Slew rate and rise time

They are two different ways of looking at the same thing.

Slew rate is a measure of how fast a signal is changing. How many volts it changes in a given period of time. Usually stated in volts per microsecond.

Rise time tells you how long it takes to get from 10% of the peak to 90% of the peak and ignores the beginning and end of the signal. If you had a signal that went from 0 to 10 volts, the rise time would be how long it took to get from 1 to 9 volts.

To use an automobile analogy: Slew rate would equal mph and rise tine would be the time it took to travel a certain distance. You can calculate one from the other.

Both are related to the maximum frequency a device can reproduce. If the slew rate is too low it will not be able to reproduce the higher frequencies. This is rarely a limiting factor in audio devices although some feel that the higher the slew rate the better the device.

Sean, your analogies are very colorful, one might say even fiery, but I am afraid they are not exactly right. Given the fact that part of what you say is correct and some of it isn't makes it hard to follow.

"Think of how fast the signal can make it through the hose ( circuit ) from one end to the other on demand. This is a measure of accelleration and is equivalent to the rise time." No, how fast it makes through the hose would be propogation delay. The signal could take all day to make it from one end to the other and still have a very fast rise time once it got to the output. The two are unrelated.

"Slew rate is equivalent to how much flow the hose ( circuit ) is capable of." You also refer to it as "volume of water." No, this would be the equivalent of electrical current.

Slew rate, by definition, is simply the maximum rate of change of the output voltage for all possible inputs. In simple terms, how fast the voltage can change.

Mathematically it is the slope of the line on a graph plotting voltage versus time. Take the amount the voltage has changed, divide it by the time it took to change, and you have the slew rate, usually expresed in volts per microsecond.

Since music is made up of sine waves, and higher frequency sine waves have faster rates of change (the fastest being where it crosses zero) at some frequency this rate of change will exceed the slew rate of the amplifier. It will distort this frequency and all of those higher.

Therefore, we can say that the bandwidth of an amplifier is slew rate limited.

Rise time is how long it takes the voltage to get from 10 to 90 percent of it's peak as I stated above. You are correct that there is also a fall time and it can be different.

I admit I may have oversimplified the relationship between risetime and slew rate. Even though you can calculate a rate of change based on the risetime it is not the same as the slew rate. It is possible that a circuit can have a high enough slew rate to handle a signal but still be unable to do so because it is limited by the rise time, and vice versa.

From a practical point of view it makes more sense to talk about rise time with digital circuits since they are always switching between 2 voltage levels. For instance, a zero represented by zero volts and a one represented by 5 volts. The rise time would be how long it takes to get from .5V to 4.5V. The falltime how long it takes to get from 4.5V to .5V. In an analog circuit that has an infinite number of different levels it probably makes more sense to describe it in terms of slew rate.

I could go into a long winded mathematical explanation of the two and show how they are both related to the RC time constants of a circuit, and therefore both are limiting the bandwidth of a circuit, but that is probably more than is needed and it is very difficult to do mathematical equations on this forum.

The term acceleration is not used correctly in Sean's analogy. The correct term would be velocity, but the analogy is still wrong. Velocity is how fast something is moving, how much distance you can travel in a given period of time. Acceleration is how fast the velocity is changing, you are moving but either speeding up or slowing down. Neither slew rate nor rise time have anything to do with speeding up or slowing down, only moving at a constant rate.

Velocity is a rate of change.
Acceleration is a changing rate of change.

If you want to use a speed analogy then slew rate is the velocity of the voltage. It is not related to the "volume" of the signal, at least I don't think it is because in 25 years I've never heard anyone talk about the volume of a signal except in terms of current.