Slew rate question

renx said:

Hi,

I have revisited my claims in the last couple of posts, and I did the math again, and these are my conclusions:

There exists such a complex signal that when "passed" through a 1st order butterworth lpf of 20kHz @(-3db), gets minimally linearly distorted (a couple of degrees of phase shift and less than 0.5db in amplitude) but requires 10 times larger slew rate than the slew rate required by the 20kHz pure tone signal of the same amplitude peak.

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Another hypothetical? What natural source is this supposed to model, some random combination of chaotic sources?

Much simpler to start with an arbitrarily fast rise time square wave (rifle shot, lightning strike), then LPF that with one pole at some still fast but reasonable rate. If you want to go old school jangle some keys in front of a fast microphone. If the circuitry can't keep up you'll hear the IMD under the key noise.

As soon as I get my Mathematica graphs uploaded, I will post them here to back up my claims, and would kindly ask all of you to check for any errors in my theory or calculations.
The reason I am doing this is that I remember reading an article from Yamaha, I think, on how the slew rate impacts the sound of power amplifiers. If I recall correctly they were playing the same material through a couple of amplifiers different by their slew rate only, and same speakers of course, and have concluded that larger slew rate is needed than that of a max freq. Unfortunately I can't find it anywhere!

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Sounds like some marketing blather. An amplifier with marginal or inadequate slew rate, will likely have other shortcomings (like gain bandwidth product, etc) that can impact sound quality. Like PRR already mentioned, amplifiers at their slew limit are essentially clipping wrt to their rate of change so severely distorted. While i don't want to generalize, the slew rate limiting behavior of different amplifiers in the region just before slew limiting can also be different, so it is always prudent to have a safety margin.

Normalizing for power supply voltage a 20khz sine wave peak or max rate of change is only around 60mV/uSec/Vp-p. I personally like to design for a power bandwidth of 40kHz so maybe double that for a hard target, but we want a safety margin on top of that. 

The good news is that even inexpensive widely available opamps (NE5532/TL074) have been spanking those slew rates for several decades.

An earlier rule of thumb suggested 1V/uSec/V of power supply. That seems more than a little conservative to me.

Nobody is saying make it "just" fast enough for 20kHz, and for decades we haven't had to.

The slow part of this thread's dynamic duo at 15V/sec will deliver a power bandwidth a few octaves above human hearing (>160khz clean sine wave for +/-15V rails).  This seems adequately fast to me. While I would also include input RF filtering since even lowly AM radio is higher slew rate than that. 

The fact that I have been designing electronics under wrong assumptions for so long is just killing me!
That is why I have to get to the bottom of this.

Regards, Renx.

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I'm afraid to ask what that premise is. I recall when we actually had to deal with slow opamps, but thankfully that was a long long time ago.

JR

PS: I seem to recall a thread around here a few years ago about making a bench circuit with variable slew rate that could be listened to with the slew rate necked back just to learn what it sounds like. But this artificial slew limiting would be be cleaner below slew limiting thresholds than we encounter in practical circuits.

> larger slew rate is needed than that of a max freq.

Just as clip-level must be higher than peak signal.

One difference: older simpler amplifiers (tubes and few-transistor) had rising THD/IMD even before clipping. We often kept signal far below the clip-point. See "broadcast line drivers" with two 6V6 capable of over 5 Watts at 5% THD, rated for +28dBm (under 1 Watt) to get sub-1% THD performance.

Fancier more complex 49-transistor "stages" often have "no" THD/IMD until 99% of clipping. We are quite able to build an amplifier with +/-36V rails, +/-32V clipping, work it up to +/-31V signal peaks, and have "no" distortion.

However the more common slew issues do not have this kind of extended linearity. (That's a problem for another decade+.) So we like to stay 10X below the hard limit. Hence if we slew 1.5V/uS and want dead-clean, we aim for 15V/uS to stay in the middle of the nonlinearity, where it is nearly-linear. As JR says, "a safety margin".

There's another side to this. We don't push +28dBm along phone lines. The most critical level is the ADC input. The new Line Level should be ADC level. And this is often 2.5V peak. Therefore we should be using +/-3V supplies and striving for at least 3V/uS. A decompensated '741 (AKA '101) is ample (except it needs more than 3V rail to make 2.5V swing). (The flaw in this ointment is that the better ADCs have lower hiss level than some legacy analog signal processing; we may have to push larger signal through patchbay then pad-back at the ADC.)
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> bench circuit with variable slew rate

Differentiator. Clipper. Integrator.

There's some bother getting the variable diff and int to track. Or you can vary the clipping, but good clean clipping of differentiated audio is already tough, KISS may be the best bet.

You could go crude with an AM radio cap across the compensation pins of a '301. 0.1V/uS is well within reach, if the '301 would be stable with its comp pins extended and a hand hovering near. The other drawback is that this way gain-bandwidth also falls. Even at unity-gain, 365pFd would give 80KHz closed bandwidth, little NFB and a raucous sound in the top octave or so.

> marketing blather

Yamaha often takes truth and dresses it up extra nice. I recall a boast about wiring unity-gain buffers as noise-gain-of-2 differential amps to avoid marginal stability. Yeah, but I suspect they were also looking at ground-crap rejection, essential in larger systems, but who wants to boast about rejecting their own crap? The core truth is: most buyers don't know squat, entertain them long enough to hammer a hint about buying.

Ah.. the old LM301,, 10V/uSec in feedforward compensation mode, I don't miss having to worry about speed, and playing games to get there.

The modern ICs are such a luxury to work with.

JR

Hi to all,


EDIT: This statement is wrong, I checked and rechecked!

I can now confirm my claims from two posts before.

In theory, there exists such a signal that when passed through a single pole lpf @20kHz, has a higher "rise" than that of a single 20kHz sine wave of the same amplitude, implying the need of a higher slew rate than of a max freq.

I won't go into mathematical details (except if requested), but this is my theory and I would kindly ask other members to check for eventual mistakes I made.

The signal I used is an exponential function gated in such a way that it never exceeds a value of 1. One could use a very steep ramp as well. Than I convolved it with a single pole lpf at 20khz, than found the maximum rise of the filtered function. The resulting rise can be much larger that that of a single 20kHz sine wave depending on the rise of the initial signal.

So if this theory is correct you would indeed need a higher slew rate than required by the max freq.

Now if a real life signal will ever have such a rise time is another question. It sure is possible but I don't know how probable.
And if it did have such a rise time how much of a distortion would it cause and most important of all, would it be detectable by human ear.

Regards, Renx.

This is perhaps not that mysterious. A full scale square wave at any low-mid frequency passed through a one polle LPF at 20 khz, will have

renx said:

Hi to all,

I can now confirm my claims from two posts before.

In theory, there exists such a signal that when passed through a single pole lpf @20kHz, has a higher "rise" than that of a single 20kHz sine wave of the same amplitude, implying the need of a higher slew rate than of a max freq.

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Like a square wave? Or saw tooth? or...

I won't go into mathematical details (except if requested), but this is my theory and I would kindly ask other members to check for eventual mistakes I made.

The signal I used is an exponential function gated in such a way that it never exceeds a value of 1. One could use a very steep ramp as well. Than I convolved it with a single pole lpf at 20khz, than found the maximum rise of the filtered function. The resulting rise can be much larger that that of a single 20kHz sine wave depending on the rise of the initial signal.

So if this theory is correct you would indeed need a higher slew rate than required by the max freq.

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Indeed...

Getting back to my practical solution a simple rise time limited input, either a passive filter in the input or incorporated into the amplifier (leach published an AES paper on the subject)

A simple one-pole LPF -3dB at 50kHz will slew rate limit an infinitely fast square wave to less than 10V/usec peak for a 30Vp-p square wave.  This seems adequately fast and well within the capability of general purpose opamps for the last few decades.

Now if a real life signal will ever have such a rise time is another question. It sure is possible but I don't know how probable.
And if it did have such a rise time how much of a distortion would it cause and most important of all, would it be detectable by human ear.

Regards, Renx.

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But even if your hypothetical is possible it is avoidable with rise time limited design.

IMO

JR

PS; I've made some math mistakes lately so check my math but i come up with 9.7V/usec at instant of square wave transition up/down/up.

PPS: a power amp capable of more than 30Vpp needs more than 10V/usec. to accommodate similar rise time.

renx said:

Hi to all,

I can now confirm my claims from two posts before.

In theory, there exists such a signal that when passed through a single pole lpf @20kHz, has a higher "rise" than that of a single 20kHz sine wave of the same amplitude, implying the need of a higher slew rate than of a max freq.

I won't go into mathematical details (except if requested),

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Please elaborate. I've toyed with pulses and after 20k LP, they are all slower (or equal) than the sinewave. That's due to the temporal displacement of harmonics, so their max slew doesn't coincide. If you shift the harmonics prior to LP, you also increase the amplitude.

Wrong, wrong, wrong. I was wrong!!!

I just realized an error in my inverse laplace transform and have to admit it in order to finally get to the bottom of this.

There is NO such complex signal which has a larger rise time than the the rise time of the max freq., implying that the maximum required slew rate is indeed the slew rate required by the max freq. after the lpf.

This is my final statement, and will not bother you with this topic any more.

This is the time where I would like to thank John Roberts, PRR, Samuel Groner and other members for this enlightning discussion. I did learn a lot!

Regards, Renx.