# Maximum typical slew rates in audio

#### HalFoster

Paid Member
I came across a topic yesterday that had me thinking about the slew rates present in audio and the max/min required for processing equipment - specifically, how to fill in the blanks in the following statement:

The highest slew rates are in the vicinity of <slew rate> and are frequently found in the waveforms generated by <instrument/voice/etc>.

My first guess (admittedly a WAG) would be the initial hard strike of a cymbal or something along those lines. Does anyone have any specific numbers and/or references on this topic?

Thanks,

Hal

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#### lineup

How can we measure slewrate in an amplifier?
With SPICE or in real circuit?

#### HalFoster

Paid Member
Get a estimate in spice, see the real numbers using the actual circuit. Just need a fast risetime signal and a scope fast enough to capture the (preferable both) waveforms. Couple of things to keep in mind, especially if referencing the above given article: 1) the slew rate is not the risetime and 2) The formula for the minimum required slew rate applies to a perfect sine wave - not at all a given in a music source.

Hal

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#### HalFoster

Paid Member
For the initial signal to to input of the circuit I like to use a pulse generator that has configurable rise and fall times (the falling slew rate of an circuit is just as important to signal integrity and just about always is different from the rising slew rate.) - change them until you notice a difference. You can either view both at the same time or, preferably use use the A-B function on the scope to only show when the signals start to differ. While you can use a fast digital scope for this, it is a use where a good fast analog scope really shines - I use a Tektronix 2465B.

Hal

#### tomchr

Paid Member
How can we measure slewrate in an amplifier?
With SPICE or in real circuit?
It's pretty easy to measure on a real circuit. All you need is a function generator and an oscilloscope. Pretty fundamental... You can also look at it in simulation, but unless you're really meticulous you won't have the layout parasitics included, so the simulation will be pretty optimistic (i.e., show an unrealistically high slew rate).
Simulation can still be useful, though. If your simulation shows the circuit doesn't have sufficient slew rate you'll need to change the design so that it does.

So the question becomes: How much slew rate isneeded? I'll answer that below.

Any signal can be reconstructed using a sum of sine waves. The bandwidth of audio is typically considered to be 20 kHz. So the highest frequency your audio system will need to produce is 20 kHz. We can derive the rate of change (i.e., the slope of the curve aka the derivative) for the sine wave like this:

∂/∂t [Vpeak * sin(w*t)] = w * Vpeak * cos(w*t), where w = 2*π*f.

A sine wave has the highest rate of change at the zero crossing and the first zero crossing happens at t = 0. So let's find the maximum rate of change for the sine wave:

∂/∂tmax = w * Vpeak * cos(w*0) = w * Vpeak, where w = 2πf.

So the minimum slew rate required of the circuit in order to reproduce a 20 kHz sine wave is:

SR = 2*π*20000*Vpeak

For a line level circuit where Vpeak is typically 15 V this works out to 1.88 MV/s ... or in more common units 1.88 V/µs. For a power amp specified to provide 100 W into 8 Ω (which corresponds to 40 V, peak) you need: 2*π*20000*40 = 5.02 V/µs.

Or if you prefer to use the 22.4 kHz bandwidth of a digital reproduction chain: 2.11 V/µs for line level, 5.63 V/µs for the 100 W power amp.

Tom

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#### lineup

Get a estimate in spice, see the real numbers using the actual circuit. Just need a fast risetime signal and a scope fast enough to capture the (preferable both) waveforms. Couple of things to keep in mind, especially if referencing the above given article: 1) the slew rate is not the risetime and 2) The formula for the minimum required slew rate applies to a perfect sine wave - not at all a given in a music source.

Hal
I use SPICE function generator with squarewave and the built in oscilloscope.
The square looks perfect with 5 kHz but not with 10kHz.
How much slewrate is this? What is the number like?

#### HalFoster

Paid Member
Tom's answer is indeed correct for calculating the required slew rate for a nice, symmetrical sine wave. Just keep in mind that real world signals frequently do not present as a classical sine and as such, even though the periodic frequency of the waveform gives a fixed number using the classical formula, portions of the waveform may have a much higher (or lower) DV/DT and require higher order frequencies to represent. My original question refers to these exceptions.

Hal

#### HalFoster

Paid Member
@lineup - The difference more than likely is in how the circuit processes the higher frequencies and is not due to slew rate limitations as they are not changing - but the frequency response of the circuit is. With most SPICE simulators the rise/fall time of the square wave will not change as the frequency is changed so whatever effects you are seeing are due the the circuit simulation itself. With SPICE it all comes down to the accuracy of the models for the components - and that information is usually not given or even intentionally changed to protect the manufacturers IP. Really the best way short of actually building the physical circuit is to study any datasheets available and understand how the component(s) will react in the application. In short, calculating something like DV/DT from SPICE is pretty much a crapshoot - and the real result will be changed by parasitics that will not be present in the SPICE simulation.

Hal

#### HalFoster

Paid Member
Anyway, getting pretty off topic - anyone that can help with the original question?

Thanks!

#### bucks bunny

The answer has been given already by Tom. Whatever complex waveform you consider - it is band limited to audio. Anything else is audio mystic. And, btw, slewrates calculated are based on the assumption of 20kHz full bandwidth - which is far above real audio events.
In fact the audio content in the upper octave is small. Otherwise, the tiny voice coils of tweeters would burn, did you ever see these in real life?

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#### HalFoster

Paid Member
Well, he answered a question... just not mine.

#### bucks bunny

he did, but you do not like the answer

#### HalFoster

Paid Member
Although I will give that I should have added "in music"

#### HalFoster

Paid Member

"The highest slew rates are in the vicinity of <slew rate> and are frequently found in the waveforms generated by <instrument/voice/etc>."

#### Mark Johnson

Paid Member
This sounds like a DIY design project. The slew rate (dVoltage / dTime) of a signal is merely that signal, differentiated. So just design yourself a differentiator circuit (Google Advanced Search finds 36 million search hits for Differentiator Circuit Schematic), put it into a peak hold circuit (12 million search hits), and display the output. Job Done.

Calibration will be simple: just have your function generator output a triangle wave, and measure its (dVoltage / dTime) with your scope. Then attach your Peak Slew Rate DIY project and twirl its calibration pots until your meter shows the known, measured, Correct Answer the scope gave.

Now you can connect your Peak Slew Rate meter to either the input of your power amp, or the output of your power amp, or the output of your DAC, or anything else you may be curious about.

If the maximum slew rate ever seen at the input of your power amp is S volts per microsecond, and your power amp has a voltage gain of G volts out per volt in, then the power amp output will need to slew at (S * G) volts per microsecond. Maybe you'd prefer to be conservative, and insist upon buying (or DIY building!!) a power amp whose slew rate is at least (1.5 * S * G) volts per microsecond. Now you've got some safety margin.

You could have some fun tabulating the peak slew rate for different albums / CDs / streaming tracks. You might discover that your personal favorite musical selectionss, are among the very highest slew rates of all. Or your personal favorites might have the lowest slew rates. Different musical genres might have different "footprints" of slew rate distributions. You may enjoy finding these things out, and organizing your results so that others can benefit too.

#### HalFoster

Paid Member
Mark-

Not sure if you are answering me or not (apologies if not - very good response) but if so:

I'm not asking how to measure slew rate - that is trivial and I have plenty of equipment that can measure it and I do so, fairly often. Rather, I was just curious what the maximum naturally occurring slew rate in typical live (NOT recorded) music or voice would be. Someone was trying to justify using a GHz op-amp in a preamplifier and, after I stopped laughing, I started to wonder what would actually be required in a perfect solution. Really should have stated it that way in the first place and eliminated a lot of the confusion.

Thanks,

Hal

#### Mark Johnson

Paid Member
I myself use a 200 MHz opamp in the input stage of the M2x power amp. My circuit is named Milpitas and it's here on diyAudio; search will find it easily.

#### von Ah

Paid Member
I think at some point we would come up against microphones vs ears here. Whether it’s Volts per microsecond or walnuts per cubit, there may be a fundamental measurement vs. experience divide.

#### MarcelvdG

Many years ago, before CD was introduced, there was an article from Matti Otala's research group about audio signal rates of change published in the Journal of the Audio Engineering Society. I can look up the details if you like. They played records and measured the peak signal voltages and peak rates of change, with both normal and direct to disc recordings.

When they looked at the ratio of the peak rate of change to the peak audio voltage, the highest value was about 0.05 (V/us)/V, equivalent to an 8 kHz sine wave. That was on a recording called Deutsche Marschmusik: Einzug der Gladiatoren.

I have no idea if the ratio got larger with (high-resolution) digital recordings.

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