Slew Rate

DonH50

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I have seen a few discussions about slew rate and thought it might be a worthwhile thread. Slew rate is defined as the amount a signal (voltage, current, power, whatever) changes in a given time period. For the math types, it is the first derivative with respect to time. For a single-frequency sinusoid, e.g. a single tone, the slew rate (SR) is given by

SR = 2*pi*f*A where

pi = 3.14159…
f = frequency
A = amplitude

The amplitude is the peak (pk) value of the signal. For example, a 1 Vrms signal is 2.828 Vpp or 1.414 Vpk. At 1 kHz, the slew rate is 8,886 V/s, or 0.0089 V/us (Volts per microsecond, a typical unit). This is the maximum slew rate, which occurs at the sinusoidal signal’s center crossing. It decreases away from the center, though stays fairly close to the maximum value for most of the amplitude range (it does decrease to zero at the very top and bottom).

Since slew rate seems to be more a concern for power amplifiers, I calculated the slew rate for various power levels (rms) into an 8-ohm load and plotted it versus frequency below. The log-log plot presents the slew rate as a straight line at each power level (1, 10, 100, and 1k W).

Slew Rate..JPG

The slew rate may be lower than some expected given the 50 to 100 V/us rates specified by some manufacturers. At 20 kHz, a 100 W signal only requires 5.03 V/us slew rate. There are pros and cons with higher slew rates:

A few pros about high slew rate:

  1. Greater design margin for high-frequency signals.
  2. A higher slew rate allows the amplifier to better control high-frequency ringing in the load (speaker).
  3. Higher slew may require higher bandwidth, which can make it easier to close the feedback loop without instability.

The cons tend to mirror the pros:

  1. High slew rates can push design margin to the edge, decreasing amplifier stability.
  2. High slew rate can cause excessive high-frequency content, potentially damaging drivers. If the speakers cannot respond quickly enough, power turns to heat that can damage or destroy the drivers.
  3. Greater bandwidth and/or fast edges (possible with a high slew rate) can cause high-frequency peaking and ringing, or even oscillation, with certain loads. Higher bandwidth also means more noise, and more (higher-frequency) distortion components.
There are always trades, naturally…

HTH - Don
 
Last edited:

andy_c

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Higher slew requires higher bandwidth, which can make it easier to close the feedback loop without instability.

Not true. For a conventional voltage feedback power amplifier, the slew rate in Volts/second is given by:

SR = I/C

where I is the tail current of the input stage diff amp and C is the Miller compensation cap. The gain-bandwidth product in rad/sec is given by:

GBW = gm/C

where gm is the transconductance of the input stage diff amp and again C is the Miller compensation cap. The bandwidth in Hz is the GBW divided by the product of 2pi and the nominal low-frequency gain (determined by the ratio of the feedback resistors).

One way to double the slew rate of an amplifier without changing its bandwidth is to first reduce the compensation capacitor C by a factor of two, then reduce the input stage transconductance gm by a factor of two by adding or increasing the emitter degeneration of the input stage.

Another way is to keep C constant, double I, then adjust the emitter degeneration of the input stage as necessary to keep gm constant.
 

DonH50

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Depends on the topology, and of course you are right for that one; I'll correct to "may require". I should have stated I have little experience designing power amps; my background runs to much higher frequency (GHz) circuits so I do not think about LF op-amps much. For me, sometimes Miller compensation (or any other compensation scheme) works and sometimes not for a given design. I don't really want to get into that; if you know it, you don't need this thread, and if you don't, it's probably too deep to get into here. I wasn't going to dive quite as deep into amplifier topologies and was thinking primarily of the output stage, which is just one place slew-limiting can occur, and where degeneration is limited (mainly to ballast resistors to equalize power dissipation among the multiple output transistors). Also, at the terminals we do not usually control the load impedance, and I was not addressing the internals (not saying I should not have, again figured it was too deep for the bulk of the audience).

Actually, microstrip already PM'd me about mixing SR and frequency response. Hopefully he'll chime in as well. I'll just preface what he might say by noting that there is a relationship but it can be complicated, and my pros and cons are very general statements with plenty of qualifications and exceptions depending upon the actual design and load. I freely admit that in trying to simplify complex material it is easy to over do it and mislead folk. Nor do I have any claim to being anywhere close to perfect!

An interesting thread might be one that discusses amplifier design in more detail, including various topologies and classes of operation.
 

microstrip

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Hi Don,

Your analysis is very interesting, but you approach risks mixing the effects of slew rate and frequency response as an unique parameter. Although they have similar consequences, in practical implementations they are due to different reasons.

Slew rate represents the maximum rate of change of output voltage of an amplifier. It is mainly due to limitations in the output stage of the amplifier, than can not change voltage and supply current instantaneously.

Frequency response or bandwidth, as it is called some times, is usually a limitation imposed at the input stage by frequency compensation at the input stage. Most designers will voluntarily limit the high frequency bandwidth at this stage, but we can not be sure of that in every design.

I think we can not analyze the pros and cons without taking this in account - sometimes it is not possible to simplify a problem.
 
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amirm

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Thanks for the write-up Don. I think you did a great job of explaining what slew rate is in general. Engineers as always, can different a bit on details :).
 

DonH50

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Not just engineers, Amir, but thank you! :)

microstrip -- One minor point: I would append the word "voltage" to your definition of amplifier slew rate. I have designed various amplifiers and whilst slew rate was almost always a parameter of interest, sometimes it was current or something other than voltage that mattered. Thank you very much for adding your insights to this thread!

I started thinking about counters to the "practical implementations" part but realized that, like andy_c, you may well be more on target for audio amps where my circuit designs have targeted other applications. In some of those, FR and SR are tightly coupled, but that is probably not true in general.

Thanks for keeping me honest! - Don
 

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