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Non ideality in output square wave of a differentiator circuit

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IanB:

--- Quote from: rstofer on February 13, 2019, 07:22:46 pm ---Except that both of my Comdyna 6 Analog Computers are loaded with 741s and replacements are expensive.  I'm somewhat reluctant to substitute but at some point that may just be the way it works out.

--- End quote ---

On an analog computer we would do both amplitude and frequency scaling for any given problem. So if the desired frequencies in the system being modeled exceed the limiting slew rate of the amplifiers, one could just change the frequency scale to bring things into range.

There may be other performance limits of the 741, but if the analog computer was designed around those amplifiers, then substituting them for more modern amplifiers with higher performance may just introduce new compatibility problems with the rest of the system? I would be cautious.

bonzer:
Thanks a lot for you answers. I also wanted to notice that these are the results of a simulation circuit.
I'm still a bit confused, I'd like to point out the problem in an accurate way because it's for an university work (but it's a brief comment so feel free to add here whatever comes to your mind).
I attached differentiator's bode diagram of the gain.
So what we have from what you said is that:

* Gibbs phenomenon is a math abstraction so is not exactly rappresented by the circuit as it is real and has attenuation therefore high frequency harmonics get attenuated and not truncated. What we see is then an approximation of the Gibbs fenomenon, not at both ends of the edges because of the real behaivor of the circuit (phase shift and so on, as said by emence67) 
* The problem of non differentiable points of the triangular wave doesn't convince me enough, why wouldn't it just saturate at those points then? Anyway it might be, I'm not sure
* Phase non linearity - could be the biggest contribution to those overshoots as we don't have here a linear phase system
In confirmation to the last point, I've just found an example of a butterworth filter vs bessel filter (bessel has linear phase) having a square wave at the output on this link. The case looks similar but I don't know how much it is related.

https://www.allaboutcircuits.com/technical-articles/how-to-low-pass-filter-a-square-wave/

rstofer:
If you stop and think about a C-R differentiator where the signal goes in the C and comes out the junction between the R and C, you will see the same spike when the triangle or square wave changes shape.

https://www.electronics-tutorials.ws/rc/rc-differentiator.html

Look at the waveforms about 1/2 way down the page.  The bottom waveform is a typical differentiator used to generate a clock pulse from a square wave.  It would be cleaned up with a Schmitt Trigger perhaps but the idea is to find the edges of the square wave where dv/dt heads off toward infinity and the output waveform has the characteristic differentiator spike.

This is exactly what you have except your circuit is more elegant.  But a differentiator is a differentiator and the derivative at the point of inflection or jump discontinuity is undefined.

In my view, Gibbs Phenomenon is a completely different animal and will always affect all 4 corners whereas the differentiator only looks at the 2 edges and the direction of the pulse is in the same direction as the edge transition.

Actually, GP is just a math problem.  Add another harmonic and it will be reduced.  Add a dozen more and it will be reduced further.  Include an infinite number of terms and it will disappear.  As you build up a square wave from a sine wave and its harmonics, it is the corners that are the last to fill in.

http://recordingology.com/in-the-studio/distortion/square-wave-calculations/


MANY years ago, logic systems weren't always synchronous and it was quite common to use the edge of some signal to create a pulse to clock some part of the circuit.

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