I am considering using two identical 4-ohm rated woofers in a series connection to both increase the impedance rating and the total driver radiating area. This would be for a bi-amplified speaker directly driven by a solid-state amplifier with a very low output impedance and no filter elements in series with the drivers.
It seems to me that with the DC resistances of each driver in series with the other driver that both the Qts value of the drivers and the damping factor of the amplifier would change. My research has not yielded a satisfactory answer, so I am asking the good people here to help with these two questions:
Will the Qts of each speaker change when two identical woofers are connected in series? If so, why? If not, why not?
Will the damping factor of the amplifier change? If so, why? If not, why not?
Thanks to any and all who can help.
It seems to me that with the DC resistances of each driver in series with the other driver that both the Qts value of the drivers and the damping factor of the amplifier would change. My research has not yielded a satisfactory answer, so I am asking the good people here to help with these two questions:
Will the Qts of each speaker change when two identical woofers are connected in series? If so, why? If not, why not?
Will the damping factor of the amplifier change? If so, why? If not, why not?
Thanks to any and all who can help.
The damping factor is simply the inverse of the output impedance.
That output impedance has other impedances/resistances added to it before it gets to the speaker driver terminals. Add all those together to arrive at the source impedance seen by the speaker drivers.
Then you'll see that damping factor is almost totally irrelevant.
The output impedance of the amplifier at any fixed frequency does not change as you change the load impedance. But the output impedance does change when the frequency at which it is measured changes. It can change a lot.
If I remember correctly two identical drivers connected in series behave as one driver with double the impedance. But do go and check this.
The downside to using series drivers is that they are not identical and as a result there are some errors in the way each is driven. Read about that as well.
That output impedance has other impedances/resistances added to it before it gets to the speaker driver terminals. Add all those together to arrive at the source impedance seen by the speaker drivers.
Then you'll see that damping factor is almost totally irrelevant.
The output impedance of the amplifier at any fixed frequency does not change as you change the load impedance. But the output impedance does change when the frequency at which it is measured changes. It can change a lot.
If I remember correctly two identical drivers connected in series behave as one driver with double the impedance. But do go and check this.
The downside to using series drivers is that they are not identical and as a result there are some errors in the way each is driven. Read about that as well.
Qts will be the same, so bass response will be the same, but ... acoustic coupling between drivers will make sound different, let's say, sound fuller, because of boosting power response as much as 3dbs at frequencies under wavelength corresponding to distance between these two drivers acoustic centers.
Nothing to see with drawing twice the power from the amp because of halving impedance. Not at all an electrical question: acoustical coupling, same effect regarding less of parallel or serial connecting.
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How about getting it right. 
For a given voltage across the terminals two drivers in series radiate the same acoustic power at long wave length (compared to separation) but there is a 3dB increase in efficiency as 1/2 the total power is input to the drivers. In parallel it's similar. 6dB increase in radiated power for a given voltage, but twice the power input, thus, again a 3dB increase in efficiency.
For a given voltage across the terminals two drivers in series radiate the same acoustic power at long wave length (compared to separation) but there is a 3dB increase in efficiency as 1/2 the total power is input to the drivers. In parallel it's similar. 6dB increase in radiated power for a given voltage, but twice the power input, thus, again a 3dB increase in efficiency.
Thanks for the replies. I still hope to get the why and the wherefore on these questions. Perhaps it will help if I post some of the notions that I understood as facts:
Every speaker driver, in addition to its nominal AC impedance rating, has a DC resistance value and a Qts value for the raw driver. If a series resistance is added between the speaker and the amplifier, the Qts value will increase. This is why, for example, when we are tuning a bass reflex box, we must treat the woofer crossover coil, which has its own resistance, as a unit with the driver to obtain the new Qts value for box tuning. Why would or would not the DC resistance of one driver affect the Qts of the other?
Damping factor, as I understand it, is a value determined by dividing the load impedance by the amplifier output impedance. So, for example, if we have a speaker rated at 8 ohms and the amplifier output impedance is .25 ohms, the damping factor of this combination will be 32. It would seem that the same amplifier into a 4 ohm load would combine with that load to give a damping factor of 16. Is this or is it not correct?
If you can school me here or direct me to other sources I would be grateful. Thanks again.
Every speaker driver, in addition to its nominal AC impedance rating, has a DC resistance value and a Qts value for the raw driver. If a series resistance is added between the speaker and the amplifier, the Qts value will increase. This is why, for example, when we are tuning a bass reflex box, we must treat the woofer crossover coil, which has its own resistance, as a unit with the driver to obtain the new Qts value for box tuning. Why would or would not the DC resistance of one driver affect the Qts of the other?
Damping factor, as I understand it, is a value determined by dividing the load impedance by the amplifier output impedance. So, for example, if we have a speaker rated at 8 ohms and the amplifier output impedance is .25 ohms, the damping factor of this combination will be 32. It would seem that the same amplifier into a 4 ohm load would combine with that load to give a damping factor of 16. Is this or is it not correct?
If you can school me here or direct me to other sources I would be grateful. Thanks again.
Yes, that is generally how one calculates the 'damping factor' in theory but in reality it is quite meaningless and misleading as the impedance of a 'passive' loudspeaker is hardly representative of a constant impedance as a load.
Just taking a look of an individual driver's spec's will show that voice coil resistance (Re) plays a major part in a driver's impedance. That voice coil resistance of the driver by itself limits the effectiveness of any damping factor the amplifier might offer, let alone that of the crossover and cabling.
As said in other posts 'damping factor' is essentially irrelevant for that simple reason, though 'active' systems seem to do a bit better audibly due the lack of a intervening 'passive' crossover.
C.M
Question is summing radiations requires those drivers relatively close together.
The total SPL of the left and right speaker of a typical stereo set up playing a mono program is not +6dbs because the distance between them make them uncorrelated sources. Though probably the bass will sound louder, because of coupling at large wavelengths. An effect similar to bass boost thanks to boundary proximity.
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Once again it is not a question of drawing more or less power from the amp because of changes in impedance. It is an acoustical question, electrical power involved being the same.
In answering this part of the question I would suggest with two identical drivers in series the QTS of the combination doesn't change because the back EMF's generated by both voice coils are additive, as are the voice coil inductances.
So too are the voice coil resistances additive, thus the amplifier 'sees' this series combination of drivers as being one driver with a voice coil of twice the inductance and twice resistance and generating twice the back EMF of a single driver, thus nothing has changed to effect the overall QTS nor that of the SPL.
If the Sd is doubled but the current (the driving force on the voice coil) is halved through a doubling of the impedance (in a series connection), the cone displacement for a series combination is now halve of that of a single driver for any given input signal. So the overall result is a SPL that is unchanged but the acoustical efficiency has now doubled.
C.M
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