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Maximum slew rate typically found in music/voice
SeanB:
Pretty much most audio at some point or the other went through the venerable 741 opamp, or any of the clones, with the 1v/us slew rate it has. Works for low level audio, so pretty much should be a minimum, though better is not going to be easy to hear.
SiliconWizard:
--- Quote from: tggzzz on September 15, 2023, 06:47:03 pm ---The question is ill-formed. The slew rate is a function of frequency and amplitude.
A 1kHz 100V signal has a slew rate 10 times higher than that of a 1kHz 10V signal.
--- End quote ---
Obviously. To this I will add: a reasonable approximation for the minimum required slew rate would be to start with the classic relationship between bandwidth and rise time.
For a 10%-90% rise time Tr, and a bandwidth BW, it is approx.:
Tr = 0.35 / BW
If we take a typical "line" level for audio, amplitude in the order of 1V, so a p-p amplitude of 2V, we can approximate the 10%-90% section with 80% of the p-p amplitude, so 1.6V.
Let's call the p-p amplitude App.
The minimum required slew rate to accomodate a given bandwidth at the max amplitude given above would thus be (all values are in SI units, so App in V, BW in Hz and SR in V/s):
SR = 0.8 * App / Tr = 0.8 * App * BW / 0.35 = 2.29 * App * BW
With a typical 20kHz BW for audio and the typical amplitude mentioned above, that yields: SR = 2.29 * 2 * 20e3 = 91600 V/s = 0.0916 V/µs
At +/-10V you have 10 times that, so ~ 0.916V/µs.
Edit: Fixed a silly calculation mistake. We get a value within about 80% of the SR found classicaly from the derivative of a sine wave, which is perfectly normal since with the derivative method, you use the maximum of the signal's slope (the max of the derivative of the sine wave), while using the above rule of thumb, this is equivalent to using the slope of a line between the 10% and 90% points, considering sin(x) is relatively close to a straight line around the origin.
(Finding the equivalence between the two formally takes a little while in calculation, but it is, within a factor.)
As an extra exercise, you may consider what happens to a pure sine wave with the max frequency (= BW) if we limit the slew rate to the value calculated with the method above, rather than using the derivative at the origin.
wraper:
--- Quote from: tom66 on September 15, 2023, 06:40:51 pm ---Would it matter - if the human ear can't typically hear above 20kHz, the maximum slew rate is a function of frequency, since any energy above that frequency is going to be ignored by the low pass filter that is the human auditory system. There will be some audiophiles who claim that sampling above ~44kHz is necessary for one reason or another but AFAIK there's no scientific basis for those claims.
I'd imagine it's possible that striking a cymbal could produce frequencies well above 20kHz and therefore slew rates well above what we would see from e.g. voice or wind instruments.
--- End quote ---
Sampling frequency above that is needed because 2x sampling frequency from Nyquist's theorem does not really work IRL because real low pass filters are not perfect and thus you want more margin. 44kHz sampling works good enough not because it works fine for 20kHz but because even though humans can hear high frequencies, they do it poorly. And neither actual sound contains much in that part of spectrum.
TimFox:
--- Quote from: SeanB on September 15, 2023, 09:32:27 pm ---Pretty much most audio at some point or the other went through the venerable 741 opamp, or any of the clones, with the 1v/us slew rate it has. Works for low level audio, so pretty much should be a minimum, though better is not going to be easy to hear.
--- End quote ---
The 1 V/us slew rate of the 741 should be adequate for signal levels below, say, 1 V rms.
Note that before you see the tell-tale straight line on the output waveform, the differential input stage has gone non-linear (large-signal behavior of differential pair).
The decompensated 5534 op amp (Ccomp = 0) has a slew rate of 13 V/us, decreasing to 6 V/us with 22 pF, according to the 1994 Philips datasheet.
(22 pF is needed for unity-gain stability, but 0 works for higher closed-loop gains.)
Nominal Animal:
Slew rate must be at least \$2 \pi f V_{pk}\$ for a sinusoidal signal of frequency \$f\$ and amplitude \$V_{pk}\$ to be reproduced perfectly. This is well documented for amplifiers.
This is because the voltage of the signal with respect to time is
$$V(t) = V_{pk} \sin \left( 2 \pi f t \right)$$
and the slew rate is the magnitude of its derivative with respect to time,
$$\left\lvert \frac{d V(t)}{d t} \right\rvert = \left\lvert 2 \pi f V_{pk} \cos\left( 2 \pi f t \right) \right\rvert$$
which reaches the extrema when \$\cos\left(2 \pi f t \right) = \pm 1\$. Therefore, the maximum slew rate is \$2 \pi f V_{pk}\$.
For \$f = 20000 \text{ Hz}\$ and \$V_{pk} = 1 \text{ V}\$, the slew rate must be at least \$125663.7 \text{ V/s} = 0.126 \text{ V/µs}\$.
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