Pretty much any modern amp is made to work with a load range from 4 ohms to 16 ohms. Typically, people mistake the power rating (as in 100w @ 8 ohms) as an impedance requirement, generally not so.
The simple formula for combining two speakers of unequal size in parallel is -
Rt = (R1xR2)/(R1+R2) = (8x4)/(8+4) = 32/12 = 2.67 ohms
Though it is fairly obvious, we are of course talking about speakers PER CHANNEL; not how many speakers on an amp, but how many speaker on a channel with a channel being one internal amplifier of a mutli-amplifier power amp.
Others are right, there is a phase angle introduced, mostly because of the crossover, but for the most part in simple calculation like this, it is not necessary to consider.
Also, keep in mind, as I sure those of you who build speakers know, impedance is not fixed. It will typically go slightly below the rated impedance and also go noticeably above. An 8 ohm rated speakers will likely drop down to 6 or 7 ohms and will rise as high as 15 to 20 ohms.
Recently I came across a well known speaker model of a respected brand that was rated at 8 ohms nominal but had a side note that it was possible for the impedance to drop as low as 3.2 ohms.
But keep in mind that both speaker manufacturers and amplifier makers are well aware that speaker impedance is not fix and that rated impedance is 'nominal', so that knowledge is built into the building of amps.
It is virtually a standard for all modern consumer amps since the invention of the transistor amp, to be able to handle a combined single channel speaker load in the range of 4 ohms to 16 ohms. The only amps not conforming to this virtual standard are going to be cheap bargain basement crappo amps.
Any modern HiFi audiophile amp, even a low powered one is going to handle a combined speaker load of 4 ohms to 16 ohms.
I suspect amps that have a stamp on the back that says '8 ohms to 16 ohms' means two 8 ohm or two 16 ohms speakers. Stereo amps have A/B swithced, or A and B speaker connnection. For the most part we can just consider 'A' the front speakers and 'B' the rear speakers. If you use two 8 ohm speakers, one on the front left channel and one on the back left channel, the combination is 4 ohms which is the limit of the amp. Two 16's would create an 8 ohm load.
As I said, among reasonable amps, it is virtually an industry standard for each amp channel to handle a speaker load in the 4 ohm to 16 ohms range.
As to the idea of adding a 4 ohm resistor in series with a 4 ohms speaker to raise it's impedance, that will work from an electrical perspective, but not from a sound perspective. Let's say you have a 8 ohm speaker in parallel with a seried 4 ohms resistor and 4 ohms speaker. The 8 ohm speaker is going to get the full music signal, but half of that signal is going to be lost in th e 4 ohm resistor leaving only half available to your 4 ohm speaker. Better in this case to simply wire the 8 ohm and the 4 ohm speaker in series.
There are a very few comsumer amps and many commercial amps that can handle loads as low as 1 ohms, though it is unlikely you will ever have one of these to play with.
Here is my take on combined speaker impedance calculations -
On the last formula I go through the calculation keystroke by keystroke an a calculator. It looks complicated, but it's actually very easy, if you follow along with my keystrokes, you should get the hang of it quickly.
This is probably more than you want to know, but here is
how you combine the impedance of several speakers -
1.) When you are combining two speaker of equal size, they
simply divide in parallel and add in series.
- two 8 ohm speakers per channel, wired normally
(parallel)
Rt = R1/n
Rt = 8/2 = 4 ohms
Actually, this holds true for any number of equal sized
(impedance) speakers in parallel. Divide the value of a
single speaker by the total number of speakers.
three 8 ohm speakers in parallel-
Rt = 8/3 = 2.667 ohms
four 8 ohm speakers in parallel-
Rt = 8/4 = 2 ohms
- wired in series or in a chain, they add
Rt = 8 + 8 = 16 ohms
Actually, in series for any combination of sizes, they just add -
Rt = R1 + R2 + R3 + R4 + R...
a 6 ohm, an 8 ohm, and a 16 ohm in series-
Rt = 6 + 8 + 16 = 30 ohms
2.) Two speakers of unequal impedance in parallel.
Rt = (R1 X R2) / (R1 + R2)
Example: 6 ohm with 8 ohm
Rt = (6 X 8) / (6 + 8) = (48) / (14) = 3.43 Ohms
3.) Multiple speaker of unequal value in parallel
Rt = 1 / [(1/R1) + (1/R2) + (1/R3) + ...]
If you have a common calculator this is easy. Most cheap
calculators have a reciprocal key [1/x] meaning ONE
divided by 'X' where 'X' is the number.
So, using a calculator with the key strokes shown in
square brackets [] and numbers in round () brackets, here
is the sequence for 6 ohm with 8 ohms with 16 ohms -
Rt = 1/(1/6 + 1/8 + 1/16)
(6) [1/x] [+] (8) [1/x] [+] (16) [1/x] [=] [1/x]
Here is what you should see -
6 [1/x] = 0.166666666
[+]
8 [1/x] = 0.125
[+]
16 [1/x] = 0.0625
[=]
= 0.3541666666
[1/x]
= 2.824 ohms
Steve/BlueWizard
