Help me with OHM's law and output transformers

Since I have them, I want to try stacking two pairs of Dynaco A-10's for the workshop system. They are a claimed 8 ohm speaker. So, does that make a pair of them a 4 ohm load? A sixteen ohm load? The tube amps have taps for 16, 8, and 4. Should I worry about overtaxing the amplifiers? I can understand how an inefficient speaker like an Appoge can be refered to as a dead short circuit since it has wide bands of aluminum foil connected at each end by the + and - amp output. It is almost like shorting out the amp. Does that mean that a speaker with many drivers will be very efficienct since the signal goes through many more feet of voice coil wire? Or, is it the opposite since the signal has to work harder to drive all those cones? In the early days of solid state it was known that connecting multiple speakers together could be harmfull to amps. If the amp had a speaker selection switch, it would let you choose one or the other but usually not both at the same time. Something I don't understand here, I guess I don't understand Ohms law since this seems to be contrary. While we're at it, I have often wondered which transformer tap sends the signal through the most length of wire, the 4 or 8 Ohm tap? This may all be elementary to some of you and I apologize for that, can anyone clear this up for me, Thanks, Chris
Chris -- If you connect the two speakers in parallel, the combined nominal impedance is 4 ohms. If you connect them in series, the combined nominal impedance is 16 ohms. Of course, depending on the speaker the actual impedance at some frequencies could be significantly lower and higher than those numbers.

Parallel connection is far preferable sonically to series connection, if the amp can handle the increased (lower impedance) load. Given that the amp has 4 ohm taps, it should be able to in this case, assuming the speaker stays reasonably close to its nominal impedance over most of the frequency range.

In case it's not clear, "parallel" means connecting the plus (red) output of an amplifier channel to the plus input of each of the two speakers on that channel, and the minus (black) output of the amp to the minus inputs of each of the two speakers on that channel. "Series" means the positive amp output to the positive terminal of one speaker; the negative terminal of that speaker to the positive terminal of the second speaker; and the negative terminal of the second speaker to the negative terminal of the amp.

The 8 ohm tap of the output transformer includes more turns of wire in the transformer secondary (output winding) than the 4 ohm tap. That results in greater voltage at the 8 ohm tap, such that the output power into an 8 ohm speaker is approximately the same as the output power into a 4 ohm speaker. Similarly, the 16 ohm tap has more turns and greater output voltage than the 8 ohm tap.

The reason parallel connection is better than series connection sonically, if the amp can handle the load, is that in a series connection the source impedance driving each speaker is the amp output impedance plus the impedance of the other speaker. That will degrade bass damping, and if the speakers are not identical (fortunately they are in your case) frequency response irregularities will be introduced into each speaker by the impedance variations of the other speaker.

-- Al
Thank you for a simple and very understandable explanation! I am still confused though on the comparisons I pointed out about the Apogee speaker's voice coil compared to a multi driver cone speaker. Would you care to comment on that issue? Thanks so much, Chris H.
Chris -- I think you are referring to speakers that have multiple drivers handling the same part of the frequency range, such as a large speaker having two or three 10 inch woofers all handling the same part of the spectrum, and perhaps multiple mid-ranges and tweeters as well (as opposed to say a conventional 3-way speaker with one woofer, one mid-range, and one tweeter). Correct me if I'm misunderstanding the question.

Assuming everything else to be equal, a speaker with two or more identical woofers handling the same frequency range will be more efficient than a similar speaker with only one woofer, for the reason that it has more total cone area, that can move more air. Everything else being equal, though, that would result in a lower total impedance, due to the paralleled drivers. A speaker with say a half dozen paralleled woofers would have to be designed with higher impedance drivers, to prevent the combined impedance from becoming unreasonably low.

Keep in mind, also, that most (but certainly not all) kinds of solid state (but not tube) amplifier designs can provide greater power into lower impedances than into higher impedances, up to a point. Current capability becomes more important working into lower impedances, while voltage swing capability may limit the power output into a higher impedance.

If your question referred to more conventional speaker designs which have only one driver for each part of the spectrum, the presence of multiple drivers does not in itself directly affect efficiency, since any given frequency coming into the speaker is basically handled only by one driver element (aside from the cross-over regions, where the incoming energy is split between two driver elements). Obviously, however, different driver designs will tend to have differing efficiencies, due to many other design variables that are involved, and the design of the cabinet will be a major factor as well.

-- Al
Thank you again Al. Yes I was refering to speakers with many drivers doing the same frequencies. Something like the Pipedream speaker which looks like it has a dozen or so drivers comes to mind. If I understand you, all those drivers must be designed for very high impedance to keep the total impedance from being too low. So, if you just made something like that with a bunch of off the shelf drivers it would be a difficult load for an amp I guess.
Thanks for sharing your knowlege, C. Harvey
Chris -- I took a look at the Pipedreams at the Nearfield Acoustics site. As you've no doubt seen, there is surprisingly little specification information there, not even the speaker impedance.

But on their largest model, it looks like on each channel there are two woofer cabinets each with just two drivers, but a total by my count of 18 midranges and 40 tweeters(!).

I would guess, and it's just a guess, that to keep the combined impedance of that many midrange and tweeter elements within reasonable bounds, while having individual driver impedances that are not too far out of the ordinary, they must be using some sort of serial-parallel arrangement. In other words, connecting several groups of drivers in parallel, where each group contains several drivers in series.

The drawbacks of serial connection which I mentioned above would be pretty much inapplicable in this case. Damping factor would not be degraded significantly because the woofers are not connected in series. And the fact that the series connected drivers are identical would minimize or eliminate any frequency-response irregularities that would occur if the drivers had differing impedance vs. frequency curves.

-- Al