“What are the general rules about matching impedance of speakers and amplifiers? I’ve tried reading textbooks and articles on sound recording but I still come away with a blank stare. Basically, I’ve got two 80 watt 6 ohm speakers that I would like to connect to a mini stereo system. The speakers that come with the system are two small 20 watt 4 ohm speakers. On the back of the amp it says “SPEAKER IMPEDANCE MIN 4 ohm”. Would it be safe to replace the smaller speakers with the bigger ones?”
Your blank stare is probably the result of reading a lot of theory that isn’t explained in a way that is congruous with your common sense. They don’t need to be “matched” (in the sense I think you mean) at all.
The basic concept here is really pretty simple. Ohms represent a resistance to current flow. The more resistance there is (more Ohms) the less current will flow in the circuit, which also happens to mean less overall power gets delivered to the load (the speaker in this case). Conversely lower resistance will allow more current to flow, and more power to be delivered…up to a point. If the resistance (technically the impedance in this case) of the load drops too low the current source (the amplifier in this case) will be unable to continue to supply the necessary current and continue to function properly (every power source has its limits). Sometimes this will result in damage to the power source or some of the components delivering the power (potentially including the wire – this is why you have circuit breakers in your house), and sometimes the power source is designed with current limiting circuitry to protect itself in these cases.
So amplifier manufacturers are concerned with the minimum net impedance of the loads connected to them because they have a direct impact on the performance of the amp, and in fact can sometimes be the difference between the amp working or breaking.
Part II of your question is implied. Unlike the impedance ratings of your speakers the wattage ratings don’t have much to do with whether they can be safely connected to a particular amp. It’s just a specification that lets you know about how much average power the speakers can handle. Practically speaking you probably wouldn’t want to plug a 40 watt speaker into a 1000 watt power amp, but even if you did it would work fine so long as you don’t turn the level up enough to blow the speaker. (Surprisingly, most speakers are blown from too little power rather than too much – see below.)
So (finally, the answer) you can certainly plug in those bigger speakers and they should work fine. The have a higher impedance so there is no risk to the amp, and they have a higher wattage rating so there is no significant risk to the speakers. Do be careful though. We don’t know the sensitivity rating of the speakers or how much power it will take to drive them to a given volume. You may find they are not as loud as the smaller ones, which could be due to lower sensitivity and/or the higher impedance. Sure, you can turn the amp up more, but when you reach a point where the amp is distorting (clipping) you run great risk of harming the speakers even though you may not be anywhere close to their wattage rating. There have been several past Tech Tips that covered this concept more thoroughly so feel free to search the archives for them.