A Question on Speaker Driver Efficiency

Hey Willie,

You know, you could grab a speaker crossover simulator and try this out for free, it may help you. I use XSim. There you can use the virtual 8 Ohm drivers to explore various different wirings and output. 

Yes, the amp matters. If it's a tube amp, you probably want to shoot for 8 Ohms. 

If we compare a single 16 Ohm driver vs. 2 in parallel, you get 8 Ohms, but +6 dB in output. 

If you wire 2 x 16 Ohms, you end up with 32 Ohms, and no gain in sensitivity. 

@erik_squires  - if I understand you correctly...

I will be using drivers that ....
- have a sensitivity of 96 db
- and come in 4, 8, or 16 ohms impedance

To get a total impedance of  8 ohms my choice would be...

2 - 16 ohm drvers in parallel  - which gets me a 6db increase -  102 db

Whereas...

2 - 4 ohm  drivers in series - simply stays at 96db?

I hope I have interpreted you correctly

Thanks - Steve 

Double check the sensitivity on each! :) It is very unusual that the same driver has the same sensitivity regardless of impedance! It's not impossible, but usually manufacturers cut the sensitivity by 3dB as impedance doubles. 

Yes, your math is correct.  Again, I encourage you to grab XSim Crossover Simulator for PC or equivalent to try these ideas out. 

Best,

E

If the amp puts out x watts at 8 ohms, and you split it between two speakers totalling 8 ohms, each speaker sees the half the power and puts out the same dB level.  When you add them together, the net result is the same.

That said, I would think that, if the net volume in dB for the speakers truly are the same regardless of the impedience, two 16 ohms speakers would be the better choice.

Speakers in parallel work independent of each other.  Speakers in series work together and can have an effect on each other.

Also, speakers with higher impedience tend to have a high Bl, and therefore follow the signal more accurately.

@toddalin - what is -  "high Bl"

Thanks

Placing woofers in series will double the resistance and inductance.  This will cause a more steep frequency response roll off on the upper end and will show how sensitive the drivers are at half their standard drive level sensitivity rating. In theory, half the voltage applied to a driver will result in half the sound pressure in the output (-3db). But if two drivers outputs are combined, in theory, output should be doubled - thus cancelling out the effect that halving the applied voltage generates. That's the theory. In practice, the summation of separate but identical woofer responses is somewhat complicated because the way sound pressure waves combine in free space depends largely on the size of each sound source relative to the frequency wavelengths of interest, the relative proximity of the sources in space to one another, and the location in space that response is being detected. In general, you will find that the parallel/series arrangement of multiple drivers can improve overall acoustic efficiency and "apparent sensitivity" at lower frequencies. The essential reason for this is that more driver surface area improves acoustic coupling of the energy source (voltage) to the media being acted upon (air molecules). Try connecting four identical woofers with two series pairs in parallel. You should witness increased output at low frequencies over a single driver for the same applied voltage at most voltage levels Again, however, what is detected in response is heavily dependent on the spatial and frequency characteristics outlined above. Electrically, you should have the same nominal net impedance as one driver but acoustical coupling improvements should provide increased output for the same applied voltage and current draw (the series/parallel arrangement of the 4 woofers should restore the net final inductance value to approximately that of one woofer). All of the above ignores issues pertaining to  the driver's inherent non linearity caused by electrical/mechanical energy loss/storage. For the purposes of the above explanation, one should just assume a "linear" driver.

" If the amp puts out x watts at 8 ohms, and you split it between two speakers totalling 8 ohms, each speaker sees the half the power and puts out the same dB level. When you add them together, the net result is the same.

That said, I would think that, if the net volume in dB for the speakers truly are the same regardless of the impedience, two 16 ohms speakers would be the better choice.

Speakers in parallel work independent of each other. Speakers in series work together and can have an effect on each other.

Also, speakers with higher impedience tend to have a high Bl, and therefore follow the signal more accurately. " -toddalin

I'm afraid very little of what toddalin said above is true. Loudspeaker drivers don't "divide up" power. They respond to a driving force we call voltage. Placing them in series means that voltage is divided between them. Placing them in parallel means that voltage is shared. In the former case, the current drawn from the source is cut in half. In the case of the latter, current drawn from the source is doubled. Sensitivity is professionally expressed as acoustic output generated (typically at one meter distance) for 2.83 Volt RMS input.  It is not expressed in acoustic output (db) per watt of input. That technically, is a measure of efficiency - not sensitivity. With 2.83 Volts applied to two identical drivers in parallel, sensitivity is nearly doubled - BUT SO IS THE CURRENT DRAWN. So there's no net improvement in EFFICIENCY. With two identical drivers in series, current is cut in half because resistance is doubled. Sensitivity may be marginally reduced or improved depending on the sensitivity curve of the driver (how linear the driver's output changes with changes in drive level)

As for the 16 ohm explanation toddalin provided - it is completely bupkiss. A loudspeaker's force factor has nothing to do with its electrical impedance. Force factor is the force exerted on a voice coil that is traversing a magnetic field. A 16 ohm resistance voice coil can have the same force factor curve as a 4 ohm voice coil. Voice coil resistance is not an accurate predictor of driver non linearity (accuracy).

I think you missed the point.

He uses two 4 ohm speakers to produce 8 ohms or two 16 ohm speakers to produce 8 ohms.  Nothing else matters!

If the amp put out 100 watts at 8 ohms, it does so into either of the two noted loads..., because either load totals 8 ohms and the amp puts out 100 watts at 8 ohms.

As for the speakers.  There are two and they share the 100 watts between them.  If they have the same impedience, they share this 100 watts equally, so they each get 50 watts, regardless of whether they are in series or parallel.

Do you think that one will get 25 watts and the other 75 watts or some other crazy combination if they have the same impedience and share the power equally?  That's nuts.

As for Bl, wrong again.  

The Bl is the product of magnetic field strength in voice coil gap and length of wire in magnetic field (T•m), and has a direct impact on how well the speaker reacts to the signal.

A higher impedience voice coil will typically put more wire in the voice coil and therefore has the ability to result in a higher Bl.

But, just look at the TS parameters for JBL speakers of the same type in 4 and 8 or 8 and 16 ohms and this becomes apparent.

e.g., 2265G (4 ohms) Bl=13.6, 2265H (8 ohms) Bl=19.5
2268G = 15.2, H=21.5
2269G = 19.2 H=26.4

etc.

@toddalin

Hi Todd

I've been reading JBL specifications since the late 1970s. I didn't just fall off the turnip truck. The discussion  was about sensitivity changes resulting in parallel versus series arrangement. You got it completely wrong by falling into the "watts" trap - which is a reference to EFFICIENCY- not SENSITIVITY. Paralleling increases sensitivity. Series arrangement typically reduces overall sensitivity somewhat - depending on the driver's response curve and other factors I mentioned.  And as I pointed out, series arrangements increase inductance the amplifier sees which rolls off response - an obvious qualitative judgment you also missed.
As for 16 ohm voice coils and as you alluded to - "the length of the wire in the magnetic gap", did it ever occur to you that voice coil windings can have several layers and in JBL's case, also be "edgewound" aluminum ribbon? The force factor BL is a function of the magnetic field strength within the gap and that of the voice coil with current traveling through it as it traverses said magnetic field. The amount of flux  that is cut and results in  magnetic force on the voice coil is a function of the fixed voice coil gap height, the magnetic field strength within that gap, the magnetic field strength produced by the current running through the voice coil, and a host of factors associated with electrical and magnetic losses of the system. The number of turns of wire of the coil that at any given time is cutting across the gap is but one of many factors that affect overall force strength. A longer voice coil which has the same winding density as a shorter voice coil has no impact on BL - particularly if the Xmax of both designs is similar and both are operated well within their linear region. And if the applied voltages are the same, guess what - the higher impedance coil draws less current which produces a weaker magnetic field which in turn weakens the force exerted. You are clearly way over your head at this point and it might be a good idea for you to quit while you're behind. Voice coil resistance is only one small factor in loudspeaker design which by itself, has no bearing on the linearity or fidelity of the end product - the complete opposite of what you attempted to conclude. Time to pick up a book on electrical engineering or ask an engineer for an explanation. Nothing you have said in this thread has been accurate or useful. Misleading and irrelevant, yes. Useful? No.

Thanks to all for all the input - Once again Agon members have proven to be very insightful.

@erik_squies

- I double checked the sensitivity numbers and 4, 8, and 16 ohm speakers have identical sensitivity - 95db, but it's definitely something to verify going forward - different brands may vary

The XSim Crossover Simulator  seems to be for audio crossovers
- In guitar amps/Speaker cabinets for the majority of cases there is no crossover, so I'm wondering if it would be of any use?

FYI, since I know a few of you play instruments - I have now tried a Celestian 8" mid freq driver and an Eminence Legend 10": bass driver.. Both of these are excellent and significantly better than the original drivers in the areas of  sensitivity, dynamics and clarity.

One last question for everyone...
- In parallel - each driver would move at EXACTLY the same time (pretty much)
- in series - would the second speaker in the "chain" be moving slightly behind the first speaker due to lag time through the voicecoil of the first speaker ?
- also, would one speaker be affected by the other?
- Would the human ear be able to discern this?

Thanks again for all the feedback - it's very useful

Cheers - Steve :-)

@williewonka

Excellent questions

1)  yes (in phase)
2) yes but it should be virtually undetectable
3)  In series, there will be increased inductance which will roll off high frequencies (yes). In parallel, inductance seen by the amp is cut in half just like the resistance is. Also, increased current draw from the amp almost always affects linearity (increased distortion). Whether or not this is noticeable depends on the amp and how hard you drive it.
4) the human ear should be able to discern the increased sensitivity of the parallel arrangement without any problem. All the other aspects - highly debatable and largely dependent on the person.

All of the above - my opinion based on experience - certainly not the end all be all as I'm sure others might have different experiences.

"Speaker sensitivity is measured in decibels per 1 watt per 1 meter, but is usually referred to as just decibels [source: JBL]."

For an 8 ohm load, this equates to 2.83 volts. But for a 4 ohm load it’s 2.00 volts and for a 16 ohm load its 4.00 volts. Because the OP said the speakers have the same "sensitivity," this has been accounted for.

And yes, JBL does put more wire and turns in the gap for their higher impedience speakers leading to a high Bl.

In fact, there are cases where the higher impedience model looses travel (Xmax) because of this difference.

And seeing as how JBLs are the only make of speaker that matter in my household, I stand behind the logic that a higher impedience typically leads to a higher Bl.

As to the effects of inductance, I did note that there is interaction between the two speakers in a series set-up (goes beyond inductance) that does not exist in the parallel set-up, and for these reasons I would choose a parallel set-up.  

@ toddalin

The industry standard for as long as I can remember relies on a fixed voltage to assess a loudspeaker's sensitivity - not power input. In this way, it doesn't matter what the loudspeaker's impedance is. All are judged on the same level playing field. No one has to adjust drive level to compensate for a "nominal" impedance rating. All drivers under test get the same voltage applied and no concern is paid to the current drawn - simply the acoustic output that is generated. If the driver or loudspeaker under test's efficiency is sought, then the unit of power  (watt) is a concern - not the unit of force applied (volt). If you had any electrical engineering experience, you'd know this and would stop quoting a JBL cut sheet as "your Bible".

As to the 16 ohm bit, I give up. I did my best to explain it to you and have obviously failed. Know one thing though. You aren't the only knowledgeable JBL "fanboy". I happen to be listening to a pair of 250ti Limiteds that I've had since new (1992). My first pair of speakers was the L19s I bought - probably before you were born...ugh....that hurts to say.... In any case, please take some heartfelt advice that is not meant to demean you or put you down - there is alot more to learn about electrical, acoustical, and mechanical engineering than what you will find in a JBL cut sheet. I know. Before engineering school, I studied the very same cut sheets you clearly obsess over.

The L19 made it’s debut in the 1979 catalog. Seeing as how I’ve been into JBLs since the 60’s, it sounds like you are the newcomer.

I've even developed and make products for use with classic JBLs.

https://youtu.be/pbbS0QYK2_o

http://www.audioheritage.org/photopost/data//500/medium/Resized1.jpg

http://www.audioheritage.org/photopost/data//500/medium/Tweeters1.jpg

I never said that the higher impedience meant that the speaker would have a higher Bl, but allowed for it, and showed several examples to that effect.

You’ve not shown one model that demonstrates otherwise.

As for sensitivity, you are using your definition,. and I am using mine, and both exist in many places on the internet.

How can you know that the manufacturer for the speakers from the OP isn’t using the same definition that I am using?

BTW, when someone types "You’re out of your league," this typically indicates that they are at the limits of their own understanding and just don’t want to show their ignorance by pushing it further or are too head strong to consider another point of view.

"Also, speakers with higher impedience tend to have a high Bl, and therefore follow the signal more accurately. " - toddalin

" And seeing as how JBLs are the only make of speaker that matter in my household, I stand behind the logic that a higher impedience typically leads to a higher Bl. " - toddalin

" I never said that the higher impedience meant that the speaker would have a higher Bl, but allowed for it, and showed several examples to that effect." - toddalin


Have you posted these revelations in any other forums? I'm curious what the response was. At this point, I'm starting to get embarrassed that I even responded to you in the first place - clearly, this must be your idea of a joke.  On the other hand, I suppose it is possible that you could just be utterly clueless or that you simply enjoy talking in circles.. Either way, it's a waste of my time to try to convince you of anything since you're so convinced of your special "expertise". Have a nice day!

I look at PV, Eminence, and others..., and yes, for the same models, the higer impedience version typically has the higher Bl.

So, contrary to what some would say, I guess that JBL is not the only one who does this and the OP is advised to check the specs for the selected speakers for himself.

Obviously, someone else around here hasn't even bothered to look at the various manufacture's similar offerings to confirm or deny their beliefs.

One last question for everyone...
- In parallel - each driver would move at EXACTLY the same time (pretty much)
- in series - would the second speaker in the "chain" be moving slightly behind the first speaker due to lag time through the voicecoil of the first speaker ?
- also, would one speaker be affected by the other?
- Would the human ear be able to discern this?

@williewonka , a previous answer was incorrect.

Both speakers will move at EXACTLY the same time regardless of the hookup.

Usually tube amps like higher impedances, so usually its to your advantage to put the speakers in series if you want cleaner sound. In the scenario you described though it will work fine either way if 8 ohms is your goal; two 4 ohm speakers in series or two 16 ohms speakers in parallel. You will not be able to hear any difference other than the differences that might be in the drivers themselves.

To clear up some obvious confusion on this thread, Sensitivity is a voltage measurement and efficiency is a Power measurement. Into 8 ohms both are the same, since sensitivity is 2.83 volts at one meter and that works out to 1 watt.

Into a 4 ohm load, 2.83 volts is 2 watts not 1. So the amp must make twice as much power and thus there is a 3 db increase in sensitivity (but note that the increase in volume is because the amp is making more power, not because the speaker is more efficient). The converse is true into 16 ohms- now the amp makes 1/2 watt to make 2.83 volts so the sensitivity is 3 db less.

So if you have a 97 db 1 watt/1 meter 8 ohm driver, two in series will have the same efficiency (since each is absorbing 1/2 watt) while the sensitivity is 94 db. If you put the two drivers in parallel for a 4 ohm load, the efficiency is the same as 1/2 is absorbed by each driver if 1 watt is applied. However the sensitivity is now 100db.

The trick is that you are using a tube amp and since they can't double power as impedance is cut in half, the efficiency spec is easier to use since it tells you how loud the speaker will play with your amp. 

Hi OP! 

XSim will help you evaluate the impedance and relative output. You can try making up circuits of various speaker drivers, and the output volume AND impedance will change when you do. :) So it gives you immediate feedback to possible choices. 

Notes:

Sensitivity: Volume in dB at 2.83V. 

Efficiency: Volume in dB at 1 Watt. 

For 8 Ohms, this value is the same. 

Best,

E

@atmasphere

atmasphere said - " a previous answer was incorrect.

Both speakers will move at EXACTLY the same time regardless of the hookup. "

Incorrect? Really? In theory, they move at EXACTLY the same time only when no capacitance exists in the circuit. Current through the coils is the same at any given time only when the circuit doesn’t have capacitance. We know this is not the case. All circuits have some level of capacitance and inductance. The question is whether or not the amount of capacitance in the circuit and how it interacts with the series inductance is readily detectable. In practice, it is not. However, because it is not readily detectable doesn’t mean it doesn’t exist. I stand by what I said above - there will in fact be a phase delay between the two loudspeaker drivers but it will be virtually undetectable.

If you had any experience designing or building amplifiers, you’d know that every energy storing element within a circuit contributes to phase lead or lag between voltage and current. Loudspeaker coils are no different. This becomes immediately apparent when trying to maintain a safe phase margin with a typical feedback amplifier. The frequency at which inadequate phase or gain margin results in oscillation might be well over 50khz - certainly much higher than any loudspeaker woofer can deal with - hence undetectable but still there nonetheless.

As for "obvious confusion" regarding efficiency and sensitivity, there was nothing inaccurate or "confused" about my explanation - which you essentially repeated until you said this:

"So if you have a 97 db 1 watt/1 meter 8 ohm driver, two in series will have the same efficiency (since each is absorbing 1/2 watt) while the sensitivity is 94 db. If you put the two drivers in parallel for a 4 ohm load, the efficiency is the same as 1/2 is absorbed by each driver if 1 watt is applied. However the sensitivity is now 100db. " - atmasphere

With that, you clearly blew it. Two identical drivers in series will draw half the current of one driver but acoustic output of the two drivers in series will be essentially the same as one driver - not 3db down or 94 db as you indicated. Their accoustical output will sum depending on the factors I noted in my original post. So acoustical efficiency is not the same as you indicated - but roughly double.

You try to draw a distinction between efficiency and sensitivity but clearly don’t understand the essence of the difference - you aren’t "applying a watt". The only thing you’re applying is voltage. The device(s) draws whatever current the resistance dictates. In the case of two 97db drivers in parallel, you’ll only get 100db output if a pair are in parallel and are drawing current sufficient for two watts - not 1 watt. Go back and read what you said. Two 8 ohm drivers in parallel that normally produce 97db at 2.83v drive level individually, will only produce 100db when they draw two watts in the parallel arrangement. In series, they will draw half the current but each device's acoustic output will sum to roughly 97db. Efficiency is doubled with the series arrangement and remains unchanged with the parallel arrangement.

Since your confidence level appears to be far ahead of your knowledge level, it might be a good idea to say " I THINK what the previous poster said might be incorrect". A little humility goes a long way and alleviates the need to on occasion eat crow.

@erik_squires

Simple and accurate erik - Kudos!

In theory, they move at EXACTLY the same time only when no capacitance exists in the circuit. Current through the coils is the same at any given time only when the circuit doesn’t have capacitance. We know this is not the case. All circuits have some level of capacitance and inductance. The question is whether or not the amount of capacitance in the circuit and how it interacts with the series inductance is readily detectable.

OMG, Do you really think that electric current slows down thru inductance in the circuit and accelerates after? Please simulate this before you place more of this nonsense.

:"OMG, Do you really think that electric current slows down thru inductance in the circuit and accelerates after? Please simulate this before you place more of this nonsense. " - kijanki

OMG....educate yourself before you go online and make yourself look foolish attempting to educate others.

Current through an inductor is defined by the following equation:

V=Ldi/dt

Current through a capacitor is defined by the following:

I =Cdv/dt

When the above elements are combined with resistance in a series circuit and excited by a time varying voltage, the following equation results:

R I ( t ) + L 1 d I ( t ) d t +  L 2 d I ( t ) d t + V ( 0 ) + 1 C ∫ 0 t I ( τ ) d τ = V ( t ) .
From the above, one can see that voltage - V(t) is not simply split between the two "ideal" drivers L1 and L2. The capacitor's voltage buildup and drop off over time changes the equation. While the value of C is likely very small in this particular circuit, it's STILL THERE.

CJ1965 4-17-2018
If you [Atmasphere] had any experience designing or building amplifiers, you’d know that every energy storing element within a circuit contributes to phase lead or lag between voltage and current. Loudspeaker coils are no different.

FYI, "Atmasphere" is the designer and owner of Atma-Sphere Music Systems, Inc., which for more than 40 years has produced some of the world’s most unique and highly regarded amplifiers and preamplifiers.

Also, my belief and my perception has been that his frequent contributions to this forum are more highly valued and more widely respected than those of any other designer or manufacturer who participates here.

A little humility goes a long way ....

+1

Regards,
-- Al

@almarg

That’s all well and good, however, the laws of physics and the mathematical descriptions of those laws haven't changed much in the past century. Every circuit has capacitance, inductance, and resistance - of that there is very little doubt. Given this salient fact, one should be careful giving blanket answers to questions raised on this forum without deferring to the underlying equations that DEFINE as accurately as currently possible, the conditions associated with the questions being asked. It’s one thing to provide blanket answers that leave out the details in response to a question raised here. It is quite another to "correct" someone with the same "blanket answers that leave out details" when the person you’re attempting to correct has provided those missing details.

+1 Al

Thank you. People need to learn to express their opinions without the need to insult others, especially the ones whose knowledge and experience as well as their contributions are unique in this industry. 

" Thank you. People need to learn to express their opinions without the need to insult others, especially the ones whose knowledge and experience as well as their contributions are unique in this industry. " - kalali

If I had known that atmasphere was some "world class" amplifier designer, I probably would have used a different circuit analogy to make my point. In this case, I didn't have a clue who he/she was which re enforces a point I've been making elsewhere - when it comes to sharing accurate information with others, the credentials of the person attempting to share  information are irrelevant . Only the facts and accuracy of the information matter.

Secondly, when you are a professional in an industry and put yourself out on a forum sharing "facts" to help educate others, you should accept the possibility that you will be "incorrect" or "wrong" on occasion and all of the downside associated with that potential. This underscores the need to be  careful, exercise restraint, and double check your "advice" before you give it out. The outcome can solidify your reputation for expertise or weaken it - that's the inherent risk in sharing with others.

Wow, I am soooo glad that I didn't spot this thread before now..... 
giving way to all the theory and mathematics,  
@williewonka 
If all things are equal,  meaning a 4 ohm 8 ohm and 16 ohm driver would all sound equivalent in a given cabinet, Paralleled wired speakers sound better overall than series.  I would also recommend that you add a simple impedance correction circuit.   Many amplifiers react better to a consistent impedance.  Not all, but No amplifier sounds worse with it. (unless you are dropping impedance too low for a few tubes) still within tubes impedance operating range,  even tubes sound better with impedance correction circuits on speakers.  
NO PROOF,  this is my experience. 
Good Luck,  Tim 

CJ1965, I believe that what your analysis about phase differences between voltage and current in reactive circuit elements may not be taking into account is that the motion of a dynamic driver results from the current it is conducting, rather than from the voltage that is applied to it. And the current in a series circuit is of course identical at all points in the circuit, aside from the consequences of the propagation delay that will exist along that path. Which in turn will be completely negligible for path lengths that would be present in a home environment, putting aside reflection effects for which timing may have relevance in digital applications.

Regards,
-- Al

CJ1965 4-17-2018
"So if you have a 97 db 1 watt/1 meter 8 ohm driver, two in series will have the same efficiency (since each is absorbing 1/2 watt) while the sensitivity is 94 db. If you put the two drivers in parallel for a 4 ohm load, the efficiency is the same as 1/2 is absorbed by each driver if 1 watt is applied. However the sensitivity is now 100db. " - atmasphere

With that, you clearly blew it.

Ralph’s (Atmasphere’s) statement is entirely correct, if (as he is assuming, consistently with commonly seen usage) efficiency is defined on a 1 watt basis. And if sensitivity is defined on the basis of 2.83 volts.

Strictly speaking, I would define speaker efficiency as being the ratio of acoustic power out to electrical power in. But that definition would have little practical use, and the term is widely (and IMO very reasonably) used to refer to the SPL produced at 1 meter in response to an input of 1 watt.

Regards,
-- Al

@cj1965 Current in the circuit is still the same. You are confusing voltage across the speaker with current. Imagine simple circuit consisting of voltage source and bunch of inductors and capacitors in series. Now you insert speaker into it. Do you think it will sound differently in different places of insertion? There is only one current in the circuit and two speakers in series have to respond at the same time (unless there is place where "faster current" can escape).

@almarg 

Do the math. Take two 8 ohm nominal woofers, connect them in series, and apply 2.83v.

2.83 divided by 16  = .176875 Amps (current "I")

power dissipated into each woofer in this circuit then becomes:

R(I X I) or resistance of each woofer times the square of the current running through it. Thus
8(.176875 X .176875) = .25 Watts or 1/4 watt - not 1/2 watt as atmasphere and you have suggested -

 " two in series will have the same efficiency (since each is absorbing 1/2 watt) while the sensitivity is 94 db "- atmasphere

The above can be expressed another way.
Power dissipated in two woofers in series = net voltage drop across both times the net current flowing through both.
2.83 Volts times .176875  = .5 watts or 1/2 watt total between both drivers in series. If together both woofers are dissipating 1/2 watt, then individually they must dissipate 1/4 watt - thus agreeing with the above calculation. At half the voltage drive level (voltage divided when connected in series), each woofer should produce half the acoustic output and consume 1/4 the power.When their acoustic outputs are summed, the net acoustic result is the same as if for one driver - however the power consumed is cut in half.

This jives with measurements I've made of acoustic output of drivers in series.

" @cj1965 Current in the circuit is still the same. You are confusing voltage across the speaker with current. Imagine simple circuit consisting of voltage source and bunch of inductors and capacitors in series. Now you insert speaker into it. Do you think it will sound differently in different places of insertion? There is only one current in the circuit and two speakers in series have to respond at the same time (unless there is place where "faster current" can escape)." - kijanki

Please read and study the equation I posted above for two inductors (speaker coils) in series with a resistance and capacitance. The equation doesn't lie. Current and voltage are constantly varying and as the equation shows  the voltage representations of each woofer are NOT equivalent to the applied votlage input [V(t)] ,minus the other woofer's voltage. The voltage represented by the capacitance must also be accounted for and it is time dependent. If you disagree with the equation and what it is saying - address your comments/concerns with that equation and its applicability to the subject at hand. I didn't invent Kirchoff's law - I'm merely reciting it in the context of a series connected loudspeaker pair.

You're telling Almarg to do the math?  LOL, Man, you got big mouth.

Incorrect? Really? In theory, they move at EXACTLY the same time only when no capacitance exists in the circuit. Current through the coils is the same at any given time only when the circuit doesn’t have capacitance. We know this is not the case.

@cj1965 It seems that you are forgetting about Kirchoff's Law. Obviously one woofer cannot move if current is not also flowing through the second in a series connection! So that means the other woofer has to move **at the same time** otherwise Kirchoff's Law is violated, which is an impossibility. Further, the current has to also flow the other way (it is an audio waveform after all), so the situation with the woofer's relationship is reversed; it is quite obvious that they will move at exactly the same time and this is true even if the drivers are of different inductance.

Kirhoff's Law was also taught to me in school as the 'Law of energy conservation'. It basically states that there cannot be more energy in a circuit than is put into it, nor can there be any less. So if a watt is put in, the individual parts in the circuit will all dissipate some fraction of that watt in such a way that if you added it all up, it would be exactly 1 watt. Here is the Wikipedia page:
https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws

Now if the drivers are dissimilar, they might not *sound* the way you want (one might have a greater voltage drop across it than the other), but if they are the same driver there isn't a downside unless higher impedance is problematic as with a solid state amp (however the solid state amp will be seen to be making less distortion).

If all things are equal, meaning a 4 ohm 8 ohm and 16 ohm driver would all sound equivalent in a given cabinet, Paralleled wired speakers sound better overall than series. I would also recommend that you add a simple impedance correction circuit.   Many amplifiers react better to a consistent impedance. Not all, but No amplifier sounds worse with it. (unless you are dropping impedance too low for a few tubes) still within tubes impedance operating range, even tubes sound better with impedance correction circuits on speakers

This bit is problematic. The drivers are going to sound the same whether in parallel or in series. What **won't** sound the same is the amplifier, which reacts very differently to impedance depending on the amp.

Now in the case of this thread, the amp in question is a tube guitar amp. Tubes, generally speaking, prefer a higher impedance and will make less distortion if the higher impedance is accommodated by a tap on the output transformer. The transformer will run cooler as it is more efficient, so with most tube amps you get a tiny bit more power as well, as well as more extension into the bottom octave of the amp.

Reducing distortion may not be the goal in a guitar amp, where the guitarist's individual 'sound' that he is going for is highly subjective and varies greatly from one guitarist to another, even using the amp amp.

So ultimately, the OP will simply have to try it both ways. The amp won't be damaged by this, and if there are taps for each impedance, they should be employed.

Again, current (and not voltage) is what moves the coil.

"Again, current (and not voltage) is what moves the coil." - kijanki

That statement is utterly clueless and contradicts a widely held definition that has been born out in countless measurements of voltage and current in coils. Once again, the definition of voltage as it RELATES to current in any given inductor coil is:

V(t)= Ldi/dt

where  voltage across an inductor at any given time is directly proportional to the time rate of change of current running through said inductor. Voltage and current in an inductor are INEXTRICABLY LINKED to one another and the precise mathematical representation has been given earlier in this thread. If you disagree with the above equation, good for you. You might be on to a new discovery in electronics and physics. Somehow, I doubt it. You could know something that no one else on the planet knows and we're all in for a new, amazing discovery. But then again, you just might be another clueless individual trolling around on the internet in search of a pointless argument....

This bit is problematic. The drivers are going to sound the same whether in parallel or in series. What **won’t** sound the same is the amplifier, which reacts very differently to impedance depending on the amp.
Hi Ralph, 
I believe that I did elude to the fact that it is the amp that sound differently, but I want to stress that in this case, compensation circuitry should sound better with tubes that the speaker without the circuitry.
Using 2 - 16 ohm speakers, depending on frequency, you will see impedances normally rise to 30 or 40 ohms if not higher. You can obviously go into why and amp sounds better on 8 ohms than 4. Impedance compensation circuitry normally only lowers the peaks (stated for others on the thread), it never raises an impedance dip. So when we can make a speaker consistent from say 8 to 9 ohms, in my experience A tubed amplifier putting out consistent power across all frequencies has always sounded better than an amp that sees a speaker that strays radically. Again, this is only my experience, today, I seldom build a speaker without compensation, there are a few exceptions, but Few.

I'm giving up - you won't get it.

I encourage anyone wanting to follow along, to grab XSim crossover simulator, and examining the Frequency Response, Watts Dissipated and Impedance charts. 

http://www.diyaudio.com/forums/software-tools/259865-xsim-free-crossover-designer.html

The "blank" driver is an ideal 8 Ohm driver with an 80 dB efficiency. This will put to rest any questions about power, efficiency and sensitivity you may have. 

Best,

E

This jives with measurements I've made of acoustic output of drivers in series.

Sounds like you are running a solid state amp. Solid state amps, generally speaking, are usually built to behave as a voltage source. If that is the case, it will make double the power into half the impedance, and thus also half the power if the impedance is doubled. So such an amplifier will make 1/4 of its 4 ohm power into 16 ohms (drivers in series).

@atmasphere

I'm the only one in this thread actually citing equations based on Kirchoff's law while you hand wave generalizations about tube amps.

I'm the only one in this thread actually citing equations based on Kirchoff's law while you hand wave generalizations about tube amps.

Really? Hand-waving seems to be what you are doing with this quote...

Somehow you don't seem to make the connection that current has to flow if a circuit is complete. Its Circuit Basics 101 first day stuff.

CJ1965, re your last post that was directed to me, your math is of course correct. However, once again, if efficiency is defined as the SPL produced at 1 meter in response to an input of 1 watt, if that 1 watt is provided to two speakers connected either in series or in parallel each speaker will absorb half of a watt. So when efficiency is referred to, and defined as the SPL produced at 1 meter in response to 1 watt, the results of your calculation need to be normalized to 1 watt of supplied power. Which in turn makes Ralph’s statement that you alleged to have "blown it" entirely correct.

You [Kijanki] could know something that no one else on the planet knows and we’re all in for a new, amazing discovery. But then again, you just might be another clueless individual trolling around on the internet in search of a pointless argument....

For someone who has only been participating in this forum for a couple of months you certainly are quick to direct insulting comments at some of the forum’s most knowledgeable and widely respected members. And that certainly includes Kijanki, as well as Atmasphere. I suggest that some modification to your manner would result in your contributions being better received, and discussions in which you participate being more constructive.

Regards,
-- Al

" Really? Hand-waving seems to be what you are doing with this quote...

Somehow you don’t seem to make the connection that current has to flow if a circuit is complete. Its Circuit Basics 101 first day stuff. " - atmasphere

What a clueless statement. When a capacitance is present, current flow is dependent on the time rate of change of voltage across the capacitor. Since it is a series circuit, this time rate of change affects the flow of current with time through both inductors - Circuit Basics 102.

I= Cdv/dt

Your simplistic view assumes that current through all reactive elements in a circuit is steady state (constant). And that is pretty scary for someone who has experience building amps. But then again, it’s tube amps and this is the year 2018 - so that kinda makes sense.

" For someone who has only been participating in this forum for a couple of months you certainly are quick to direct insulting comments at some of the forum’s most knowledgeable and widely respected members. And that certainly includes Kijanki, as well as Atmasphere. I suggest that some modification to your manner would result in your contributions being better received, and discussions in which you participate being more constructive. " - almarg

Perhaps you should direct your comments to the folks with vast, impeccable credentials who say things like this:

" You're telling Almarg to do the math? LOL, Man, you got big mouth. " - kijanki

Btw, I know my math is correct, thank you. I should hope after four years of electrical engineering, I would know  a little about basic addition, subtraction, multiplication, and division....

" re your last post that was directed to me, your math is of course correct. However, once again, if efficiency is defined as the SPL produced at 1 meter in response to an input of 1 watt, if that 1 watt is provided to two speakers connected either in series or in parallel each speaker will absorb half of a watt. " - almarg

Please, I cannot take you seriously if you (or anyone else for that matter) continues saying things like - "if that one watt is provided" to loudspeakers. You can't apply or "provide a watt". All you can do is apply a voltage and the load draws whatever current it draws based on its resistance. The accuracy of my math above stands and it stands in stark contrast to the erroneous statement atmasphere made and you supported which suggested two 8 ohm speakers in series would each dissipate 1/2 watt with a total of 2.83V applied as input. Wrong is wrong. Math is either correct or incorrect. 1/2 watt DOES NOT equal 1/4 watt. Period.

.

I'm voting to remove cj1965 from our forum.  Administrator should already observe that he calls respected members "clueless".  I wonder who would join me and what is the procedure to remove such obstacle. 

CJ1965 4-18-2018
... the erroneous statement atmasphere made and you [Almarg] supported which suggested two 8 ohm speakers in series would each dissipate 1/2 watt with a total of 2.83V applied as input.

Neither I nor Ralph (Atmasphere) said or even implied that.

You can't apply or "provide a watt". All you can do is apply a voltage and the load draws whatever current it draws based on its resistance.

What we were referring to is applying whatever voltage is necessary to result in a total of 1 watt being consumed by the two speakers, whether they are connected in series or in parallel. Which is what is relevant if what is being referred to is the overall efficiency of the speaker combination, and if efficiency is defined as the SPL produced at 1 meter in response to 1 watt.

I'm not sure how that can not be clear, after all that has been said.

Regards,
-- Al

" So if you have a 97 db 1 watt/1 meter 8 ohm driver, two in series will have the same efficiency (since each is absorbing 1/2 watt) while the sensitivity is 94 db " - atmashpere

Each is not absorbing 1/2 watt when placed in series (with the required 2.83 V applied) and the net acoustical sum of output is approximately 97db - not 94db. Two obvious errors in one sentence. The math doesn't lie and frankly, I'm getting a little tired of the verbal gymnastics at this point. The math is simple and anyone who wants to read the details above can readily see where the error was established. Yeah, you can double the input drive voltage to 5.7v and then the series arrangement will have each woofer dissipating 1/2 watt. You can also multiply the input voltage by 10,000 - it won't tell us anything about the effect placing two identical drivers in series has. Sorry, wrong is wrong. And with that, I have to move on. I have better things to do with my time.

As quoted by CJ1965:

" So if you have a 97 db 1 watt/1 meter 8 ohm driver, two in series will have the same efficiency (since each is absorbing 1/2 watt) while the sensitivity is 94 db " - atmashpere [sic]

Given that efficiency is defined as the SPL produced at 1 meter in response to 1 watt, when he said "since each is absorbing 1/2 watt" he clearly meant "since each is absorbing 1/2 watt if a total of 1 watt is being provided." Also, the paragraph in which that statement appeared certainly made no reference to 2.83 volts.

If that was not clear then it certainly should have become clear during the course of the subsequent posts, especially mine.

... you can double the input drive voltage to 5.7v and then the series arrangement will have each woofer dissipating 1/2 watt. You can also multiply the input voltage by 10,000 - it won’t tell us anything about the effect placing two identical drivers in series has.

Specifying the efficiency of a series combination of speakers, defining efficiency as the SPL produced at 1 meter in response to 1 watt, will tell us whatever can be told by an efficiency spec. As Ralph alluded to earlier, efficiency specs tend to be especially relevant in the case of tube amps, since for example in the case of an amp providing 4 and 8 ohm output taps maximum power ratings (in watts) will typically be the same or similar when an 8 ohm load is connected to the 8 ohm tap as when a 4 ohm load is connected to the 4 ohm tap.

Regards,
-- Al