So my Sony home theater in box just died after after nearly 5 years. I'm looking to take the next step to achieve awesome home theatre sound on a $400 budget. I will mostly be doing movies and gaming but music is very important as well. Where do I start? The watage and impedance numbers have me in a state of confusion. I've done some shopping and came up with:
http://www.amazon.com/gp/aw/d/B00B7X2OW6/ref=ox_sc_act_image_4?ie=UTF8&smid=AKR88PAWTQVN2
http://www.amazon.com/gp/aw/d/B00064JWSG/ref=ox_sc_act_image_2?ie=UTF8&smid=A1WPEQCN6WJKZG
http://www.amazon.com/gp/aw/d/B000TQ4D8K/ref=ox_sc_act_image_1?ie=UTF8&smid=ATVPDKIKX0DER
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Receiver power ratings are typically based on single channel driven and while this may be mentioned in the fine print, manufacturers tend to be very deceptive. For example they may have a receiver that is 100 watts x 7 channels and call it "700 watts" when in fact it may be less than 200 watts total. If you listen to only one channel you can get up to 100 watts but if you listen to all 7 it must divide that less than 200 by 7 for less than 28 watts/ch. Depending on demand, you may get more than that at any one instant, the power is not regulated to any particular amount per channel, it's more of a first come first serve. If for example it's a quiet scene in the movie and all channels are using only a small amount of power and then suddenly something happens that demands a lot of power in only one speaker, that one channel may still get up to 100 watts. If however it is a very noisy scene and all speakers are playing loud, the single power supply in the receiver cannot provide 100 watts to each of the 7 channels all at the same time.
It's really hard to get anything decent on a $400 budget but I like your first three links over any of the other suggestions so far.
As for ohms, there is no impedance "matching" between receiver and speaker. Impedance matching only applies to transformers, not solid state audio amplifiers. The impedance rating you see on a receiver is actually a current capacity rating expressed in terms of minimum load impedance. If it can't handle lower than 6 ohms for example, don't put a 4 ohm speaker on it and don't double up 8 ohm speakers on it.
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As for power, don't pay much attention to speaker power ratings, actual power ratings are more complex than particle physics and thus a simple number like "100 watts" is virtually meaningless.