consider how the attenuation arises. Take the case of two
resistances in series, R1 and R2. Given an impressed voltage
of Vs, we can calculate the voltage across . The current
through the entire circuit, will, by Ohm's law, be:

Vs
I = ---------
R1 + R2

Given that current, again, by Ohm's law, the voltage across
R2 will be:


Vr2 = I R2

And, combining these two equations and simplifying, we find
that:

R2
Vr2 = Vs -------
R1 + R2

Now, in the case where R1 = R2, this reduces to simply:

1
Vr2 = --- Vs
2

Now, this can be generalized for impedances. If the
impedances are the same, we can say that:

Z2
Vz2 = Vs ---------
Z1 + Z2

Z1 and Z2 represent the complex, frequency dependent
impedances of our loudspeakers. If Z1 = Z2, which would be
the case if our two speakers are the same (and this includes
the frequency-dependent impedance variations as well), then
our equation reduces to the fact that the voltage across
each speaker would be:

1
Vz = --- Vs
2

Notice the complete absence of any frequency-dependent terms
in this final equation: with two identical speakers in
series, the voltage across each is simply 1/2 that of the
voltage the amplifier is producing across the total, and is
independent of frequency. There are, thus, no
frequency-dependent variations in frequency as a result of
putting two identical speakers in series. Q.E.D.

-----------------------
Footnotes

(1) One often encounters hi-fi accessories, for example,
that utilize "mass damping" to control resonances. That
adding a mass will change a resonant system is hardly in
dispute, that it "damps" a resonance is altogether a
different and quite incorrect claim.

(2) There are other loss mechanisms, most notable the
acoustical losses. However, for direct radiator
loudspeakers, these loss mechanisms are quit
insignificant, most often representing less than 1% of
the total losses. Not coincidentally, this number is not
too dissimilar form the acoustical efficiency of such
speakers as well, because in order to produce sound,
real work has to be done, and it is the work done into
these acoustical "losses" that actually is the produced
sound. Eliminate the acoustical loss, say by taking away
the radiation load by putting the speaker in a vacuum,
and you've eliminated the sound. Not an entirely useful
exercise for something like a loud "speaker."

(3) While the case of non-identical drivers or systems is
more complicated, the general principles apply, though
there are confounding factors such as
frequency-dependent attenuation resulting from different
frequency-dependent impedances.

(4) "Falsification" is a vital part of the scientific
method. A theory must be falsifiable, that is, it must
make a prediction that, by experiment or observation,
can be clearly shown to be right or wrong. In the case
we have here, either one theory, the other theory, or
neither theory will be supported by the experimental
data. No data can support both. If a theory makes a
prediction that can't be tested, it's no good as a
theory. You might have a theory: "I can levitate myself
while no one is looking." It's impossible for anyone
else to construct a test, because they can never look at
you doing what you claim, thus the "theory" has no value
scientifically.
-----------------------
Copyright (c) 2000-2001 by Dick Pierce.
Permission given for one-time no-charge electronic
distribution with subsequent followups.
All other rights reserved.

--
| Dick Pierce |
| Professional Audio Development |
| 1-781/826-4953 Voice and FAX |
| |

[GregS[_3_]]

In article , (GregS) wrote:
In article ,
Mark wrote:
On Dec 3, 9:31=A0am, "William Sommerwerck"
wrote:
This long and currently pointless (or at least meandering) thread began w=
hen
someone largely ignorant of the most-basic electronics theory asked a
question he probably had no real interest in the answer for.

I see this over and over. People trying to be helpful spend huge amounts =
of
time answering questions that are covered in library books. There has got=
to
be a better way to direct people to the information they need.

I rarely ask broad questions, limiting myself to something specific that =
I
couldn't readily find the answer for. I consider it my own responsibility=
to
educate myself, and not to abuse other peoples' generosity.

yes the original question from the OP was basic...

the secondary question re the impact series/parallel connection has on
speaker damping factor is not basic and is not covered in any book I
have seen...

if you find this long and pointless, please feel free to not
participate...

This is long, as I may quote....sorry...I'm leaving part 2 out.


Damping: Loudspeakers In Series
Dick Pierce
Professional Audio Development

1 INTRODUCTION


I got that from Google.


greg

[Richard Crowley]

"Scott Dorsey" wrote ...
William Sommerwerck wrote:
This long and currently pointless (or at least meandering) thread began
when
someone largely ignorant of the most-basic electronics theory asked a
question he probably had no real interest in the answer for.

I see this over and over. People trying to be helpful spend huge amounts
of
time answering questions that are covered in library books. There has got
to
be a better way to direct people to the information they need.

That IS what the FAQ is for, isn't it?

If only it were posted online in a reliable place.
www.recaudiopro.net has been offline for what, several years now?

[GregS[_3_]]

In article , "Richard Crowley" wrote:
"Scott Dorsey" wrote ...
William Sommerwerck wrote:
This long and currently pointless (or at least meandering) thread began
when
someone largely ignorant of the most-basic electronics theory asked a
question he probably had no real interest in the answer for.

I see this over and over. People trying to be helpful spend huge amounts
of
time answering questions that are covered in library books. There has got
to
be a better way to direct people to the information they need.

That IS what the FAQ is for, isn't it?

If only it were posted online in a reliable place.
www.recaudiopro.net has been offline for what, several years now?



Should be here just fine.....

http://www.faqs.org/faqs/AudioFAQ/

[Mark]

1 INTRODUCTION

I got that from Google.

greg-

thanks that was a good paper

but it did not include the effect of the amplifer output Z which Arny
correctly pointed out will be reduced to 1/2 for speakers in series.
Not an important factor these days..

Mark

[[email protected]]

On 2008-12-03 said:
"Scott Dorsey" wrote ...
This long and currently pointless (or at least meandering) thread
began when
someone largely ignorant of the most-basic electronics theory
asked a question he probably had no real interest in the answer
for.
That IS what the FAQ is for, isn't it?
If only it were posted online in a reliable place.
www.recaudiopro.net has been offline for what, several years now?

I think it's still on recordist.com however.
wOuld it be helpful to have it posted actually *in* the
group occasionally?
k


Richard webb,
replace anything before at with elspider

"They that can give up essential liberty to obtain a little temporary
safety deserve neither liberty nor safety."
--- Benjamin Franklin, NOvember 1755 from the
Historical review of Pennsylvania

[Chris Hornbeck]

On Wed, 3 Dec 2008 06:20:58 -0800 (PST), Mark
wrote:

For four identical speakers in series-parallel, the load
to the amplifier is the same as that of one of the speakers,
and each speaker gets 1/2 the voltage and 1/2 the current
from the amplifier, so sees the same source impedance as
a single speaker.

the question is not about what load the AMP sees, you are correct what
you said about what load the amp sees but that is not in question, the
question I am discussing is not what load that the amp sees but rather
what does each speaker see as a source Z driving it...this is what
determines the damping factor for the speaker..

in the case of one speaker, the speaker obviously sees the output Z
of the amp.

The question at hand is what does each speaker see as a driving Z when
two speakers are connected in series.. and it is not a simple
question as it first appears.....

It's certainly interesting, and Don's analysis assuming perfect
similarity is great. Duh, the guy's solid.

But I think that the key to the puzzle is contained in the identity
of the series-parallel quad load and a single speaker load. The
amplifier cannot distinguish between the quad and the single. It
operates exactly the same with either load at any particular
electrical output level.

But also, each of the drivers in the quad gets 1/2 of the voltage
and 1/2 of the current from the amplifier. No single (identical!
by definition) driver can deviate from its 1/2 and 1/2 allotment
(because identical by definition), so the quad of drivers behaves
electrically exactly like a single driver. (*Noting that real drivers
couple acoustically, usually pretty weakly, but still...)

So, at the interface between amplifier and speaker, there's no
difference between single or identical quad. And, no individual
driver of the quad can (by definition) behave differently than a
single...

Long way around the topic, but, as you've said, it's an interesting
'un.

Much thanks, as always,
Chris Hornbeck