What is the relationship, if any, between speaker cabinet resistance (as measured by ohms) and amp wattage?

For example, I have a bass amp combo rated at 80 watts into 8 ohms (the combo speaker), and 100 watts into 4 ohms (combo + extension cab.) I thought that if resistance dropped by half, the wattage doubled. Obviously not!

Similarly, I have an amp head rated 180w into an 8 ohm cab, and 280 into 4 ohms. Again, not a doubling of watts, but also not the same apparent relationship as the combo.

Just curious what the math is, and what other factors I'm missing. Anyone have an idea?

Ignorant as I am about solid state electronics, I'll just point out a couple of factors that keep the actual output power ratings with different load impedances from following a simple mathematical relationship:

1) The actual output impedance of the amplifier is unknown, and at the nominal output impedance rating may be more or less well matched to the nominal impedance of the speaker. Everything's not ideal in the real world.

2) The power supply of the amp may not be up to providing the higher peak current demanded by the amp as the output impedance is reduced.

3) The output resistance of the power transistors is a fixed quantity, and as the output current goes up, the heat produced goes up linearly with it. The heat sinks may not be capable of dissipating the increased heat, so it may be unsafe to run the amp "wide open" with a lower load impedance.

Some quick Googling turned up this page on matching speaker impedance to a solid state amp:

http://www.tedpavlic.com/teaching/osu/ece327/extra/impedance_matching.pdf

Tube amps with beam power tube or pentode outputs are a different animal. The fixed voltage on the screen grid is what mainly controls the output power, and as it doesn't fluctuate much with the varying voltage on the plate that the load influences, output power is pretty much fixed even with different loads. Plate resistance of these tubes is so much higher than practical output loads that the actual load chosen is arbitrary. Going up or down 2-4X will affect the power very little. It's normally picked to be around the point of lowest harmonic distortion, so changing speaker load from the nominal one will increase distortion. With pentode tube amps it also increases the plate voltage swing as speaker load increases, so it may overstress the insulation in the output transformer or cause arcing at the tube socket. (Doubling the load won't cause a problem in most amps.) Reducing the load impedance won't hurt a tube amp, whereas it may overheat a solid state amp.

"A cheerful heart is good medicine."

Thanks Ricochet! Yeah I figured there were a few more things involved. From what I've been able to learn, my example (half the resistance gets double the wattage) is "perfect world," and as you said, everything's not ideal in the real world.

in any circuit, the voltage and wattage will be affected by the Resistance

Actual Total Wattage/voltage = total voltage/wattage DIVIDEDBY Resistance

Fortune, Fame, Mirror, Vain, Gone Insane But The Memory Remains

Yes, but we're dealing with alternating current and *impedance* with speakers, not resistance. The above Ohm's Law formula doesn't tell you how the power output of an amplifier changes with the impedance of the load. There are empirical formulas, but actual amps don't always seem to know them.

"A cheerful heart is good medicine."

It seems solid state state play more by the rules. Tube amps flex. Keep in mind I really don't know alot about this stuff and half of what I know came from the guy that posted before me. :lol:

"Work hard, rock hard, eat hard, sleep hard,

grow big, wear glasses if you need 'em."

-- The Webb Wilder Credo --