Increase total Speaker Impedance Question

P.S. to my previous post. Another calculation method, which gives the same 37.8 watt answer but is somewhat simpler:

For many solid state amps, especially those for which the 4 ohm power rating is equal to or close to twice the 8 ohm power rating, the power capability into (1.6 + 3) = 4.6 ohms can be approximated as (4/4.6) x the 4 ohm rating.

125 watts x (4/4.6) = 108.7 watts.

Max power into the 1.6 ohm speaker combination, when in series with a 3 ohm resistor, would be:

108.7 x (1.6/4.6) = 37.8 watts.

Regards,
-- Al

Instead of killing useful power and also useful bandwidth per given load, I'd use single pair of speakers replacing quantity by quality. Another option is to use zone preamp and drive each pair of speakers with separate identical stereo amp.

Hi Bill and Almarg,

Thanks again for your detailed explanation. I understand the power loss in this setup. However, I am still having difficulty grasping why the sound quality would also take a turn for the worse. Will the frequencies be improperly passed or cut off by the resistor? If not, then, all frequencies will still be passed to the speakers, but at lower power, and that shouldn't affect the sound at all theoretically isn't it?

Thanks!!

I did make an error in my initial calculations above resulting in the discrepancy, and Al's math is of course correct. I believe that the primary difference in sound quality will be due to a loss of damping factor from the amp when driving the additional series resistance. The only way to really know how significant the difference will be is to try it with your specific setup. I can't predict it beyond that with any real degree of confidence.

Angelgz2, see this Wikipedia writeup on the voltage divider effect. In Figure 1 consider Vin to be the voltage the amplifier (or receiver) is "trying" to output to the speakers at any given instant. Consider Z1 to be the sum of the amplifier's output impedance and the 3 ohm series resistance. For nearly all solid state amplifiers the output impedance will be negligible, and so Z1 will be essentially 3 ohms. Consider Z2 to be the combined impedance of the paralleled speakers (nominally 1.6 ohms), and Vout to be the voltage applied to the speakers.

As you will see in the writeup, the voltage applied to the speakers will be proportional to Z2/(Z1 + Z2). Since Z2, the combined impedance of the paralleled speakers, will inevitably vary significantly as a function of frequency (to a greater or lesser extent depending on the particular speakers), Vout will vary significantly as a function of frequency. The result will be significant frequency response irregularities.

That will be similar to what happens, as we discussed earlier, when two non-identical speakers are connected in series, except that it will probably not occur to as severe a degree in this situation since Z1 is constant.

Also, whatever damping factor the amplifier may provide will be reduced to the rough vicinity of 4/3 = 1.33 for 4 ohm speakers that may be included in the combination of speakers, or 8/3 = 2.67 for 8 ohm speakers that may be included in the combination of speakers. (The reason I'm saying "the rough vicinity of" is that I'm ignoring the damping effect of each speaker on the other speakers). Those are very low damping factors. Chances are the result will be loose and flabby bass, to a greater or lesser degree depending on how critical woofer damping is for the particular speakers.

Finally, to the extent that woofer damping is degraded by the presence of the resistor it seems conceivable that "back emf" generated by the woofer of each speaker in the parallel combination, instead of being effectively damped by the amplifier's low output impedance, could to some degree enter the other speakers and be reproduced as sound, thereby adding distortion to the sound each speaker should be reproducing.

Regards,
-- Al