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How to automatically find the final x-value of a waveform to be used by the integ() function

Dear Community

I want to compute the "smoothness" of a waveform, that is, the integral of the absolute value of the second derivative of a signal. The problem I encounter is that the derivatives of a waveform are a little bit shorter than the simulation time (logically). The final value of the time vector is not consistent (depends on accuracy settings and such). I would like to find a way to automatically extract this final value of the time axis such that the integral can be computed over the whole range. The second derivative of a waveform can be very "noisy", so using the integ() function with extrapolation "on" leads to inaccurate results if the final value lies outside.

Suppose that the signal is simply called vout and the corresponding waveform is VT("/vout"). I can extract the final value of the x-axis with some workarounds, e.g.

ymax(xval(abs(deriv(deriv(VT("/vout"))))))

xmax(xval(abs(deriv(deriv(VT("/vout"))))))

The latter one works because the waveform has its "maximum" at the final value (the name xmax is misleading; that function does not return the highest x-value). The output of this expression, however, cannot be used as an argument for the integ() function, probably because it is also a waveform object or so? Using

integ(abs(deriv(deriv(VT("/vout")))) 0 ymax(xval(abs(deriv(deriv(VT("/vout")))))) nil )

yields a evaluation failed error.

What is the easiest way to accomplish this? Thanks for any help.

Andrew Beckett over 1 year ago
Two approaches:

If you provide integ() with only a single argument, it will integrate over the whole x-range without you needing to specify the limits

Or you can use the lastVal() function on a waveform to find the final x-value.

Andrew
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DomiHammerfall over 1 year ago in reply to Andrew Beckett

Thanks for the fast reply, much appreciated.

A quick comment on my approach: I noticed that not only the end time is shorter if you calculate the derivative, but also the start time is unequal to zero. So to make anything work, one also needs to extract the start time and pass it as an argument to the integration function; it then works.

Of course, Andrew's approach is even better. I can confirm that both ways work and yield the same result.

On a side note: that call of integ() with a single argument is not documents (or at least I couldn't find it).
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Andrew Beckett over 1 year ago in reply to DomiHammerfall

See: https://support.cadence.com/apex/techpubDocViewerPage?xmlName=oceanref.xml&title=OCEAN%20Reference%20--%20Predefined%20and%20Waveform%20(Calculator)%20Functions%20-%20integ&hash=pgfId-1028686&c_version=IC23.1&path=oceanref/oceanrefIC23.1/chap10.html#pgfId-1028686

In particular:

You should specify either both the limits or neither. In case you do specify the limits, they become the end points of the range on the X-axis for definite integration. If you do not specify the limits, then the range for definite integration is the entire range of the sweep on the X-axis.

Note there's also a firstVal as well as lastVal function should you need that.

Andrew
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