copyright 1997 by rick chinn. all rights reserved.

distribution permitted, with the stipulation that this copyright notice be retained and distributed with the information.

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more speakers than amplifier

this article resulted from a question that curt taipale of the churchsoundcheck listserv asked me one day.

curt: i've taught, when i get to the subject of impedance and the usual problem in a church - connecting too many stage monitors to one amp channel - i usually get one person who says they've solved that problem by (1) adding resistors to bring the load back to 8 ohms, or (2) by connecting the monitors in a series-parallel arrangement.

for example, beyond the awkwardness of the series-parallel wiring job, and the possibility of the system not working at all because someone hooked it up wrong that sunday morning, i've often wanted to investigate what happens to the phase relationship between the speakers, and/or the damping factor. do you know of any other interaction besides just a power issue?

rick: the answer is a bit long, but it is fairly complete, and (i think) avoids errors caused by oversimplification.

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here's the problem(s).

we know that a solid-state amplifier (i.e. one with a transformerless output) emulates a perfect voltage source, up to a point. if it were perfect, we could hang an infinite number of speakers on it, and the amount of power delivered would simply increase, according to ohm's law. wouldn't that be nice?

of course, this can't happen, at least not in this world, and should you be tempted to try it, either the amplifier will complain (consider yourself lucky) or it will go bang and release its smoke.

so, up to a point, you should load a solid-state amplifier at it's minimum load impedance...if you're interested in getting as many watts as possible out of it.

if the amplifier were perfect, then the 4-ohm power would be twice the 8-ohm rating, and the 2-ohm rating would be twice the 4-ohm rating. the degree to which the amplifier's actual performance conforms to this model is a reflection on it's 'stiffness.' some amplifiers may come close to the 2:1 relationship between 8-ohms and 4-ohms, and then the ratio may get closer to 1:1 between 4-ohms and 2-ohms. this is an indication that the amplifier is becoming current limited, and while 2-ohm operation may be allowed, performance is probably suffering, which may become evident upon examination of the distortion performance.

series or parallel?

i think that the best way to illustrate the multiple speaker problem may be via example. let's take a case of two 8-ohm speakers connected to an amplifier that delivers 200 watts into a 4-ohm load, and where 4-ohms is the minimum load impedance.

in this case, the load impedances are equal, and the speakers share (equally) the amplifier's output: 100 watts each.

now, let's double the number of speakers (four). how to connect them? if we put them all in parallel, then the load impedance is the individual speaker impedance divided by the number (8 / 4 = 2). nope. won't work.

if we put them all in series, then the total impedance is the speaker impedance multiplied by the number (8 * 4 = 32). while this will deliver sound, the amplifier will not deliver nearly it's full output power, in this case 25 watts, divided four ways. nope.

if we put them all in series-parallel, then the total impedance is the same as any one speaker (i'll leave it to you to work the numbers). so, the amplifier gets loaded at 8-ohms, which it maybe delivers 125-150 watts into this load, divided four ways. maybe. if you do this, the speakers should be identical.

so, stick a resistor in series with it!

so, some bright-eyed person says: just put a resistor in series with each one, and then connect them all in parallel. (or you could put them all in parallel and add a resistor to bring the total up to the amplifier's minimum load impedance). either way, the answer is the same. in this case, we'll use the second method (easier). put them all in parallel. 2-ohm total impedance. amp can drive 4-ohms, we add 2-ohm resistor in series, now overall load is 4-ohms, amp is happy, we have sound. sort-of.

what we have here is a series circuit consisting of a 2-ohm resistor and a 2-ohm (net) loudspeaker. equal impedances, so the power divides equally. amp delivers 200-watts into 4-ohms, so 100 of those watts goes to the speakers, divided four ways, the other 100 watts goes to the resistor, which converts it into heat.

don't use a resistor, use a transformer.

finally, we'll use the transformer cure. we'll use a transformer to step the 2-ohm total load back up to 4-ohms. ignoring transformer losses, we'll have 200 watts delivered to the 2-ohm load, which turns into 50 watts per speaker, more or less.

these transformers are not easy to find. definitely not something you can go to radio shack to buy.

analysis

ranking the solutions according to performance:

- the transformer, because it gets more watts to more speakers
- series resistor. the amp gets loaded to 4-ohms, but we turn half of this into heat.
- series parallel. the amp gets loaded to 8-ohms, where it possibly delivers more power, and this gets divided 4-ways

series connected loudspeakers…not!

now, let's tackle what happens when you put loudspeakers in series. whether you know it or not, any speaker's impedance is highly dependent on frequency, and the 'nominal' rating that you see on a spec sheet is more like a pinprick on a moving target.

starting with the low frequencies and moving to higher frequencies, the impedance starts out low, rises to several times the nominal value (cone resonance), dips slightly, rises again (box resonance), and then falls back towards the nominal value. going even higher, we reach a point where the impedance begins to climb, albeit at a much slower rate. the inductance of the voice coil causes this rise.

remember damping factor. in most cases, this is a number that the sales guy drags out to impress you with the amplifier's specs. reality is that damping factors beyond about 32 don't mean much (diminishing returns), and that's a topic for another time. still, the amplifier presents a low source impedance to the speaker, which helps the amplifier tell the speaker exactly what to do, and how to do it. raising the source impedance reduces the ability of the amplifier to boss the speaker around, and this is what happens when you put speakers in series. what's worse, if they're not identical, then the impedance curves don't match up, which means that the series-connected speakers interact in a deleterious fashion.

in simple audio terms: the bass gets boomy, and if the impedances aren't equal, then the division of power between the two becomes unequal. in simpler terms: avoid this if at all possible.

how bad is the resistor, really?

the series resistor does the same thing as far as the damping factor goes, but the resistor's value is unchanging with frequency, which is a better thing. all speakers are connected in parallel, which is a simpler hookup that even a monkey should be able to do. the effect of the resistor on the damping factor is probably less than the effects of putting the speakers in series-parallel.

**Moral**: the series resistor thing is probably the lesser of all the evils, but still not the optimum solution.

another solution

the solution that i use in my own live-sound system is that of a multi-channel amplifier. in this case, it is a rane ma-6, which is 6 100 (or so) watt channels in a single 3u chassis. in a pinch, i can put 2 monitors on one channel, but for the most part, it's one monitor per channel, and this also gets me a level control for that particular monitor. you can argue that 100w isn't enough power, and for some folks it arguably isn't. but for me, i use it as a decision point for accepting jobs: if it isn't enough power, then the job is likely to be louder than i like, which for me is a good reason to send them elsewhere. i realize that this may not be an option for some of you. btw, the ma-6 can be run with the outputs bridged, which gives you 3 300-watt channels. oh yes, each output has an individual limiter, which helps make the 100w channels seem louder than they are. works for me.

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