Talk about confusing !!!!
"Frequency response" on an amp is typically rated at 1 watt of output whereas "power bandwidth" is rated at full rated power. An amp that may have a frequency response of 1 MHz at 1 watt may only have a "power bandwidth" at full rated power of 20 KHz ( extreme case for demo purposes ). This will obviously vary with how linear the amplifier is at various output levels. It is therefore possible to have both a high slew rate yet still be limited in bandwidth. In most cases though, designers that strive for high slew rates also strive for wide power bandwidths too.
Other than that, slew rate tells how much voltage the device can swing in a given period of time. The more voltage that it can swing in a shorter period of time, the more likely that it is to remain truer ( more linear ) to the input signal without adding its' own distortions to the signal. This takes into account that the device is stable in design as changing the load or impedance that it sees could very well change the slew rate.
As i've stated before, high levels of speed and stability are what make for good performance but one without the other makes for a less consistent, less desirable product. As either performance attribute ( speed or stability ) is reduced, the more that "system synergy" comes into play. That's because you have to start balancing out the flaws of one component with the strengths of another & vice-versa. Problem here is that when you chance one factor in the equation by "upgrading" a component, you now have different "strengths & weaknesses" that need to be balanced out.
As to what is an acceptable level of slew rate for an amplifier, most of the acknowledge "audio experts" ( like John Curl & Nelson Pass ) teach that 40 V/uS is more than acceptable. I would say that this is a good starting point, but is nothing to sneeze at in itself.
Others like Douglas Self teach that, so long as the circuit is capable of providing more signal than it is ever called upon to deliver during normal conditions, it is "plenty". As such, Self proclaims that preamps with a slew rate of 2V/uS are "plenty fast enough". His reasoning? 2 volts is typically more than enough to drive most amps to full output, so the preamp ( during normal operation ) will probably never be called upon to deliver more than that amount of output at any given time. Very simplistic logic that really only works when everything is perfectly optimized / best case scenarios.
Having said that, some amps are MUCH slower than others. For instance, some of the older Quad amps slewed at 5 V/uS, which is very slow. Some B&K amps slew at appr 14 V/uS, which is still pretty slow. If you look for common sonic signatures between both of these brands, you'll find that neither is known for "slam" ( the ability to deliver high quantities of power very rapidly ) or "high frequency articulation". The latter has to do with the fact that the higher the frequency one tries to reproduce, the "faster" the amp has to be to accurately reproduce the signal.
Now what happens when you connect an amp to a highly reactive load that is very low in impedance? If the amp is unstable and / or lacking in current capacity, the slew rate is reduced. Why is that? Simple. The amp can only climb in voltage as fast as it can deliver current. If the amp can't load into the speaker due to a lack of current or stability factors into the equation with a "tough speaker load", the amount of voltage that the amp can deliver in a given period of time ( slew rate ) is reduced accordingly. This is a fact that most EE's never think about and is commonly overlooked. That's because these spec's are based on tests conducted into non-reactive "dummy" loads, not actual speakers.
As such, one is ALWAYS better off with an amp that is as fast as possible. That's because there will always be conditions presented to it that reduce effectively it can operate. This has to do with the dynamic nature of music and the reactive load that most speakers present during those dynamic changes in amplitude.
Obviously, selecting an amplifier with a high rail voltage ( more dynamic headroom ) with gobs of current capacity ( less potential for clipping & better overall driver "control" ) that is of a stable design ( remains consistent in performance regardless of the load impedance it is connected to ) and can respond quickly to signal changes ( high slew rate ) over a wide bandwidth ( frequency response ) at full power ( power bandwidth ) while maintaining high levels of linearity ( various distortions i.e. THD, IMD, TIM, etc.. ) without the need for a lot of error correction ( negative feedback ) is what we are looking for.
As one can see, there are MANY spec's that tie into making a "good performing" and "good sounding" amplifier. Lose any portion of the above stated "requirements" of good performance and you compromise the overall level of reproduction and versatility ( more variation from speaker to speaker ) of the component. The end result is that the engineer / designer that developed the product has to take all of this into consideration when sitting at the drawing board AND select parts that will more than hold up under duress. Marginal designs using marginal parts are easy and less costly to produce, hence the fact that many products perform quite similarly ( poorly ) overall. Sean
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PS... Slew Rate and Rise Time are somewhat the same spec's. Given the limited voltage output required for a preamp, the spec of "rise time" is more appropriate here whereas "slew rate" would apply more directly to a power amp. That's because the preamp is voltage limited in real world operating conditions to less than 2 volts, so we want to know how long it takes ( duration ) it can deliver a specific amount of voltage. On the other hand, speakers require high levels of voltage, so slew rate tells us how much ( quantity ) voltage the amp can deliver in a given time period. In effect, slew rate tells us how much voltage the device can swing in a given period of time and rise time tells us how long it takes to deliver a specified amount of voltage. Even though they are kind of the same thing expressed in different manners, good manufacturers actually provide both spec's with the specific parameters for each test result involved. If a manufacturer provides both specs, you should look for lower rise times and higher slew rates for better performance.